NACA Conference on Aircraft Loads, Structures, and Flutter

airplane span, the results obtained by the two methods w i l l differ (see appendix). I n the following material, t h i s property w i l l be used i n assessing the significance of spanwise variations i n the turbulence on the t e s t results.

RESULTS FOR THE B-29 AIRPLANE The measurements obtained i n t h e course of the B-29 flight investi- gation have been used t o estimate t h e frequency-response function f o r the bending s t r a i n s at the various stations by application of the spec- trum method described i n the preceding section. I n estimating the frequency-response function, it was necessary t o assume a shape f o r the w a s not measured i n t h e B-29 inves- gust spectrum since the gust spectrum tigation. The gust spectrum used f o r t h i s purpose is given by the f o l - lowing expression: where R = 2sf/V and V i s the airplane speed. This spectrum has been found t o approximate the atmospheric conditions covered by flight meas- urements of gust spectra when a value of about 1,000 is used f o r the scale of the turbulence L. The intensity of the turbulence which is described by the root-mean-square gust velocity (I is, however, not known f o r the B-29 measurements.

I n order t o permit direct comparisons of the frequency-response functions a t the various wing stations, the results were converted t o "equivalent accelerations" by dividing the s t r a i n s at each station by t h e s t r a i n per g measured at the station during slow pull-ups. The results obtained f o r the amplitude of the frequency-response function on t h i s basis are shown i n figure 2. The ordinate represents the ampli- tude of the bending-strain response f o r a u n i t sinusoidal gust velocity a t the various frequencies. The four solid-line curves shown i n the figure a r e the r e s u l t s f o r the four spanwise stations whose locations

of the semispan b % . Also

a r e designated i n terms of the fraction shown i n figure 2, by the dashed-line curve, i s the frequency-response function obtained from the masured nodal accelerations and which can be considered as a reference f o r s t a t i c loading. Thus, the difference between t h i s reference and the other curves gives an indication of the effects of wing f l e x i b i l i t y . (Flexibility also has an effect on the nodal accelerations, but t h i s effect i s small. ) Comparison of the solid curves of figure 2 w i t h the reference curve of nodal- acceleration s effects of f l e x i b i l i t y

f 23

are associated w i t h a large peak at the first bending mode, which i s at 2.7 cps. The amplification i s highest f o r the 15-percent-semispan sta- t i o n and progressively decreases w i t h outboard wing span station. Above

about 4 cps, the curves are somewhat disorderly, probably because of the

effects of higher structural modes.

I n order t o see how w e l l the frequency-response functions could be determined analytically, calculations were also made. The calculated s t r a i n frequency-response functions were converted t o equivalent accel- erations f o r direct comparison w i t h the resul%s of figure 2 and a r e shown i n figure 3. These r e s u l t s are f o r three modes or degrees of freedom, that is, airplane v e r t i c a l motion and the first and second symmetrical bending modes. Comparison of the results i n figures 2 and 3 shows that, i n general, the character and trends of the experimental and calculated frequency-response functions are i n f a i r l y good agreement i n regard t o f l e x i b i l i t y effects. Both figures indicate t h a t the principal e f f e c t s of f l e x i b i l i t y are associated w i t h the first bending mode and that t h e amplification i s largest at the root station and progressively decreases w i t h outboard wing span station.

It is of interest t o note that the calculated and measured frequency- response functions (figs. 3 and 4) differ below about 1 cps. This d i f - ference i s due principally t o the omission of the pitching motion i n the calculations. Because of t h e high gust input power at these low frequen- cies, it would thus appear t h a t t h e inclusion of the pitching mode i s quite important i n determining the actual output response.

The effect which the frequency-response functions have on the over- allbending-strain amplification i s shown i n figure 4. I n the upper part of the figure, the ordinate i s the r a t i o of the root-mean-square s t r a i n f o r the flexible airplane t o the root-mean-square s t r a i n f o r the reference condition Q The reference s t r a i n s were based on the €,REF' nodal-point accelerations measured i n rough air and the s t r a i n per g as measured at t h e various spanwise stations i n slow pull-ups.

This refer- ence condition represents the s t r a i n s f o r the s t a t i c application of loads, and thus t h i s r a t i o provides a measure of dynamic-strain amplification.

The circles represent the measured amplification factors, and the curves represent calculated results. The dashed curve was obtained by consid- ering two modes': airplane v e r t i c a l motion and the first symmetrical mode i n bending. The solid curve w a s obtained by using three modes: airplane v e r t i c a l motion and the first two symmetrical bending modes.

The measured results show t h a t the overall s t r a i n amplification is approxi- mately 10 percent at the root station and is somewhat lower at the out- board wing stations. Both the two-mode and three-mode c'alculations are i n rather good agreement w i t h the measured r e s u l t s except a t the far- thest outboard station.

A second s e t of strain-amplification f a c t o r s is shown i n the lower p a r t of figure 4. This ordinate i s the r a t i o of the s t r a i n s that would occur with equal frequency f o r the f l e x i b l e airplane fiFmX and f o r the reference airplane condition E ~ . "he frequency l e v e l at which t h i s s t r a i n r a t i o was taken corresponds t o a value of s t r a i n equal t o about twice t h e root-mean-square strain. These experimental amplifications are about twice as large as those shown i n the t o p figure based on root- mean-square s t r a i n s . This is a consequence of f l e x i b i l i t y having a greater e f f e c t on the number of peak s t r a i n s than on the root-mean-square values. The calculations which use only two modes underestimate the s t r a i n amplifications at t h e outboard stations, whereas the analysis using three modes gives a good approximation t o the measured results.

The foregoing results Fmply that, f o r t h i s straight-wing airplane, calculations using only v e r t i c a l motion and the fundamental bending mode are adequate f o r determining t h e e f f e c t s of f l e x i b i l i t y on the roat- mean-square s t r a i n values but that the second bending mode must also be included when considering peak strains.

RESULTS F O R TI-IE B-47A AIRPIANE Frequency-Response Functions The r e s t of t h i s paper w i l l cover test results obtained from the

B-47A airplane investigations . Figure 5 shows t h e measured frequency-

response functions f o r the rear-spar bending s t r a i n s f o r various wing stations. Similar results were a l s o obtained f o r t h e s t r a i n s on the f r o n t spar but are not included. The results sham are f o r both t h e amplitude and the phases and were obtained by the cross-spectrum m e t h o d .

The gust input spectrum was obtained from t h e vane angle-of-attack meas- urements corrected f o r airplane motions according t o t h e method given i n reference 4. For present comparisons, the measured s t r a i n s at the var- ious stations were converted t o equivalent accelerations by dividing by the s t r a i n s per g i n pull-ups at the same test conditions. The reference curve shown i n t h e figure was based on t h e center-of-gravity accelerations which appear t o be r e l a t i v e l y uninfluenced by the fundamental airplane vibration mode and provides a measure of t h e s t r a i n s f o r s t a t i c loading.

(The use of the center-of -gravity accelerations f o r the reference loading is discussed i n more detail later.) The differences between the reference curve and t h e other curves thus provide a direct measure of the e f f e c t s of t h e dynamic f l e x i b i l i t y on t h e l o c a l strains. A s i n the case of the B-29, the e f f e c t s of f l e x i b i l i t y show up principally as a large peak at t h e first bending mode frequency which is around 1- cps. I n contrast t o t h e B-29, however, t h e magnitude of the peak is now smallest a t the root sta- t i o n and progressively increases f o r the outboard stations. Another significant difference between the frequency-response functions f o r the B-47A and t h e B-29 airplanes is the closer proximity of the first bending mode t o the short-period mode which is a% about 0.6 cps. A s a consequence, the gust input, which decreases rapidly w i t h frequency, w i l l be r e l a t i v e l y much higher a t the first bending mode i n t h i s case, and larger overall amplification effects may be expected.

The phases shown i n figure 5(b) indicate a l i n e a r increase i n phase l a g with increasing frequency, as i s the case f o r a simple system with a moderate amount of damping. Above 2 cps, the curves appear t o be e r r a t i c .

The r e s u l t s above 2 cps are not, however, considered t o be r e l i a b l e .

Strain-Amplif ication Factors Figure 6 shows t h e variations i n the bending-strain-amplif ication factors w i t h spanwise positions. Again, the r e s u l t s a r e shown based on both root-mean-square values and s t r a i n s having an equal frequency of occurrence. Note t h a t the ordinate scale i s compressed and covers a wider range of amplification values than the scale used earlier f o r the corresponding B-29 results.

For t h e swept-wing airplane, the effects of f l e x i b i l i t y are com- plicated by large s t a t i c aeroelastic or twist effects which a c t t o reduce t h e gust loading and the s t r a i n response. Thus, the derivation o f ampli- f i c a t i o n factors f o r t h i s case i s not straightforward, and several pro- cedures m i g h t be used. For present purposes, three s t r a i n responses are considered.

These are the actual measured strains, the numerator of t h e ordinate, and two reference s t r a i n conditions. These reference s t r a i n s are (1) The s t r a i n s obtained by the s t a t i c application of t h e same loads t o the airplane.

(2) The s t r a i n s obtained by the s t a t i c application of the loads t o an essentially "rigid" airplane, t h a t is, an airplane embodying no s t a t i c aeroelastic effects.

The r a t i o of the measured s t r a i n s t o the s t r a i n s i n the s t a t i c a l l y e l a s t i c airplane yields the solid-line curves and provides a measure of the purely The r a t i o of the measured dynamic s t r a i n amplification. (See f i g . 6.)

s t r a i n s t o the s t r a i n s f o r the airplane without s t a t i c aeroelastic e f f e c t s yields the dashed-line curves and provides a measure of the combined e f f e c t s of t h e s t a t i c alleviation and the dynamic amplification.

The procedure used i n t h e determination of the reference s t r a i n s was based upon the use of the actual measured center-of-gravity acceler- ations as a measure of t h e airplane loading i n rough air.

Examination of the power spectra of the normal accelerations had indicated t h a t the first mode had only a minor effect on the center-of-gravity accelerations.

A s a further check, the average airplane acceleration w a s determined f o r a short section of the t e s t run by using the accelerometer measurements from 22 locations along the wing and fuselage of the test airplane along w i t h their associated masses. The results obtained indicated that, except f o r the presence of high-frequency fluctuations associated w i t h the higher s t r u c t u r a l modes, the center-of-gravity acceleration provided a good meas- ure of the airplane acceleration. O n t h i s basis, the center-of-gravity acceleration measurements were faired t o remove the e f f e c t s of the higher structural modes and used as a measure of the airplane loading. The loads obtained on t h i s basis were then converted t o s t r a i n s f o r the various sta- tions on a s t a t i c basis by using the s t r a i n s per g as measured i n slow pull-up maneuvers at the test dynamic pressure. "he s t r a i n s obtained on t h i s basis provide a measure of the s t r a i n s f o r a s t a t i c a l l y e l a s t i c air- plane and were used i n obtaining the solid-line curves of figure 6.

I n order t o provide a measure of the static-aeroelastic effects on the strains, t h e s t r a i n s per g i n pull-ups were also determined f o r the condition of l o w or zero dynamic pressure. A t low dynamic pressure, the s t a t i c aeroelastic effects tend t o be minimized, and thus the s t r a i n s per g obtained at low dynamic pressure provide a basic "rigid" airplane reference condition. Figure 7 i l l u s t r a t e s the values of bending s t r a i n per g obtained at one s t a t i o n f o r various values of dynamic pressure. The variation of th; ;train per g appears l i n e a r over the w i d e range of dynamic pressure represented. A l i n e a r extrapolation t o a value of dynamic pressure of 0 was therefore used. The difference between the s t r a i n per g (0.65) f o r a dynamic pressure of 0 and the value (0.51) f o r the t e s t dynamic pressure provides a measure of the s t a t i c aeroelastic s t r a i n allevia'tion f o r t h i s station. The amount of t h i s alleviation is about 22 percent f o r t h i s s t a t i o n and varied somewhat f o r the other stations .

The s t r a i n s per g f o r the condition at a dynamic pressure of 0 were used with the airplane center-of-gravity acceleration t o obtain the sec- ond set of reference strains. These reference s t r a i n s constitute s t r a i n s f o r an airplane embodying no dynamic f l e x i b i l i t y or s t a t i c aeroelastic effects and w e r e used t o obtain the dashed curves of figure 6.

I n t h e upper part of figure 6, the dynamic amplification, shown by the solid curve, i s about 10 percent a t the root but increases rapidly along the span and reaches a value of about 2 a t the 60-percent-semispan station. The amplification factors obtained by considering both the s t a t i c alleviation and dynamic effects, shown by the dashed line, are below 1 a t the inboard stations but reach values of about 1 . 5 at the 60-percent -semi span st at i on.

-.

E The amplification factors based on the r a t i o s of s t r a i n s f o r equal frequency of occurrence, shown i n the lower part of figure 6, follow the same pattern as those based on the root-mean-square values but are every- where higher. It thus appears that, f o r the swept-wing B-47A airplane, the effects of d y n d c f l e x i b i l i t y are quite large, particularly at the m i d - span stations, but t h a t favorable s t a t i c aeroelastic alleviation moderates the large dynamic amplifications. In addition, it is evident t h a t several values f o r the amplification factor may be obtained depending upon t h e particular definition or reference used. The particular amplification factor of significance depends upon the specific application.

EFFECTS OF SPANWISE VARIATIONS I N TURBULENCE A s a f i n a l point, some indirect evidence of the e f f e c t s of spanwise variations i n turbulence on airplane gust response w i l l be presented.

A s mentioned previously, two methods could be used i n determining the frequency-response functions f o r the B-47A: t h e spectrum and the cross- spectrum methods. A s indicated, if no spanwise variations i n turbulence existed, then the gust input would be adequately reflected by the point measurements of the angle-of-attack vane. For t h i s case, both methods should yield identical r e s u l t s f o r the frequency-response function. Fig- ure 8 shows the frequency-response functions obtained by the two methods f o r the airplane center-of-gravity normal acceleration. It is quite clear t h a t the cross-spectrum r e s u l t s are consistently lower than those obtained by t h e spectrum method. Similar differences a l s o have been found between s t r a i n frequency-response functions obtained by the two The differences between these two results are suggestive of methods.

the effects of spanwise variations i n gusts which have received consider- able attention recently i n analytical studies by Diederich, Drischler, and Liepmann.

(See refs. 2, 6, and 7.)

By making use of some r e s u l t s obtained by Diederich (ref. 5 ) , first- order adjustments f o r the effects of spanwise variations of turbulence the condition of isotropic turbulence w e r e made t o these two results f o r i n accordance w i t h the analysis given i n t h e appendix. The adjusted frequency-response functions obtained are shown i n figure 9. Two e f f e c t s may be noticed from t h i s adjustment. the two frequency-response F i r s t , functions are now i n much b e t t e r agreement, and second, the adjustment has raised the two curves by from 10 t o 20 percent over most of the fre- quency range i n accordance with the span averaging functions of figure 10.

The basis f o r the underestimation and distortion i n the apparent frequency- response function of figure 8 stems from the f a c t that the point gust input used i s too high. The effective gust input i s the average gust velocity across the span which, as indicated i n reference 5 , tends t o f a l l below the point input at a l l frequencies. A s a consequence, the airplane acceleration response is lower than w h a t would be expected f o r uniform turbulence across t h e span i n accordance w i t h the point measurements.

These r e s u l t s thus suggest that the e f f e c t s of spanwise variations i n turbulence are significant f o r such airplanes as t h e B-47A. I n addition, since analytic r e s u l t s indicate that the e f f e c t s of spanwise variations i n turbulence are primarily a function of span, these e f f e c t s may he even more important f o r airplanes with larger span than t h e present airplane.

CONCLUDING REMARKS It has been indicated t h a t , f o r the B-29 airplane, the e f f e c t s of the first and second symmetrical bending m o d e s yield moderate s t r a i n ampli- f i c a t i o n s i n rough air a l l along the airplane span. Calculations involving one or preferably two s t r u c t u r a l modes appear t o yield r e l i a b l e estimates of f l e x i b i l i t y on t h e s t r a i n s .

For swept-wing airplanes, the e f f e c t s of f l e x i b i l i t y a r e complicated by the importance of s t a t i c aeroelasticity e f f e c t s i n addition t o t h e dynamic response. I n the case of the B-47A airplane, the dynamic a n r p l i f i - cations appear t o be quite large, particularly i n the midspan region.

These amplifications are a t least p a r t i a l l y balanced by large and favor- able s t a t i c aeroelastic e f f e c t s associated with sweep. Finally, some indirect r e s u l t s suggest that spanwise variations i n tukbulence have a significant e f f e c t on t h e responses of the B-47A airplane.

1 1 APPENDIX EFFECTS O F SPANWISE VARIATIONS I N TURB-CE ON MEASURFD FREQUENCY-RESPONSE FUNCTIONS I n the main body of t h i s paper, it was indicated t h a t , f o r uniform turbulence across the airplane span, the amplitude of the frequency- response function f o r gust disturbances can be obtained experi-

I H ( f ) I

mentally by two methods; the spectral method which i s based on t h e relation and the cross-spectral method which i s based on the r e l a t i o n The subscripts s and c a r e used t o differentiate between the e s t i - mates obtained by the two methods. I n t h i s appendix, the e f f e c t s on these estimates of spanwise variations of turbulence w i l l be outlined.

The material t o be presented is based on t h e analysis of the e f f e c t s of spanwise gust variations given i n reference 5 .

The response of an airplane z ( t ) t o two-dimensional turbulence, t h a t is, turbulence varying along the f l i g h t path and along the spanwise direction, may be expressed as where b wing span v e r t i c a l gust velocity impinging at wing leading edge a t x(t,y) time t and span location y h(t,y) response at time t due t o u n i t impulse gust impinging

a t wing between s t a t i o n y and y + dy a t time zero

.

1 ; : The power spectrum of z ( t ) as derived i n reference 5 i s given by where 4Z(f> power spectrum of response z ( t )

4x (f , y2-y1) cross-spectrum between gust velocities impinging at

wing leading edge at stations y2 and yl influence function describing response of airplane H(f,Y) t o unit sinusoidal gusts impinging at wing leading at s t a t i o n y and i s given by edge "he a s t e r i s k designates the complex conjugate.

I n these terms, the frequency-response function obtained by t h e spectral method can be expressed as where 4(f,O) is the power spectrum of the gust input at span s t a t i o n 0 (such as measured w i t h the vane).

The expression f o r given by equation (A5) may be viewed

1 H s ( f ) I

as an average frequency-response function. Further insight i n t o t h i s result can be obtained by considering the special case where For t h i s case Equation ( A 7 ) indicates t h a t the quantity determined from

1 Hs ( f ) I

measurements represents the "frequency part" of the frequency-response function and is.multiplied by the term i n brackets, which m i g h t be con- sidered a span averaging function. For the case of uniform turbulence across the span, equation ( A 7 ) reduces t o If the turbulence is isotropic w i t h a known spectrum, the averaging function given by the term i n brackets i n equation ( A 7 ) can be evaluated.

Evaluations of the numerator of the term i n brackets are given i n refer- ences 5 and 6 f o r several assumed power spectra of turbulence and f o r several assumed span distributions y. By using these results, t h e func-

t i o n 7 ( f ) was evaluated f o r a particular case and the results obtained

a r e shown i n figure 10. The r e s u l t shown i n figure 10 i s f o r the case of a uniform span distribution (7(y) = l/b) and a spectrum of v e r t i c a l gust velocity given by 25rf where Q = - and V i s the airplane forward speed. In equation ( A 8 ) ,

v

crw is the root-mean-square gust velocity and L is the scale of turbu- lence. A value of L = 1,000 f e e t appears t o be representative of con- ditions f o r atmospheric turbulence. For present purposes, a value of b / L = 0.1 was assumed.

A similar analysis may be applied t o the cross-spectrum case and yields the following results:

.. .. , I , > . _ I . I _ _ -

where t h e weighting function given by the term i n brackets may also b e

viewed as an average span weighting function The function T2( f )

y2( f ) .

can also be evaluated from figure 4 of reference 5 f o r the case of mi- form span loading and the gust spectrum of equation ( A 8 ) . This func- t i o n Y2(f) i s also shown i n figure 10.

If the weighting functions Yl(f) and T 2 ( f ) given i n equations (A7) and (Ag) are divided i n t o the measured values of I H s ( f ) I and l H c ( f ) 1, respectively, of figure 8, estimates of I H ( f ) l may be obtained which a r e compatible. The r e s u l t s obtained i n t h i s manner a r e shown i n figure 9.

REFERENCES 1. Mickleboro, Harry C., and Shufflebarger, C . C.: Flight Investigation of the Effects of Trpnsient Wing Response on Wing Strains of a Twin-Engine Transport Airplane i n Rough A i r . NACA TN 2424, 1951.

2. Murrow, Harold N., and Payne, Chester B.: Flight Investigation of the Effect of Transient Wing Response on Wing Strains of a Four- Engine Bomber Airplane i n Rough A i r . NACA TN 2951, 1953.

3. Houbolt, John C., and Kordes, Eldon E.: Structural Response t o Discrete and Continuous Gusts of an Airplane Having Wing-Bending F l e x i b i l i t y and a Correlation of Calculated and Flight Results.

NACA Rep. 1181, 1954. (Supersedes NACA TN 3006; also contains e s s e n t i a l material from TN 2763 and TN 2897.)

4. Crane, Harold L., and Chilton, Robert G.: Measurements of Atmospheric Turbulence Over a Wide Range of Wavelength for One Meteorological Condition. NACA TN 3702, 1956.

5. Diederich, Franklin W.: The Response of an Airplane t o Random Atmos- pheric Turbulence. NACA TN 3910, 1957.

6. Diederich., Franklin W., and Drischler, Joseph A.: Effect of Spanwise Variations i n Gust Intensity on the L i f t Due t o Atmospheric Turbu- lence. NACA TN 3920, 1957.

7. Liepmann, H. W.: Extension of t h e Statistical Approach t o Buffeting and Gust Response of Wings of F i n i t e Span. Jour. Aero. Sci., vol. 22, no. 3, Mar. 1955, pp. 197-200.

TEST AIRPLANES Figure 1 MEASURED 6-29 STRAIN FREQUENCY RESPONSE FUNCTION IH(f)l, STRAIN GUST VELOCITY 1 I I I I I 0 I 2 3 4 5 f , CPS . . . .

'E CALCULATED B -29 STRAIN FREQUENCY RESPONSE FUNCTION Y/+= 0.15

A

IH (f ) I , STRAIN GUST VELOCITY 0 I 2 3 4 5 f,CPS Figure 3 B -29 S T R A I N A M P L l F I C A T I O N %, FLEX 1.1 v€, REF

--_

--*_

-----_------

I .o I I I I I I I I 1 1 0' o EXPERIMENTAL CALCULATED -----VERT. MOTION + 1st WING BENDING \ - V E R T . MOTION + 1st AND 2d WING BENMNG € F L E X € R E F a 0 .2 .4 . 6 .8 1.0 y/+ Figure 4 MEASURED B - 4 7 A STRAIN FREQUENCY- RESPONSE F U N C T l O N

/\

I 4, 4

STRAIN GUST VELOCITY 0 I 2 3 f , C P S Figure 5 ( a ) MEASURED B-47A STRAIN FREQUENCY-RESPONSE FUNCTION PHASE ANGLE h PHASE ANGLE I DEG I I I I I I I 0 I 2 3 f, CPS Figure 5(b) B-47A STRAIN AMPLIFICATION %, a i , FLEX REF : :

3 - o-- DYNAMIC AMPLIFICATION

o---- STATIC ALLEVIATION + 'FLEX 'REF

-----

I - 0 .2 . 4 .6 .8 I .o y/* Figure 6 VARIATION OF STRAIN PER g IN PULL-UP WITH DY NAMlC PRESSURE

---- -\ I

STRAIN - . 4 INDICATION PER g

GUST TESTA

CONDITION

-

I

-2

I

I I I I I , Figure 7 2c B-47A NORM4L-ACCELERATION FREQUENCY- I?ESPONSE FUNCTION ACCELERAT I ON G U S T VELOCITY 0 .5 I .o L 5 20 2.5 f ,CPS Figure 8 B-47A NORMAL-ACCELERATION FREQUENCY- RESPONSE FUNCTION ADJUSTED FOR SPANWISE GUST VARIATIONS I H ( f ) l A D J 3 ACCE L E R ATlON GUST VELOCITY 0 .5 I .o 1 5 2 . 0 2.5 f , C P S .

-0

&&9

Figure 9

SPAN AVERAGING FUNCTIONS 7 ( f ) AND % ( f ) FOR b/L= 0 . 1

-

. 7 Figure 10 LOADS lMPLICATI0NS OF GUST-ALLEVIATION SYSTESIS By W i l l i a m H. Phillips Langley Aeronautical Laboratory SUMMARY I A review is presented of the factors affecting gust loads and the methods or devices which reduce these loads. Aerodynamic devices which reduce the lift-curve slope include spoiler-deflector controls, f o r which some data are presented i n the Mach number range from 0.4 t o 1.1.

Systems are also considered i n which a sensing device is used t o operate gust-alleviation controls. Two basically different types of sensing devices are possible, the load-sensing type and the angle-of -attack-- sensing type. These devices are compared and t h e i r limitations discussed.

Some preliminary f l i g h t measurements of wing-root bending moment due t o turbulence are presented f o r a gust-alleviation system installed i n a small twin-engine transport airplane. This system increased the wing- root bending moments as compared with those of the basic airplane. This increase resulted from the f a c t that the system as tested w a s adjusted t o reduce acceleration and, as a result, overcompensated f o r the wing-root bending moments due t o gusts. Some f l i g h t measurements of the e f f e c t s of a yaw damper on the t a i l loads of a bomber airplane are also presented.

INTRODUCTION G u s t alleviation has been of continued i n t e r e s t t o almost every group i n aviation since its inception, but it has not been incorporated i n production airplanes. Apparently the reason f o r the lack of use of gust alleviation is that detailed analyses of promising devices e i t h e r pose problems insoluble at a given stage i n aircraft development or result i n practical disadvantages t h a t seem t o outweigh the potential benefits. Systems have been studied by various organizations with the objectives of providing improved riding comfort, increased safety due t o load reductions, reduced structural weight, and more stable gun platforms.

Inasmuch as the various systems are perennially proposed as m e a n s of improving a i r c r a f t , a need f o r a summary of the methods available f o r gust alleviation and the problems associated with these methods is apparent.

The present report considers the loads implications of gust-alleviating methods.

'3 SYMBOLS wing chord C lift-curve slope cLa dynamic pressure U gust velocity true airspeed V drag-coefficient increment ACD M Mach number angle of attack a velocity a t stall V S cruising speed vC maximum speed VMAX DISCUSSION The factors affecting gust loads are shown i n table 1. The first factor is the d i r e c t load due t o the gust. As indicated by Vne CL, the formula, this load is proportional t o the lift-curve slope q, and the change i n angle of attack due t o the gust, dynamic pressure U/V, where U is the gust velocity and V is the true airspeed. This or by reducing q. The load may therefore be reduced by reducing cL,.

second factor is the airplane motion due t o gusts o r due t o controls.

The airplane motion is dependent on the basic airplane s t a b i l i t y , and may a l s o be influenced by the operation of controls manually o r by an autopilot. The t h i r d factor t o be considered is the action of special controls t o o f f s e t the gust load directly. This category would include the relieving effects due t o wing bending, the use of hinged surfaces or and f i n a l l y the use of special gust-alleviating 'controls, such as w i n g s , w i n g flaps, operated by a sfrvome2l-jpgsm.

t 3 ,CI Effect of Spoiler-Deflector Control Aerodynamic devices which reduce the lift-curve slope include t h e use of sweep o r reduced aspect r a t i o , the effects of which are well known, and the use of chordwise s l o t s which, i n effect, reduce the aspect r a t i o .

Another device f o r reducing the lift-curve slope is the spoiler-deflector control ( r e f . 1). The e f f e c t s of this device as a function of Mach num- ber on a swept wing are shown i n figure 1. This figure shows the percent of the basic wing load produced by the wing with a spoiler-deflector con- t r o l covering 18 percent of the span. The increment i n drag coefficient The spoiler height i s a l s o shown. These data are taken from reference 2.

above the w i n g w a s 0.02’3 and the deflector projection below the wing w a s 0 . 1 5 ~ . I n t h i s case, the reason f o r the short span of the spoiler- deflector control w a s t o locate it inboard of the aileron and outboard of the horizontal tail. T h i s device provides a large increase i n drag as well as a reduction i n lift-curve slope. For t h i s reason, this control might be useful f o r slowing an airplane down when rough air is encountered but it would not be desirable f o r continuous use i n high-speed f l i g h t .

Tests on specific configurations have shown t h a t this control may be located so as t o minimize longitudinal t r i m changes. Location of the spoiler-deflector control ahead of a n aileron, however, has been found t o reduce greatly the aileron effectiveness, as might be expected. Possibly, the spoiler-deflector control could be operated i n conjunction with the aileron t o overcome t h i s d i f f i c u l t y .

Effect of Sensor and Servo System Operating Special Controls I n systems which use a sensing device t o detect the gusts and t o operate gust-alleviation controls, two basically different types of sensing devices are possible: one, the load-sensing type such as s t r a i n gages or an acceleroneter, and the other, the angle-of -attack-sensing type. The effects of these devices d i f f e r i n several important respects.

F i r s t , as shown i n figure 2, these sensing devices exhibit different trends of effectiveness as a function of airspeed.

The gust envelope f o r a typical transport airplane i s a l s o shown i n this figure. With the load-sensing type of gust alleviation the percent a l l e v i a t i o n increases with increasing speed, whereas with the angle-of-attack-sensing type the percent alleviation tends t o remain constant. Thus, i f the two systems are designed t o have the same effectiveness a t a given speed, the load- sensing type w i l l show greater effectiveness a t higher speeds. These results apply only i f the system gain i s held constant as might occur with the use of some simple types of aerodynamically operated gust a l l e v i - ators. If a servo system i s used, of course, it is possible t o vary the gain of the system as a function of speed and thereby change the e f f e c t s of speed from those sham.

The second difference between the two systems i s concerned with the different nature of the effects which l i m i t the m a x i m u m alleviation obtainable. The usual limitation i n the case of the load-sensing system is the occurrence of a high-frequency instability. Figure 3 shows the percent.load experienced with a load-sensing system as a function of the r e l a t i v e gain. A relative gain of 1 on this scale represents a condition i n which, f o r example, a load increment corresponding t o 1 g on the sensor w i l l operate the controls t o produce a load increment of on the airplane. Very high gains are required t o obtain a large - l g percent of alleviation. A load-sensing system, however, is a typical closed-loop system, f o r which high gains are l i k e l y t o result i n i n s t a b i l i t y . Analog-computer studies f o r certain typical cases have shown t h a t reduction i n load below 50 percent of the unalleviated case resulted i n an oscillatory response and that these oscillations became unstable a t a higher gain as shown.

With the angle-of-attack-sensing system, t h i s type of i n s t a b i l i t y is much less l i k e l y t o be encountered because this arrangement i s much more nearly an open-loop system, that is, operation of the angle-of- attack sensor causes deflection of the alleviation controls but opera- t i o n of the alleviation controls has only a minor e f f e c t on the indica- tions of the angle-of-attack sensor. For t h i s reason, the limitation is less on the amount of gain ,which may be employed, and systems are designed usually so t h a t the e f f e c t of a uniform gust i s completely counteracted by the alleviation controls. With t h i s type of system the limits on the load reductions obtainable r e s u l t primarily from the f a c t that sensing the gust at one point does not give a representative indi- cation of the average angle of attack across the wing span. Unpublished theoretical studies have shown t h a t the e f f e c t of nonuniform gust veloc- i t y across the span f o r the angle-of-attack-sensing system is a function of the r a t i o of the w i n g span t o the scale of turbulence. Because of the large scale of atmospheric turbulence, values of alleviation as high as 80 percent may be obtained with a single sensor located ahead of the nose which operates the controls with no lag. The addition of a suitable f i l t e r t o the output of the sensor which reduces the response t o high-fre- quency gusts further improves the alleviation theoretically attainable.

Such a filter may also be desirable i n order t o reduce the effects of structural feedback, which might cause the system t o reinforce structural modes of oscillation i f the system response were not attenuated a t high frequencies.

Flight Tests of Gust-Alleviation System Installed i n Airplane A f l i g h t investigation has been made of a gust-alleviation system i n a small twin-engine transport airplane. Some preliminary 4 i n s t a l l e d of t h i s study have been reported previously (refs. 3 and 4).

, I w a s designed improvement of passenger camfort. The system uses an angle-of-attack vane t o operate wing flaps through a servo system. The reduction i n acceleration obtained with The r e l a t i v e values of normal accel- t h i s system is shown i n figure 4.

eration as a function of frequency, obtained w i t h t h e basic airplane and the gust-alleviated airplane f o r comparable conditions of turbulence, and The r e l a t i v e the e f f e c t of the system on pitching velocity are shown.

values plotted i n t h i s figure are proportional t o the square root of the power spectral density of the response and show the correct r e l a t i v e values as well as the variation of the response with frequency. The nor- mal acceleration f o r the alleviated airplane w a s reduced to.30 o r 40 per- cent of t h a t f o r the basic airplane i n the frequency range from 0 t o 2 cyles per second. The pitching velocity, which w a s small f o r t h e basic airplane, w a s further reduced f o r the alleviated case.

Extensive strain-gage measurements have been made t o determine the e f f e c t of this system on the structural loads. These data have not been completely evaluated a t this t i m e . The e f f e c t of the system on wing-root bending moment is sham i n figure 5 . The wing-root bending moment is actually increased by the gust-alleviation system. The explanation of this increase i s indicatedby the i n s e r t on the figure which shows the change i n span load distribution f o r basic and alleviated airplanes due t o a small positive increment of angle of attack. I n the alleviated case, the flaps on the wing are deflected up on the outboard sections and dawn near the root. This arrangement provides downwash conditions a t the tail which minimize pitching moments due t o the gusts. The resultant l i f t due t o this combination is about zero, but because the t i p sections are much more effective i n producing bending moment, the result is a negative bending moment due t o an up gust. The magnitude of this nega- t i v e bending moment is actually greater f o r a given gust than the posi- t i v e bending moment on the basic airplane.

These r e s u l t s apply only s o long as the system is operating i n its lineax range. A t a gust velocity of about 10 f e e t per second, the f l a p s reach t h e i r stops. For greater up-gust velocities, the bending moments would increase i n the positive direction as on the basic airplane. Thus, f o r a gust velocity of 20 f e e t per second, the bending moment would be expected t o come back t o about zero, and f o r higher gust velocities would again become positive. This sytem i s therefore one which serves t o improve passenger comfort i n the frequently encountered small gust veloc- ities, but which reduces the structural loads due t o severe gusts. No f l i g h t data are available, however, t o show the characteristics of t h e system i n severe turbulence. The system increased the magnitude and frequency of t a i l loads as well as the stresses i n minor s t r u c t u r a l com- ponents such as the rear spar, the wing flaps, and so forth. This result indicates that fatigue loads would be a more serious problem f o r the gust- alleviated airplane.

Effect of Yaw Damper on Vertical-Tail Loads Some measurements have been made t o determine the e f f e c t of a yaw damper on the v e r t i c a l - t a i l loads experienced by a bomber airplane i n rough air a t various altitudes. These r e s u l t s are shcwn i n figure 6, which presents the probability of exceeding a given value of vertical- t a i l spar s t r a i n with the yaw damper on and off at two altitudes, 35,000 f e e t and 5,000 f e e t .

The yaw damper reduces the magnitude of The damping of the Dutch loads considerably i n the high-altitude case.

r o l l motion of 'the airplane under these conditions is l o w so that a The e f f e c t of large resonance a t the Dutch roll frequency is obtained.

the yaw damper is primarily t o reduce t h i s amplification of load due t o the Dutch roll motion. A t l o w altitude where the damping of the air- plane i s better, the gains due t o the yaw damper are small.

Sane studies have been made t o determine the f e a s i b i l i t y of reducing the loads on the wings by use of the normal elevator control. The r e s u l t s are similar t o those obtained i n the l a t e r a l case; that is, i f the air- plane has very l o w damping i n pitch the loads may be reduced through elimination of the resonant peak of the short-period mode ( r e f . 5 ) . How- ever, any attempt t o reduce the direct e f f e c t of the gust on the l i f t of the surfaces by heading the airplane into the gusts requires large pitching motions of the airplane.

CONCLUDING R E M A F K S A brief review has been given of the basic methods of gust allevia- tion, and some results obtained i n f l i g h t t e s t s of a gust-alleviation system have been presented. A system designed f o r improvement of pas- senger comfort did not reduce structural stresses while operating i n its linear range.

The system would be expected t o reduce the wing loads due t o severe gusts, but loads i n the t a i l and other structural components were increased.

* REFERENCES 1 . Croom, Delwin R., Shufflebarger, C. C., and Huffman, Jarrett K . : A n Investigation of Forward-Located Fixed Spoilers and Deflectors as Gust Alleviators on an Unswept-Wing Model. NACA TN 3705, 1956.

2 . Croom, Iklwin R., and Huff'man, Jarrett K.: Investigation at Transonic Speeds of Deflectors and Spoilers as Gust Alleviators on a 35' Swept

Wing - Transonic-Bump Method. (Prospective NACA paper. )

3. Kraft, Christopher C., Jr.: Initial Results of a Flight Investigation TN 3612, 1956.

of a Gust-Alleviation System. NACA Initial Results of a Flight 4. Cooney, T. V., and Schott, Russell L . : Investigation of the Wing and Tail Loads on an Airplane Equipped With a Vane-Controlled Gust-Alleviation System. NACA TN 3746, 1956.

5 . Vitale, A. James, Press, H . , and Shufflebarger, C. C . : An Investiga- tion of the Use of Rocket-Powered Models for Gust-Load Studies With an Application to a Tailless Swept-Wing Model at Transonic Speeds.

NACA TN 3161, 1954.

TABLE I FACTORS AFFECTING GUST LOADS A LOAD = SUM OF I-DIRECT LOAD DUE TO GUST- (a C L ,

oq

2-AIRPLANE MOTION DUE TO GUST O R CONTROLS (A) BASIC AIRPLANE STABILITY (B OPERATION OF CONTROLS MANUALLY OR BY AUTOPILOT 3-ACTION OF SPECIAL CONTROL TO OFFSET LOAD (AI WING FLEXIBILITY (B) HINGED SURFACES (c] SENSOR AND SERVO SYSTEM OPERATING SPECIAL CONTROLS LOAD ALLEVIATION AND DRAG OF A SPOILER-DEFLECTOR 0 .4 .6 .8 I .o 1.2 M Figure 1 EFFECT OF SENSING SYSTEM ON VARIATION OF LOAD WITH AIRSPEED LOAD, g UNITS I .5 I .o 4 . 5 " P C

Figure 2 233

lo LOAD REDUCTION WITH LOAD- SENSING SYSTEM

loo 80 R /SCILLATIONS

I I I I I I I I I 0 1 2 3 4 5 6 7 8 RELATIVE GAIN Figure 3 EFFECT OF GUST- ALLEVIATION SYSTEM ON AIRPLANE MOTIONS BASIC AIRPLANE ACCELERATION AMPLITUDE 0. \ PITCHING- VELOCITY AMPLITUDE 1-

------

0 I 2 3 FREOUENCY, CPS Figure 4 EFFECT OF GUST- ALLEVIATION SYSTEM ON ROOT BENDING MOMENTS SPAN LOAD DISTRIBUTIONS BENDING- GUST-ALLEVIATED AIRPLANE MOMENT BASIC AIRPLANE AMPLITUDE I I I I I I I 0 I 2 3 FREQUENCY, CPS Figure 5 EFFECT OF YAW DAMPER ON VERT1 CAL- TAIL LOADS DAMPER OFF

--- DAMPER ON

M = 0.35 M = 0.65

.I I- ’\ \ t \\

\ ’ .001 0 0 VERTICAL-TAIL SPAR STRAIN Figure 6 RECENT DATA ON TI33 FRICTION DURING LANDING By Sidney A. Batterson Langley Aeronautical Laboratory SUMMARY A n investigation w a s made a t the Langley landing-loads track t o obtain data on the coefficient of f r i c t i o n during wheel spin-up. A landing gear w a s tested a t horizontal velocities ranging from 0 t o 180 f e e t per second together with v e r t i c a l velocities of 7.0 and 9.3 f e e t t i r e per second. The results indicate the e f f e c t of forward speed and inflation pressure on the coefficient of f r i c t i o n .

INTRODUCTION The National Advisory Committee f o r Aeronautics has been engaged for some time i n an experimental study of the wheel spin-up phenomenon during landing. A s a r e s u l t of these investigations, it has been possible t o separate the effects of a number of parameters on the coefficient of f r i c - tion. Until recently, however, data could not be obtained under controlled conditions f o r either the large landing gears or the high forward speeds which are required f o r modern airplanes. I n order t o obtain such data the NACA has put into operation a new research f a c i l i t y called the landing- loads track. This paper presents the f i r s t data obtained at the track and indicates the e f f e c t of forward speed and t i r e inflation pressure on the coefficient of f r i c t i o n . Although the trends are clear it i s not yet pos- s i b l e t o define the variations accurately because of the limited number of available t e s t results.

TEST CONDITIONS The t o t a l dropping weight w a s 20,000 pounds. The t e s t covered a horizontal velocity range from 0 t o 180 f e e t per second and v e r t i c a l velocities' of 7 and 3 . 3 f e e t per second. The landing gear w a s equipped with a 44 x 13, type V I I , 26-ply-rating t i r e . The normal inflation pressure f o r the 20,000-pound weight is 140 pounds per square inch; how- ever, the t i r e pressure w a s varied i n one series of t e s t s . All tests were made with the s t r u t inclined a t a m angle of 15O. A l i f t force of 20,000 pounds w a s applied t o the dropping mass throughout the impact, but the airplane f l e x i b i l i t y characteristics were not simulated. Com- parisons made of the landing surface a t the landing-loads track and an shared the roughness of both sur- active runway a t Langley Field, V a . , faces t o be about the same.

RESULTS AND DISCUSSION Effect of Horizontal Velocity Figure 1 shows the e f f e c t of forward speed on the v e r t i c a l and drag reactions a t the ground and on the Coefficient of f r i c t i o n . Time his- t o r i e s are shown of three tests made at horizontal velocities vh of 110, 130, and 160 f e e t per second. The sinking speed Vv was 9 . 3 f e e t per second f o r all three tests. I n reference 1 it was shown that the coeffi- cient of f r i c t i o n is affected by the vertical load. However, during the three t e s t s shown i n figure 1, the maximum coefficient of f r i c t i o n occurred at approximately the same value of v e r t i c a l load. This i s apparent from the upper s e t of curves where the c i r c l e s appearing on the curves indicate the value of the vertical load a t the instant of maximum coefficient of f r i c t i o n f o r each t e s t . These data, therefore, i s o l a t e the e f f e c t of forward speed on the maximum coefficient of f r i c t i o n , and show that increases i n forward speed reduce the maximum coefficient of f r i c t i o n .

A t the present time insufficient data are available a t constant v e r t i c a l load t o define this variation accurately.

I n figure l i t can be seen that the maximum drag reaction as well as the maximum coefficient of f r i c t i o n changes over a limited range of forward Figure 2 shows the variation of maximum drag reaction over a much speed.

The v e r t i c a l velocity is 9 . 3 f e e t larger range of horizontal velocities.

per second. This v e r t i c a l velocity is the same as f o r the data i n f i g - Each point represents a separate t e s t , and the maximum drag reac- ure 1.

t i o n is plotted against the horizontal velocity of the t e s t .

The curve reaches a maximum a t a forward speed of about 110 f e e t per second.

It can be seen i n figure 1 that t h i s is the forward speed where wheel spin- up occurs just as the v e r t i c a l load roughly levels off. A t forward speeds l e s s than 110 f e e t per second spin-up occurs sooner and a t a lower value of vertical load and results i n smaller drag loads. A t the higher forward speeds, although the v e r t i c a l loads remain approxi- mately constant, the decrease i n maximum coefficients of f r i c t i o n causes smaller drag loads.

Effect of Tire Pressure Figure 3 shows the effect of variation i n t i r e pressure on the coef- f i c i e n t of f r i c t i o n . Four t e s t s were made a t a horizontal velocity of .

160 f e e t per second and a vertical velocity cf 7 f e e t per second. The t i r e inflation pressures p covered a range from 35 t o 210 pounds per square inch. I n figure 3 the coefficient of f r i c t i o n is plotted against the instantaneous skidding velocity. Skidding velocity is defined as the difference i n velocity between the peripheral speed of the t i r e and the runway. Since the skidding velocity is maximum a t the instant of touchdown, spin-up occurs from right t o 3 . I n the region l e f t i n figure where the skidding velocity is large, the curves form two groups. Although the difference between the two curves which form each group is small, the difference between the two groups is large. Furthermore, the curves obtained a t the higher t i r e pressures exhibit lower coefficients of f r i c - tion. It is believed that t h i s is caused primarily by differences i n t e m - perature i n the t i r e footprint region. Since as the t i r e inflation pres- sure i s increased the tire footprint areas decrease, the heat generated during skidding i s distributed over a smll area, and the rubber is hot and primarily molten and exhibits a low coefficient of f r i c t i o n . However, a t the low inflation pressures, where the t i r e footprint areas are larger, the heat i s distributed over a greater area; the rubber i s cooler and p r i - marily i n the solid s t a t e and exhibits a higher f r i c t i o n coefficient.

Evidently, the transition region from s o l i d t o molten rubber occurs some- where i n the region of t i r e pressures between 70 and 140 pounds per square inch. All the curves reach approximately the same maximum value a t the low skidding velocities. This indicates that the t i r e has turned sufficiently so that cool rubber predominates i n the footprint region when spin-up occurs.

Figure 3 shows that the maximm coefficient of f r i c t i o n obtained a t a t i r e inflation pressure of 35 pounds per square inch occurs a t an appreciably higher skidding velocity than those obtained a t the higher t i r e pressures. This is attributed primarily t o the method used i n measuring the skidding velocity. I n order t o obtain the peripheral speed of the t i r e , measurenents are made of the rotational velocity of the wheel, and the rotational motion of the t i r e with respect t o the wheel is neglected. As the t i r e pressure i s decreased the response of the wheel t o the motion of the t i r e i s lowered. This i s not too c r i t i c a l i n the early stages of the impact where the increase of the drag load is rela- t i v e l y slow. However, appreciable errors are introduced as spin-up is approached since the wheel i s unable t o follow the rapid changes of the t i r e motion caused by the rapidly changing drag load.

Effect of Braking and Wet Landing Surface Figure 4 shows time histories of drag reactions obtained f o r tests made a t a horizontal velocity of 160 f e e t per second and a v e r t i c a l veloc- i t y of 7 f e e t per second.

Wheel spin-up i n all cases occurred subsequent t o the leveling off of the vertical-load curve. The curve indicated as "braked" w a s obtained during a landing made with p a r t i a l brake pressure applied t o the wheel. The curve labeled "free" w a s obtained during a Braking caused reduced normal landing with the wheel free t o rotate.

spin-up accelerations and, t o a certain degree, simulated the e f f e c t of increasing the moment of i n e r t i a of the wheel. It can be seen that, even .

though the braked wheel skidded f o r a longer time, the maximum drag load i n both cases w a s the same.

The curve labeled "wet" i n figure 4 w a s obtained from a landing made on a wet runway with the wheel free t o turn. The other curye w a s obtained from a landing made with the wheel locked, ant! the rubber i n the footprint area w a s undoubtedly molten. For both curves the skidding velocities are it can be seen that the drag high, up t o 0.10 second after impact, and loads are approximately the same during t h i s time. This indicates t h a t the lubricating effects of w a t e r and molten rubber are about the same.

is I n the case of the landings on wet concrete where the lubricant spread along the runway, an appreciable reduction is seen i n the m a x i m u m drag load when compared with the maximum drag loads occurring i n e i t h e r the free or the braked landing. This 'indicates t h a t runway lubrication, i n addition t o reducing the coefficient of f r i c t i o n at high skidding velocities, a l s o r e s u l t s i n a reduction i n the coefficient of f r i c t i o n a t F the very l o w skidding velocities where the f r i c t i o n i s of the s t a t i c ,or interlocking type.

S W Y OF RESULTS The principal results indicated by these tests are as follows: 1. The m a x i m u m coefficient of f r i c t i o n developed during wheel spin- up appeared t o decrease as the horizontal velocity w a s increased.

2. Landings made with varying t i r e inflation pressures indicated that a t the high skidding velocities the coefficient of f r i c t i o n w a s lower f o r the higher t i r e . i n f l a t i o n pressures. However, a t the low skidding velocities, the value of the maximum coefficient of f r i c t i o n appeared t o be substantially independent of the t i r e inflation pressure.

3. The maximum drag load obtained during a landing made with p a r t i a l brake application w a s the same as that obtained during a landing with the same initial conditions and with the wheel free t o rotate.

4. A t high skidding velocities the lubricating e f f e c t of water on the runway is approximately the same as that of molten rubber.

REFERENCE 1. Milwitzky, Benjamin, Lindquist, Dean C., and Potter, Dexter M.: A n Experimental Study of Applied Ground Loads i n Landing. NACA Rep. 1248, 1955. (Supersedes NACA TN 3246.)

€ GROUND REACTIONS AND COEFFICIENT OF FRICTION 5 0 r x IO3 GROUND ,REACTIONS, L B I I

COEFF. OF 4 1 4

’ ;\

F R I C T I O N !\ I I :I I I I I 0 .I .2 .3 .4 TIME AFTER IMPACT, SEC Figure 1 M A X I M U M DRAG REACTIONS VERTICAL VELOCITY, 9.3 F P S

20 -

M A X I M U M DRAG 15- REACT1 ON, LB 0 50 IO0 150 200 HORIZONTAL VELOCITY , V h , FPS

. a . a a . L . a 1 , 1 - , - - -

F 'IN.

- .2 - . I I I I I Figure 3 DRAG REACTIONS HORIZONTAL VELOCITY, 1 6 0 FPS; VERTICAL VELOCITY, 7 FPS I I J 0 .IO .20 .30 T I M E AFTER IMPACT,SEC 1.

- 4 A SUMMARY O F GROUND-MADS STATISTICS . b

% f b 2

By John R. Westfall, Benjamin Milwitzky, s Norman S. Silsby, and Robert C . Dreher Langley Aeronautical Laboratory SUMMARY This paper b r i e f l y summarizes the more important s t a t i s t i c a l data obtained by the NACA on the subject of ground loads. The information presented r e l a t e s primarily t o landing-impact and taxiing loads; however, some limited data are a l s o presented on one' phase of ground-handling loads, namely, braking f r i c t i o n . A number of experimental and theoreti- c a l papers dealing w i t h various aspects of the subject are l i s t e d i n the bibliography.

IXLBODUCTION The NACA has f o r some time been concerned with t h e study of ground loads on aircraft; these include landing-impact loads, taxiing loads, and A number of experimental and theoretical loads due t o ground handling.

reports that have been published on various aspects of the subject are listed i n t h e bibliography. The present paper summarizes the more impor- t a n t s t a t i s t i c a l data on ground loads obtained by the NACA, which may serve as a basis f o r predicting the ground-loads experience of a i r c r a f t .

The two major phases of the ground-loads problem considered herein a r e landing impact and taxiing loads; however, some limited data are also presented on one phase of ground-handling loads, namely, braking f r i c t i o n .

The section on landing impact considers first the i n i t i a l contact conditions, then landing-gear reactions and airplane response.

!The con- t a c t conditions are i n the form of s t a t i s t i c a l data on f i v e parameters: v e r t i c a l velocity, horizontal velocity, bank angle, rolling velocity, and wing l i f t . Although there are other parameters, the ones considered appear t o be t h e most important. The discussion of ground reactions and airplane response is primarily concerned with t h e analytical prediction of v e r t i c a l and drag loads from the known i n i t i a l conditions.

On t h e subject of taxiing loads, data are available i n the form of runway profiles and acceleration measurements from VGH records i n taxiing; t h e latter are presented i n s t a t i s t i c a l form. Some considerations on air- plane structural response i n taxiing are also given.

With regard t o ground handling, some limited data are presented on t h e coefficient of f r i c t i o n as measured i n braking tests with an airplane and with a specially designed tow cart.

SYMBOLS Fv v e r t i c a l ground force, lb f frequency, cps acceleration due t o gravity, f t / s e c 2 g An incremental center-of-gravity acceleration, Q units t i r e pressure, lb/sq in.

P t i r e v e r t i c a l velocity at contact, f p s VV W airplane weight, l b P coefficient of f r i c t i o n Subscript : max maximum FKEEXJLTS AND DISCUSSION Landing Impact Statistics.- The available s t a t i s t i c s on t h e i n i t i a l contact condi- t i o n s are summarized i n figures 1 t o 4. Figure 1 shows probability curves f o r t h e v e r t i c a l velocity a t contact. The ordinate is t h e probability of equaling or exceeding a given value of v e r t i c a l velocity; the abscissa is t h e v e r t i c a l velocity. Because there appeared t o be d e f i n i t e differences i n the s t a t i s t i c s for c i v i l and military (land-based) airplanes, the prob- a b i l i t y curves f o r these two categories are shown separately. Although t h e reasons f o r t h e differences between t h e two categories are not com- p l e t e l y understood, it is probably significant t h a t , on the whole, two

different generations of airplanes are involved - t h e c i v i l airplanes

were a l l piston powered, whereas t h e military airplanes w e r e mostly jets.

Furthermore, some of t h e military landings were transitional-training f l i g h t s . The more severe character of t h e military landings is indicated e ... 0 a . I , .. ..

by the generally higher values of v e r t i c a l velocity a t a given probability level. For example, 1 i n 10,000 landings of military airplanes would be expected t o equal or exceed a v e r t i c a l velocity of about 8$ f e e t per sec- ond; the corresponding value f o r the c i v i l airplanes i s about 5 feet per second.

con- Figure 2 shows similar probability curves f o r t h e airspeed a t is the probability of equaling or exceeding a given The ordinate t a c t .

expressed as value of airspeed; the abscissa is the airspeed at contact, percent above the s t a l l i n g speed. Again, the m i l i t a r y operations appear t o give higher velocities a t a given probability level.

With regard t o bank angle and rolling velocity a t contact, which are of concern f o r unsymmetrical landings, wing span appeared t o be a better criterion f o r separating the data than types of operations. Accordingly, w i t h t h e number of engines taken as a crude measure of wing span, t h e airplanes with four and more engines were put i n t o one category and the single- and twin-engine airplanes i n t o another. Figure 3 presents t h e probability curves f o r bank angle. A s might be expected from geometric considerations, the larger span airplanes have somewhat smaller angles of bank. The probability curves for rolling velocity are shown i n f i g -

ure 4; here the differences are more pronounced than f o r bank angle. It

may be t h a t these differences r e f l e c t not only t h e geometrical span effect, but a l s o the greater moments of i n e r t i a and damping i n roll of the larger airplanes.

A study was made t o determine whether there was any s t a t i s t i c a l correlation between bank angle and rolling velocity, on the one hand, and v e r t i c a l velocity or horizontal velocity, on t h e other hand.

It was found t h a t no such correlation existed. There was a l s o no correlation between bank angle and rolling velocity.

It therefore appears t h a t a l l of these parameters may be treated as independent quantities i n calcu- l a t i n g unsymmetrical landing loads.

With regard t o the wing lift a t contact, both past and more recent studies have shownthat, f o r c i v i l transport airplanes, the most probable value of wing lift at contact is l g a n d t h a t i n 95 percent of the landings the wing lift was between O.9g and 1.1g.

The s t a t i s t i c a l analysis indicated no significant correlations between wing l i f t and v e r t i c a l velocity.

Although a f a i r l y substantial amount of s t a t i s t i c a l data has been obtained on these i n i t i a l contact conditions, the sizes of the samples are s t i l l insufficient t o permit the final resolution of the effects of such variables as airplane type, size, wing loading, and so forth.

Reactions and response.- O n the subject of landing-gear reactions and airplane response, the first problem t o be discussed i s t h e deter- mination of t h e v e r t i c a l loads when the i n i t i a l contact conditions are given.

I n recent years analytical methods have been developed f o r predicting t h e behavior of the landing gear during impact and the loads applied t o Good agreement has been obtained between the theoretical t h e airplane.

results and data from landing-gear drop tests. The analytical method also appears t o be reasonably satisfactory when compared with f l i g h t - t e s t data.

Figure 5 shows a comparison of the maximum v e r t i c a l loads obtained from f l i g h t tests of t h e SNJ airplane and calculated maximum loads based on the assumption t h a t the airplane is a r i g i d body. The ordinate is the m a x i m u m center-of -gravity acceleration obtained f o r each impact, and the abscissa is t h e v e r t i c a l velocity at contact. There i s considerable scat-

t e r i n the f l i g h t data, about 30 percent above 4 feet per second, reflec-

t i n g the e f f e c t s of such factors as shock-strut binding due t o drag loads, unsymmetrical landings, side force due t o yawed landings, and so forth, a l l of which can modify the v e r t i c a l loads developed. A t the lower values of v e r t i c a l velocity the experimental data a r e somewhat higher than t h e calculated curve, largely because of t h e e f f e c t s of shock-strut preloading and breakout f r i c t i o n which were not considered i n these calculations.

Above a v e r t i c a l velocity of about 4 feet per second, the calculated curve

seems t o l i e f a i r l y close t o the mean of the experimental data.

Figure 6 shows a similar comparison of measured and calculated maxi- mum v e r t i c a l loads f o r the larger and more flexible B-29 airplane. The ordinate is the maximum landing-gear vertical-load factor and the abscissa is the v e r t i c a l velocity.

The dashed l i n e represents t h e calculated values. The break i n the curve r e s u l t s from the effects of shock-strut breakout, which were included i n these calculations. Although there is a scarcity of test points a t the higher values of v e r t i c a l velocity, it does appear t h a t the calculated r e s u l t s are i n f a i r l y good agreement with t h e f l i g h t - t e s t data.

With regard t o the prediction of spin-up drag loads, the most impor- t a n t unknowns have been t h e magnitude and variation of t h e coefficient of f r i c t i o n between the t i r e and runway during t h e impact. Figure 7 sum- marizes the available experimental information on the variation of coef- f i c i e n t of f r i c t i o n during t h e wheel spin-up process. The ordinate i s t h e coefficient of friction, and the abscissa is the skidding velocity, which i s defined as the instantaneous difference between the forward speed of the airplane and the peripheral speed of the t i r e . The shaded bands are envelopes of t h e data obtained i n several different test pro- The two relatively narrow bands represent tests with an SNJ landing grams.

gear i n the Langley impact basin. The shorter of these two bands i s f o r true forward-speed impacts; the longer one represents impacts with forward ".

speed i n combination w i t h reverse wheel prerotation ( t o simulate higher horizontal velocities beyond the range of the impact-basin equipment) The wider dotted band shows r e s u l t s obtained with the B-29 airplane i n f l i g h t t e s t s . The lowest band represents data recently obtained with a B-57 landirig gear a t the new landing loads track.

A l l these bands illustrate the f a i r l y well-known f a c t that the coef- f i c i e n t of f r i c t i o n decreases with increasing skidding velocity. The width of the bands represents t h e effects of other factors which influ- ence the coefficient of friction, such as the! s l i p ratio, t h e v e r t i c a l load, variable-heating and contamination effects, and variations i n the runway surface conditions, plus, of course, experimental errors. It w i l l be noted t h a t the S N J and B-29 data, which are f o r r e l a t i v e l y low t i r e pressures, are generally i n good agreement w i t h one another, whereas the results f o r the B-57 landing gear, which has a much higher t i r e pres- sure, indicate appreciably lower coefficients of f r i c t i o n . These r e s u l t s appear t o verify a previously suspected trend, namely, that the coeffi- cient of f r i c t i o n decreases at higher t i r e pressures.

Although the shapes of the bands are f a i r l y consistent f o r the various tests, it i s not as yet possible t o take i n t o account quantita- t i v e l y a l l the factors that contribute t o the spread of t h e values of the coefficient of friction. Therefore, it seems that the most practi- c a l approach at present is t o select a shape f o r the curve, and then normalize it on the basis of t h e maximum value. From inspection of the data it appears that a reasonable range of the maximums might be from about 0.4 t o 0.9, the value t o be used depending on the conditions involved.

Taxiing Loads On t4e subject of taxiing loads, essentially two types of data a r e available a t present; t h a t is, measurements of runway profiles and center- of-gravity acceleration data from the impact portion of VGH records.

Two possible ways of u t i l i z i n g runway profile data are: (1) as specific displacement inputs in analog computations, or (2) as statisti- c a l power spectra i n generalized harmonic analysis. these Both of approaches present certain practical d i f f i c u l t i e s . In the case of the one of the major problems is t o define a representative analog method, A s t o the use of generalized harmonic analysis, t h e main stumb- runway.

l i n g blocks are as yet unsolved problems of nonlinear landing-gear a unique transfer function.

response and the determination of With regard t o the VGH acceleration data, several general relation- ships have been found which appear t o be applicable t o a number of different types of airplanes and which provide a common basis f o r e s t i - These a r e shown i n the following mating the loads experience i n taxiing.

table : AIRPLANE APPROX. 5 MIN TAXIING T I M E I TO 2 CPS 5 C.G. RESPONSE < 20 MPH SPEED AT A n M A X

<

SCATTER AT CUM. 1.5 I 4

FREQ. = 104 I

F i r s t , an analysis of the time spent i n taxiing, for three transport airplane types, showed that t h i s time was remarkably constant, averaging within a few seconds of 5 minutes.

Second, it was found that the predominant frequency i n t h e center-

of-gravity accelerations - that is, the frequency a t which the airplanes

respond most t o the runway roughness inputs - is also remarkably constant

f o r f i v e , d i f f e r e n t types of airplanes ranging f r o m t h e 13-36 bomber t o a small j e t fighter. This predominant frequency varied only from about 1 t o 2 cps, with an average value of about 1-73 cps, despite a very wide range of wing bending frequencies f o r the airplanes involved. This fre- quency of about 1 . 7 7 cps appears t o be associated with the natural vibra- t i o n of the airplane on its t i r e s .

Third, it was found that, f o r four transport t y p e s , i n several hundred taxi runs, t h e maximum taxiing loads occurred at speeds usually below 20 q h .

Fourth, detailed analysis of a l l the loads experienced i n taxiing f o r four airplane types shared that the probability distributions w e r e very similar, and the s c a t t e r i n the load l e v e l at a given probability was small, being about 1.5 t o 1, or less than the s c a t t e r f o r such param- e t e r s as v e r t i c a l velocity or horizontal velocity.

Consequently, it may be assumed that a combined distribution of taxiing loads can be used t o a l l taxiing operations.

represent Figure 8 shows distributions of center-of-gravity accelerations i n taxiing, per 1,000 f l i g h t s . The ordinate is the number of times a given value of center-of-gravity acceleration is equaled or exceeded i n 1,000 flights; the abscissa is the center-of-gravity incremental accel- eration. The ordinate scale can be ratioed i n direct proportion t o the -b

254 L

number of f l i g h t s considered. I n calculating these curves, the approach used was first t o construct a cumulative frequency distribution of a l l t h e individual incremental load peaks, both positive and negative, based on a very detailed analysis of a , r e l a t i v e l y few VGH records; these results were ratioed up t o represent 1,000 flights, and are shown by the upper curve. Then, on the basis of data f o r 7,000 f l i g h t s , a cumulative fre- quency distribution was obtained f o r the maximum taxiing load i n each f l i g h t . This distribution of maximum loads was also ratioed t o represent 1,000 f l i g h t s and i s shown by the lower curve. I n the l i m i t , the two curves should coincide a t a cumulative frequency of 1. I n view of the nature of the assumptions involved and the fact that the two distribu- tions were obtained independently, the convergence appears t o be quite good.

If the predominant frequency of t h e input t o t h e airplane is assumed t o be 1 . 7 5 cps, one can make a straightforward response calculation f o r steady-state forced vibration and, thus, determine the variation of the acceleration along the span, which can then be compared w i t h the accelera- t i o n a t the center of gravity. The r a t i o s resulting from such a compari- son would permit converting the abscissa scale i n figure 8 from center- of-gravity acceleration t o acceleration at any point along the span.

As an example, such a response calculation has been made f o r the B-29 airplane; two f l e x i b l e symmetrical bending modes were considered and a steady-state sinusoidal input force at 1.75 cps was assumed t o act at the landing-gear attachment point. Figure 9 shows a plot of the accel- eration response of the B-29 as a function of position along the span.

The dashed l i n e is the rigid-body response; the solid l i n e is the t o t a l dynamic response. For the input frequency of 1.75 cps, the r a t i o of incremental wing-tip acceleration t o incremental center-of -gravity accel- eration i s about 7.9. It i s of interest t o note t h a t data obtained i n taxiing tests of a B-29 a t t h e W r i g h t A i r Development Center showed acceleration r a t i o s of the same order. However, there are s t i l l some aspects of the problem which are not f u l l y understood; f o r example, even though the B-29 records showed frequencies of about 1 . 5 t o 2.0 cps at t h e center of gravity, the frequencies at the wing t i p were, i n sane cases, considerably higher.

Braking Loads The last topic t o be discussed is t h e subject of braking friction.

Recent NACA tests w i t h a special tow cart and with a C-123B airplane have provided the data shown i n figure 10. Here the maximum coefficient of f r i c t i o n i n braking on dry concrete i s plotted against the horizontal velocity. The circles are data obtained with the C-l23B airplane; the squares are results obtained with the tow cart at lower speeds. A l t h o u g h t h i s type of information can be useful i n the calculation of maxhm

2 ,:5

' braking loads, no s t a t i s t i c a l data are as yet available regarding p i l o t operating practice i n applying the brakes, t h a t is, the magnitude and frequency distributions of braking loads.

CONCLUDING REMARKS The foregoing material swmnarizes t h e more important NACA data Additional work applicable t o the calculation of repeated ground loads.

w i l l be necessary t o extend t h e s i z e and scope of t h e s t a t i s t i c a l samples arid t o f i l l i n the several analytical gaps which s t i l l e x i s t .

BIB LJ: OGRAPHY S t a t i s t i c a l Data Silsby, Norman S., Rind, Emanuel, and Morris, Garland J.: Some Measure- ments of Landing Contact Conditions of Transport Airplanes i n Routine Operations. NACA RM L33E05a, 1953.

Silsby, Norman S. : S t a t i s t i c a l Measurements of Contact Conditions of 478 Transport-Airplane Landings During Routine Daytime Operations.

NACA Rep. 1214, 1953. (Supersedes NACA TN 3194.)

Silsby, Norman S., and Harrin, Eziaslav N.: S t a t i s t i c a l Measurements of Landing-Contact Conditions of a Heavy Bomber. NACA RM L55EO3, 195.

Ianding Conditions f o r Large Silsby, Norman S., and Harrin, Eziaslav N.: Airplanes i n Routine Operations. NACA RM LfS>E18c, 1955.

and Morris, Garland J.: S t a t i s t i c a l Measurements of Kolnick, Joseph J . , NACA RM L55H24, Landing Contact Conditions of t h e Boeing B-47 Airplane.

Lindquist, Dean C.: A S t a t i s t i c a l Study of Wing L i f t at Ground Contact f o r Four Transport Airplanes.

NACA TN 3435, 1975.

Silsby, Norman S. : S t a t i s t i c a l Measurements of Landing Contact Conditions of Five Military Airplanes During Routine Daytime Operations. NACA RM L56F21a, 1956.

Harrin, Eziaslav N. : Comparison of Landing-Impact Velocities of F i r s t and Second Wheel To Contact From S t a t i s t i c a l Measurements of Transport Airplane Landings. NACA TN 3610, 1956.

Dreher, Robert: A Method f o r Obtaining S t a t i s t i c a l Data on Airplane

Vertical Velocity at Ground Contact From Measurements of Center-of -

Gravity Accelerations . NACA TN 3541, 1956 .

Loads and Response Milwitzky, Benjamin, and Cook, Francis E. : Analysis of Landing-Gear Behavior. NACA Rep. 22-54, 1953. (Supersedes NACA TN 2735.)

Cook, Francis E., and Milwitzky, Benjamin: Effect of Interaction on Landing-Gear Behavior and Dynamic Loads i n a Flexible Airplane Structure. NACA Rep. 1278, 1956. (Supersedes NACA TN 3467.)

* . * n . . * = c m . w 0 mm' a - , 1 *

An Milwitzky, Benjamin, Lindquist, Dean C., and Potter, Dexter M.: NACA Rep. 1248, Experimental Study of Applied Ground Loads i n Landing.

1955. (Supersedes NACA TN 3246.)

Vertical and Sawyer, Richard H., H a l l , Albert W., and McKay, James M.: Drag Ground-Reaction Forces Developed i n Landing Impacts of a Large Airplane. NACA RM L55E12c, 1955.

Evaluation of the Reduced- Milwitzky, Benjamin, and Lindquist, Dean C.: Mass Method of Representing Wing-Lift Effects i n Free-Fall Drop Tests NACA TN 2400, 1951.

of Landing Gears.

An Impulse-Momentum Method Yntema, Robert To, and Milwitzky, Benjamin: f o r Calculating Landing-Gear Contact Conditions i n Eccentric Landings.

NACA TN 2596, 1952.

Some Measurements Walls, James H., Houbolt, John C., and Press, Harry: and Power Spectra of Runway Roughness. NACA TN 3303, 1954.

On Spectral Houbolt, John C., Walls, James H., and Smiley, Robert F.: Analysis of Runway Roughness and Loads Developed During Taxiing. NACA TN 3484, 1953.

VERTICAL VELOCITY FOR CIVIL AND MILITARY AIRPLANES PROBABILITY ,0-2 - I 0 I 2 3 4 5 6 7 8 9 I O vv, FPS Figure 1 AIRSPEED AT CONTACT FOR CIVIL AND MILITARY AIRPLANES MILITARY I, 347 LANDINGS PROBABILITY 10-4 - I I I I I I I I I I 0 20 40 60 80 IO0 AIRSPEED AT CONTACT, % ABOVE STALL Figure 2 BANK ANGLES FOR SMALL AND LARGE AIRPLANES PROBABILITY 257 LANDINGS 10-4 - I I I I I I 1 I 0 2 4 6 8 BANK ANGLE, DEG Figure 3 ROLLING VELOCITY FOR SMALL AND LARGE AIRPLANES I 4-AND MORE ENGINE CIVIL AND MILITARY 153 LANDINGS I-AND 2-ENGINE CIVIL AND MILITARY 686 LANDINGS I I I I I I I I 0 4 8 1 2 ROLLING VELOCITY, DEG/SEC ,TOWARD FIRST WHEEL TO CONTACT Figure 4

--. . e l -

CALCULATED AND EXPERIMENTAL MAXIMUM VERTICAL LOADS IN FLIGHT TESTS OF S N J AIRPLANE 0 I 2 3 4 5 6 7 8 9 1 0 V, , FPS Figure 5 CALCULATED AND EXPERIMENTAL MAXIMUM VERTICAL LOADS I N FLIGHT TESTS OF 6-29 AIRPLANE 1.8 / I’ /’ 0 / / .

.a’ I .2 CALCULATED #’ 5.6 I I I I 1 I I J 0 1 2 3 4 ’ 5 6 7 8 9 V , ,FPS Figure 6 3 1 e ? e m em e * e c e m e a = e r 7 .

COEFFICIENT OF FRICTION DURING I-UP PTI RE * LB/SQ IN.

IMPACT-BASIN TESTS ,SNJ ---------32

~~ 1

FLIGHT TESTS, B -29 ------------- 7 5 I , I .Or I 0 40 80 I20 1 6 0 200 240 280 SKIDDING VELOCITY, FPS Figure 7 DISTRIBUTIONS OF TAXIING LOADS PER 1,000 FLIGHTS

lo5 ‘“n

TOTAL ACCELERATIONS

lo4

CUMULATIVE lo3 FREQUENCY IO2 IO

u MAXIMUMS

I Figure 8 RESPONSE OF 8-29 AIRPLANE f = 1.75 C PS

ACCELERATION -

RESPONSE FACTOR 5 r

1 I I I I I I I I I I

0 I70 340 510 680 850 SPANWISE DISTANCE,IN.

BRAKING TESTS ON DRY CONCRETE 0 TOW CART 0 C-1238 AIRPLANE - 1 . 0 - .E - . 6 MAX. COEFF.

OF FRICTION, PMAX .4 - - .2 I I I I I I J 40 60 80 1 0 0 120 140 160 HORIZONTAL VELOCITY, FPS

Figure 10 263

. ' , 1 1 . 1 . -1

. c m . l I r

STRUCTURES

.

7 5 3 9 9

- - AERODYNAMIC HEAT ?IRANSFEB I;o WING SURFACES AND WING LEADING E D G E S By Aleck C. Bond, W i l l i a m V. Feller, and W i l l i a m M. Bland, Jr.

Langley Aeronautical Laboratory A canpilation is presented of sane recent r e s u l t s obtained a t various f a c i l i t i e s of the Langley Aeronautical Laboratory on the heat transfer t o wing surfaces and wing leading edges. Data obtained f’ran hypersonic tunnel t e s t s , rocket-powered-model f l i g h t t e s t s , and high-stagnation- temperature j e t t e s t s are included and canpared with applicable theories.

Measured heat transfer t o wing surfaces exposed t o high-heat fluxes, i n general, showed good agreement w i t h theory. w a s also shown t o be Theory adequate in predicting the heat transfer t o wing surfaces Over a range of local Reynolds numbers fran 1 x lo6 t o 20 X 106. Heat-transfer meas- urements on a blunted slab wing a t a Mach number of 6.86 showed t h a t surface heating a t zero angle of attack was essentially t h e sane f o r sweep angles of Oo, 40°, and 600; also, increasing the angle of attack of the slab wing increased the heating of the windward surface and decreased the heating of the leeward wing surface. Measurements a t high Reynolds numbers showed that rates of heat transfer that are much higher than laminar rates can be experienced on leading edges in the region of the wing-body juncture. Transpiration-cooling t e s t s on a wedge surface showed that theoretical predictions on the effectiveness of nitrogen as a transpiration coolant apply equally as well for conditions of e i t h e r high or low heating potentials. Further cooling t e s t s showed t h a t helium is about f i v e times more effective as a transpiration coolant than nitrogen.

INTRODUCTION Considerable emphasis has recently been placed on the experimental study of the aerodynamic heat transfer t o wing surfaces and wing leading The wing leading edge has received a large amount of considera- edges.

tion and has been treated both theoretically and experimentally i n refer-

ences 1 t o 4 . A qualitative type of investigation on wing leading edges

a t conditions of high stagnation temperature has been reported i n refer- ence 5. Investigations are reported in references 6 t o 8 of the

c o e e e I e o o o . *-. -- ..I

F .

r i aerodynamic heating of wing surfaces at angles of attack a t low super- sonic speeds; however, data on the effects of leading-edge bluntness, sweep, and angle of attack, particularly a t hypersonic speeds, as well as the effects of high heating potentials and high Reynolds numbers on wing-surface heating are indeed lacking i n the current literature.

Results of experiments conducted a t various f a c i l i t i e s of the Langley Aeronautical Laboratory have recently becane available which provide some extension of the s t a t e of the art regarding the heat transfer t o wing leading edges and wing surfaces. Rocket-powered-model f l i g h t t e s t s have provided some large-scale measurements of the heat transfer t o wing surfaces as well as of the heating of blunt leading edges i n the vicinity of the wing-body juncture. Hypersonic wind-tunnel t e s t s have provided information on both the effects of sweep md m g l e of attack on the heat transfer t o a wing having large leading-edge blunt- ness. Tests in a j e t having a high stagnation temperature have also provided results on the heating of wings under conditions of high r a t e s of heat transfer. Furthermore, data on the effectiveness of transpira- t i o n cooling of f l a t surfaces, under conditions of high stagnation tem- perature, have also recently become available *can tests i n a hot-jet f a c i l i t y . It is, therefore, the purpose of this paper t o present a canpilation of these recent r e s u l t s which are applicable t o the high- speed wing-heat ing problem.

SYMBOLS F injection parmeter, P 2V2 M Mach number h Stanton number based on l o c a l conditions,

N s t

Cp2PZVZ h Stanton number based on free-stream conditions, % t , m C p , P m V m PVS

R Reynolds number, -

IJ PmVCQd

-

Reynolds number based on diameter, Rd IJW T temperature, OF or ?R

v velocity, ft/sec

Btu/slug specific heat of a i r a t constant pressure, OF d diameter of cylindrical leading edge, f t B t U h l o c a l aerodynamic heat-transfer coefficient,

(sq ft) (set> (9)

9 dynamic pressure, lb/sq f t S length from stagnation point t o measurement station, as indicated when used, f t A sweep angle, deg U angle of attack, aeg viscosity of a i r , lb-sec/sq f t P P density, slugs/cu f t Subscripts : A W adiabatic w a l l C coolant EXP experimental 2 conditions outside boundary layer 0 zero coolant flow r a t e TH theoretical t t o t a l conditions W conditions pertaining t o skin of model 03 f r e e -stream conditions 1 - 0 0. 0 . 0 6 .*. . I m .

RESULTS AND DISCUSSION Heat Transfer a t H i g h Stagnation Temperature w i t h high-heat f l u e s , In order t o study heating problems associated one of the f r e e jets of the Langley preflight j e t of the Pilotless Aircraft Research Station a t Wallops Island, Va., has been modified t o allow t e s t i n g of relatively large t e s t specimens a t stagnation tempera- 3,fsoOO R which corresponds t o a Mach number of about tures up t o about The t e s t Mach number is maintained the same (M = 2.0); 6.5 at altitude.

however, the stream temperature is increased by burning ethylene gas upstream of the e x i t nozzle. This mode of t e s t i n g provides heating rates corresponding t o Mach numbers much higher than the stream Mach number i n a t e s t medium not much different fram a i r . Recent t e s t s w i t h wings subjected t o high heating r a t e s have yielded heat-transfer data which show good agreement w i t h theory. Results f o r a wing tested a t a stag- nation temperature of 3,476' R, a stream Mach number of 2.0, and a stream

Reynolds number of 2.4 X lo6 per foot are shown i n figures 1 and 2. The

wing w a s a tapered unswept wing of hexagonal cross section, w a s constructed of magnesium, and had a span of 1 1 inches. The leading edge which was blunted t o a 1,/16-inc% radius was covered with a 1/32-inch Inconel cap t o increase its endurance at the t e s t temperature. Sweep of the leading edge was 17O. A t the 63-percent spanwise station (coinciding with the cen- t e r l i n e of the j e t ) , temperature measurements were made at four chordwise locations: the stagnation-point and the 1-, 2-, and 3.77-inch stations.

Temperature time histories measured on the wing are shown i n figure 1.

The temperature at the stagnation point rises rapidly and i n approximately 2.1 seconds (time of f a i l u r e of the leading-edge cap) has reached 2,731' R, j u s t about 22g0 R below the melting temperature of Inconel. The tempera- tures at the three reaxward stations show a maximum rise of about one-half the stagnation-point value. It should be noted, however, t h a t the temper- ature of the 2-inch station, which is immediately behind the end of the leading-edge cap, is generally about X)Oo higher than the temperatures of the other two stations during most of the t e s t .

In figure 2 these wing heating data are reduced t o the nondimensional Stanton number evaluated at local conditions and a r e also plotted as a function of time. In the p l o t a t the upper l e f t , the stagnation-point data are cmpmed w i t h the average laminar stagnation-point theory of Goodwin, Creager, and Winkler (ref. 4).

Caparison w i t h the average theoretical stagnation-point values rather than w i t h local values is made it w a s f e l t that, because of the small physical s i z e of the leading since edge, the measurements a t t h i s point more nearly represented average values rather than local point values. The first data point shows good agree- ment w i t h the theory; however, w i t h increasing time, the data show increasing deviation fran the theory. This disagreement is believed t o be due mainly t o l.arge l a t e r a l conduction losses fram the stagnation

F

point as the leading edge increases i n temperature, since it is known that the temperature gradient across t h e j e t i s not uniform but tends t o peak i n the v i c i n i t y of the jet center line. The data f o r t h e other three stations are compared w i t h the f l a t - p l a t e theories of Van Driest (refs. 9, 10, and 11) and, i n general, show good agreement. The theo- r e t i c a l curves were determined by using calculated l o c a l condi!!xLons and a Reynolds number length equal t o the streamwise distance f r c x n t h e stag- nation point t o the measurement station. These data show that the flow was i n i t i a l l y laminar a t the 1-inch s t a t i o n and t h a t t r a n s i t i o n took place between t h e 1- and 2-inch stations and then gradually moved forward w i t h time. I n i t i a l l y , t r a n s i t i o n could have been caused by t h e abrupt discontinuity a t the end of the leading-edge cap, and the forward move- ment w i t h time may have been due t o t h e increased temperature (i.e., It i s obvious that, had temperature r a t i o ) of the surfaces w i t h time.

the t r a n s i t i o n point not moved forward, a serious hot spot would have developed a t or near.the 2-inch measurement station. The ccxnparison of t h e data f o r the three downstream stations w i - those of t h e stagnation point show that t h e turbulent l e v e l of heating of t h e downstream s t a t i o n s w a s of the order of one-half that of t h e stagnation point.

It might be mentioned a t t h i s time that, i n t h e reduction of the heating data f o r the 1-inch s t a t i o n t o l o c a l Stanton number, t h e l o c a l conditions were determined by considering t h e losses through t h e normal shock caused by the blunted leading edge. This procedure gave much b e t t e r agreement w i t h the theory than w a s obtained when t h e losses w e r e neglected. For t h e two stations downstream, t h e agreement between theory and experiment was not enhanced when taking these losses i n t o account; thus, t h e effects of t h i s small amount of bluntness did not propagate very far downstream i n t h i s case.

Large-Scale Heat-Transfer Measurements In recent rocket-powered-model flight t e s t s , sane r e l a t i v e l y large- scale heat-transfer measurements have been obtained on two d i f f e r e n t wing configurations a t free-stream Reynolds numbers up t o approximately 27 X lo6 based on t h e wing chord. This Reynolds number is equivalent t o that of a wing of 120-inch chord flying a t an a l t i t u d e of 50,000 feet and a Mach number of 2.5. In order t o show t h e general agreement which w a s obtained w i t h theory over t h i s large Reynolds number range, repre- sentative data from these t e s t s are shown i n figure 3 as t h e r a t i o of experimental t o theoretical Stanton number as a function of the l o c a l Reynolds number. It m i g h t be mentioned a t this time that there w a s no indication of laminar heating on either of t h e wings throughout the usable portion of the flight tests; however, a t the beginning of t h e t e s t s there w a s some indication of t r a n s i t i o n a l flow a t t h e most forward measurement stations. The theoretical Stanton numbers were, therefore, evaluated from the turbulent f l a t - p l a t e theory of Van Driest (refs. 10 and 11) by using calculated local conditions and a value of 0.6 f o r t h e r a t i o of Stanton number t o skin-friction coefficient.

One of the t e s t wings was unswept, untapered, of approximately 20-inch chord and span, employed a ?-percent circular a i r f o i l section, and had f o r a l l practical purposes a sharp leading edge. The other the heating data of which are reported i n reference 12, had a wing, leading-edge sweep of 30°, a span of 25 inches, and employed a hexagonal a i r f o i l section w i t h a leading-edge radius of approximately 1/8 inch.

The data f o r the unswept wing are shown by the circular symbols and represent measurements at seven chordwise stations (35.7-percent. span) and a free-stream Mach number range f r m 1.75 t o 2.66. The data f o r the swept wing, indicated by the square symbols, were obtained a t f i v e chord- wise stations (42-percent span) and are f o r a free-stream Mach number range from 2.0 t o 3.64. Local Reynolds numbers up t o about 20 X 106 were obtained on the unswept wing; however, on t h e swept wing the maximum

l o c a l Reynolds nunber iSLonly- of the order of 10 X 10 6 . Even though the

stream Reynolds numbers of the t w o wings were of the same order of magni- tude, the l o c a l Reynolds numbers for the swept wing were lower as a r e s u l t of its blunted leading edge.

In the lower Reynolds number range t h e agreement w i t h theory i s generally within k l 5 percent, with the majority of the points showing agreement within k10 percent. A t the higher Reynolds numbers the data show agreement within about 20 percent of the theory. The decreasing trenii w i t h increasing Reynolds number which is exhibited by the data may be due t o t h e reduction i n the r a t i o of Stanton number t o skin-friction coefficient w i t h increasing Reynolds number which w a s observed by Seiff i n reference 13. Since the present data were obtained i n the presence of temperature, pressure, and Mach number variations, it is f e l t t h a t no d e f i n i t e conclusions can be drawn on t h i s point. The important feature of these data is t h a t reasonable agreement w i t h theory is shown f o r two t o t a l l y different wing configurations over a rather wide variation of Reynolds number.

Heat Transfer at Angle of Attack and Sweep Theory and experiment have shown t h a t both leading-edge sweep and bluntness have t h e general effect of reducing the l o c a l r a t e s of heat transfer t o t h e leading edge. In order t o study the effects of sweep as well as the effects of angle of attack on the heating of the surfaces of a wing w i t h a blunt leading edge, t e s t s have been conducted i n the Langley 11-inch hypersonic tunnel a t a Mach number of 6086 on a slab wing w i t h a s a i c i r c u l a r leading edge. In figure 4 are presented some of t h e r e s u l t s of these t e s t s which show the effect of sweep on t h e wing-surface heat transfer a t zero angle of attack. The data are f o r a stream Reynolds i number of 0.151 x 106 based on the 3/4-inch diameter of the leading edge and correspond t o an actual flight a l t i t u d e of about 76,000 f e e t at the t e s t Mach number. The data are plotted as Stanton number based on free- stream conditions as a function of s/d, where s is the surface length, measured i n a streamwise plane, froan the stagnation point t o the measure- ment station, and d is the leading-edge diameter. Data a r e presented In order t o show the r e l a t i v e f o r sweep angles of Oo, 40°, and 60'.

magnitude between the leading edge and surface heating, theory curves f o r the cylinder are presented for each of the sweep angles; however, since heat transfer t o swept cylinders has been presented i n the past (refs. 3 and 4 ) , attention i s called t o the f l a t - p l a t e portion of the wing. The measured data f o r a l l sweep angles l i e essentially on one l i n e and show no effect of sweep angle on the surface heating. The theory curve included in figure 4 w a s ccaqputed by using the Van Driest theory f o r laminar boundary layer (ref. 9 ) w i t h l o c a l conditions determined by taking into account the losses through the normal shock and by assuming the local s t a t i c pressure on the surface equal t o stream s t a t i c pressure. In the vicinity of the leading edge (s/d = 1 t o 2) the data a r e considerably t h i s theoretical calculation, mainly as a r e s u l t of the higher than higher-than-stream pressures which are known t o e x i s t there; but as the pressure f a l l s off w i t h distance downstream, the data show better agree- ment w i t h the theory. Measured pressure distributions on the wing showed that, just behind the leading edge, the surface pressures were several times higher than stream s t a t i c pressure and dropped off t o s/d of about 7.5.

about twice the stream s t a t i c pressure a t values of zero The theory curve shown i n the figure was actually computed f o r sweep, but it is Tnteresting t o note t h a t calculations f o r the 40° and 6 0 ' sweep angles showed only small variation from t h e 0 ' sweep condition.

Measured surface heat transfer a t angle of attack f o r the 40° swept slab wing is presented in figure 5 as being generally typical of the effect of angle of attack on the wing surface heating f o r a l l the sweep angles. Here, again the data are plotted as Stanton number based on free-stream conditions as a function of streamwise s/d. Measurements are presented of surface heating of the lower or windward surface w i t h the wing at angles of attack of 5 ' and 7.5' and of the upper or lee- w a r d surface with the wing a t angles of attack of 5 O and loo. The curve of zero-angle-of-attack data, of course, applies t o both upper and lower surfaces of the wing. Increasing the angle of attack increases t h e heating of the lower surface and decreases the heating of the upper sur- face. The variation of heating with angle of attack is essentially linear for both the upper and lower surfaces; however, the r a t e of increase of heating on the lower surface is about twice the r a t e of decrease of heating on the upper surface.

1 . 6 e .e.

.e

a

Heating of Wing Leading Edge in Vicinity of Wing-Body Juncture The heat transfer to swept cylinders in an undisturbed flow f i e l d has been studied over a wide range of conditions and, in general, the experimental data agree well w i t h existing theories. A rocket-powered- model f l i g h t t e s t was recently conducted for the purpose of measuring the heat transfer t o leading edges in the vicinity of the wing-body juncture a t relatively high Reynolds numbers. A sketch i s shown i n f i g - ure 6 of the rocket-powered model which carried small stubs representing only the leading-edge portions of Oo and 750 swept wings. The stubs had cylindrical leading edges of 3/4-inch diameter which became tangent t o f l a t surfaces inclined a t 4 . 3 O t o the chord plane. Thermocouple measure- ments were made i n a direction perpendicular t o the leading edge of each stub a t locations shown in the cross-section sketch. Four measurement points were obtained on the Oo swept stub; however, on the 75O swept stub, the most rearward thermocouple failed t o operate properly and, hence, measurements a t only the three forward locations were obtained.

Measured heating data f o r the two leading edges a t a stream Mach

number of 3.12 and a stream Reynolds number of 18.7 X lo6 per foot a r e

presented in figure 7 along w i t h appropriate theoretical curves f o r c m - parison. The data are presented as the nondimensional Stanton number evaluated a t free-stream conditions as a function of s/d where s is the surface length, measured i n a plane normal t o the leading edge, frm the stagnation point t o the measurement station and d is the leading- edge diameter. The measured data on the cylindrical portion of the leading edge f o r both the 0 ' and 75' swept stubs are considerably higher than t h a t predicted by the laminar leading-edge theory in reference 4.

O n the Oo swept leading edge, the heating a t the stagnation point is of the order of 2 times t h a t which i s predicted by laminar theory, and on the 7 5 O swept leading edge, the heating i s of the order of 4.5 times as great. Since there is such a large difference between the measured values and the laminar theory f o r the cylindrical portion of the leading edges, it was f e l t t h a t the f l o w over t h i s portion must be turbulent.

This w a s verified f o r the 0 ' swept leading edge by integrating the meas- ured values over t h e cylindrical portion t o obtain the average heat transfer. This average value (Nst = 34.96 >< 10-4) was found t o agree ,* very well w i t h the theoretical average (NSt

= 34.85 x lo4) cmputed

,*

from the turbulent theory i n reference 3. Comparison of the measured data on the f l a t portion following the cylinder w i t h the Van Driest turbulent f l a t - p l a t e theory (refs.. 10 and 11) also shows good agreement and tends t o establish further t h a t the flow on the Oo swept leading edge w a s turbulent. f o r turbulent heating on the 75O swept The analysis leading edge w a s not carried out because of the absence of information on the local flow conditions a t t h i s sweep angle and Mach number.

The reason f o r turbulent f l o w over the Oo swept leading edge cannot be deduced f r a n the measurements made on the model. Since the measure- ments were made a t a distance of only 11 inches fra the body, the heating t o the leading edge could have been influenced by conditions existing i n the body boundary layer. The Reynolds number for the body a t the leading-

edge body juncture w a s approximately 66 x lo6 and the body boundasy-layer

With these con- thickness was estimated t o be of the order of 1/2 inch.

ditions prevailing, it is possible t h a t interaction between the bow shock ahead of the leading edge and the thick turbulent boundary layer of t h e body could have increased the heating of the leading edge t o the turbu- l e n t level. Although exact simulation of the flow f i e l d a t the wing-body juncture may not have been provided by the short leading-edge stubs, these data indicate that r a t e s of heat transfer much higher than l a m i n a r r a t e s can be experienced on leading edges i n the region of the wing-body juncture, and that, further, more canplete investigations are needed t o understand t h i s phenomenon.

Transpiration Cooling at H i g h Stagnation Temperatures A t lower flight speeds the problem of convective heating of an air- c r a f t surface can generally be handled by designing the surface as a heat sink and allowing the skin t o a t t a i n some allowable equilibrium temperature. A s f l i g h t speeds increase, the idea of sane type of cooling f o r the hotter surfaces appears more attractive. One type of cooling which shows promise i s transpiration cooling, in which the coolant passes from the i n t e r i o r of the a i r c r a f t through a porous skin i n t o the hot boundary layer. Experimental data on transpiration cooling a t r e l a t i v e l y low heating potentials have been reported in references 14, 15, and 16, and have shown appreciable reduction i n the convective heating w i t h trans- piration cooling. In order t o investigate the effectiveness of trans- piration cooling a t higher heating potentials, exploratory t e s t s have been conducted a t high stagnation temperatures i n the Langley preflight j e t of the Pilotless Aircraft Research Station at Wallops Island, Va.

The model employed f o r the tests was a blunted wedge of 200 half-angle which had a porous stainless-steel segment inserted i n one surface through which coolant was ejected. Tests were conclucted a t a ncminal free-stream dymmic pressure of 5,000 pounds per square foot and a free-stream Mach 2.0; however, the local-surface Mach number on the wedge was number of of the order of 1.2. Results of these t e s t s showing the effect of trans- piration cooling on the wedge-surface temperature f o r both nitrogen and helium coolants are presented i n figure 8. The ordinate is the non-

TW - Tc

dimensional wall-temperature pwameter where Q is the

TAW,O - Tc

porous-wall temperature, T, i s the coolant temperature, and TAW,O is the boundary-layer recovery temperature f o r zero coolant flow rate. The abscissa is the coolant flow r a t e i n pounds per square foot per minute.

Such a presentation of cooling data shows d i r e c t l y the reduction i n w a l l temperature which can be achieved f o r a given coolant flow rate.

Data are presented f o r stagnation temperatures i n the range from 2,35'j0 R t o 3,370° R f o r nitrogen coolant and frcm 1,755O R t o 3,195O R f o r helium coolant. For t h e various tests, r a t i o s of w a l l temperature t o l o c a l temperature ranged from 0.2 t o 0.5 and the l o c a l Reynolds numbers ranged It m i g h t a l s o be mentioned that the present from 0.6 X lo6 t o 8.2 X 106.

data were obtained f o r average operating temperatures of t h e porous w a l l Comparison of t h e nitrogen i n t h e range frm about 20O0 F t o 1,300° F.

and helium data i n figure 8 shows t h a t the helim performs as a much as would be expected because of more effective coolant than nitrogen, For example, i n order t o main- the higher specific heat of t h e helium.

t a i n t h e skin a t a t a p e r a t u r e of about 0.3 of the uncooled value, approximately 10 pounds of nitrogen per square foot per minute would be required as ccmpared w i t h 2 pounds per square foot per minute for helium.

It m i g h t be added that this r a t i o of 5 t o 1 i n required coolant flow rates is roughly the same as the r a t i o of the specific heat of helium t o t h a t of nitrogen.

In order t o show how tZlese high-temperature data canpare w i t h theory and other low-temperature data, as w e l l as t o show t h e e f f e c t of cooling on t h e heat transfer, the data were reduced t o heat-transfer coefficients and are presented i n dimensionless form i n figure 9. The ordinate i s t h e r a t i o of the Stanton number with cooling t o the Stanton number f o r zero cooling, and t h e abscissa is t h e injection parameter F (the r a t i o of coolant weight flow t o l o c a l stream w e i g h t flow) divided by t h e Stanton number f o r zero cooling. In the reduction of t h e measured data t o Stanton nmber, the recovery temperature w i t h coolant flow w a s evaluated by using recovery-factor values ccanputed from the theory of reference 17, which gives the variation of recovery factor w i t h Mach number, coolant flow r a t e , and Reynolds number. Included f o r comparison are the theo- r e t i c a l curve applicable t o nitrogen from the theory i n reference 18 f o r M = 1.0 and a r a t i o of w a l l temperature t o l o c a l temperature of 0.2, and the experimental data i n reference 14 f o r the transpiration cooling of an 8 ' cone w i t h both nitrogen and helium coolants a t R stag- 1 , 0 6 0 ' R. The experimental wedge data for nitrogen nation temperature of coolant form E band which has the same trend as t h e t h e o r j and shows s l i g h t l y greater cooling effectiveness.

The present data f o r the nitrogen a l s o show good agreement w i t h the trend established by the 8 ' cone data.

The present he1i.w data do nut show as good agreement w i t h t n e p r i o r w i t h heliuni coolant as is observed i n the case w i t h nitrogen.

cone data Since both s e t s of data f o r the helium coolant are f o r s m a l l flow rates, t h e discrepancy between the two s e t s of data may be due t o t h e l e s s e r accuracy i n determining the flow r a t e s i n the lower range of flow rates.

With t h i s type of correlation, t h e canparison of t h e effectiveness of helium with nitrogen as transpiration coolants i s about i n t h e same

2; 4

relation as noted i n figure 8. The theory which is s t r i c t l y derived for transpiration of a i r t o a i r but is applicable also t o nitrogen because of the similarity of the physical characteristics may be said t o apply equally as well f o r either high or low heating potentials.

CONCLUSIONS The pertinent conclusions which may be drawn f'ran the foregoing canpilation of wing-heating data may be summarized briefly as follows: 1. Measured heat transfer t c wing surfaces exposed t o high-heat fluxes have, i n general, shown good agreement w i t h theory. Theory has also been shown t o be adeqmte i n predicting the heat transfer t o wing surfaces over a wide range of Reynolds number.

2. Heat-transfer measurements on a blunted slab wing e=t a Mach number of 6.86 showed t h a t the surface heating a t zero angle of attack was essentially the same for sweep angles of Oo, 4 0 ° , and 60°. Increasing the angle of attack of the slab wing increased the heating of the wind- ward surface and decreased the heating of the leeward surface.

3 . Measurements a t high stream Reynolds nmbers have shown t h a t r a t e s 02 heat transfer much higher than laminar r a t e s can be experienced on leading edges i n the region of the wing-body juncture.

4. Theoretical predictions of the effectiveness of nitrogen as a transpiration coolant have been shown t o apply equally as w e l l f o r con- ditions of either high or low heating potentials. Measurements have shown t h a t helium i s about f i v e times more effective as a transpiration coolant than nitrogen.

1. Reshotko, E l i , and Cohen, Clarence B.: Heat Transfer a t the Forward Stagnation Point of Blunt Bodies. NACA T N 3513, 1955.

2. Beckwith, Ivan E.: Theoretical Investigation of Laminar Heat Transfer on Yawed I n f i n i t e Cylinders in Supersonic Flow and a Comparison W i t h Experimental Data. NACA RM L55FO9, 1955.

3. Beckwith, Ivan E., and Gallagher, James J.: Experimental Investigation of the Effect of Boundary-Layer Transition on the Average Heat NACA RM L56E09, Transfer t o a Yawed Cylinder i n Supersonic Flow.

Investiga- 4. Goodwin, Glen, Creager, Marcus O., and Winkler, Ernest L . : a t i o n of Local Heat-Transfer and Pressure Drag Characteristics of NACA RM A55H.31, 1956. Yawed Circular Cylinder a t Supersonic Speeds.

5. Bland, W i l l i a m M., Jr., and Bressette, Walter E.: Some Effects of Heat Transfer a t Mach Number 2.0 at Stagnation Temperatures Between 2,310' and 3,50O0 R on a Magnesium Fin With Several Leading-Edge Modifications. NACA R M L57C14, 1957. (Prospective NACA Paper. ) 6. Carter, Howard S.: Heat Transfer on the Lifting Surfaces of a 60° Delta Wing a t Angle of Attack f o r Mach Number 1.98. NACA m ~ 5 6 ~ 2 3 , 19%.

7. Bartlett, G. E., Hilton, J. H., Vidal, R. J., and Woolard H. W.: Experimental Investigations of Heat Transfer on a 10-Percent Double- Rep. No. CAL/CM-832 (Contract Wedge Airfoil at Mach No. 2.0.

NOrd-14>23), Cornell Aero. Lab., Inc., Jan. 1955.

8. Sterbutzel, Gerald A., and Kajencki, Stephen S.: Experimental Inves- tigation of Heat Transfer Frcxa Aerodynmic Bodies i n Supersonic Flow. Rep. No. AF-473-A-9 (Contract 03-038-ac-16701), Cornell Aero. Lab., Inc., Apr. 1950.

9. Van Driest, E. R.: Investigation of Laminar Boundary Layer i n Compressible Fluids Using the Crocco Method. NACA TN 2597, 1952.

10. Van Driest, E. R.: The Turbulent Boundary Layer f o r Compressible Fluids on a Flat Plate With Heat Transfer. Rep. No. AL-997, North American Aviation, Inc., Jan. 27, 19%.

11. V a n Driest, E. R.: The Turbulent Boundary Layer With Variable Prandtl Number. Rep. No. AL-1914, North American Aviation, Inc., Apr. 2, 1 9 % .

Akii?

12. Swanson, Andrew G., and Rumsey, Charles B.: Aerodynamic Heating of a Wing A s Determined From a Free-Flight Rocket-Model Test t o Mach Number 3.64. NACA RM LfS6Flla, 1956.

Examination of the Existing Data on the H e a t Transfer 13. Seiff, Alvin: From the Point of Turbulent Boundary Layers a t Supersonic Speeds NACA TN 3284, 1954.

of View of Reynolds Analogy.

14. Chauvin, Leo T., and Carter, Howard S. : Ekploratory Tests of M = 2-03 Using Transpiration Cooling on a Porous 8 O Cone at Nitrogen Gas, Helium Gas, and Water as the Coolants. NACA RM L55C29, 1955- 15. Leadon, B. M., and Scott, C. J.: Measurement of Recovery Factors and H e a t Transfer Coefficients W i t i n Transpiration Cooling i n a Using A i r and Helium as Turbulent Boundary Layer a t M = 3 Coolants. Res. Rep. No. 126, Univ. of Minnesota Inst. Tech., Dept.

Aero. Eng. (Contract A J ? 18(6oo)-1226), Feb. 1956.

16. Rubesin, Morris W., Pappas, Constantine C., and Okuno, Arthur F.: The Effect of Fluid Injection on the Compressible Turbulent

Boundary Layer - Preliminary Tests on Transpiration Cooling of

a Flat Plate a t M = 2.7 With A i r as the Injected G a s . NACA RM A551193 1955- 17. Rubesin, Morris W.: An Analytical Estimation of the Effect of Transpiration Cooling on the Heat-Transfer and Skin-Friction Characteristics of a Compressible, Turbulent Boundary Layer.

NACA TN 3341, 1954.

The Effect of Mass Transfer 18. Dorrance, W i l l i a m H., and Dore, Frank J.: on the Cmpressible Turbulent Boundary Lsyer Skin Friction and Heat Transfer. Rep. ZA-7-013, Convair, Aug. 5, 1954.

TIME HISTORIES OF WING TEMPERATURES Mm.2; Tt= 3,476O R STATION I" 3.77" 3,OOOr 1/32" INCONEL CAP

2.500 1 1

STAGNATION POlNT

I I I I I I

0 .5 I .o 1 5 2.0 2.5 TIME, SEC Figure 1 WING-SURFACE HEAT TRANSFER Moo= 2 ; T+ = 3,476O R ; R , = 2.4 X IO' PER FT STAGNATION POINT

80 4!914L------ THEORY

I" STATION o o o o o o rTURBULENT THEORY

60 F

n POINT LAMINAR THE~RYO 0 0 80 X I O - ~

1 2" STATION 1 3.77" STATION

60 0 0 0 INCREASING TIME- Figure 2 P COMPARISON OF EXPERIMENT AND THEORY FOR LARGE-SCALE HEAT-TRANSFER TESTS 1.2r I .o .8 NSt, EXP .6 - 5"/0 CIRCULAR A R C HEXAGONAL NSt, TH - .4

- .. . ... . 19.9"

- . 2 M,=1.75 To 2.66 Maz2.00 T O 3.64 I I I I I I EFFECT OF SWEEP ON HEAT TRANSFER TO A BLUNT L.E. WING a=Ooi M.6.86; Rd=0.151~106 A ,DEG 0 0 n 40 A 60 THEORY, L A M INAR FLAT PLATE On

-

A d A m I I I I I I I 0 I 2 3 4 5 6 7 8 STREAMWISE s/d Figure 4 \ TRANSFER EFFECT OF ANGLE OF ATTACK ON HEAT TO A B L U N T L.E. WING -4 JUNCTURE 0 2 4 6 0 I O STREAMWISE S/d Figure 5 LEADING-EDGE HEAT-TRANSFER MODEL 4 2 . 4 ' 1 - 4 MEASUREMENT STATION LEADING-EDGE CROSS SECTION Figure 6 HEAT TRANSFER T O LEADING EDGE IN VICINITY OF WING-BODY JUNCTURE M =3.12; R = 1 8 . 7 X 1 0 6 PERFT; Rd= 1.17x106 OD OD A =Oo A = 75' 50 6 x 1 0 - 4 c

40 - -

N s t p --LAMINAR L.E.

I I 0 .4 .8 1.2 1 . 6 0 .4 .8 1.2 s/d s/d Figure 7 EFFECT OF TRANSPIRATION COOLING ON WEDGE-SURFACE TEMPERATURE LB M a = 2 q , S J 5,000 SQFT i T+ .OR 1 - NITROGEN HELIUM 0 3,370 0 3,195 0 2,921 b 2,591 ' * O r .8 0 2,355 A 1,.755

" : ; .2

"%' NITROGEN

O . 0 0 HELIUM 0 0 0 A OOcQJ 4 ,

L I I I I I I I I 1

0 2 4 6 8 IO 1 2 1 4 1 6 I8 LB/SQ FT COOLANT FLOW RATE, MIN Figure 8 I EFFECT OF TRANSPIRATION COOLING ON HEAT TRANSFER T+ , O R NIT.ROGEN HELIUM o 3,370 a 3,195 200 WEDGE 0 2,921 b 2,591

I.OK

c 0 2,355 A 1,755

8" CONE 6 1,060 1,060 -8kA NITROGEN DORRANCE AND DORE HELIUM 0 . 5 1 . 0 1.5 2.0 2.5 3.0 3.5 F/Nst,o c .

.a a.

TOTAL BEAT TRANSFER To BLUNT-NOSE SHAPES W I T H LAMINAR BOUNDARY LAYERS AT HIGH SUPERSONIC SPEEDS By John 0. Reller, Jr.

Arnes Aeronautical Laboratory SUMMARY A method of designing blunt shapes has been devised which proposes t o reduce the heat transfer t o a body by v i r t u e of low-velocity flow A typical body over the nose and low-density f l o w over the afterbody.

consists of a f l a t nose and a highly curved afterbody surface defined by a modified Newtonian theory.

Tests w e r e conducted i n the Ames 10- by &inch supersonic wind tunnel at Mach numbers from 3.0 t o 6.3 and it w a s found that t o t a l heat- transfer rates f o r these flat-nose shapes is less than t h a t of a cone Comparison of experimental r e s u l t s with theory of about the same drag.

indicates higher than average heat-transfer rates near the shoulder of a typical shape and r e l a t i v e l y low values over most of the afterbody.

INTRODUCTION It is a well-known fact that blunting can reduce the rate of heat transfer t o the nose of a body i n supersonic f l o w . The problem is, however, t o determine a type of blunting which tends t o minimize the heat-transfer rate. The purpose of this paper is t o describe an inves- t i g a t i o n of t h i s problem i n which it w a s undertaken first t o devise a method of designing blunt shapes and then t o check by experiment the effectiveness of these shapes i n reducing heat transfer.

"he basic heat-transfer equation, i n t h e form of Reynolds analogy, Although t h i s analogy i s not s t r i c t l y is shown at the top of figure 1.

applicable f o r blunt shapes, i n general the convective heat-transfer coefficient i s proportional t o the product of the l o c a l density, local velocity, specific heat, and l o c a l skin-friction coefficient. The spe- c i f i c heat is a factor over which relatively l i t t l e control can be exerted. Likewise, control over the skin-friction coefficient is limited primarily by the extent t o which laminar boundary-layer f l o w can be Attention is therefore focused on the product of the local preserved.

density and the l o c a l v e l o c i t y . This product, and hence the local heat- transfer coefficient, m a y be kept low over a shape designed t o have low Such a velocities at the nose and low densities over the afterbody.

shape would, i n i t s simplest form, be a truncated cone, inasmuch as the f l a t nose minimizes l o c a l v e l o c i t i e s , while the highly inclined sides minimize local pressures and hence densities. The f a c t is, however, t h a t the sharp corner a t the intersection of the face and afterbody of a truncated cone tends t o cause local separation and reattachment of the flow with an attendant shock wave and unfavorable pressure gradient.

These conditions tend t o promote transition t o a turbulent boundary layer, which increases the local heating rate. Therefore, the surface i n t h i s shoulder region should be curved t o avoid l o c a l separation and possible tripping of t h e boundary layer. I n order t o promote laminar flow over the e n t i r e afterbody it is desirable t o have a contour which Such a contour generates a continuously favorable pressure gradient.

is easily determined w i t h the modified Newtonian theory of Eggers, Resnikoff, and Dennis (ref. l ) , providing the square of hypersonic s i m i - l a r i t y parameter M is large compared w i t h unity. "his condition is I D this satisfied by blunt bodies at the high supersonic Mach numbers of The resultant expression defining the shape of the after- investigation.

body surface i s shown as the second equation i n figure 1. Note t h a t the coordinates iT and axe the local x and y dimensions, resp.ectively, divided by the radius of the f l a t nose. The parameter K i n t h i s expres- sion fixes the l e v e l and gradient of pressure on the afterbody.

Two families of blunt-nose bodies of revolution were designed according t o t h i s equation. The f i r p t family is shown at the l e f t i n figure 1 and consisted of eight bodies of the same fineness ratio, but of varying diameters of the flat nose. family of bodies, For the second shown at the r i g h t i n figure 1, the nose and base diameters were held The constant and the fineness r a t i o was varied f r m about 0.3 t o 1.6.

are shown on the superimposed sketches of corresponding values of K The bodies of t h i s second family have approximately the these bodies.

same pressure drag and for t h i s reason two reference bodies of similar pressure drag w e r e included i n the t e s t program. These were the sharp- pointed and hemispherical-tipped 6 0 ' cones shown i n figure 1. A f u l l hemisphere of the same base diameter w a s also tested.

Tests were conducted i n the Ames 10- by &inch supersonic wind tunnel at Mach numbers fram 3 t o 6 . 3 . As shown i n figure 2, models were s t i n g supported fram the rear and were i n effect insulated t o prevent

. ,. r . .. 4

., b ' 0 - l: : heat loss tm the support system by a guard heater which w a s used t o H e a t input was through equalize the temperature i n the support shell.

From the a resistance heater of Inconel wire wound on a copper spool.

known resistance and measured voltage the overall heat-transfer rate could be determined f o r equilibrium conditions. This apparatus did not m a d e permit the measurement of local heat-transfer rates. Models were of aluminum and provided essentially constant-temperature heat-transfer Thermocouples were installed surfaces because of t h e i r high conductivity.

within the models t o measure temperatures near the outer surface. N o correction w a s made t o the measured data t o account f o r the heat flow through the exposed portion of the m o d e l bases. This heat f l o w w a s esti- mated t o be a small fraction of the t o t a l and hence has been neglected since the primary i n t e r e s t of t h i s investigation is the r e l a t i v e effects of shape on heat transfer.

EFFECT OF BLUNTNESS ON HEXT T R P L N S F E R The effect on heat transfer of varying nose diameter w h i l e holding fineness r a t i o constant i s shown i n figure 3 . Representative data a t zero angle of attack and free-stream Mach number M .of 4.24 are presented i n the form of nondFmensiona1 heat-transfer coefficients, that is, Stanton numbers, based on free-stream properties. A t the top of the figure, Stanton numbers are referenced t o model base area and as such are a direct comparison of the total heat-transfer rates. As nose diameter i s increased frm zero, Stanton number first decreases slightly, then remains nearly constant up t o a diameter r a t i o of one-half, and there- after increases substantially up t o a diameter r a t i o of 1. The Stanton numbers presented i n the lower p a r t of figure 3 are referenced t o wetted surface area, exclusive of t h e base, and hence are indicative of the average heating r a t e per unit surface area. They decrease significantly with increasing diameter r a t i o up t o about one-half and then remain essentially constant. These r e s u l t s suggest t h a t a body w i t h a nose- to-base diameter r a t i o of about one-half i s a good comprmise f o r l o w values of both t o t a l and average heat transfer. Furthermore, t h i s amount of bluntness yields drags which are i n the range of practical i n t e r e s t f o r b a l l i s t i c m i s s i l e shapes. It was f o r t h i s reason that a diameter r a t i o of 0.32 was used i n designing t h e second f a m i l y of bodies.

EFFECT OF FINENESS RATIO ON HEAT TRANSFEZ To BLUNT 'BODIES Total heat transfer t o the bodies of different fineness r a t i o at zero angle of attack is shown i n figure 4 as a function of free-stream Mach number. Camparative data f o r a hemisphere are also presented.

Stanton numbers are referenced t o model base area. The upsweep of the data with increasing Mach number results frm the decrease of free- stream Reynolds number R typical of a wind tunnel operating w i t h a fixed supply pressure. As determined frm shadowgraph pictures the boundary layer w a s laminar over the flat-nose bodies at a l l t e s t condi- tions. This is i n contrast t o the reference cones on which transition occurred a t low Mach numbers and is an i l l u s t r a t i o n of the effect of blunting on the length of laminar run. In fact, at M = 3, the length of laminar run w a s increased by as much as a factor of 4. Total Stanton numbers f o r the flat-nose shapes were less than corresponding cone values a t a l l Mach numbers. Thus, by blunting it was possible t o increase sur- face area and volume by a factor of 3 with no heat-transfer penalty.

t o wetted surface area, a When the Stanton numbers are referenced pronounced effect of fineness r a t i o i s apparent as shown i n figure 5.

Note, f o r example, t h a t values of average Stanton number f o r the shape are 35 percent lower than those f o r the cone with all-laminar K = 6

boundary lqyer (M > 4). The maximum reduction i n average Stanton number

w i t h all-laminar f l o w is 70 percent f o r the shape at M = 4.24.

K = 9 These data are, as are a l l the data discussed previously i n t h i s report, f o r zero angle of attack. It should be pointed out, however, t h a t no measurable change i n Stanton-numbers has been observed f o r the flat-nose shapes at angles of attack up t o 3'.

The f a c t should not be overlooked that the r a t e of aerodynamic' heating i s actually proportional t o the product of Stanton number and Thus, it i s a t a c i t assumption of the tpmperature recovery factor.

discussion i n previous sections t h a t recovery factor i s essentially con- stant. The validity of this assumption is i l l u s t r a t e d i n figure 6 where average temperature recovery factors based on free-stream conditions are shown as a function of free-stream Mach number. It i s apparent t h a t shape has l i t t l e effect on recovery factor; hence, t h i s factor plays no significant r o l e i n t h i s discussion of the effect of shape on heating.

DISTRIBUTION O F IxlCAL HEAT-TRANSFER COEFFICIENTS * The measurement of overall rates of heat transfer described i n this paper can, at best, give only a qualitative idea of local heating rates.

It was undertaken t o determine a theoretical distribution of heat-transfer coefficients around one typical shape and t o make a limited experimental comparison. The method of Stine and Wanlass (ref. 2) w a s used t o calcu- l a t e heat-transfer coefficients. This calculation requires a knowledge of the local f l o w properties j u s t outside the boundary layer. These proper- t i e s were derived from experimental pressure distributions such as those shown i n figure 7. Also sham i n figure 7 are the predicted pressures D * .* .

..

of the modified Newtonian theory which was used t o design the blunt-nose bodies. These predicted pressures are i n good agreement w i t h experiment, the differences being most pronounced i n the region of the shoulder of the body. The calculated variation of local heat-transfer coefficient w i t h &istance along the body surface i s shown i n figure 8 where the r e s u l t s of the Stine-Wanlass method, which includes the effect of pres- sure gradient, are compared at free-stream Mach numbers 3 and 5 w i t h flat7plate values taken from the laminar boundary-layer theory of All heat-transfer coefficients are based on l o c a l Van Driest ( r e f . 3 ) .

flow properties j u s t outside the boundary layer. Reference values near the stagnation point were computed by the method of Sibulkin (ref. 4 ) .

Predicted heat-transfer coefficients remain essentially constant over t h e first half of the nose f l a t but then increase t o 2 t o 3 times this value near the shoulder. (A portion of the curve i n t h i s region has been shown as a dashed line because spacing of the pressure taps did not per- m i t an accurate determination of the maximum.) Subsequently, local coefficients decrease sharply t o l e s s than one-half the i n i t i a l value The notable feature of and continue i n a gradual decline t o the base.

t h i s prediction i s the pronounced increase of heat-transfer coefficients over the forepart of the body as a r e s u l t of three-dimensional and pressure-gradient effects. These relatively large local heating rates somewhat over- indicate t h a t perhaps the design of these bodies has been simplified. Very qualitatively, it appears that a slightly convex nose would tend t o reduce the heat-transfer peak at the shoulder by reducing the l o c a l density, although a t the expense of a s l i g h t increase i n heat transfer t o the nose.

COMPARISON OF TBEIORY WITH EXPERlMENT Integrated values of the theoretical heat-transfer coefficients f o r portions of the body surface are compared w i t h experimental measurements The flat-nose a d nose-shoulder data were obtained w i t h i n figure 9.

camposite models t h a t isolated the heat-transfer surfaces fram the r e s t of the body. Agreement is reasonably good except for the f l a t nose at free-stream Mach numbers above 3 . Both camputed and measured Stanton numbers show t h a t roughly 55 percent of the t o t a l heat transfer was concentrated i n the nose-shoulder region which has less than X) percent of the surface area. Thus, on an average basis, heat-transfer r a t e s i n t h i s region are greater by a factor of 5 than those f o r the rest of the body.

These r e s u l t s apply only when boundary-layer flaw i s entirely laminar. A qualitative indication of the effect of transition on t o t a l heat transfer w a s obtained, i n one case, by a r t i f i c i a l l y tripping the boundary layer i n the shoulder region. The resultant Stanton number i s shown as the solid point i n figure 9. It i s indicated that the overall heating rate is not substantially increased by the presence of a turbu- l e n t boundary layer i n t h i s region of relatively low density flow.

CONCLUDING REMARKS The r e s u l t s of t h i s investigation c m be summarized as follows: 1. A method of designing blunt shapes has been devised which reduces the heat transfer t o a body by virtue of low-velocity flow o%er the nose and low-density f l o w over the afterbody.

2. An afterbody curvature has been found which augments the favor- able effect of a flat nose i n promoting long runs of laminar boundary layer.

3. Total heat transfer t o these shapes is the same o r less than t o a cone of about the same drag, although heat-transfer rates per unit of surface area are considerably lower.

.

4. Camparison of theory and experiment indicates higher than average heat-transfer rates near the shoulder of a typical flat-nose shape and relatively low values over most of the afterbody.

1. Eggers, A. J . , Jr., Resnikoff, Meyer M., and Dennis, David I S . : Bodies of Revolution Having Minimum Drag a t Ugh Supersonic Airspeeds.

NACA TN 3666, 1956. (Supersedes NACA RM's A51K27 by Eggers, Dennis,

and Resnikoff and A52D24 by Resnikoff . )

2. Stine, Howard A . , and Wanlass, Kent: Theoretical and Experimental Investigation of Aerodynamic-Heating and Isothermal Heat-Transfer Parameters on a Hemispherical Nose With Laminar Boundary Layer at Supersonic Mach Numbers. NACA TN 3344, 1 9 % .

3 . Van D r i e s t , E. R.: The Laminar Boundary Layer With Vasiable Fluid Properties. Rep. No. AL-1866, North American Aviation, Inc., Jan. 19, 1 9 9 .

Heat Transfer Near the Forward Stagnation Point of a 4. Sibulkin, M. : Body of Revolution. Jour. Aero. Sci. (Readers' Forum), vol. 19, no. 8, Aug. 1952, pp. 570-571.

BODY SHAPES USED IN HEAT-TRANSFER INVESTIGATION REYNOLDS ANALOGY h a pucpcf BODIES FOR LOW HEAT TRANSFER FAMILY # 2 BODIES FOR LOW HEAT TRANSFER FAMILY # I REFERENCE BODIES Figure 1 HEAT TRANSFER APPARATUS .010" CLEARANCE ALL AROUND Figure 2 EFFECT OF BLUNTNESS ON HEAT TRANSFER AT M54.24 .0045r .0030L I nl I I I I I I .0026{ Z L I D = -767

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Figure 5 AVERAGE TEMPERATURE-RECOVERY FACTORS OF BODIES

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Figure 7 THEORETICAL LOCAL HEAT-TRANSFER COEFFICIENTS FOR A BLUNT BODY; LAMINAR BOUNDARY LAYER

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.'

BLUNT NOSES AT HIGH SUPERSONIC SPEEDS L O C A L HEAT TRANSFER TO By W i l l i a m E. Stoney, Jr.

Langley Aeronautical Lab or at ory A brief summary i s presented of :he recent theoretical and experi- mental work on l o c a l heat-transfer rates on blunt-nose bodies. Compari- sons of theoretical and measured heating r a t e s indicate the following conclusions: The calculation of l o c a l conditions over noses of high radius of curvature needs more study and t e s t i n g at t h e present time.

If l o c a l flow conditions are known, the laminar heating r a t e s over the whole nose shape can be calculated h i t h i n most engineering accuracy For t h e requirements f o r the whole range of Mach numbers up t o 13.8.

case of turbulent flow, turbulent f l a t - p l a t e theory based on l o c a l flow properties can provide good estimates of the heating r a t e s possible.

at present t h e biggest unknown.

The prediction of t r a n s i t i o n remains INTRODUCTION The importance of blunt-nose shapes has increased i n recent years because such shapes have many advantages i n comparison with the more common sharp-nose shapes f o r missiles having high heating rates.

High drag is sometimes desirable f o r b a l l i s t i c missiles and does not penalize t h e t o t a l efficiency of these missiles since they operate at essentially drag-free a l t i t u d e s f o r t h e major part of t h e i r f l i g h t .

As shown i n ref- erence 1, extremely blunt noses develop lower t o t a l heating rates than do sharp noses of about the same s i z e and d r a g .

Finally, and perhaps most importantly, there are many indications that extremely blunt shapes f o s t e r longer runs of laminar flow than do sharp shapes.

For these reasons the calculation of t h e l o c a l heating rates on such shapes has become extremely important.

The present paper gives a brief summary of present-day techniques and their effectiveness. T h i s summary together w i t h t h e attached l i s t of references should be helpful t o those orienting themselves i n t h i s fast-changing f i e l d .

I pressure coefficient

CP

2 surface.distance measured from stagnation point M Mach number P pressure heating rate, Btu/( sec) (sq f t ) free-stream Reynolds number based on body diameter k, d r b base radius nose radius or radius of curvature rh surface distance f r o m stagnation point t o junction of hemisphere S and cylinder; on f l a t face, distance from stagnation point t o edge, t h a t is, cylinder radius T temperature, OF X distance along center l i n e measured from apex of nose e angle between f r e e streaan and noma3 t o surface of nose CI- viscosity of a i r P density of a i r Subscripts : HEMIS hemispherical nose 2 l o c a l W based on temperature of w a l l surface 0 a t stagnation point m free stream I .

DISCUSSION Calculation of Local Flow Conditions Before any attempt can be made t o calculate heat-transfer rates, the l o c a l flow conditions must be calculated. Blunt noses can be classi- f i e d roughly into two groups: those f o r which the Newtonian flow concept (Cp,z/Cp,o = cos20) i s applicable and thus f o r which the l o c a l conditions can be e a s i l y calculated, and those f o r which the Newtonian flow concept is not applicable and f o r which no simple solutions exist.

A rough boundary can be fixed between these two groups of nose shapes by consideration of a series of noses having constant r a d i i of curvature.

Such a series i s i l l u s t r a t e d i n figure 1; t h i s s e r i e s progresses from t h e hemispherical nose on the l e f t t o the f l a t nose ( i n f i n i t e radius) on t h e r i g h t . The intermediate case f o r t h i s series would be the nose shown i n

the center - the nose f o r which, according t o Newtonian theory, t h e flow

j u s t before the corner i s a t a Mach number of 1. Until s t r i c t e r c r i t e r i a are provided, Newtonian calculations should be checked with experiment o r with a more comprehensive theory f o r noses having a radius of curva- t u r e a t t h e stagnation point greater than Recently, several theo- r e t i c a l approaches have been presented t o the blunt-nose problem. (See 2 t o 5; theories presented i n r e f s . 4 and 5 may also be found i n r e f s .

appendix D of r e f . 6. ) Some of these appear t o be promising, but more experience w i t h them i s needed before t h e i r general usefulness can be determined.

This paper considers only shapes whose l o c a l conditions are known.

Experimental data and theoretical r e s u l t s are applied t o the hemispherical and the f l a t noses t o bring out the following points: (1) If the r a t e of change of velocity a t the stagnation point i s known, the heat-transfer r a t e a t t h i s point can be calculated accurately enough f o r most engineering purposes.

(2) With the proper pressure distribution t h e laminar heating r a t e s over t h e e n t i r e nose can be calculated s a t i s f a c t o r i l y , and reasonably good estimates of the possible turbulent heating rates can be made.

Prediction of Stagnation-Point Heating Rates The prediction of stagnation-point heating rates is well proved f o r the lower Mach number range and needs demonstration only at t h e higher Mach numbers where r e a l gas effects come i n t o play.

I n figure 2 t h e r a t i o s of measured stagnation-point heating r a t e s t o theoretical calculations are presented as functions of free-stream Mach number. The t e s t r e s u l t s were obtained from a f l i g h t of t h e Lockheed X-17 rocket having a nose defined by the equation r / r b = (X/*b) 1/3 ( r e f . 6 ) , a flat-face cylinder i n f r e e f l i g h t ( r e f . 7), and shock-tube experiments performed by Alexander P. Sabol of the Langley Aero-Physics Section f o r 1-inch-diameter spheres. The l i n e f o r the Lockheed data repre- sents the Mach number t h e history f o r t h e f l i g h t , the lower portion being t h a t f o r the accelerating p a r t of the f l i g h t and the upper portion repre- senting t h e decelerating Mach numbers. The difference between accelerating and decelerating values at any given Mach number i s probably a measure of t h e t e s t accuracy rather than a r e a l e f f e c t due t o t h e higher Reynolds numbers of the deceleration portion of t h e f l i g h t path. The NACA rocket as preliminary data.

data should be considered The theoretical heating rates f o r both rockets were calculated by t h e stagnation-point theory of Fay and Riddell, c i t e d i n appendix B of reference 6, f o r t h e equilibrium boundary layer w i t h a Prandtl number of 0.71 and a Lewis number of 1.4. The stagnation-point theory of Lees ( r e f . 8) w a s compared w i t h t h e shock-tube experiments. The theories a r e different because Lees assumes through the pp = p w h = Constant boundary layer while Fay and Riddell use an approximately correct varia- (ref. 9) notes that, f o r hypersonic f l i g h t conditions, t i o n . Probstein t h e heat-transfer r a t e f o r a r e a l i s t i c variation of pp across the bound- ary layer is significantly lower than t h a t calculated from t h e approxi- mation pp = p+w. If F'robstein's conclusions are assumed t o apply d i r e c t l y t o Lees' calculations, t h e l e v e l of t h e r a t i o of t h e shock-tube

experimental values t o Lees ' calculated values shown i n figure 1 would be

raised t o somewhere between 1.1 and 1.4. This would not change the general conclusion derived from t h i s figure that, although the s c a t t e r shown indi- cates t h a t many d e t a i l s of t h e heat-transfer processes under these high- temperature conditions are s t i l l unknown, the agreement of these data is close enough so t h a t it can be f e l t that t h e i r general nature is understood .

Calculation of Heating Rates Over Entire Nose I n t h e calculation of heating r a t e s over t h e e n t i r e nose, the stagnation-point heat-transfer r a t e s of the hemispherical noses are used as datum points, and a l l t h e data and calculations are presented as r a t i o s of these values.

3 presents the r a t i o s of l o c a l laminar heating r a t e s on a Figure hemispherical nose t o stagnation heating rates plotted as functions of position along t h e surface of the hemisphere. The t e s t points are f o r a variety of conditions from Moo = 2 t o 6.8 and free-stream Reynolds numbers based on diameter of 1.0 x 106 t o 14.3 x 106. (Data f o r M = 2 and M = 3.9 are presented i n r e f . 10 and data f o r M = 6.8 i n r e f . 11.

The data f o r M = 2.5 were obtained from a free-flight investigation conducted by James J. Buglia a t the Langley Pilotless Aircraft Research Station a t Wallops Island, Va.) Good agreement with the theoretical dis-

tributions, which were calculated by the method of Lees ( r e f . €9, can be

seen immediately. Corrections by the Probstein theory t o Lees' stagnation- point theory mentioned previously would probably not affect the r a t i o s gre- sented i n figure 3 . It is also important t o notice t h a t the distribution of heating rates does not vary markedly w i t h Mach number.

Another interesting condition hriicated by the data i n figure 3 is the extremely high Reynolds number (14.3 x 106) f o r which laminar flow was obtained i n one f l i g h t t e s t . This model, however, was a special case for which extreme pains were taken t o obtain a mirror f i n i s h on the nose

of the order of 2 microinches - not an ideal process f o r assembly-line

fabrication.

S i m i l a r agreement w i t h t e s t results can be shown f o r the other

extreme i n the series of nose shapes - the perfectly f l a t face. I n fig-

ure 4 the l o c a l heating rates were not divided by the flat-face stagna- t i o n heating rates but by the appropriate hemispherical stagnation heating rates. T h i s allows a direct comparison of the f l a t and hemispherical values. The s o l i d l i n e gives the theoretical laminar results for the f l a t face by the method of Lees ( r e f . 8); and the dashed l i n e above it, the same r a t i o calculated by the method of Stine and Wanlass ( r e f . 1 2 ) .

The l a t t e r calculations d i f f e r from Lees' because they include a cor- rection f o r the effect of pressure gradient. (For the relatively l o w pressure gradients of the hemisphere, the two methods agree closely.)

A s can be seen from the figure the agreement w i t h either theory is rea- sonably good and the uncertainties i n the measurements do not permit a choice between them.

Since the f l a t nose i s a shape f o r which Newtonian f l o w concepts do not work a t all, obtained experi- a pressure-ratio distribution pz/po mentally a t a Mach number of 2 (see ref'. 13 and theoretical work of r e f . 14) was assumed t o be constant f o r a l l higher Mach numbers and was used i n the theoretical calculations. The agreement of the data, which cover Mach numbers from 2 t o 13.8, indicates that t h i s approximation was adequate f o r t h i s case. (Data f o r M = 2 are presented i n r e f . 13; data f o r M = 13.8 are presented i n r e f . 7; and data f o r M = 5 were deter- mined i n an investigation of 2-inch flat-face cylinders conducted by Morton Cooper in the Mach number 5 axisymmetric blowdown j e t a t the Langley Gas Dynamics Branch.)

What i s gained by the f l a t face in lower l o c a l heating r a t e s i n the center i s l o s t a t its edge. However, it must be remembered t h a t high l o c a l heating r a t e s are not necessarily the c r i t i c a l points i n a p a r t i - ..

cular design, as can be shown by the time history of temperature profiles on the front and side of the flat-face rocket model on which the heating r a t e s a t a Mach number of 13.8 were obtained. These temperature profiles and a sketch of the nose are presented i n figure 5. The nose was made of copper and was three-sixteenths of an inch thick on the front and one- eighth of an inch thick at the sides. The datum points represent the temperatures as measured along the front surface and down the side f o r three different times during the high Mach number part of the f l i g h t .

A t the e a r l i e s t time not much hea%ing has occurred and the temperature p r o f i l e i s relatively f l a t . A t peak Mach number the effects of conduc- t i o n i n the skin can be seen since the highest temperature is reached a t 0.82/s i n s p i t e of the peak heating which occurs a t the corner. The reason t h a t the sides are able t o act as good heat sinks l i e s i n t h e i r extremely l o w heating rates.

Measurements of these rates f o r the f i r s t two side thermocouples are shown in figure 4.

Seven seconds l a t e r , the model has slowed down t o a Mach number of 7, and the l a t e r a l flow of heat i n the skin w a s so large t h a t the maximum temperature of the f l i g h t

occurred i n the center of the model - not a t the corners. T h i s is, of

course, only an example but it does show t h a t a f a i r l y detailed study of the particular nose m u s t be made i f i t s effectiveness i s t o be evalu- ated correctly.

There are some indications ( f o r example, r e f . 1) t h a t f l a t noses o r closely a l l i e d shapes may have some advantages in retaining l a m i n a r flow, and, as is shown, on a hemispherical nose t h i s retention can be very high. I n fig- very important since turbulent heating rates can be ure 6 the r a t i o s of local heating rates t o stagnation heating rates are presented as functions of surface location. The t e s t points were deter- mined f r o m an investigation conducted by Ivan E. Beckwith and James J.

Gallagher i n a blowdown j e t a t the Langley G a s Dynamics Branch. For t h i s investigation a Mach number of 2 and free-stream Reynolds num- bers (based on body diameter) of 2.7 x 106 and 3.4 x 106 were used.

Transition obviously took place forward on the hemisphere f o r both t e s t s and heating rates nearly 2- times the stagnation r a t e were reached. The s o l i d l i n e represents f l a t - p l a t e turbulent values based on the l o c a l Reynolds numbers around the body. T h i s comparison and similar compasi- sons f r o m other t e s t s indicates that even t h i s relatively crude theoreti- c a l approach may have considerable value in estimating the turbulent heating rates. (See a l s o r e f s . 15 and 16. The theoretical approach of r e f . 16 may a l s o be found i n appendix C of r e f . 6.)

F CONCLUDING REMARKS The calculation of the l o c a l heating conditions over noses of high radius of curvature needs more investigation a t the present time, although data obtained i n low Mach number t e s t s may be adequate at much higher Mach numbers f o r use i n these calculations. However, if the l o c a l conditions are known, the laminar heating rates over the whole nose shape can be calculated within most engineering accuracy requirements f o r the whole range of Mach numbers up t o a t l e a s t 13.8.

For turbulent f l o w , flat-plate theory may provide good estimates of the heating rates possible. O f course, the prediction of t r a n s i t i o n s t i l l remains and is the biggest unknown at the present time.

1. Reller, John O., Jr.: T o t a l Heat Transfer t o Blunt-Nose Shapes With Laminar Boundary Layers at High Supersonic Speeds. (Prospective NACA paper.)

2. Maslen, Stephen H., and Moeckel, W. E.: Inviscid Hypersonic Flow Past Blunt Bodies. Preprint No. 665, S.M.F. Fund Preprint, Inst. Aero.

Sei., Jan. 1957.

3. Probstein, Ronald F.: Inviscid Flow i n the Stagnation Point Region of Very Blunt-Nosed Bodies at Hypersonic Flight Speeds. WADC TN 56-39? (Contract No. AF 33(616)-2798), Wright A i r Dev. Center, U. S. Air Force, Sept. 1956. (Also available from ASTIA as Doc.

No* AD97273.1 4. Hayes, Wallace D.: Some Aspects of Hy-personic Flow. The Ramo-Wooldridge Corp., Jan. 4, 1955.

5. Hayes, Wallace D.: Hypersonic Flow Fields at S m a l l Density Ratio.

Doc. No. 34, The Ramo-Wooldridge Corp., May 12, 1955.

6. Anon. : X-17 Re-Entry Test Vehicle - R-3 Fin& Flight Report. Rep.

No. MSD-313 (Contract No. A F 04 (645)-7), Lockheed Aircraft Corp., Oct. 31, 1956.

7. Stoney, W i l l i a m E., Jr., and Swanson, Andrew G.: H e a t Transfer on a Flat-Face Cylinder Measured in Free Flight at Mach Numbers Up t o 13.8. (Prospective NACA paper.)

8. Lees, Lester: Laminar Heat Transfer Over Blunt-Nosed Bodies at Hyper- sonic Flight Speeds. J e t Propulsion, vol. 26, no. 4, Apr. 1956, PP. 259-269.

9. Probstein, Ronald F.: The Effect of Variable Fluid Properties on the Equilibrium Laminar Boundary Layer Surface Heat Transfer Rate a t Hypersonic Flight Speeds.

WADC TN 56-2 (Contract No. AF 33(616)- 2798), Wright Air Dev. Center, U. S. Air Force, Dec. 1955.

10. Garland, Ben jamine J., and Chauvin, Leo T. : Measurements of Heat T r a n s f e r and Boundary-Layer Transition on an 8-Inch-Diameter Hemi- sphere Cylinder in Free Flight f o r a Mach Number Range of 2.0 t o 3.88.

(Prospective NACA paper. ) U. Crawford, D a v i s H., and McCauley, W i l l i a m D. : Investigation of the Laminar Aerodynamic Heat-Transfer Characteristics of a Hemisphere- Cylinder in the Langley 11-Inch Hypersonic Tunnel at a Mach Number of 6.8. NACA TN 370

f - 30%

t - ._ 12. Stine, Howasd A., and Wanlass, Kent: Theoretical and Ekper b e n t al Investigation of Aerodynamic-Heating and Isothermal Heat-Transf e r Parameters on a Hemispherical Nose With Laminar Boundary Layer at Supersonic Mach Numbers. NACA TN 3344, 1954.

13. Maskley, J. T., and Stoney, W i l l i a m E., Jr.: Heat-Transfer and Pres- sure Measurements on a Flat-Face Cylinder at a Mach Number of 2.

(Prospective NACA paper. ) 14. Maccoll, J. W., and Codd, J.: Theoretical Investigations of the Flow Around Various Bodies i n the Sonic Region of Velocities. British Theoretical Res. Rep. No. 17/45, B.A.R.C. 45/19, Ministry of Supply, Armament Res. Dept., 1945.

15. Van Driest, E. R.: The Problem of Aerodynamic Heating. Aero. Eng.

Rev., vol. 15, no. 10, Oct. 1956, pp. 26-41.

16. Denison, M. Richard: Turbulent Boundary Layer on Blunt Bodies of Revolution a t Hy-personic Speeds. Res. Memo., Lockheed Aircraft Corp., Missiles Systems Div., Apr. 13, 1956.

f BLUNT-NOSE FLOW FIELDS r S O N l C LINE Figure 1 COMPARISON OF MEASURED AND CALCULATED STAGNATION HEAT-TRANSFER RATES

F \

- QcALc -6

-

-

.4

--

- X-17 ROCKET, LOCKHEED

0 SHOCK TUBE -

.2

} NACA

- ~//l//////l ROCKET

1 1 1 1 1 1 1 1 1 1 1 1 1 ~ LAMINAR HEATING RATES ON HEMISPHERICAL NOSES Ma, R@,d TEST 0 2.0 2.7X106 ROCKET o 2.5 14.3 ROCKET A 3.9 5.1 ROCKET v 6.8 1.0 TUNNEL 1.2 1.0 Ma, .8 LAMINAR

=4 =*I

MaJ THEORY .6 .4 .2 0 .2 . 4 .6 .8 1.0 1 /s Figure 3 LAMINAR HEATING RATES ON A FLAT-FACE CYLINDER M a Ra,,d TEST A 2 4.7x1O6 TUNNEL 0 5 4 . 6 TUNNEL I I I I I I l n j 0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 z/s Figure 4 5 2 1EMPERATURE HISTORY ON FACE AND SIDES OF ROCKET MODEL 1 , 8 0 0 1,600 1 , 4 0 0 1 , 2 0 0 1 , 0 0 0 T,OF 0 .2 . 4 .6 .8 1 . 0 1 . 2 1 . 4 1 . 6 1 . 8 2.0 2 . 2 2.4 2 . 6 1 / 5 Figure 5 TURBULENT HEATING RATES ON A HEMISPHERICAL NOSE TUNNEL TESTS AT M a = 2 R q d 0 2.7X106 0 3.4 LOCAL TURBULENT FLAT-PLATE THEORY \ -

.4 \ -,p LAMINAR THEORY

- . 2 I I I I 1 0 .2 .4 .6 .8 1.0 1 /s Figure 6

t acs

i HEAT TRANSFER TO BODIES AT A N G U S O F ATTACK By W i l l i a m V. Feller Langley Aeronautical Laboratory SUMMARY Heat-transfer rates were measured on a modified Ka.rman nose shape a t an angle of attack of Oo a t Mach llumbers of 6.86 and 3.69, and a t angles of attack up t o 2 5 O a t a Mach number of 3.69. Data are presented f o r a smooth model, which showed natural transition, and f o r the model with roughness s t r i p s , which caused f u l l y turbulent flow.

INTROGUCTION The heat transfer t o bodies of revolution a t zero angle of attack with laminar flow has been extensively studied, both theoretically and experimentally, so t h a t i n general calculations can be made f o r a given configuration with confidence. For turbulent boundary layers a t zero angle of attack, the solutions f o r cones and f l a t plates have been used with the l o c a l flow conditions along the body t o obtain good approxi- mations. Very l i t t l e study has been made of the heat transfer t o bodies a t angles of attack. A t very lasge angles of attack, it might be expected t h a t the r e s u l t s found f o r swept i n f i n i t e cylinders would be applicable, but there i s a decided lack of information on heat transfer a t inter- mediate angles of attack.

This paper presents some of the r e s u l t s from an experimental study of the heat-transfer rates t o a particular body of revolution a t angles of attack up t o 25O, i n order t o give some idea of the distribution of heat-transfer rates t h a t can be expected a t supersonic speeds on an air- plane fuselage.

SYMBOLS Stanton number based on free-stream air properties NSt Reynolds number based on body maximum diameter and free-stream *D air properties I X axial distance measured from nose D body maximum diameter A sweep angle, deg a angle of attack, deg M Mach number APPARATUS The body tested i s shown'at the top of figure 1. It is a Karman nose shape of fineness r a t i o 5 , modified by t h e addition of a tangent 1 0 ' half-angle cone i n front, and a length of cylindrical section behind.

Tests w e r e made a t zero angle of attack i n the Langley 11-inch hypersonic tunnel a t a Mach number of 6.86, and a t angles of attack from Oo t o 2 5 O i n the Langley Unitary Plan wind tunnel at a Mach number of 3.69.

RESULTS I n figure 1 are shown the r e s u l t s of the tests a t the two Mach num- bers a t zero angle of attack f o r laminar flow. The laminar correlating

parameter NStK i s plotted on a logarithmic scale against the axial

s t a t i o n along t h e m o d e l i n diameters, X/D. The c i r c l e s are the data from t h e t e s t s a t M = 6.86 and t h e squares a t M = 3.69. The dashed curves, calculated by t h e theory of Stine and Wanlass (ref. 1) f o r the two Mach numbers, f i t the data w e l l over the body, except t h a t , a t axial s t a t i o n s behind X/D = 4.2 a t M = 3.69, the r i s e i n the data indicates t r a n s i t i o n t o turbulent flow. Also shown i n figure 1 are curves calcu- l a t e d f o r M = 6.86, by t h e f l a t - p l a t e theory of Van Driest (ref. 2) f o r t h e cone and flat p l a t e . The calculated curves f o r the cone and flat p l a t e agree fairly w e l l with the experimental data on t h e p a r t s of the body t h a t are nearly conical and cylindrical, respectively.

I n figure 2 are shown data f o r the same model a t M = 3.69 and zero angle of attack but with turbulent flow tripped by roughness applied i n a r i n g near the nose as indicated i n the sketch a t t h e top of t h e fig- ure. The same parameter N s ~ F D is presented i n order t o f a c i l i t a t e comparison with t h e laminar values i n figure 1. The data near the nose are not quite up t o the values calculated i n turbulent cone theory (ref. 3) but show t h e same trend along t h e length as did t h e laminar data, and agree w e l l with t h e turbulent f l a t - p l a t e theory (ref. 4 ) toward the rear of the body.

C' ..

1F Figure 3 shows the variation of the Stanton number based on the free-stream conditions along the lower or windward meridian l i n e of the body at several angles of attack. O n the left are shown the data f o r the smooth model. The curve at zero angle of attack is the same as w a s shown i n figure 1, with transition s t a r t i n g at As the X/D = 4.2.

angle of attack increases, the heat-transfer r a t e s increase, as would be expected, and the point of transition moves forward, up t o 14' angle of attack. The curves a t angles of attack of 21' and 25' show a some- w h a t different trend.

I n order t o obtain turbulent heat-transfer data, a s t r i p of rough- ness was applied i n a band along the lower meridian l i n e as well as i n a ring ne= the nose. The results are sham on the r i g h t i n figure 3.

As i n the case of laminar f l o w , the Stanton numbers increase w i t h angle of attack from Oo t o 140. !&e curve f o r a = 21° does not follow the trend with angle of attack, and i s i n f a c t lower than t h a t f o r a = 14O.

The curve f o r i s very irregular and w i l l be discussed l a t e r . a = 25O The behavior of the Stanton number distribution curves suggests that the flow around the body changes t o a mainly crosswise flow a t some angle between 1 4 ' and 21'.

I n figure 4 the distribution of Stanton number along three meridian lines i s shown f o r two angles of attack, 7' on the l e f t , and 25' on the right. Again, roughness was applied t o produce turbulant flow. A t an angle of attack of 7' the Stanton number drops from i t s value a t the windward meridian t o about half a t 900, and about l/3 on the leeward side (180°). O n the leeward side, behind X/D = 3, the Stanton number i s independent of X/D, so that separated flow i s indicated.

A t an angle of attack of 25O, the values on the windward meridian are very e r r a t i c , ranging from values near those found f o r laminar flow up t o values i n good agreement with the turbulent swept-cylinder theory.

This behavior is due t o the f a c t t h a t the local Reynolds numbers over the roughness s t r i p are very low, so t h a t t r a n s i t i o n i s not f u l l y com- pleted a t a l l stations. The range of values of the data represents var- ious stages i n the t r a n s i t i o n t o fully turbulent flows. The curves a t meridian stations goo and 180° are smooth. Values of Stanton number a t the 9 0 ' station f o r a = 25' are not very different from those found f o r a = 7 O , but a t the 1 8 0 ' station are somewhat lower than a t a = 7 O .

Figure 5 shows a polar plot of Stanton number around the circum- ference of the body a t X/D = 5.12, where the body is cylindrical, f o r several angles of attack. O n the r i g h t side are the distributions f w M l y turbulent flows, produced by a roughness s t r i p along the windward meridian. On the l e f t side of t h i s figure are values obtained on the As the angle of attack increases, the fully turbulent smooth model.

Stanton numbers increase on the windward side and decrease on the lee- ward side up t o 14O. The curve for a = 21' nearly coincides with that f o r a = 14O, and the curve for a = 2 3 O shows a further increase. The i s calculated by a semiempirical long-short-dash curve f o r a = 250 The basis of the calculatian i s method developed f o r swept cylinders.

the theory f o r the average heat-transfer coefficients over the front half of swept circular cylinders with fully turbulent boundary layers presented by Beckwith and Gallagher i n reference 5 . This theory w a s conibined w i t h an unpublished experimentally measured distribution of l o c a l heat-transfer coefficients around a swept cylinder obtained a t the Langley Laboratory by Beckwith and Gallagher, on the assumption t h a t the distribution curve i s independent of sweep angle and Mach number ( 8 s has been shown f o r laminar flow). The agreement with experiment i s very good.

O n the l e f t side of the figure are shown the distributions of Stanton number obtained on the smooth model a t a = Oo, 70, and 250.

a , = Oo, w i t h natural transition, are i n fair agreement The values a t with the a s t i f i c i a l t r a n s i t i o n values on the right. A t an angle of attack of 7 O , the 'boundary layer i s laminar near the windward meridian and low heat-transfer values are obtained. Transition starts a t a meridian angle about 4 5 O . a = 25O, transition starts e a r l i e r , A t about 2 0 ° from the lower meridian line, a f t e r which the Stanton numbers increase and fair i n t o this curve f o r f u l l y turbulent flow a t a = 25' which w a s transposed f r o m t h e data on the r i g h t .

In figure 5 the data at a = 2 5 O agree well with crossflow theory.

The behavior of the curves at a = 14O and 21° indicates t h a t the ty-pe of flow may be changing i n the interval between. To show the trend more clearly, the Stanton numbers on the windward meridian are plotted i n figure 6 against angle of attack f o r two stations on the model; X/D = 2.8 and 5.1. The curve labeled "longitudinal-flow theory" was calculated by f l a t - p l a t e theory, by use of the l o c a l flow conditions outside the boundary layer f o r the equivalent free stream. The curve labeled "crossflow theory" w a s calculated by use of the semiempirical method described e a r l i e r for swept cylinders, the body being considered t o be made up of a series of cylinders of varying diameter and sweep from a = 0 ' t o 14' angle. The experimental values increase uniformly but the trend does not agree with that predicted by the modified flat- p l a t e (longitudinal-flow) theory. A t a = 2 1 ' and 25O, the data agree well w i t h the crossflow theory curve.

CONCLUDING REMARKS The experimental r e s u l t s presented i n t h i s paper have shown that at zero angle of attack, the available theoretical methods give a good estimate of the heat-transfer coefficients on a body of revolution. A t large angles of attack, the methods based on the cross flow over swept cylinders are applicable. For intermediate angles of attack, however, there is as yet no theoretical approach, and reliance w i l l have to be placed on extrapolation from experimental studies. It is believed that the results presented in this paper can be considered typical of simple fuselages of moderate fineness ratio at supersonic Mach numbers for which the air may still be considered an ideal gas.

REFERENCES 1. Stine, Howard A., and Wanlass, Kent. : Theoretical and Experimental Investigation of Aerodynamic-Heating and Isothermal Heat-Transfer Parameters on a Hemispherical Nose With Laminar Boundary Layer at Supersonic Mach Numbers. NACA TN 3344, 1 9 % .

2. Van Driest, E. R.: The L d n a r Boundary Layer With Variable Fluid Properties. Rep. No. AL-1866, North American Avaiation, Inc . , Jan. 1 . 9 , 1 9 % .

3 . Van Driest, E. R.: Turbulent Boundary Layer on a Cone in a Super- sonic Flow at Zero Angle of Attack. Jour. Aero. Sci., vol. 19, no. 1, Jan. 1952, pp. 55-57, 72.

4. Van Driest, E. R.: Turbulent Boundary Layer in Compressible Fluids.

Jour. Aero. Sci., vol. 18, no. 3, Mar. 1951, pp. 145-160, 216.

5. Beckwith, Ivan E., and Gallagher, James J.: Experimental Investiga-

tion of the Effect of Boundary-Layer Transition on the Average Heat Transfer to a Yawed Cylinder in Supersonic Flow. NACA m ~56~09, 1956.

c

HEAT TRANSFER TO KARMAN NOSE AT ZERO ANGLE OF ATTACK LAMINAR FLOW oM.6.86 OM = 3.69 CONE, M.6.86 a . I - I I I I I I I 1 I 0 I 2 3 4 5 6 7 8 D Figure 1 HEAT TRANSFER TO KARMAN NOSE AT ZERO ANGLE OF ATTACK TURBULENT FLOW I O 0 M13.69; RD= 1.25 X IO6

NSt 6

I I I I I I I I 0 I 2 3 4 5 6 7 X

-

D Figure 2

i 31%

HEAT TRANSFER TO LOWER MERIDIAN KARMAN NOSE j M.3.69 j R D = 1.2 x I 0 6 SMOOTH MODEL ARTIFICIAL TRANSITION a,DEG 0 0 0 7 0 1 4 A 2 1 A 25 I I I I I 0 1 2 3 4 5 0 1 2 3 4 5 X/D X/D Figure 3 HEAT TRANSFER TO KARMAN NOSE M.3.69 j R D = 1 . 2 ~ 1 0 ~ j ARTIFICIAL TRANSlTlON Q = 7 O Q =25O MERIDIAN ANGLE, DEG 6 o 0 (WINDWARD) TURBULENT CROSS FLOW 0 90 THEORY

'1 0180

0 0 . -

--

---E NS t 0 1 2 3 4 5 0 1 2 3 4 5 X/D X/D Figure 4 C I R C U M F E R E N T I A L D I S T R I B U T I O N O F H E A T T R A N S F E R K A R M A N NOSE;$ ~5.12; M~3.69; Rj-j=1.2XI06 Figure 5 HEAT TRANSFER TO LOWER MERIDIAN LINE AT ANGLES OF ATTACK M.3.69; R ~ ' i . 2 3 x I o ~ ;TURBULENT FLOW X X

- ~ 2 . 8 - = 5.1

D D 8 X 1 0 - 3 8 10-3 CROSSFLOW THEORY CROSSFLOW THEORY 6 - NSt

m M = 3.69

4 4 - 2 2 - 0 FLOW THEORY C FLOW THEORY I I I I I I I 1 0 20 30 40 0 1 0 20 30 C a, DEG a, DEG Figure 6 HEAT TRANSFER IN REGIONS OF SEPARATED AND REATTACHED FLOWS By Davis H. Crawford and Charles B. Rumsey Langley Aeronautical Laboratory SUMMARY Past experimental work has indicated that separated flow can greatly increase the heat transfer to a surface; whereas, some theoretical studies have indicated a possible decrease. Recent investigations have helped to clarify the effects of separation on heat transfer and have indicated This paper considers the results of a method of reducing separation.

some of these investigations and shows the heat transfer in regions of separation and reattachment for a few specific shapes. These results have shown that the heat transfer in a separated region is strongly affected by the extent of separation, the location of the reattachment point, and the location of transition along the separated boundary.

INTRODUCTION Recent experimental and theoretical investigations have shown that the separation of the boundary layer from a surface can have a great effect on the heat flow to the surface.

At high altitudes and high Mach numbers, the presence of separation is more likely, and the regions of separation are more extensive because of the thicker boundary layers characteristic of this type of flight. Past experimental work has indi- cated that separated flow can greatly increase the heat transfer to a surface (ref. l), whereas some theoretical studies have indicated a pos- sible decrease (ref. 2 ) . Recent investigations have helped to clarify the effects of separation on heat transfer and have indicated a method of reducing separation.

This paper considers the results of some of these investigations and shows the heat transfer in regions of separation and reattachment for a few specific shapes.

For one of these shapes, boundary- layer bleed was used to delay separation and to alter the heat transfer in the region of possible separation.

SYMBOLS b distance along surface from zero station to sphere-cylinder juncture drag coefficient CD d diameter of vehicle a t characteristic station, as indicated i n figures 2 length M Mach number Stanton number NSt heat transfer per unit area per unit time heat transfer per u n i t area per unit time a t zero station with %,ns no spike R Reynolds number based on characteristic length along surface Reynolds number based on d Rd S distance along surface from zero station X distance along axis of t e s t vehicle, as indicated i n figures DISCUSSION Flare Skirt One interesting case of separation i s the flow about an ogive- cylinder body with a 3 0 ' t a i l f l a r e ( r e f . 3 ) . The t a i l f l a r e i s a pos- s i b l e stabilizing device as well as a drag brake f o r many missile shapes.

The lower curve of figure 1 shows the position of the start of separation as a function of Reynolds number. Figure 2 shows the approximate shape of the flow pattern f o r three Reynolds numbers. A t low Reynolds numbers t h e s t a r t of separation moves forward s l i g h t l y with increasing Reynolds number as i s expected from laminar theory ( r e f . 4 ) . The shape of t h e flow pattern when the separation i s a maximum is shown i n the top diagram of figure 2. A s the Reynolds number increases, the boundary layer near t h e start of separation tends t o become transitional which delays the separation. Then the position of the start of separation moves back along the model u n t i l a t a Reynolds number of 0.5 x 106 the flow pattern appears as i s shown i n the center diagram of figure 2. A t high Reynolds numbers, the boundary layer i s f u l l y turbulent ahead of the separation, as i s shown i n the lower diagram of figure 2, and t h i s causes the flow t o EFFECT OF WING ON TAIL LOADS M=2.46; azoo; (L= 20" 1.5

-. 5

-I \ \ \ Figure 19 EFFECT OF TAIL ROLL CONTROL ON VERTICAL-TAIL LOAD I 1 I I I I

-.3 '

. 4 .6 .0 I .o MACH NUMBER Figure 17 EFFECT OF WING ON TAILLOADS M=2.46; 8=0"; a=6O 1 . 0 .5 Z

-

C

-. 5

-1.0 0 I -I CN

1-5 or -

CN&W Figure 18 FLIGHT MEASUREMENTS OF AIRPLANE S T R U C T U R A L TEMPERATURES AT SUPERSONIC SPEEDS By Richard D. Banner NACA High-speed Flight Station SUMMARY Skin and s t r u c t u r a l temperatures have been obtained on the X-lB and X-IE research airplanes under transient aerodynamic heating condi- tions at speeds up t o Mach numbers near 2.0. Extensive temperature measurements w e r e obtained throughout t h e X-u3 airplane, and temperature distributions are shown on t h e nose cone, the wing, and t h e v e r t i c a l tail. Temperatures f o r the X-1E wing leading edge and internal wing structure w e r e compared w i t h similar data f o r the X-lB.

P N o c r i t i c a l skin and structural temperatures were obtained on the two airplanes over t h e range of these tests.

Simplified calculations of t h e skin temperatures i n t h e laminar- flow regions of the nose cone and the leading edges agreed favorably w i t h t h e general trends i n the measured data. The f l a t - p l a t e skin- temperature calculations i n t h e turbulent-flow regions agreed favorably w i t h the measured data on t h e nose cone and at t h e midsemispan s t a t i o n of the wing but overestimated the v e r t i c a l - t a i l skin temperatures and a l s o the upper wing skin temperature near t h e wing t i p . The r e l a t i v e l y low values of the upper skin temperatures t h a t w e r e measured at t h e wing t i p were believed t o be caused by separated-flow e f f e c t s i n t h i s region.

INTRODUCTION I n t h e design of supersonic a i r c r d t , aerodynamic heating is becoming increasingly important. Analytical studies and controlled t e s t i n g represent t h e basic methods u t i l i z e d ' i n t h e design of complex structures t o withstand t h e effects of aerodynamic heating.

Concurrent with t h e basic research studies, t h e National Advisory Camittee f o r Aeronautics i s conducting a program a t the NACA High-speed Flight Station at Edwards, C a l i f . , t o investigate t h e skin and s t r u c t u r a l temperatures actually experienced by airplanes during f l i g h t at super- sonic speeds. The purpose of t h i s paper is t o summarize t h e results of t h i s program t o the present time. The r e s u l t s of simplified calculations of the skin temperatures are compared w i t h the measured data i n the regions of the fuselage nose cone and the wing and vertical-tail skins and leading edges.

.

SYMBOLS wing semispan b/2 C chord length average heat-transfer coefficient, Btu/sq f t -hr-% hav pressure altitude, f t M Mach number P l o c a l surface pressure, lb/sq f t free-stream s t a t i c pressure, lb/sq f t P m free-stream dynamic pressure, lb/sq f t r recovery factor T skin temperature, ? F adiabatic w a l l temperature, ? ?

Taw free-stream stagnation temperature,

T,(I + 0 . a 2 ) , OF

TT free-stream ambient air temperature, % T m t time, sec a angle of attack, deg r thickness, in.

TESTS .-.) -.

-.

-c- . c *, -.: . 2 " .

' .,.

Data have recently been obtained on the X - U airplane at Mach num- ..-.,,pp---' bers up t o 2.10 and on the X-lB at Mach numbers up t o 1 . 9 4 .

(See fig. 1.)

These speeds do not necessarily represent the maximum speed capabilit5es of the airplanes. Both airplanes are constructed primarily of aluminum.

Temperature measurements were made a t approximately 60 locations on the X-lE, and approximately 300 temperatures were measured on t h e X-lB.

Figure 2 shows the f l i g h t conditions f o r both airplanes under which the temperatures were obtained. The Mach number, pressure a l t i t u d e , ambient air temperature, and angle of attack are shown as time histories.

As can be seen, t h e two f l i g h t s are generally similar.

Transient heating conditions were experienced by both airplanes The maximum heating r a t e was experienced on the during t h e f l i g h t s .

thinner skinned X-IB and was on t h e order of 3 ' per second. This heating r a t e is r e l a t i v e l y low i n comparison w i t h t h e rates being obtained on missiles and rocket models and i n controlled wind-tunnel tests; however, it is believed t o be representative of the heating r a t e s which a r e being experienced or which will be experienced i n t h e near future by f i g h t e r and interceptor a i r c r a f t .

For laminar flow i n t h e stagnation regions, approximate heat-transfer coefficients were calculated from expressions r e l a t i n g the Nusselt number and the Reynolds number given by Stine and Wanlass.

(See ref. 1. ) I n t h e regions of flat-plate turbulent flow, approximate heat-transfer coef- f i c i e n t s w e r e calculated by using Colburn's expression.

These calcula- t i o n s w e r e greatly simglified by t h e use of free-stream conditions.

This procedure was considered j u s t i f i e d i n t h a t only the overall effects were desired. A detailed theoretical analysis i s not considered t o be within t h e scope of this report.

The results of t h e calculations j u s t described indicated r e l a t i v e l y small variations i n t h e heat-transf er coefficients with t i m e ; theref ore, were determined and used i n calculating t h e skin average values temperatures.

Newton's l a w of heat flow t o the skin, which considers the heat capac- i t y of t h e material and neglects the effects of conduction, was assumed.

RESULTS AND DISCUSSION The X-IB i n s t a l l a t i o n provides a rather detailed case history of the temperatures that exist throughout an actual airplane; and, i n view of t h i s fact, more at-f;ention i s given t o t h e X-IB data i n t h e present paper.

c T h 6 - X - l E data are used t o point out any differences t h a t e x i s t i n the measured temperatures due t o either t h e configuration or t h e construction or both.

r Some of the maximum temperatures t h a t w e r e measured on the X-IB and an indication of the higher temperature areas on t h e airplane are shown i n figure 3 . The nose of t h e airplane and the leading edges of the wing and t a i l surfaces are shaded i n figure 3 t o indicate the higher tempera- ture areas. The approximate thermocouple locations are indicated by the dark points. The maximum stagnation temperature f o r the flight was 220' F.

A maximum skin temperature of 1 8 5 ' F was measured at the forward point of t h e nose cone. O n the w i n g leading edge the maximum temperature w a s 1 6 8 ' F. A maximum temperature on t h i s order was a l s o measured on t h e leading edge of t h e v e r t i c a l tail. The maximum temperatures i n other general areas are also shown. Some of the temperatures shown a t these locations are appreciably affected by i n t e r n a l heat sources and heat sinks; f o r instance, the fuselage skin temperatures adjacent t o the liquid oxygen tank are r e l a t i v e l y low (130 F); whereas, j u s t ahead of that area on the fuselage skin a maximum of 1 2 2 ' - F w a s measured. Other areas of i n t e r e s t are the windshield and canopy and the rearward part of the fuselage i n the region of the rocket engine.

It should be pointed out that the maximum temperatures shown i n f i g - ure 3 did not a l l occur at the same t i m e . I n areas where internal con- duction is negligible, skin thickness, boundary-layer temperature, and t h e heat-transfer coefficient are the primary factors affecting the skin temperature rise .

Figure 3 gives an overall picture of the measured temperatures.

I n subsequent figures, the temperature distributions i n t h e areas of the nose cone, the wing skins, the leading edges and t h e v e r t i c a l t a i l are considered i n greater detail; and comparisons are made with calculated results. Attention i s given only t o t h e supersonic portion of the f l i g h t s , since at t h e subsonic speeds the combined e f f e c t s of increasing Mach num- ber and decreasing ambient air temperature produced only small changes i n the skin temperatures.

Figure 4 shows the nose of the X-IB, where both skin-temperature and pressure measurements w e r e made at intervals along the nose between sta- t i o n 0 and s t a t i o n 55.0. The pressure data are plotted as pressure coef- f i c i e n t s at t h e bottom of the figure. The measured skin temperatures a r e shown i n t h e upper part of the figure as the open symbols. The skin t e m - perature decreases over the forward part of the nose cone, the laminar f l o w calculations showing f a i r l y good agreement. This variation i s f o l - .

lowed by a region of no change i n the skin temperature and then an increase L' t-oward t h e rear of the nose cone where the calculated turbulent f l a t - p l a t e

. --

and cone temperatures a r e approached. It i s about here t h a t the nose-cone I . .

F shape asymptotically approaches the cylindrical shape of the fuselage, and the pressure drops t o near the free-stream value. The overall t e m - perature variations that are shown suggest t h a t t r a n s i t i o n from laminar t o turbulent flow takes place along the nose at about 25 t o 30 percent of the nose-cone length, f u l l y turbulent flow developing - a t the r e a r o f - A summary of various wind-tunnel data on cones and bodies the nose cone.

of revolution indicated t h i s general transitional area.

was relatively t h i n i n comparison The skin here on the nose cone w i t h that on other areas on the airplane. The effects of varying skin thickness on the skin temperatures can be seen i n figure 5. Figure 5 shows the spanwise distributions of maximum temperatures on t h e upper wing skin at the 66-percent-chord line and at the leading edge. The spanwise variation i n the skin thickness i s shown below. The temperature variations indicate an inverse relationship between the skin temperature and the skin thickness a t both chordwise positions. The trend which would give r i s e t o thermoelastic considerations at higher temperature levels i s clearly seen i n the data here.

The calculated temperatures, shown by the dashed l i n e s i n figure 5 , were based on a constant spanwise heating input, laminar f o r the leading edge and turbulent f o r the 66-percent-chord line; and the same variations due t o thickness are seen i n the calculated temperatures.

The d&ta i n figure 5 also i l l u s t r a t e the differences i n the skin temperature w i t h chordwise position. Both top and bottom skin tempera- tures were measured at several chordwise positions at about midsemispan and near the t i p of the wing. These data are presented i n figure 6.

I n t h i s figure the calculated temperatures were estimated on t h e basis of zero angle of attack. No detailed consideration i s given t o the effects of angle of attack on the measured temperatures; however, from an overall standpoint it should be recalled from figure 2 that t h e angles of attack were positive during the flight and were on the order of 2 ' t o loo.

The data of figure 6 i l l u s t r a t e several interesting trends.

F i r s t , notice the chordwise temperature gradients that are shown at the mid- semispan station. The higher temperatures are experienced a t the leading edge and the t r a i l i n g edge (which at t h i s location i s the outboard t i p of the f l a p ) , and the lower temperatures are experienced on the thicker skinned wing box section.

Secondly, note the differences i n temperature between t h e top and bottom skins at the two span stations, the bottom skin temperature being higher i n both cases. A t the t i p station, the f a i r l y large differences seen between the top and bottom skin suggest that the flow might be p a r t l y separated i n t h i s Etrea.

The approximate calculations, which were based on the assumption of laminar flow over the leading-edge section and turbulent f l a w over t h e remainder of the chord, give a f a i r l y good overall estimate of the skin temperatures at the midsemispan stations. A t the t i p s t a t i o n the calculations agree f a i r l y well with t h e bottom skin temperature; however, they indicate an overestimate of the top skin temperature, probably because of the flow effects previously mentioned.

An example of the internal temperatures that were measured through the wing i s seen i n figure 7. Shown i n the figure are the front wing spars at about midsemispan on the X-U3 and the X-lE. The temperatures w e r e measured a t the locations shown by the black dots on the structures, and the values are given on the right-hand side of the figure. The higher temperatures shown f o r the X - l B were measured on the skin a slight dis- tance from the spar.

I n order t o give an indication of the temperature rise t h a t has taken place i n the internal structure, it i s worthwhile t o mention that the ambient air temperatures were between -TO0 F and -90' F and that the assumed turbulent adiabatic w a l l temperatures were on the order of 200' F f o r the highest Mach numbers shown here. The measured internal tempera- tures are r e l a t i v e l y low and show only slight temperature gradients across the thickness of the X-lB wing, the lower temperature being obtained on the spar center line. Essentially no differences are seen on the t h i c k spar construction of the X-IE wing, the heavier type of construction of the X-IE having a temperature-neutralizing tendency due t o the higher heat capacity. The thermal l a g effect i s a l s o seen i n figure 6 by the increase i n the measured temperatures as t h e Mach number decreases i n the later portions of the flights.

Effects of material thickness differences are a l s o seen i n the m e a s - ured leading-edge temperatures. These data are shown i n figure 8 i n time-history form together w i t h time histories of the assumed laminar adiabatic w a l l temperatures. The locations a t which the temperatures were measured a r e shown by t h e dark points on the leading-edge sketches, and the material thicknesses are given at these locations. Values of the average heat-transfer coefficients u t i l i z e d f o r the calculated t e m - peratures are shown below the sketches. The calculated temperatures are seen t o agree very w e l l with the measured data.

M a x i m u m temperatures on t h e same order of magnitude were measured on the wing and v e r t i c a l - t a i l leading edges of the X-lB. For comparison, the temperatures that were measured a t the rear of the solid leading edge o f ' t h e X-IE are seen i n the middle of the figure. It w i l l be noticed here that t h e maximum measured temperature was on the order of 2 0 ' F.

! ! $ e high heat capacity of the solid leading edge is the contributing factor t o the small rise i n t h e temperature measured at t h i s location.

The calculated skin temperature is shown t o agree .very w e l l w i t h the measured data; however, t h i s r e s u l t is not considered significant because the measured temperatures are relatively low. (For example, a 50-percent reduction i n the assumed heat-transfer coefficient a t t h i s point would produce a decrease i n the calculated maximum temperature of 7 O F.)

shown The chordwise variation i n the v e r t i c a l - t a i l temperatures i s The i n figure 9 f o r a time near maximum Mach number a t near midspan.

temperatures were measured on t h e skin and spar center l i n e s at t h e loca- tions shown by the black dots on t h e sketch. No appreciable gradients are seen i n the chordwise variation of the measured skin temperature.

Transition from laminar t o turbulent flow w a s assumed t o take place a t the point where the leading-edge section attaches t o the front spar because inspection revealed a relatively large discontinuity i n the skin at t h i s point. Skin temperatures calculated from the average heat- transfer coefficients shown and based on these assumptions agree f a i r l y well with the measured trends i n the leading-edge region but deviate somewhat over the remainder of the chord and give a conservative overall estimate i n t h i s region.

CONCUTDING REMARKS Skin and structural temperatures have been obtained on t h e X-IB and X-IE research airplanes under transient aerodynamic heating condi- tions a t speeds up t o Mach numbers near 2.0. Extensive temperature measurements were obtained throughout t h e X-IB airplane, and temperature distributions are shown on the nose cone, the wing, and the v e r t i c a l tail. Temperatures f o r the X-1E wing leading edge and internal wing structure were compared with similar data far the X-U3.

No c r i t i c a l skin and structural temperatures w e r e obtained on the two airplanes over the range of these tests.

Simplified calculations of the skin temperatures i n the laminar- flow regions of the nose cone and the leading edges agreed favorably w i t h the general trends i n the measured data.

The flat-plate skin- temperature calculations i n the turbulent-flow regions agreed favorably w i t h the measured data on the nose cone and at the midsemispan s t a t i o n of the wing but overestimated the v e r t i c a l - t a i l skin temperatures and a l s o the upper wing skin temperature near t h e wing t i p . The relatively low values of the upper skin temperatures t h a t were measured at the wing t i p were believed t o be caus6d by separated-flow e f f e c t s i n this region.

REFERENCE 1 . Stine, Howard A . , and Wanlass, Kent: Theoretical and Experimental Investigation of Aerodynamic-Heating and Isothermal Heat-Transfer Parameters on a Hemispherical Nose With Laminar Boundary Layer at Supersonic Mach Numbers.

NACA TN 3344, 1954.

RESEARCH AIRPLANES X-IE X-IB Mz2.10 Mz1.94 60 TEMP. GAGES 300 THERMOCOUPLES

d d

Figure 1 FLIGHT CONDITIONS X - l E X - I 6 M 0.5

hp, FT " l i : 7 1 -fl

T a ° F " 7 L-'

-100 a, DEG

-

0 100 200 300 4000 100 200 300 400 TIME, SEC TIME, SEC Figure 2 MAXIMUM MEASURED TEMPERATURES, X- I 6 THERMOCOUPLE LOCATIONS 122OF Figure 3 NOSE CONE TEMPERATURES AND PRESSURES, X- I B M = 1.94, t = 270 SEC 0 MEAS.

----- LAMINAR 1 CALC.

- TURBULENT

STA 55.0

TEMP, "I0 - - CONE

O F o - . o o o 0 0 0 , , , o , u 0 T F : PRESSURE ORIFICES '0 I O 2 0 30 40 5 0 60 DISTANCE, INCHES

Figure 4

MAXIMUM SPANWISE SKIN TEMPERATURES, X-IB WING L.E., M = 1.90, t = 290 SEC 66O/oc, Mz1.32, t = 3 2 5 SEC

.F 66 % c

r

CHORDWISE SKIN TEMPERATURES, X-IB WING M a = 1.90, TT'212 O F

-+- BOTTOM SKIN I

-0- TOP SKIN \ CALC (CY=O) 200 r r

---- ~ ------------

\TOP AND BOTTOM BOTTOM 0 % C 100 0 % C I O 0 Figure 6 MEASURED INTERNAL WING TEMPERATURES X-18 0 40 80 120 TP F X-IE M 2.04 //1.30 .40 TYF!

L 0 40 80 120 T: F LEADING-EDGE TEMPERATURES

0 MEAS ---- CALC - Taw (r=0.85)

X-IB WING X-IE WING X-IB VERTICALTAIL 54% b/2 63.3% b/2 M I D -SPAN 150 250 350 150 230 310 150 250 350 t, SEC t, SEC t, SEC 1- Figure 8 IF CHORDWISE TEMPERATURES -X- I B VERTICAL TAIL M= 1.90. t = 290 SEG TURBULENT ha,,

BTU/SQ FT - HR-"F

3 L k - L - 0 20 40 60 80 100

To CHORD Figure 9

1 b.. -

TWO FACTORS INFLUENCING TEMPERATURE DISTRIBUTION&

*g N ?

AND THERMAL STRESSES IN STRUCTURES By W i l l i a m A. Brooks, Jr., George E, G r i f f i t h , and H. K u r t Strass Langley Aeronautical Laboratory The influence of j o i n t conductivity and internal radiation on t e m - perature distribution and thermal stresses has been discussed. Joints of poor conductivity can occur i n normal fabrication procedure and greatly a l t e r temperature distributions and increase thermal stresses.

O n the other hand, internal radiation tends t o make the temperature distributions more uniform and thereby relieves thermal stress.

INTRODUCTION Thermal stresses arre unquestionably an important consideration i n Such stresses a r e usually produced the design of supersonic a i r c r a f t .

by nonuniform temperature distributions - the greater the tanperature

varriation within the structure, the larger the thermal stresses. The present paper deals b r i e f l y w i t h t w o factors which may affect the tem- perature distribution, and thus the thermal stresses, within a structure; theae two factors are j o i n t conductivity and internal radiation. In order t o indicate some of the effects of these two factors without unnecessary structural ccanplications, the basic structure considered consists of a length of skin w i t h an integral or an attached web. I n addition t o theoretical results, experimental data were obtained by heating the structure either aerodynamically or by laboratory radiant- heat sources.

SYMBOLS U coefficient of thermal expansion C spec if i c heat

33.8

E modulus of e l a s t i c i t y

- . A

E s-miss i v i t y h heat-transfer coefficient j o i n t conductivity coefficient h j k thermal conductivity M Mach number heating rate t skin thickness T temperature i n i t i a l temperature TO maximum skin temperature T1 minimum web temperature T2 equilibrium temperature Taw 7 time W spec if i c weight CT thermal stress Subscripts : RC radiation and conduction .

C conduction MAX maximum DISCUSSION Simgle Integral Structure Consider first the simplest possible type of skin-web combinstion, one without joint; and without internal radiation effects. Figure 1 shows such h structure, a symmetrical integral H-section w i t h a flange ( o r skin) of thickness t symmetrically heated a t a constant r a t e q; .-- . 1 within t h i s structure heat transfer takes place by conduction only. The actual temperature T minus the i n i t i a l temperature To, multiplied by the material thermal conductivity k and divided by the heating r a t e q and skin thickness t is plotted against a time parameter i n which T i s the elapsed time, c the specific heat, a,nd w the specific weight.

The choice of these dimensionless parameters makes it possible t o present on the same p l o t the r e s u l t s f o r a given cross section of different materials subjected t o different heating rates. The calculated results, shown by the s o l i d lines, are obtained by a simple an-sis assuming constant material thermal properties and no heat losses. Point 1, which is f a r t h e s t f r o m the heat sink afforded by the web, w i l l be the h o t t e s t point i n the structure, whereas point 2, which is f a r t h e s t frm t h e heat source, w i l l be the coolest. A s a consequence of assuming no heat losses and a constant heat input, the average temperature of the structure is proportional t o the mass of the section and varies linearly w i t h time.

In order t o check the theory, three tests were made involving constant heating r a t e s of 5 , 16, and 41 Btu/ft2-sec. Each t e s t is represented by a different symbol, and the experimental temperatures a r e plotted f o r various times until the maximum skin temperature reached 4500 F. The parameters are such t h a t the data for the highest heating r a t e , shown by the diamonds, appear a t t h e extreme lower end of the curves, whereas the data f o r the lowest heating r a t e extend the f u l l length of the curves.

The t e s t r e s u l t s a r e i n f a i r l y good agreement with t h e theory; any dis- crepancy is due largely t o the assumption of constant thermal properties used i n the theory.

A t any point i n the structure, the thermal stress is proportional t o the difference between the average temperature and t h e temperature When multiplied by the appropriate material of the point i n question.

properties, these differences can be converted into thermal stresses, such as shown i n figure 2.

In t h i s figure thermal-stress distributions are shown f o r both the l o w and high heating r a t e s of 5 and 4 1 Bu/ft2-sec f o r the times when the maximum skin temperature reached 450° F. The skin stresses appear i n region A and the web stresses, i n region B. The solid l i n e s represent thermal stresses calculated from measured temperatures s h m i n figure 1, and the symbols represent experimental stresses obtained from strain-gage readings corrected f o r d i f f e r e n t i a l expansion between the gage and speci- nen. The agreement between theory and experiment is quite good. As would be expected, the higher heating r a t e allows less time f o r heat t o web, thus provides M g e r tem-prature differences be conducted into the in the struct-we, and consequently yields larger thermal stresses. For the heating r a t e of 41 Btu/ft2-sec the maximurn skin stress, shown a t the extreme right, and the maximum web stress, a t the extreme left, are more than twice the values shown for the r a t e of 5 Btu/ft2-sec, despite the f a c t t h a t t h e skin temperature r i s e was the same.

- 4 Another significant point is t h a t the maximum stresses are not related i n the same proportion as the heating rates, which have an 8 t o 1 r a t i o . The stresses shown here are those which existed when the skin temperature Tl w a s 4 p o F. If, however, the skin temperature were not limited t o 430° F and a ccanparison made a t t h e same time, then, indeed, the stresses would be proportional t o t h e heating rate.

It is also possible t o present the stresses i n a dimensionless form as w a s done f o r the temperatures. Figure 3 shows the dimensionless thermal stresses at various times during the progress of the three t e s t s a t heating r a t e s of 5 , 16, and 4 1 13tu/ft2-sec. It is again evident t h a t t h e high-heating-rate data are grouped at the lower end of the theoretical curves which are represented by the solid lines, whereas the data f o r the low heating r a t e extend the full length of t h e curves. The theoretical stresses are obtained by using t h e theoretical temperature of figure 1.

The agreement between theory and experiment is about the same as t h a t i n figure 1, and any discrepancy is due t o the same reason.

The r e s u l t s of these three figures indicate that f a i r l y accurate temperatures and stresses can be predicted i n a simple integral structure where only conductive heat transfer need be considered and, further, t h a t strain-gage readings, if treated properly, can give reasonable s t r e s s results. However, if t h i s structure had contained any joints, greater temperature differences would have resulted, and accurate calculations would have became smewhat more d i f f i c u l t .

Structure With Attached Webs In order t o show sane of the effects of joints, the temperatures i n one skin-web canbination of a multiweb wing, a more r e a l i s t i c a i r c r a f t - type structure which contains riveted joints, w i l l be examined. When s i x 20-inch-chord, m u l t i w e b wings identical i n cross section - that is,

w i t h the same overall size, skin thickness, material, and so f o r t h - were

tested a t sea-level conditions at a Mach number of 2 i n a blowdown j e t , t h e r e s u l t s were as shown i n figure 4. This figure shows the temperature difference

T 1 - T2 between the maximum temperature i n t h e skin (point 1)

and t h e minimum web temperature (point 2) divided by the maximum possible

skin temperature r i s e Taw - TO plotted against time. The upper dot-

dash curve gives the theoretical temperature-ratio drop if no heat i s conducted i n t o the stiffener, that is, i f the j o i n t conductivity is h j equal t o zero, and the lower dot-dash curve gives the theoretical r e s u l t s f o r perfect j o i n t conductivity. The experimental data f o r f i v e of the wings, indicated by the shaded area, l i e close t o the curve for perfect j o i n t conductivity. O n the other hand, the data f o r the sixth wing show t h a t t h e increased temperature drop is sanewhat closer t o the curve f o r no j o i n t conductivity. Since the temperature distribution depends mainly e a.

s34

I upon heat conduction within the structure, this increased temperature difference can be attributed almost solely t o a lower j o i n t conductivity.

The much poorer thermal conductivity of the joints of the one wing, con- pared w i t h the other f i v e wings, w a s not obtained by design but rather r e s u l t s frm the small variations i n otherwise identical structures expected frcpn normal fabrication techniques. The 50-percent increase i n temperature drop of the one wing over the average of t h e other f i v e wings also resulted i n a substantial increase i n thermal s t r e s s . In fact, the wing w i t h the largest temperature drop f l u t t e r e d and then suffered a dynamic failure; whereas, the orie wing among the other five, which w a s identical i n every d e t a i l , survived its test without damage.

Construction details, such as the inclusion of ribs, invalidate further comparison w i t h the other models. However, it seems obvious that j o i n t and sanetimes adverse, e f f e c t on the conductivity can have an important, temperature variation i n a structure and hence on the thermal s t r e s s e s and, as a r e s u l t , on the structural integrity.

In figure 5 the maximum nondimensional temperature drops have been plotted against a dimensionless joint conductivity parameter h j t / k where h j i s the thermal conductivity of the joint. Calculated r e s u l t s are shown by the solid lines. In the calculations the value of 0.013 f o r ht/k, the B i o t number (an index of the r a t e of external t o internal heat t r a n s f e r ) , w a s determined by the experimental aerodynamic heat-transfer coefficient h. The symbols indicate data obtained from the tests and show a 6 t o 1 variation i n which apparently can be expected even h j from good shop practice. Data obtained by Barzelay, Tong, and Hollmay (refs. 1 and 2) cover an even wider range i n Although a consider- h j .

able s c a t t e r i n h j is shown by the f i v e lowest t e s t points, these points are i n good agreement w i t h the theory since they l i e i n a region where a fairly large change i n joint conductivity has l i t t l e e f f e c t on the temperature drop. Thus, the b a d f o r the f i v e wings shown in f i g -

ure 4 masks a considerable variation i n The sixth point, which

hj.

does not show such good agreement, is i n a region where a small change i n h j can a l t e r the temperature drop appreciably. The spread of h j within the band shown i n figure 4 is of the same order of magnitude as the variation frm the top of the band t o the curve f o r the one wing.

If the maximum skin or stiffener s t r e s s were plotted instead of t h e

temperature drop, a similar variation w i t h could be observed - the

h j t / k lower the value of h j , the higher the thermal stress, as evidenced by the f a i l u r e of the one wing.

A c t u a l f l i g h t - t e s t results are shown i n figure 6 for a duplicate of one of the f i v e ‘wings which had very good joint conductivity. The Mach number and a l t i t u d e f o r the f l i g h t are shown a t the top of the figure.

frm the skin t o the s t i f f e n e r The temperature difference

TI - T2

I center l i n e is plotted against time. When this wing w a s attached t o a rocket model, the r e s u l t s were as shown by the solid line, which l i e s much closer t o the calculated curve f o r h = 300 Btu/ft2-hr-* than J t o the curve f o r perfect j o i n t conductivity. Since a value of h j = 300 would l i e s l i g h t l y t o the l e f t of the t e s t point f o r the one wing w i t h the l a r g e s t temperature difference shown i n figure 5 , t h e f j o i n t s of t h i s wing would be considered poor from the standpoint of thermal conductivity.

I n this case f a i l u r e of the wing w a s prevented by the inclusion of a chordwise r i b .

Internal Radiation i n an Integral Structure As w a s mentioned previously, the effect of joints is t o increase the magnitude of the thermal stresses. However, if the temperatures it is possible t h a t internal radiation involved a r e sufficiently high, i n a structure may bring about some thermal-stress r e l i e f . The h o t t e r p a r t s of the structure transfer heat t o the cooler parts by radiation and thereby lessen the temperature differences. Although there i s an increased i n t e r e s t i n t h i s phenomena, very l i t t l e information can be found on t h i s subject.

Therefore, i n order t o evaluate some of the effects of internal such radiation on the temperature distribution within a multicell beam, an analog solution w a s made t o determine the as shown i n figure 7, temperature distribution of an i n f i n i t e l y long box whose internal surfaces The procedure w a s t o assume a constant r a t e of have an emissivity of 1.

heat input u n t i l the maximum skin temperature reached a prescribed l i m i t and then t o maintain t h i s skin temperature while the web temperature approached the skin temperature.

Heat w a s put into both skins a t the rate of 5 Btu/Ft*-sec u n t i l TI reached 1,200’ F, a t which time the t h e maximum skin temperature skin temperature w a s kept constant. The maximum skin temperature Ti a r e plotted against time i n seconds.

and the minimum web temperature T2 The dashed l i n e s are the solution when internal radiation i s neglected; the solid l i n e s represent the case when radiation i s included. In t h i s s i t u a t i o n it can be seen that, when radiation is included, steady s t a t e is reached much more rapidly than when conduction only is considered. It can also readily be seen that the maximum temperature difference between t h e skin and t h e web, when conduction and radiation are considered, occurs a t approximately 75 seconds and is about two-thirds of that when conduc- t i o n only is considered.

other heating rates and skin- In order t o make a preliminary survey, temperature levels were also investigated as shown i n figure 8. Here, P

F

i n order t o show one of the effects of internal radiation, t h e r a t i o of the maximum difference between skin temperature and web t a p e r a t u r e f o r both radiation and conduction t o t h e maximum difference f o r conduction only is plotted against the skin temperature For a given heating T1.

r a t e , the r a t i o of t h e temperature differences w i l l approach a minimum q = 1 Btu/ft2-sec, value as the skin temperature increases. In the case of The curve the l i m i t i s nearly reached a t a skin temperature of 1,200° F.

f o r the highest heating rate w i l l eventually reach the lowest l i m i t but at a temperature far i n excess of 1,200° F. For the conditions i n the figure, radiation effects a r e most significant when heating rates are l o w and tea- peratures are high.

Figure 9 shows some preliminary experimental results. The specimen w a s made of -inch Inconel w i t h the cross section as shown and w a s

x

12 inches long. The emissivity of the internal surfaces w a s about 0.8.

The heating r a t e s were approximately 5 and 25 Btu/ft2-sec. Although there i s a measurable reduction i n the m a x i m u m temperature difference, the reduc- t i o n i s not as large as indicated by the idealized theoretical r e s u l t s .

CONCLUDING REMARKS In summary, two factors, joint conductivity and internal radiation, which influence tanperature distribution and therefore thermal stresses, have been discussed. Even normal fabrication techniques can produce joints of such poor conductivity as t o cause the temperature differences t o increase markedly over Those of an integral structure. O n t h e other hand, a t the higher temperatures internal radiation has the effect of making the temperature differences l e s s severe and the thermal stresses smaller. A t the higher temperatures these two effects tend t o cancel one another.

REFERENCES 1. Barzelay, Martin E., Tong, Kin Nee, and Holloway, George F.: Effect of Pressure on Thermal Conductance of Contact Joints.

NACA TN 3295, 2. Barzelay, Martin E., Tong, Kin Nee, and Holloway, George F.: Thermal Conductance of Contacts i n Aircraft Joints.

NACA TN 3167, 1954.

d TEMPERATURES IN RADIANTLY HEATED H-SECTION

- CALCULATED

k

(T-To) q

0 250 Figure 1 THERMAL STRESSES IN RADIANTLY HEATED H-SECTION

O 5 } q , BTU r r r r c

* 4' FT*-SEC F I T - B

t t t t t

c r, SEC -\ 35.0

- - e - 3 . 3

I I I -20 t - - B + A + THERMAL STRESSES IN RADIANTLY HEATED H-SECTION q

- 20

-40 L I I I I I 0 50 100 150 200 250 kr

-

cwt Figure 3 TEMPERATURE DIFFERENCES IN 6 MULTIWEB WINGS i Tl-T2 .5 TAW -TO 0 6 1 2 TIME, SEC

Figure 4

VARIATION OF TEMPERATURE DIFFERENCE WITH JOINT CONDUCTIVITY

I\ - CALCULATED

0 .I .2

y

k Figure 5 TEMPERATURE DIFFERENCE FOR MULTIWEB WING IN FLIGHT 6,000

ALT., FT M ’4

ALTITUDE 0 0

-

-

T-T2,OF 80 a 1 6 TIME, SEC Figure 6 TEMPERATURE HISTORIES FOR BOX BEAM WITH INTERNAL RADIATION e- 1.0 BTU q=5- F T ~ - S E C 0 100 200 TIME, SEC Figure 7 RATES INTERNAL. RADIATION EFFECTS FOR VARIOUS HEATING BTU q * FT*-SEC Figure 8 EXPERIMENTAL RESULTS FOR INTERNAL RADIATION Figure 9 -I EFFECT OF TRANSIENT E A T I N G ON VIBRATION FREQUERCIES OF SOME SIMPLF, WING STRUCTURES By Louis F. Vosteen, Robert R. McWithey, and Robert G. Thomson Langley Aeronautical Laboratory SUMMARY Thermal stresses caused by nonuniform temperature distributions associated with transient heating can cause changes i n the effective stiffness of wing structures. Some of the effects of this change i n s t i f f n e s s w e r e investigated experimentally by testing three types of simple wing structures under various radiant-heating conditions. The structures tested w e r e a uniform plate, a s o l i d double-wedge section, and a circular-arc multiweb-wing section. Changes i n s t i f f n e s s were i n natural frequency of vibration measured by measuring the changes during transient heating. I n order t o measure changes i n frequency, a resonance-following system w a s developed which keeps the model vibrat- ing a t i t s natural frequency.

Some of the data are compared with theo- r e t i c a l calculations and show that, a t temperature differences near those required f o r thermal buckling, distortions have a marked e f f e c t on the frequency. The conclusion w a s made that, i n order t o predict the effects of aerodynamic heating on the s t i f f n e s s of wing structures by means of laboratory radiant-heating t e s t s , care must be taken t o simu- l a t e closely the temperature distributions produced aerodynamically.

INTRODUCTION One of the effects of the nonuniform temperature distributions pro- duced by aerodynamic heating is a change i n the effective structural Changes i n s t i f f n e s s have been s t i f f n e s s caused by thermal atresses.

observed i n laboratory t e s t s of several types of simple wing structures, i n reference 1, thermal stresses were cited as the cause of failure and, of wing models subjected t o aerodynamic heating. I n order t o obtain more information on t h i s thermoelastic phenomenon, laboratory tests were conducted on several types of simplified wing structures f o r which changes i n s t i f f n e s s were measured during rapid heating. The results of these t e s t s are presented and some comparisons with theoretical calcula- tions are made.

The structures considered and the manner i n which they were heated are shown i n figure 1. The structures had a square plan form and were mounted as cantilevers. The first structure is a . p l a t e of uniform thick- The second ness which was heated radiantly along the longitudinal edges.

i s a solid double-wedge section which w a s subjected t o a constant heat input over the top and bottom surfaces. The t h i r d is a symmetrical circular-arc multiweb a i r f o i l . The heat input varied along the chord as indicated i n the figure.

TEST PROCEDURE AND NSULTS Resonance-Following System Inasmuch as the natural frequency of vibration i s a function of the model stiffness, changes i n s t i f f n e s s can be measured by measuring the changes i n natural frequency during transient heating. The mecha- nism used t o detect the changes i n frequency i s shown schematically i n figure 2. The mechanism consists basically of a forcing system, the vibrating body, a vibration pickup, and the servo detecting system. The system i s operated by setting the frequency of the signal generator so that the model i s forced i n one of i t s natural modes of vibration. The phase detector i s then set t o maintain the phase r e l a t i o n that e x i s t s between the applied force, as indicated by %he signal generator, and the response of the model, as indicated by the vibration pickup. If the natural frequency of the model changes, the phase relation between the force and the response w i l l change. The servo system detects this change, and, through a servomotor, mechanically drives the signal gen- erator until the resonant phase relation i s recovered. In this manner the model is continuously forced a t i t s resonant frequency.

Uniform Plate The plate tested w a s of aluminum a l l o y 20 inches square and 1/4 inch thick.

A s the p l a t e w a s heated, the temperature at the edges rose rapidly, but the center section remained relatively cool. The ther- m a l stresses which resulted caused a change i n the natural frequencies of the plate. I n reference 2 results were presented f o r changes i n fre- quency of the first two modes. These t e s t s w e r e repeated by using the resonance-following system; i n addition, the next three higher modes were investigated. The frequency histories which were obtained during transient heating are shown i n figure 3.

The variation w i t h time of the temperature difference AT, between the edge and the midchord i n degrees Fahrenheit, i s shown at the top of f i g u e 3 . Heat w a s applied t o the p l a t e f o r about 20 seconds a t which M

j i 344

?

time the temperature difference between the edge and the midchord w a s about 190° F. In the lower portion of the figure the r a t i o of the fre- quency measured during heating f t o that of the unheated plate f o is plotted as a function of time i n seconds f o r the first f i v e natural modes.

The mode shape and corresponding i n i t i a l frequency are sham for each curve. O f these five modes, the first torsion mode underwent the l a r g e s t a reduction of about 35 percent. The first chordwise change i n frequency, bending mode w a s l e a s t affected by t h i s type of heating. Since the plate w a s not i n i t i a l l y flat, the heating also caused the plate t o deform.

These deformations were primarily torsional and, therefore, an analysis t h a t considered only torsional deflections w a s made f o r the e f f e c t of heating on the torsional mode of vibration. is given Such an analysis i n reference 3 . Some results of t h i s analysis are shown i n figure 4.

I n figure 4 the r a t i o of the frequency of a heated plate t o t h a t of

a f l a t unheated plate is shown as a function of the r a t i o of the tempera- ture difference between the edge and the midchord AT t o the theoretical temperature difference required t o produce t h e m 1 buckling of the f l a t plate AT,,. Curves are shown f o r various values of i n i t i a l distortion which have been expressed as a t w i s t parameter For the perfect 8 , .

plate, 8 , = 0, the frequency r a t i o decreases u n t i l the buckling tempera- ture of the plate i s reached. A t this time the plate buckles; and, since the s t i f f n e s s of the buckled plate is greater than t h a t of the f l a t plate, the torsional frequency begins t o increase. For a p l a t e which has an i n i t i a l twist, the heating has two effects. The thermal stresses lower the frequency, but, since the plate is also deforming, i t s s t i f f n e s s due t o twist i s increasing. The frequency therefore reaches a minimum below the buckling temperature and any further heating causes the frequency t o increase. The plate tested had a value of 8 , of 0.06 which corresponded t o a t i p twist of about one-third degree. As the frequency history indi- cates, the s t i f f n e s s actually began t o increase w h i l e heat w a s s t i l l being applied.

Figure 5 shows a comparison between measured and calculated frequency The r a t i o of the frequency during heating t o the frequency of histories.

the unheated plate i s shown as a function of time i n seconds. A small- deflection theory which neglects the effects of distortion on the s t i f f n e s s overestimates the frequency change. When a large-deflection theory which includes the effects of distortion i s used, the agreement is substantially improved.

Double-Wedge Section The double-vedge section tested w a s made of stainless s t e e l 1 inch 20 inches square.

thick and Both the upper and lower surfaces were

3.35

subjected t o a constant heat input by means of radiant heating. The temperature distribution i n the chordwise direction i s then primarily a function of the mass distribution. Again the changes i n s t i f f n e s s were measured by measuring the changes i n natural frequency. Some of the t e s t r e s u l t s are shown i n figure 6.

The variation of temperature r i s e T with time f o r an edge, the surface a t the midchord, and a point a t the centroid of the section is shown at the top of figure 6. The changes i n frequency r a t i o with time The are shown f o r the first f i v e modes i n the lower p a r t of the figure.

mode shapes and t h e i r corresponding s t a r t i n g frequencies are shown f o r each curve.

The reductions i n frequency which occurred during heating are sur- prisingly small i n comparison with the reductions calculated by Budiansky and Mayers ( r e f . 4) f o r the aerodynamic heating of similar wings instan- taneously accelerated t o moderately high Mach numbers. The discrepancies a r i s e because of the marked difference between aerodynamic heating and this type of radiant heating. In aerodynamic heating, the temperature a t the leading and t r a i l i n g edges is limited by the boundary-layer t e m - perature. I n the radiant heating, the temperature r i g h t at the leading and t r a i l i n g edges becomes prohibitively high before a temperature dis- tribution i s obtained which r e s u l t s i n l m g e s t i f f n e s s changes. A theo- r e t i c a l calculation was made f o r the first torsion mode by using the same method as t h a t used by Budiansky and Mayers but based on the experi- mental temperature distribution obtained from the radiant-heating t e s t .

These calculations gave a frequency reduction about the same as t h a t obtained i n the t e s t . Therefore, larger reductions i n frequency probably would have been obtained i f the t e s t could have been continued f o r a longer time or i f the temperature distribution had more closely simulated that generated aerodynamically.

Multiweb-Wing Section The t h i r d section tested w a s a 5-percent-thick multiweb-wing section of aluminum-alloy construction with a 20-inch chord and span. This speci- men i s the same as one which w a s tested i n the preflight j e t of the Langley P i l o t l e s s Aircraft Research Station a t Wallops Island, Va., a t a Mach number of 2. A description of the t e s t of this model, designated MW-2, is given i n reference 1. The radiant-heating test did not simulate the aerodynamic heating correctly although an e f f o r t was made t o reproduce the average heat input. The t e s t r e s u l t s are shown i n figure 7.

The temperature i n degrees Fahrenheit is plotted as a function of time i n seconds f o r a point on the skin and a t the center of a spar a t the top of figure 7. The changes i n the frequency r a t i o with time have been shown f o r f i v e modes of vibration a t the bottom of the figure.

The largest reduction i n frequency, as shown by the lowest curve, occurred The smallest reduction i n f o r a mode which involved chordwise bending.

frequency occurred f o r the first torsion mode.

The radiant heating has not simulated the aerodynamic heating very well; therefore, these results cannot be applied d i r e c t l y t o aerodynamic t e s t s . However, the type of frequency reductions obtained here are sig- nificant. The similar model (described i n r e f . 1) tested a t a Mach number of 2 f l u t t e r e d i n a mode which involved a large amount of chord- w i s e bending as did the one which had the largest frequency reduction.

A t the present t i m e , no theoretical method is available f o r pre- dicting the effects of transient heating on the frequencies of the more complicated types of modes which are the important ones f o r this structure .

CONCLUDING REMARKS Three types of simple wing structures have been tested under various radiant-heating conditions and changes i n s t i f f n e s s as indicated by changes i n natural frequency of vibration were measured. I n order t o measure the changes i n frequency during transient heating, a resonance- following system w a s developed which keeps the specimen vibrating a t its natural frequency.

For temperature differences near those required f o r thermal buckling, i n i t i a l distortions have a marked e f f e c t on the frequency. Calculations which include the e f f e c t s of these distortions are found t o be i n good agreement with the measured frequency.

The r e s u l t s obtained from these tests indicate that the magnitude of the effects of thermal s t r e s s depends strongly on the manner i n which the structure is heated. Therefore, i n order t o determine the effects of aerodynamic heating on the s t i f f n e s s of wing structures by means of lab- oratory radiant-heating t e s t s , care m u s t be taken t o simulate closely the temperature distributions produced aerodynamically.

REFERENCES 1. Heldenfels, Richard R., and Rosecrans, Richard: Preliminary Results NACA of Supersonic-Jet Tests of Simplified Wing Structures.

R M L53E26a, 1953.

2. Vosteen, Louis F., and Fuller, Kenneth E.: Behavior of a Cantilever Plate Under Rapid-Heating Conditions. NACA RM L55E20cY 1955.

3. Heldenfels, Richard R., and Vosteen, Louis F.: An Approximate Analysis of the Effects of Large Deflections and I n i t i a l Twist on the Tor- sional Stiffness of a Cantilever Plate Subjected t o Thermal Stress, (Prospective NACA paper. )

4 . Budiansky, Bernard, and Mayers, J.: Influence of Aerodynamic Heating

on the Effective Torsional Stiffness of Thin W i n g s . Jour. Aero.

Sci., vol. 23, no. 12, %c. 1956, pp. 1081-1093, 1108.

MODEL CONFIGURATIONS PLATE WEDGE MULTIWEB Figure 1 RESONANCE-FOLLOWING SYSTEM SIGNAL PHASE MOTOR GENERATOR DETECTOR Figure 2 FREQUENCY H I STO R I E S CANTILEVER PLATE 0 5 I O 1 5 20 T I M E ,SEC Figure 3 THEORETICAL FREQUENCY CHANGES FIRST TORSION MODE 1.5 1.0 f

-

f0 . 5 i 0 .5 I .o 1.5 2.0 AT/ATcr P Figure 4 COMPARISON OF FREQUENCY HISTORIES FIRST TORSION MODE 1 . 0 f

-

- .5

f0 SMALL- DEFLECTION 0 4 8 1 2 1 6 20 24 TIME, SEC Figure 5 FREQUENCY HISTORIES D O U B L E WEDGE 1,200 T,OF 600 I .o J- .95 f0 .9 I I I I 0 2 4 6 8 TIME ,SEC

Figure 6

FREQUENCY H ISTOR IES MULT I W E B 400r T , O F 2 0 0 ~ I I , I I I 0 fo ,CPS f

-

.95 -

f0 0 I 2 3 4 5 6 TIME ,SEC Figure 7 I ?

EFFECTS O F RAPkD IlEAlcING ON STRENGTH OF AIRFRAME COMPONENTS By Richard A. Pride, John B. Hall, Jr., and Melvin S . Anderson Langley Aeronautical Laboratory SUMMARY Results of several experimental investigations axe presented which indicate the effects of rapid heating on the bending strength of multiweb beam and ring-stiffened cylinders. It is shown that thermal stresses reduce the bending load carried at buckling by both beams and cylinders.

The influence of thermal stress on maximum load is found to depend largely on the mode of buckling. For beams that buckle locally, no apparent effect of thermal Stress on the maximum load has been found.

A reduction in maximum load has been observed for beams that buckle in the wrinkling mode and for cylinders.

INTRODUCTION Aerodynamic heating rates currently contemplated in airplanes and missiles may impose severe thermal stresses on primary structures. This paper considers the influence of such thermal stresses on the bending strength of multiweb beams and ring-stiffened cylinders.

Observation of the behavior of various types of structures under combinations of loads and thermal stresses has indicated that the effect of thermal stress on buckling is to reduce the bending load which may be carried prior to buckling and that the effect of thermal stress on maximum load may be correlated with the type of stress-shortening diagram of the structure.

Some typical stress-shortening diagrams an2 associated buckling modes are presented in figure 1 .

Local buckling has a stress-shortening curve that permits considerable increase in both stress and shortening to occur after buckling and prior to failure.

Within this region of increasing stress and shortening, it is possible that a redistribution of stress would alleviate the detrimental effect of thermal stress on m a x i m load.

In contrast, the stress-shortening curve for a structure such as a ring-stiffened cylinder usually drops abruptly after buckling (fig. 1 ) .

Hence, a reduction in buckling stress produced by thermal stress should be reflected as a corresponding loss in maximum strength. A stress- shortening diagram in which considerable shortening occurs for negli- gible increase in stress exists for structures such as multiweb beams with formed-channel webs which buckle in a mode known as wrinkling.

This mode is characterizedby buckles extending across the chord of the beam.

The considerable shortening that can occur after buckling indi- cates that some influence of thermal stress on failure may be anticipated; however, this influence m y not be as great as for the cylinder.

Tests to explore themnal-stress effects on the bending strength of these three types of structures have been made and some of the results are presented in preliminary form in this paper.

SYMBOLS A cross-sectional area, sq in.

b plate width, in.

C distance from neutral axis to center of skin, in.

secant modulus for bending stress in skin, ksi

EB

secant modulus for skin, ksi ES secant modulus for web, ksi

Ew

I moment of inertia, in.

k plate buckling coefficient 2 cylinder ring spacing, in.

M bending moment, in-kips r cylinder radius, in.

S peripheral distance , in.

T temperature, OF

T average temperature, 9

?? temperature rate with respect t o time, %/see

t p l a t e thickness, in.

a coefficient of thermal expansion, per ?F ? p l a s t i c i t y reduction factor (r stress, k s i

-

(r average stress, k s i P Poisson's r a t i o Subscripts: B bending cr c r i t i c a l CY 0.2-percent-offset compressive yield f failure S skin

w web

BEAM S!EWVG'.I!K The test setup f o r applying both bending loads and rapid heating A one-cell beam i s shown supported on on beams is shown i n figure 2.

columns about one-third the distance from each end and loaded i n bending at the ends.

by t h e hydraulic jacks Rapid heating i s applied t o the top and bottom skins of the beam by means of high-intensity quartz-tube lamp radiators located behind the reflectors. Strain gages and deflec- t i o n pickups mounted on the cold webs give an indication of overall beam behavior during the test.

Failure Associated With Local Buckling A large number of tests have been made on one-cell beams t h a t buckle i n t h e l o c a l mode. (Some of the results have been reported i n ref. 1. ) A representative temperature d i s t r i b u t i o n around t h e cross section is shown i n figure 3 f o r a beam 7.35 inches square with a w a l l thickness of 0.152 inch. The variation of temperature with peripheral distance f o r one quadrant of the beam is shown. For t h e maximum heating time i n these t e s t s , t h e temperature of t h e center of t h e skin rises t o about 600° F, while t h e temperature of most of t h e webs rises t o only about 1 0 0 ' F. Temperature distributions such as t h i s w i l l produce large thermal stresses i n these beams.

For these aluminum-alloy beams, skin temperatures i n the range from 400° t o 600° F also produce deterioration i n t h e material properties.

I n order t o separate t h e loss i n beam strength caused by deterioration of material properties from the l o s s i n beam strength caused by thermal stress, a different type of test w a s made i n which al1,sides of the beam were uniformly heated at a high r a t e . The t e s t r e s u l t s f o r l o c a l buckling of these one-cell beams are shown i n figure 4.

The bending load s t r e s s i n the skin of the beam i s plotted against the average skin temperature.

For the uniform heating case t h e skin temperature i s t h e average temper- ature around t h e e n t i r e beam cross sectionj whereas, t h e average skin temperature i s indicated f o r t h e nonuniform heating case i n which t h e skins are heated at about 1 0 0 ' F/sec.

For the nonuniform heating tests t h e existence of a difference i n temperature between skins and webs i s implied as w a s shown i n figure 3 .

Results a r e given i n figure 4 f o r beams having two different values

of width-thickness r a t i o f o r t h e skin; f o r one beam proportion buckling occurred i n t h e e l a s t i c - s t r e s s range so t h a t a large increase i n stress a f t e r buckling w a s possible, and f o r the other beam proportion buckling occurred i n t h e p l a s t i c range so t h a t only a s l i g h t increase i n stress beyond buckling was obtained. The upper curve f o r b/t = 48 gives t h e calculated buckling stress f o r uniformly heated beams and shows the e f f e c t of material deterioration on the e l a s t i c buckling stress.

The buckling stress was determined from t h e following equation: The s l i g h t reduction i n buckling s t r e s s shown i s t h e ' r e s u l t of changes i n e l a s t i c modulus with temperature.

The open square t e s t points i n - , figure 4 are t h e confirming tests f o r t h i s curve.

The lower curve f o r b/t = 48 determined from the following equation i s the calculated amount of bending load s t r e s s required t o produce buckling when thermal s t r e s s i s present along w i t h material deterioration : Equation ( 2 ) follows directly from equations (1) and ( 2 ) of reference 2.

The region between the t w o lower curves i n figure 4 is a measure of the

thermal s t r e s s as calculated by the last term i n equation (2). The solid square t e s t points indicate confirming t e s t s f o r t h i s e l a s t i c thermal-stress buckling condition.

For b/t = 30 the buckling s t r e s s i s i n the p l a s t i c range f o r t h i s

material. The upper curve i n figure 4 gives the calculated e f f e c t of

material deterioration on buckling s t r e s s f o r uniform heating. The buckling s t r e s s was again determined from equation (1) by using the p l a s t i c i t y reduction coefficient The lower curve gives the 7 = Es/E.

calculated amount of bending load s t r e s s required t o produce buckling when both material deterioration and thermal s t r e s s are considered Again the region between these t w o cwves represents the (eq. ( 2 ) ) .

amount of thermal s t r e s s present at buckling. The t e s t s axe i n agree- men% w i t h the calculations. It should be noted t h a t about one-half of

the t e s t r e s u l t s presented i n figure 4 were obtained f o r beams that were

loaded first and then heated, with the remaining beams heated first and then loaded. No discernable effects of sequence could be found.

Thus, it appears that local buckling of beams w i t h integral webs can be predicted at elevated temperatures either with uniform heating o r with temperature gradients, and i n both the e l a s t i c and the p l a s t i c s t r e s s ranges.

The maximum strength of these same beams is given i n figure 5.

The curves show the maximum strength of the beams f o r uniform heating calculated from the following equation:

- - M f “

Of - -

( 3 ) I where Equation (4) is taken from reference 1 and i s dependent only on beam dimensions and material properties at elevated temperature. The calcu- lated curves of figure 5 correspond t o the same uniform heating case as the upper buckling curves f o r each value of b / t i n figure 4. A considerable difference e x i s t s between the buckling stress and failure f o r b / t = 48. A t b/t = 30 t h i s difference i n s t r e s s i s practically gone as a r e s u l t of p l a s t i c buckling; however, a considerable amount of beam deflection occurred between buckling and failure, even though the s t r e s s increased only slightly. The open t e s t points corresponding t o uniform heating indicate t h a t the f a i l u r e calculation i s valid f o r both types of beams. The s o l i d points represent test conditions at maximum load f o r the beams which had developed large thermal stresses a t buckling. As indicated by the intermingling of the open and solid test points, no e f f e c t of thermal s t r e s s is evident on the maximum load. This r e s u l t is equally t r u e f o r beams t h a t buckled either e l a s t i c a l l y or plastically.

Failure Associated With Wrinkling "he preliminary r e s u l t s obtained f o r a series of multiweb beams designed t o a i r c r a f t proportions and fabricated from 17-7 PH stainless s t e e l are given i n figure 6. The interior structure consists of t h i n formed-channel webs riveted t o the skins. I n t h i s particular configu- ration, no post-buckling strength w a s found i n the room-temperature t e s t . Therefore, the upper curve calculated from equation (1) gives the buckling strength and failure strength f o r uniform heating based on material deterioration with temperature. The lower curve gives the calculated bending load s t r e s s t h a t produces buckling under the nonuniform-heating t e s t condition (eq. ( 2 ) ) . The region between the curves then represents the amount of thermal s t r e s s t h a t w a s calculated t o be present i n t h e t e s t s . The c i r c l e s give the failure-test r e s u l t s obtained from three beams. The r e s u l t s from two of the tests f o r non- uniform heating indicate t h a t thermal s t r e s s i n the beam reduced the maximum load. The maximum possible reduction was not large i n the particular beam proportions tested, and it remains t o be determined whether o r not corresponding r e s u l t s w i l l be obtained i n beam proportions where the induced thermal stresses are a larger percentage of the beam buckling s t r e s s .

CYLINDE3 STRENGTH Tests have been completed on 2024-T3 aluminum-alloy ring-stiffened

circular cylinders (table I), and a program has been started w i t h 17-7 PH

stainless s t e e l cylinders. The test setup i s shown i n figure 7. The cyl- inder i s loaded i n bending by the large weight cage acting through a link- age system. A quartz-tube lamp radiator constructed mound the outside of the cylinder test section permits rapid heating of the cylinder skin with heat flowing into the rings primarily by conduction from the skin.

The effect of heating a t different temperature r a t e s on cylinder strength i s shown i n figure 8. The solid curve i s t h e calculated bending strength of the ring-stiffened cylinder f o r uniform heating of both skin and rings and is based on the room-temperature t e s t r e s u l t s of reference 3 The decrease i n strength shown by the curve is caused by t h e change i n e l a s t i c modulus at high temperatures.

Three nominally identical cylinders were loaded with two-thirds of the room-temperature f a i l i n g load i n bending and then heated t o f a i l u r e a t temperature rates of 1 ' F/sec, 2 0 ' F/sec, and Po F/sec. With the rate which corresponded essentially t o a uniform slowest temperature heating test, the ring temperature followed the skin temperature very closely. For t h i s case it would be expected that t h e buckling failure would be influenced mainly by the change i n e l a s t i c modulus with tempera- ture. The close agreement of the t e s t a t lo F/sec with t h e curve f o r uniform heating checks the validity of such a calculation.

For the two higher heating rates, ring temperatures lagged the skin temperature by a large amount. The lover curve i n figure 8 is faired f o r these rapid heating t e s t s and the gap between the curves indicates the effect of restrained expansion. Variations i n cylinder diameter caused by r e s t r a i n t of thermal expansion of the skin by the rings were observed i n t h e t e s t s .

The bulging between rings and circumferential compression s t r e s s produced by t h i s r e s t r a i n t a r e the most probable causes f o r t h e reduction of strength of the two cylinders subjected t o the high heating rates.

For these particular cylinder proportions, temperature rates substantially l e s s than the 20° F/sec would be required t o avoid t h i s reduction i n strength.

The effect of changing the ring spacing is shown i n figure 9 f o r a constant temperature r a t e of 9 0 ' F/sec. A t room temperature the same value of failure stress is obtained f o r equal t o 1/2 o r greater.

2/r A t a uniform elevated temperature a single calculated curve represents the strength of these cylinders. For Z/r equal t o 1/4, t h e small ring spacing r e s u l t s i n an increased bending strength f o r uniform heating con- ditions as shown by the top solid curve. The dashed curves are drawn t o t h e i r respective t e s t points f o r nonuniform heating a t the high r a t e .

The gap between the dashed curves and the corresponding solid curves is a measure of the loss in bending strength caused by the restrained skin expansion. As the ring spacing increases, the loss in bending strength also increases.

It is believed to be significant that the mode of failure of these tests was the usual diamond buckle pattern and not a circumferential bulge such as would correspond to the eccentricity of the restrained skin. This behavior and the greater reduction in failure strength with increasing ring spacing suggest that the circumferential compression due to restrained skin expansion interacts more with the bending stress than does the eccentricity. This interaction becomes more serious as ring spacing is increased, inasmuch as the ratio of the actual to the critical circumferential compression stress increases.

CONCLUDIIVG REMAHKS It may be concluded fromthese tests that thermal stresses will interact with bending load stresses to reduce the buckling load carried by a structure. Depending upon the mode of buckling, the thermal stresses may or may not affect the magnitude of the maximum lokd. In tests of structures where increases in load are required to produce deformation in the post-buckling range, no apparent effect of thermal stress on the failure load has been found; in structures which tend to deform with loss of load beyond buckling, tests indicate that a loss of strength due to thermal stress can be expected.

1. Pride, Richard A . : Transient Heating Effects on the Bending Strength Box Beams. M. S. Thesis, Va. Polytechnic Inst., 1956.

of 2. Pride, Richard A,: An Investigation of the Effects of Rapid Skin Heating on Box Beams Loaded in Bending.

NACA RM L55Bo3, 1955.

3. Peterson, James P.: Bending Tests of Ring-Stiffened Circular Cylinders.

NACA TN 3735, 1956.

F

% 3r-z k d ald c l m +I ;I d o co f c o Y ? ! ? ?

k d c d rl x u STRESS-SHORTENING CURVES FOR VARIOUS STRUCTURAL COMPONENTS STRESS SHORTENING Figure 1 TEST SETUP FOR RAPID HEATING AND BENDING OF BEAMS L-91930.1 Figure 2 TEMPERATURE DISTRIBUTION IN BEAM CROSS SECTION TEMPERATURE DISTRIBUTION IN BEAM CROSS SECTION 2014-T6 ALUMINUM ALLOY; tmlOO°F/SEC 2014-T6 ALUMINUM ALLOY; tmlOO°F/SEC - I I I 400 - 200 - I I I I I I I I I I I I I I I I I I 6 8 6 8 0 2 4 0 2 4 PERIPHERAL DISTANCE, s, IN. PERIPHERAL DISTANCE, S, IN.

Figure 3 RAPID -HEATING EFFECTS ON BEAM BUCKLING 2014-T6 ALUMlNUM ALLOY;? u 100DF/SEC - - - 4 0 BENDM LOAD - STRESS, U KS I - b

-=48 t \T

- I I I I I I I

Figure 4 3 G 3

* i 0 e. .e a . e . ... 0 . ..-

. . r < . a . . - - - -

I " RAPID-HEATING EFFECTS ON. BEAM FAILURE 2014 -T6 ALUMINUM ALLOY 100' F/SEC - 60 b -=30 - - BENDING LOAD - STRESS, KSI

-

\

- 0 200 400 600 800 SKIN TEMPERATURE, 7 Figure 5 RAPID -HEATING EFFECTS ON BEAMS (WRINKLING MODE) 17-7 PH STAINLESS STEEL; IOO'F/SEC BUCKLING AND FAILURE, UNIFORM HEATING BUCKLING WITH IO0 THERMAL STRESS

-

BENDING 80 LOAD bS

-

STRESS, KSI 60- tS

-

.025 - I tw 0.32

- t S

I I I I I I I I TEST SETUP FOR RAPID HEATING AND BENDING OF CYLINDERS Figure 7 L-90701.1 RAPID -HEATING-RATE EFFECT ON RING-STIFFENED CYLINDER STRENGTH 2024-T3 ALUMINUM ALLOY;*=+; +=300 r UNIFORM HEATING NONUNIFORM HEATING BENDING - IO STRESS, KSI

t

I I I I I I I 0 200 400 600 SKIN TEMPERATURE, O F

Figure 8 365

'.

RING SPACING EFFECT ON STRENGTH OF RAPIDLY HEATED RING -STIFFENED CYLINDERS 2024-T3 ALUMINUM ALLOY j f = 3 0 0 ; T = S O O F /SEC

-

-

- BENDING l5 LOAD STRESS, - KSI 1 0 UNIFORM HEATING 5 -

--- NONUNIFORM HEATING

I I I I I I I Figure 9 THE COMBINATIONS OF THE3MAL AND LOAD STRESSES FOR THE ONSET OF P m BUCKLING IN PLATES By George W. Zender and Richard A. Pride Langley Aeronautical Laboratory A simple and practical method for evaluating the onset of permanent buckling in plates in the presence of combined thermal and load stresses is outlined. A particular application of the method shows reasonable

agreement with tests of 17-7 PH stainless-steel square tubes. The

results indicate that the load stress which the plate can support at the onset of permanent buckling is substantially reduced as the temperature difference of the plate and adjoining members increases.

INTRODUCTION The use of high-density materials in supersonic aircraft causes con- cern with respect to buckling of the thin skin surfaces, particularly where permanent buckles may develop in the structure. Methods of analy- sis are needed which include the effects of thermal stresses in combina- tion with the usual load stresses.

In order to provide such methods, the behavior of plates due to combined thermal and load stresses is being studied; this paper presents initial results obtained for predicting the onset of permanent buckling and compares the results with experiment.

SYMBOLS cross-sectional area of skin, sq in.

AS cross-sectional area of webs or stringers restraining thermal Aw expansion of skin, sq in.

b width of skin, in.

e unit shortening of skin modulus of e l a s t i c i t y of skin materialrat average skin tem- ES perature, k s i modulus of e l a s t i c i t y of web material at average web tempera-

Ew

ture, ks i t thickness of skin, in.

average temperature of skin minus average temperature of web,

m

? F l i n e a r coefficient of thermal expansion, per ?F U s t r a i n a t which buckling i n i t i a t e s %r e las t i c l i m i t s t r a i n E e2 average s t r e s s over cross-sectional area of skin, k s i Q load s t r e s s over cross-sectional area of skin, ksi average aL average thermal s t r e s s over cross-sectional area of skin, k s i OT METHOD OF ANALYSIS A simple approximation f o r the beginning of permanent buckling i n a plate subjected t o compressive load is suggested by the experimental observation that permanent buckling begins when t h e unit shortening of the plate i s about the same value as the elastic-limit s t r a i n of the material. This concept appears useful f o r approximating the compressive load required f o r the onset of permanent buckling i n a p l a t e i n the pres- ence of thermal stresses. Consider a p l a t e which has been shortened beyond the value required f o r buckling. (See f i g . 1.) I n the usual sense, t h e shortening of t h e plate comes from compressive loads; however, i n effect, shortening also occurs when the p l a t e is heated but the ther- mal expansion i s restrained, such as would occur if t h e edges of the p l a t e were bounded by stringers or shear w e b s at a lower temperature.

This effective shortening due t o restrained thermal expansion is t h e difference i n length between the restrained and the unrestrained p l a t e when heated. The lower curve of figure 2 shows the manner i n which the effective unit shortening due t o restrained thermal expansion increases w i t h the difference i n average temperature of the p l a t e and F the adjoining member. The dashed l i n e i n figure 2 indicates the c r i t i c a l s t r a i n or t h e unit shortening f o r buckling of t h e p l a t e . The upper s o l i d curve indicates the elastic-limit s t r a i n which decreases somewhat with increasing temperature. For a given temperature difference, then, the p l a t e i s i n a state of shortening due t o restrained thermal expansion; additional shortening by compressive loading causes the p l a t e t o buckle; and further compressive-load shortening causes t h e buckles t o deepen but the buckles are not permanent u n t i l the l i m i t given by the upper curve is exceeded. The region between t h e s o l i d lines, then, defines the per- missible amount of compressive-load shortening which may be applied i n conjunction w i t h the effective shortening from restrained thermal expan- sion without causing permanent buckling.

SPECIMENS AMI =OD O F TESTING I n order t o t e s t the v a l i d i t y of t h e foregoing approximate analysis, t e s t s were performed on --inch-thick 17-7 PH s t a i n l e s s - s t e e l p l a t e s fab- ricated i n t o square tubes by welding the corners. The tubes were 32 inches long and had b/t r a t i o s of 40, 60, or 80. Two opposite walls of t h e tubes (skins) were exposed t o heat supplied by two banks of quartz-tube radiators as shown i n figure 3 . The other two w a l l s (webs) were shielded from t h e radiators by aluminum p l a t e s which ran lengthwise of the tube and projected diagonally outward from each corner of t h e tube.

The shields have been removed i n figure 3 i n order t o show the tube. Temperature dis- tributions i n the tubes were obtained w i t h thermocouples, and records of the extension near t h e corners, along 15 inches of t h e length, were obtained w i t h four d i f f e r e n t i a l transformers. Figure 3 shows t h e setup when t h e square tubes were subjected t o heat without end load.

The same t e s t setup w a s placed i n a t e s t i n g machine and compressive loads were applied i n combination w i t h heat. In addition, compression tests of tubes a t room temperature were performed. The square tubes were unloaded and/or cooled t o room temperature a f t e r loading and/or heating, and pro- of t h e amplitude of the permanent buckles were obtained with a f i l e s pantograph apparatus which multiplied the amplitude by a f a c t o r of 11.

For each run, the average of the buckle depths (measured from c r e s t t o valley or twice maximum amplitude) i n t h e skins w a s obtained. Figure 4 shows an example of t h e permanent-buckle information obtained f o r t h e square tubes subjected t o heat. The particular data shown a r e f o r t h e square tube subjected t o heat without compressive load and w i t h b / t = 60.

The ordinate shown i n figure 4 is t h e difference of the average tempera- tures of the skin and web of the tube. Before t h e tube w a s subjected t o heat, the average value of buckle depth w a s obtained from t h e pantograph measurements and is indicated i n figure 4 ( i n i t i a l imperfection). After t h e tube had been subjected t o an elevated temperature and cooled t o room temperature, the permanent-buckle depth w a s s l i g h t l y larger than t h e i n i t i a l imperfection. Subsequent t e s t s on the same tube but with pro- gressively higher values of temperature resulted i n progressively larger values of permanent-buckle depth. The temperature difference when the permanent-buckle depth began t o exceed the i n i t i a l imperfection w a s defined as the s t a r t of permanent buckling, as is indicated i n figure 4.

Similar information was obtained f o r a l l tubes tested except that load s t r e s s w a s plotted i n place of temperature difference f o r the square tubes subjected t o compressive load but not t o heat. The b a d s t r e s s i n the skin at the start of permanent buckling f o r t h e square tubes sub- jected t o both heat and compressive load w a s evaluated from the extension measurements and the t o t a l load on the tube since the compressive s t r e s s f r o m t h a t i n the webs.

i n the skin f o r t h i s case d i f f e r s considerably RESULTS AND DISCUSSION Figure 5 presents a comparisoii of the experimental r e s u l t s with The curves obtained from the approximate analysis previously given.

ordinate shown i n figure 5 i s the average compressive load s t r e s s f o r the onset of permanent buckling i n the plate, and the abscissa is the difference i n average temperatures of t h e skin and web. The d e t a i l s of evaluation of the curves are given i n t h e appendix. It is apparent that the load s t r e s s which the p l a t e can support at the onset of perma- nent buckling is substantially reduced as the temperature difference increases.

I n general, reasonable agreement of the approximate analysis and the experiment e x i s t s . Somewhat b e t t e r agreement e x i s t s when load s t r e s s only is applied than when large thermal stresses are present. The poorer agreement i s largely attributed t o the assumption that the properties of the heated skin are represented by properties f o r the average value of skin temperature. This representation is somewhat inaccurate at high values of temperature difference when rather large-temperature gradients e x i s t .

CONCLUDING R E m S A simple and p r a c t i c a l method for evaluating the onset of permanent buckling i n plates i n the presence of thermal stresses i s given. A par- t i c u l a r application of the method shows reasonable agreement w i t h t e s t s of 17-7 PH stainless-steel square tubes. The r e s u l t s indicate that the load s t r e s s which the p l a t e can support at the onset of permanent buckling is substantially reduced as the temperature difference of the plate and adjoining members increases.

APPENDIX EVALUATION OF LOAD S!?2RESS Compressive stress-strain curve"s of 17-7 PH stainless-steel material for a wide range of temperatures are presented in reference 1 and are Beyond kuckling, assumed to represent the material of the square tubes.

the average stress in the buckled skin is approximated by the expression (ref. 2 ) : which is in substantial agreement with the experimental measurements obtained on the square tubes subjected to compressive loads without ther- m a l stresses (room-temperature tests). The combined thermal and load stress for the onset of permanent buckling is then O ' +o',=E / E E

T Sb e2 cr

The thermal stress as given by equation (2) of reference 3 is OT = aEs ( 3 ) 1 + -

EWAW

Equation ( 3 ) was modified for thermal stresses exceeding the buckling

stress by employing assumptions consistant with equation (1) , in order

to allow for the effect of the reduced longitudinal stiffness of the buckled skin. After evaluating the thermal stress, the load stress uL was obtained from equation (2) and the results are shown by the curves of figure 5 .

E REFERENCES 1. Stein, Bland A . : Compressive Stress-Strain Properties of 17-7 PH and AM 350 Stainless S t e e l Sheet at Elevated Temperatures. (Pro- spective NACA paper. ) 2. Von K d d n , Theodor, Sechler, Ernest E . , and Donnell, L . H.: The Strength of Thin Plates i n Compression. A.S.M.E. Trans., APM-54-5, vol. 54, no. 2, Jan. 30, 1932, pp. 53-57.

An Investigation of the Effects of Rapid Skin 3 . Pride, Richard A.: Heating on Box Beams Loaded i n Bending.

NACA RM L55BO3, 1955.

BUCKLED PLATE Figure 1 METHOD O F ANALYSIS ELASTIC LIMIT

w

UNIT SHORTENING

-----

RESTRAINED THERMAL EXPANSION TEMPERATURE DIFFERENCE Figure 2 .

" ' . : TEST SETUP FOR THERMAL PERMANENT BUCKLING OF SQUARE TUBE Figure 3 147-64 1 MEASUREMENTS OF PERMANENT - B U C K L E DEPTH EX P E R I M E NTA L I 7 -7 PH STAINLESS S T E E L , b / t = 60 O F ':-n.l IN ITlAL IMPERFECTION I I I , 0 .02 .04 .06 OB IO '12 PERMANENT -BUCKLE DEPTH ,IN.

Figure 4 COMBINATIONS OF LOAD STRESS AND TEMPERATURE DIFFERENCE FOR THE START OF PERMANENT BUCKLING 17-7 PH STAINLESS STEEL; AS’ AW EXPERIMENT b/t 0 40 A 60 0 80 0 1 0 0 200 300 400 500 600 700 TEMPERATURE DIFFERENCE, O F Figure 5

F

SOME E X P E R m S WITH INSULATED STRUCTURES By Richasd Rosecrans, Aldie E. Johnson, Jr., and W i l l i a m M . Bland, Jr.

Langley Aeronautical Laboratory Two methods of insulating structures, one f o r short-time use and the other f o r somewhat longer protection, were studied by radiant-heating t e s t s and supersonic-wind-tunnel t e s t s . Results of these t e s t s indicated t h a t effective temporary protection can be obtained w i t h f a i r l y l i g h t - weight structures; however, it is emphasized that care should be given t o design d e t a i l s t o prevent f l u t t e r of the insulation cover i n some cases.

INTRODUCTION One proposed method of coping with the problem of aerodynamic heating is t o provide an insulating cover or radiation shield t o reduce the amount of heat entering the structural airframe. In order t o be most effective, such a covering must have high insulating value and as l i t t l e weight and thickness as possible. If it i s necessary t o protect the basic structure a simple, thin, lightweight system can be employed.

f o r only a short time, For longer protection, a more elaborate method is necessary. Even the more extensive insulating systems permit heat t o get through eventually; therefore, f o r very long time exposure t o high temperatures, cooling must

be provided. This paper discusses the f i r s t two classes - those which

do not require cooling.

TESTS Experiments have been conducted upon several devices which appeared l i k e l y t o afford significant protection.

Solid Protective Covering One short-time method involved a combination of insulation and heat I f the basic structure is of lightweight material incapable of storage.

withstanding high temperatures, it can be protected for a short period by covering it with one o r more layers of heavier material which can t o l e r a t e high temperature. Much of the heat which enters the structure c during the first few seconds is stored in t h e covering material. Heat f l o w t o the inner structure is delayed partly by the conductivity of the material and p a r t l y by thermal resistance of the joints. I f the need f o r protection ends by the time a damaging amount of heat enters the basic structure, as it might i n the case of a short-range missile, the objective i s accomplished. Such a method was used t o protect some tapered fins.

With no protection, the leading edge of a magnesium f i n melted i n l e s s than 2 seconds. With the leading edge covered with one layer of 0.008-inch- thick glass cloth and one layer of 0.031 Inconel, the temperature of the magnesium had risen t o l e s s than l25O F i n 2 seconds. A heavier covering, i n which one layer covered the entire fin and a second layer covered only the leading edge, was even more effective. Figure 1 shows that, while the temperature of the outer layer of Inconel rose rapidly and reached 1,750° F in 5 seconds, the temperature of the inner magnesium structure had r i s e n t o only 9 0 ' F i n 2 seconds, when the unprotected f i n had failed, and t o l e s s than 300' F i n 5 seconds. During the f i r s t 2 seconds, l e s s than 5 percent of the heat which entered the leading edge penetrated t o the load-carrying structure.

of the t e s t showed that, soon a f t e r the f i n entered Motion pictures the j e t stream, t h e cover becage red near midspan, where the temperature of the gases f r o m t h e j e t were highest. Because the thickness of the covering varied between the leading and t r a i l i n g sections, the tempera- After 8.4 seconds, t u r e of the cover along the chord was f a i r l y uniform.

the j e t pierced the protective cover and the fin f a i l e d almost immediately.

Double-Wall Construction Two insulating configurations ( f i g . 2), designed t o protect the a i r - One was a frame over a longer period of heating, were investigated.

single-faced, corrugated-core sandwich of Inconel X; the other was a stainless-steel honeycomb sandwich. The exposed surface w a s supported by the longitudinal corrugations i n one case and by the core and inner face of the sandwich i n the other; i n both cases the sandwich was separated from the load-carrying structure by either bulk insulation o r an a i r gap. Corrugated panels were constructed with and without bulk insulation; a l l honeycomb panels were made with only an a i r gap. Because of the very l i g h t weight of these panels, the possibility of f l u t t e r and f a i l u r e existed; consequently, t h e i r structural integrity i n a supersonic airstream, as well as t h e i r insulating qualities, was determined.

Corrugated panels.- The corrugated panels were designed and fabricated Both the surface and corrugations were by the Bell Aircraft Corporation.

of 0.005 Inconel X.

A one-quarter-inch s t e e l p l a t e constituted t h e base o r load-carrying structure.

Retaining straps held the panel against the supports, and provision w a s made f o r expansion i n both directions.

Thermo- couples on the under side of the outer face and at several locations in the i n t e r i o r measured the temperature during a t e s t .

I n order t o determine the insulating capacity of this type of con- struction, the outer surface was heated, i n a s t a t i c test, a t approxi- mately 1/2 Btu/sq ft/sec u n t i l it reached l , 5 0 O o F, a f t e r which t h e skin was maintained at t h a t temperature for about 50 seconds. Temperature histories are shown i n figure 3 . The temperature of t h e exposed surface rose at a constant r a t e f o r about 70 seconds and then w a s held steady u n t i l 2 minutes had elapsed f r o m t h e start of t h e test. The temperature of the inner surface of the corrugation lagged behind that of the exposed surface and f i n a l l y reached an equilibrium temperature about 150° F lower than that of the outer face. The combination of the radiation shield and bulk insulation protected the load-carrying structure so that it experi- enced only a negligible temperature r i s e .

Additional t e s t s were made i n a blowdown j e t at a Mach number of 1.4, sea-level s t a t i c pressure, and a stagnation temperature of 6000 F. In some of the t e s t s , added heat w a s supplied by a quartz-lamp radiator which faced the panel from just outside the j e t stream and raised the surface temperature t o nearly l,OOOo F i n some cases. Temperature his- t o r i e s f o r a test on a corrugated panel without bulk insulation are shown i n figure 4. Surface temperatures of about 800° F were reached. The temperature of the inner p a r t of the corrugation lagged several hundred degrees behind t h a t of the exposed surface and the load-carrying struc- t u r e experienced only a s m a l l temperature r i s e . The data terminate after 10 seconds because of the f l u t t e r and f a i l u r e of the corrugated cover.

Aerodynamic heating w a s augmented by the radiant heater and t h e combined effect of t h e heating and t h e air loads caused f l u t t e r t o begin about 10 seconds a f t e r the t e s t began. The panel w a s mounted as an extension of the tunnel w a l l and w a s divided into three bays by expansion joints.

From motion pictures, f l u t t e r w a s first observed i n the downstream bay.

It spread quickly t o the other bays and the panel w a s destroyed after about 12 seconds. High-speed pictures taken a t 640 frames per second show the very high frequency of the f l u t t e r and indicate that the mode shape was much l i k e that of corrugated m e t a l . The corrugations were i n the same direction as those of the supporting corrugations of the panel but appeared t o have a longer wave length by a factor of perhaps two or three. A Not a l l the tests of corrugated panels ended i n t h i s manner.

similar configuration, but with an improved design o f . t h e edges, survived However, the r e s u l t emphasizes t h e need f o r careful t h e same t e s t .

experimental checking of such designs, at l e a s t u n t i l more adequate theo- r e t i c a l methods are available.

3'78

Honeycomb panels.- The honeycomb panels were fabricated of 0.005-inch- All sandwich thick facing sheets brazed t o both sides of a honeycomb core.

material w a s 17-7 P H stainless s t e e l . The base or load-carrying structure

w a s 1/8-inch-thick aluminum plate. The same type of s t a t i c heating test w a s made on the honeycomb panels as on the corrugated panels.. Tempera- t u r e histories are shown i n figure 5 f o r the outer and inner faces of t h e sandwich and f o r the base structure. The heating cycle is evident from w a s very nearly the same as t h a t f o r the cor- the surface temperature and rugated panels. The inner-face temperature lagged behind and approached 1 , 2 5 0 ' F toward the end of the test. The aluminum base w a s heated t o about 300' F, which is a higher temperature than t h a t of the base plate behind the corrugated panel with bulk insulation, even when allowance is made f o r the difference i n heat capacities of the two base structures.

I n the wind-tunnel t e s t s , however, the bending s t i f f n e s s of the honey- comb panels w a s sufficiently high t o prevent f l u t t e r , and t h e only unde- w a s t h e pock-marked appearance of the outer s i r a b l e effect of the t e s t surface. Thermal expansion of the heated skin caused the facing sheet t o buckle over each c e l l of the honeycomb interior. This buckling reduced the smoothness of the aerodynamic surface but had the advantage of reducing the overall expansion of the panel.

DISCUSS I O N L i t t l e difference i n insulating value w a s found between the corrugated and honeycomb panels, s o long as bulk insulation was not used between t h e sandwich and the base structure. The corrugated panels with bulk insula- t i o n were considerably better from an insulation standpoint than either type without it but, when bulk insulation w a s used, the protective covering w a s three times as thick as when it w a s omitted. The corrugated panels have certain advantages because they employ only one face; they can be fabricated by seam welding instead of brazing, which makes them easier t o manufacture and, also, they can easily be bent around curved surfaces s o long as the curvature is i n only one direction. Similarly, the honey- comb panels have advantages because of t h e i r greater strength; they are considerably l e s s susceptible t o f l u t t e r and should require l e s s sup- porting structure.

CONCLUDING REMARKS These t e s t s represent only a s m a l l e f f o r t i n the f i e l d of insulated Results so far structures; many additional variations can be studied.

indicate t h a t effective short-time insulation can be achieved with f a i r l y lightweight structures; however, it is emphasized t h a t care should be given t o design d e t a i l s i n order t o insure structural integrity.

* E T H Y L E N E H O T - E X H A U S T J E T T E S T

INCONEL - PROTECTED MAGNESIUM F I N

2*ooor

TEMP., .031 INCONEL O F , 1,000 0 2 4 6 TIME, SEC Figure 1 I NSU L AT I NG PAN E LS CORRUGATED PANEL RETAINER CORRI BULK I NSU L AT ION BASE HONEYCOMB PANEL OUTER FACE INNER FACE BASE PLATE SUPPORT PIN LABORATORY RADIANT - H E A T I N G T E S T CORRUGATED P A N E L 1,500 1 , 0 0 0 TEMP., O F 0 60 I20 T I M E , S E C Figure 3 BLOWDOWN-JET TEST CORRUGATED PANEL - TEMP, O F

400 -

I 0 5 I O T I M E ,SEC Figure 4 L A B O R A T O R Y R A D I A N T - H E A T I N G TEST HONEYCOMB P A N E L 1,500 1 , 0 0 0 TE M P., O F 60 I20 T I M E , SEC Figure 5

, . , -

F SOME RESEARCH RESULTS ON SANDWICH STRUCTURES By Melvin S. Anderson and Richard G. Updegraff Langley Aeronautical Laboratory SUMMARY The results of compressive-buckling t e s t s of s t e e l sandwich plates are given, and the significant parameters which affect the strength of the plates are discussed. The various types of sandwich construction are shown t o be comparable on a weight-strength basis with conventional high-s trength aluminum- alloy construct ion.

INTRODUCTION The use of high-density, heat-resistant materials in modern a i r c r a f t has served t o reemphasize the need f o r lightweight methods of construction.

One such method receiving wide attention i s sandwich construction which permits almost full u t i l i z a t i o n of the strength of t h i n gages of materials.

Success of this approach i s t o a large extent dependent upon advances i n production techniques and practical engineering experience. For these reasons a number of sandwich Configurations have evolved, some of which are shown in figure 1. The honeycomb sandwich has been produced by adhe- sive bonding, brazing, and welding techniques. In high-temperature m t e - rials there i s considerable interest i n the welding approach and attention has, therefore, been directed toward other configurations which are more amenable t o welding. Representative of these configurations are the truss- core, tube-core, and web-core sandwiches a l s o shown in figure 1. These configurations have the common characteristic that the core elements can be joined t o the faces by welding along p a r a l l e l longitudinal lines.

Certain obvious differences exist between these configurations and the honeycomb; f o r example, they are more directional i n t h e i r s t i f k e s s and strength properties. They require a heavier core t o achieve comparable panel thicknesses, but the core carries direct loads and provides a high shear strength. The core also provides natural passages f o r the circula- t i o n of coolants i n applications where this may be desirable. The behavior of the truss-core sandwich is typical of t h i s group and is considered along w i t h the honeycomb sandwich in t h i s paper.

b p l a t e width D p l a t e flexual s t i f f n e s s per u n i t width p l a t e shear s t i f f n e s s per unit width DQ E Young's modulus of e l a s t i c i t y h overall height of sandwich k plate-buckling coefficient 2 panel length compressive load per unit width pi t p l a t e- element thickness p l a s t i c i t y reduction factor ?-I angle between face sheet and core element

e

Poisson's r a t i o s t r e s s buckling s t r e s s Qcr Subscripts : C core f face sheet 1 upper face 2 lower face EXPERIMENT Honeycomb construction effectively increases t h e thickness of the sandwich p l a t e which r e s u l t s i n a high overall bending s t i f f n e s s as com- pared with an equivalent-weight plate of s o l i d material. A t the same time, however, the l i g h t core tends t o make a sandwich sensitive t o con- centrated loads and causes shearing deformations t o play an important r o l e i n determining the stress t h a t a sandwich p l a t e can carry. Because of t h i s effect, sandwich development has required considerable experi- mental work using special t e s t techniques and fixtures.

Test Technique A f i x t u r e t h a t w a s found t o be suitable f o r a simple test of t h e strength of a sandwich panel i n compression is i l l u s t r a t e d - i n figure 2.

The panel is loaded on i t s ends by a t e s t i n g machine, and t h e panel edges are alined by a fixture designed t o give simple support. A cross-sectional view of the panel and f i x t u r e is shown i n figure 3. The I-beam and knife edges prevent lateral deflection of the panel edges but permit rotation.

They can be adjusted t o accommodate panels of different thickness and width. Clearance between the f i x t u r e and the t e s t i n g machine permits shortening of the panel without loading the fixture.

The sandwich p l a t e shown i n figure 2 has a honeycomb core. For t h i s type of sandwich it w a s found necessary t o reinforce the panel a t t h e loaded ends t o prevent end failures. The l i g h t areas of t h e test speci- men are externally applied doubler plates which are adhesive-bonded t o the panel. It i s considered significant t h a t in tests of truss-core sandwich no special end reinforcement was required. This i s attributed t o the higher shear strength of the core of t h i s construction.

T e s t Results Panels.- Test results f o r some honeycomb panels are compased i n These panels varied f i g u r m t h the buckling theory of reference 1.

i n thickness from 1/4 inch t o 3/4 inch with face-sheet thicknesses of The compressive buckling-stress coefficient 0.017 inch t o 0.064 inch.

Theory pre- i s plotted as a function of a shear-flexibility parameter.

d i c t s a large l o s s i n panel buckling; strength as core shear f l e x i b i l i t y increases. If the shear s t i f f n e s s DQ of the panel i s large, the buckling-stress coefficient approaches t h e value of 4 which i s associated Theory is capable of predicting t h e influence of the wfth s o l i d plates.

geometrical quantities which make up the shear-flexibility parameter as i s i l l u s t r a t e d by the open t e s t points f o r both brazed and adhesive-bonded s t e e l honevcomb -Danels. The core density associated with these points w a s

f$ lb/cu f t (l/k-inch c e l l with 0.002-inch f o i l ) and I 2 lb/cu f t (l/k-inch

c e l l with 0.003-inch f o i l ) .

However, when panels having a core density

of 62 lb/cu f t (l/k-inch c e l l with 0.0015-inch f o i l ) were tested, pre-

dicted strengths were not consistently obtained as indicated by the dark- ened t e s t points.

These l o w points are believed t o be caused by the low shear strength associated with the lightest core. The influence of core shear strength i s not included i n buckling theory. The loss i n buckling strength f o r these panels i s much greater than the reduction i n weight over a panel which had a heavier core but sustained the predicted load.

Hence, on a weight-efficiency basis as well as from the standpoint of obtaining consistent and r e l i a b l e results, these t e s t s indicate t h a t adhesive-bonded cores should have a density greater than 6- lb/cu f t .

In the sandwiches with the heavier cores, the stresses i n the face sheets varied up t o 200,000 psi, the compressive yield s t r e s s of the material tested.

Beams.- Since the matter of core density i s an important factor in determining the weight of honeycomb panels, further t e s t s have been made i n which sandwich panels were used as the compression covers of box beams i n bending. Figure 5 is a photograph of one of the beams a f t e r a com- pression f a i l u r e of the sandwich cover. O f the three beams tested t o date, only the one having a sandwich with a core density of 12 lb/cu f t approached t h e load predicted by theory (14 percent less than theory). The remaining

t w o beams had core densities of & and d lb/cu f t and f a i l e d a t loads

2 4 considerably l e s s than the predicted ones. These results suggest that, t o achieve adequate core shear strength, heavier cores may be required f o r a practical structure than f o r simple compression t e s t s under more ideal conditions.

LOCAL BUCKLING OF TRUSS-CORE SANDWICHES Plate-buckling theory has been applied t o truss-core sandwich plates i s again adequate.

and the available t e s t r e s u l t s indicate that the theory With the truss-core sandwich no problems wirth core shear s t i f f n e s s or strength were encountered because of the higher core densities required of the sand- t o prevent l o c a l buckling of the individual p l a t e elements wich configuration. The l o c a l buckling s t r e s s can be calculated with the By knowing the l o c a l aid of a diagram such as t h a t shown i n figure 6.

buckling s t r e s s as well as the overall plate i n s t a b i l i t y s t r e s s as a function of sandwich dimensions the proportions can be varied t o obtain In figure 6 the most e f f i c i e n t sandwich f o r any given loading condition.

the buckling coefficient f o r l o c a l i n s t a b i l i t y of the sandwich configura- t i o n i s plotted against the r a t i o of core-elemen$ thickness t o face-sheet thickness over a range of values found t o give e f f i c i e n t proportions.

It should be noted t h a t the core elements are of t h e same order of thick- ness as the face sheets i n contrast t o the f o i l in honeycomb cores which may be only a fraction of the thickness of the face sheets. Inasmuch as the sandwich is orthotropic, t h e buckling-stress coefficient is given f o r compression i n both the longitudinal direction indicated by the upper curves and the transverse direction indicated by t h e lower curves. A lower strength i s obtained f o r the transverse loading inasmuch as the face plates are subject t o column f a i l u r e between truss-panel points- I n both cases, the buckling-stress coefficient is raised because of inter- ference r e s t r a i n t s caused by the triangular arrangement of the members.

The values indicated i n figure 6 have been substantiated by crippling t e s t s on s m a l l specimens such as t h a t shown i n figure 7. This particular

specimen i s of welded construction, 17-7 PH s t a i n l e s s s t e e l , and sustained

a s t r e s s of 185,000 p s i at f a i l u r e .

By using figure 6, p l a t e proportions can be adjusted s o t h a t l o c a l buckling of the sandwich elements i s equal t o or greater than t h e overall plate-buckling stress. For example, if -it is desired t o achieve a longitudinal-compression s t r e s s of 180,000 p s i ( a typical value f o r the yield stress of high-strength s t e e l ) , the proportions given on t h e l e f t - hand portion of figure 6 meet the requirements; a l s o given i s t h e c r i t i c a l compressive s t r e s s i n the transverse direction which is almost two-thirds the value f o r the longitudinal direction. The overall height of the sand- wich, indicated by the r a t i o h/tf = 15, is such that a very favorable weight efficiency i s obtained f o r panels of t h i s sandwich loaded in edge compression.

EFFICIENCY OF SANDWICH CONSTRUCTION The weight of unstiffened plates, sandwiches, and stiffened panels subjected t o longitudinal-compressive s t r e s s is plotted as a function of the appropriate s t r u c t u r a l index i n figure 8.

The weight of these struc- tures can be compared at identical values of the s t r u c t u r a l index inasmuch as t h e p l a t e width b and panel length 2 are simply the support spacing i n an actual structure. For t h i s particular plot, t h e u n i t s are such t h a t , i f the ordinate i s multiplied by the support spacing, the weight i s given d i r e c t l y i n pounds per square foot of surface. For example, at an ordi- nate value o f 0.2, a p l a t e 10 inches wide would weigh 0.2 times 10 (or 2 lb/sq f t ) .

The weight efficiency of the honeycomb-sandwich construction taken from reference 2 has been calculated by assuming t h a t a core density of 10 lb/cu f t w a s necessary t o obtain the stresses indicated by theory.

The most e f f i c i e n t proportions f o r the truss-core sandwich involve core densities varying from 30 t o 50 lb/cu f t .

Despite the greater core density f o r the truss-core sandwich, there i s l i t t l e difference i n weight between the t w o types of sandwich construction; w i t h the honeycomb sandwich more efficient a t low values of the structural index and because of the load- carrying core, the truss-core sandwich i s more e f f i c i e n t at the higher values&-% %.l.so shown in figure 8 are the weight-efficiency curves f o r high-gtrength aluminum-alloy plates that would occur in multispar con- struction'and for conventional stiffened-panel construction.

It appears t h a t under compressive loadings sandwich construction in s t e e l is com- parable i n weight t o e f f i c i e n t conventional construction i n aluminum alloy.

THE3MAL STRESSES IN SANDWICH PLATES Aconsideration of the response of sandwich plates t o transient heat- indicates t h a t certain adjustments t o sandwich proportions may be desirable t o minimize the effect of thermal stresses. For example, i n figure 9 are shown the r e s u l t s of thermal-stress calculations f o r a typical sandwich which is heated on one face t o &IOo F a t a r a t e of 80 F per second. Heat is transferred t o the other face by conduction and radiation. The sandwich is assumed t o be constrained t o remain flat, and the resulting maximum thermal s t r e s s i n the t w o faces i s plotted against the thickness r a t i o of the two faces. T h i s r a t i o w a s varied while holding the t o t a l weight of the sandwich constant.

For equal-thickness faces, the tension s t r e s s in the cooler face is equal t o the compression s t r e s s i n the heated face: As the thickness of the cooler face i s decreased, relatively l i t t l e change occurs in the ten- sion s t r e s s while the compression stress i n the heated face i s reduced considerably. This favorable alteration in the thermal stresses is due p a r t i a l l y t o a reduction i n the maximum temperature difference between the t w o faces and p a r t i a l l y t o the change i n the r e l a t i v e areas of the faces. The decrease i n compressive thermal s t r e s s permits an increase i n load s t r e s s t o be cazried before buckling of the sandwich. I n addi- tion, the more even distribution of temperature through the thickness of the sandwich permits the absorption of a greater quantity of heat before the hotter face exceeds its allowable temperature.

CONCLUDING REMARKS A few of the factors which affect the design of any particular sand- wich configuration have been presented. For honeycomb construction, the core should be of sufficient stiffness t o give a u g h buckling coefficient in order t o obtain a minimum-weight sandwich.

In addition, t h e core should be of adequate strength t o prevent premature core failures and insure r e l i a b l e results. For sandwiches such as t h e truss core, tube core, or web core, shear strength or stiffness i s generally no problem; but t h e main consideration i s proportioning t h e sandwich so that overall p l a t e i n s t a b i l i t y i s not preceded by l o c a l buckling or crippling. Sand- wiches of t h i s type can be proportioned so that they compare favorably with honeycomb construction on a weight-strength basis. For elevated- temperature applications, a sandwich with FL thicker outer face appears b e t t e r able t o cope with the effects of heating and restrained expansion.

.. . .

.._ ...

REFERENCES 1. Seide, Paul, and Stowell, Elbridge Z.: Elastic and P l a s t i c Buckling of Simply Supported Solid-Core Sandwich Plates in Compression.

NACA Rep. 967, 1930. (Supersedes NACA TN 1822. ) 2. Johnson, Aldie E., Jr., and Semonian, Joseph W.: A Study of t h e Efficiency of High-Strength, Steel, Cellular-Core Sandwich Plates i n Compression. NACA T I ? 3751, 1956.

S A N D W I C H C O N F I G U R A T I O N S TRUSS CORE HONEYCOMB CORE WEB CORE T U B E CORE Figure 1 TEST SETUP IF GROSS SECTION OF FIXTURE AND SPECIMEN HONEYCOMB Figure 3 BUCKLING COEFFICIENTS FOR SANDWICH P L A T E S k r 2 7 ) D COR E P i = b 2 DENSITY L B K U F T 675 8.50,

0 '6 BRAZED

m n ADHESIVE BONDED m

't

I I I I I I I I I 0 .2 4 . 6 .8 8 2 D

SHEAR FLEXIBILITY PARAMETER, -

b2 DQ Figure 4 SANDWICH BOX BEAM AFTER FAILURE Figure 5 L-57 -650.1 BUCKLING OF TRUSS-CORE SANDWICH ELEMENTS 2~ I Figure 6 CRIPPLING SPECIMEN Figure 7 L-57-95 1 WEIGHT-STRENGTH CURVES .7-UNSTIFFENED PLATE ,7075-T6 .6 - CONVENTIONAL STIFFENED PANEL, 7075 -T6 TRUSS-CORE SANDWICH, 17-7PH I I I I I I I I 0 I 2 3 4 Pi P i STRUCTURAL INDEX,- OR ~ KSI b

Figure 8 393

EFFECT OF SANDWICH DIMENSIONS ON THERMAL STRESSES

50r

c-2, TENS ION -

-

T H E R M A L

Lt1

STRESS, 7- KS I

-

20 / =k

CT I , COMPRESS ION Lt2

P-

10-

/

I I I I I I I Figure 9 RECENT RESEARCH ON THE CREEF’ OF AIRFRAME ’ COMPONENTS By Eldon E. Mathauser, Avraham Berkovits, and Bland A. Stein Langley Aeronautical Laboratory The results of recent research of the National Advisory Committee for Aeronautics on the creep of airframe components at elevated tempera- tures are summarized. Experimental lifetime data from creep tests of stainless-steel plates and aluminum-alloy unstiffened circular cylinders are presented and compared with results predicted from isochronous stress- strain curves.

The results of a study to determine the magnitude of creep strains that produce significant structural deformations are included.

A comparison of structural weight determined from assumed strength and creep criteria is made to establish temperature ranges in which creep is expected to influence structural design for various materials.

INTRODUCTION Many studies have been made at the National Advisory Committee for Aeronautics during the past few years to obtain basic knowledge of the creep behavior of structural elements at elevated temperatures. These studies have ranged from analytical and experimental investigations of simple structural elements such as columns and plates (refs. 1 to 3) to the development of a variational theorem (ref. 4) suitable for applica- tion in many structural creep problems. Studies have also been made to establish approximate methods (for example, ref. 3) for predicting creep collapse of structural components.

This paper presents comparisons between experimental and predicted lifetime results for stainless-steel plates and for aluminum-alloy unstiffened circular cylinders; The results of an analysis to determine the magnitude of creep strains that produce significant structural deformations are given.

Temperature ranges in which creep is expected to influence aircraft structural design are indicated for various materials.

T C - 2 ? e - b width, in.

ES secant modulus, ksi Et tangent modulus, ksi acceleration due to gravity, ft/sec g k c onstant r radius, in.

t thickness, in.

%r critical (buckling) stress, ksi 0.2-percent-offset compressive yield stress, ksi uCY

-

O f average failure stress, ksi DE'l!T2RMINATION O F CREEP C0I;LPSSE The approximate methods that have been investigated for predicting creep collapse of structural elements are based on the use of isochronous stress-strain curves in conjunction with methods established for pre- dicting maximum strength. A n example of isochronous stress-strain curves is given in figure 1 . The dashed line indicates the material compressive stress-strain curve for 17-7 PH stainless-steel sheet (condition TH 1,050) at 800' F. The solid lines, designated as isochronous stress-strain curves, indicate the strain produced on application of a given stress plus the creep strain obtained at that stress for the various times.

Curves such as these can be obtained by cross plotting compressive creep curves to give stress as a function of strain for different times. The isochronous stress-strain curves shown in figure 1 were obtained from compressive creep tests of the stafnless-steel sheet at 800° F. The tick marks indicate the 0.2-percent-offset compressive yield stresses.

, Plates The use of isochronous stress-strain curves for the prediction of creep lifetime of plates will be considered first. A comparison between predicted and experimental lifetimes is shown in figure 2 . Applied stress .b is plotted against lifetime defined as collapse time for 17-7 PH stainless-steel plates (condition T K 1,050) at 800' F . m e symbols indicate compressive-creep-test results from V-groove edge-supported plates for width-thickness ratios ranging from 15 to 60. The solid lines indicate plate life predicted fromthe following equation:

-

t a f = 1.60 &acy where is the average applied stress to produce creep collapse of 5 f the plate, E , is the secant modulus associated with acy is the compressive yield stress, and t/b is the plate thickness-width ratio.

Equation ( 1 ) gives maximum strength of V-groove edge-supported plates

at elevated temperatures (ref. 3 ) , if the material parameter / =

is evaluated from the material compressive stress-strain curve. Evalua- tion of the material parameter from isochronous compressive stress-strain curves, in general, gives a satisfactory approximation for plate lifetime.

This equation has been used to predict creep lifetime for both 2024-T3 and 7075-6 aluminum-alloy plates. Similar agreement between experimental and predicted results was obtained.

Unstiffened Circular Cylinders Prediction of creep lifetime of unstiffened circular cylinders using isochronous stress-strain curves will now be considered.

In figure 3, bending moment is plotted against lifetime defined as collapse time for 5052-0 aluminum-alloy cylinders at 500° F . The symbols indicate experi-

mental results obtained from reference 5 for radius-thickness ratios

ranging from 125 to 250. Predicted lifetimes indicated by the curves were obtained by substituting materials data from isochronous stress- strain curves into the following relation: where Ocr is the critical or buckling stress, k is a constant assumed to be 0.6, Es and Et are secant and tangent moduli, respectively, and t/r is the cylinder thickness-radius ratio. ! T h e predicted buckling stresses were then converted to bending moments by using elementary beam theory. ! € ! h e isochronous stress-strain curves required for this study were obtained from compressive creep tests of 5052-0 aluminum-alloy sheet at 500° F. The experimental results shown in figure 3 are the only data available on the lifetime of cylinders subjected to bending.

Although the predictions are i n good agreement w i t h the experimental data, addi- t i o n a l studies w i l l be needed t o determine whether equation (2) w i l l predict lifetime s a t i s f a c t o r i l y f o r cylinders of other materials and t o establish the appropriate value of k.

CREXP DEFLECTIONS The results of the studies of creep of plates and cylinders and of other s t r u c t u r a l components investigated previously indicate that life- time defined by collapse can be estimated i n general by substituting material data obtained from isochronous compressive stress-strain curves i n t o appropriate relations that define maximum strength of the struc- tural elements. For some types of structures, it is realized that large creep deformations can be obtained i n a fraction of the actual collapse t i m e . Such deformations i n many cases may determine the useful l i f e of the structure.

A study w a s made accordingly t o determine the range of values for creep s t r a i n t h a t would be expected t o govern design of structures where deformation rather than collapse would be of primary interest.

The structure considered f o r this study w a s a constant-stress wing i n which the stresses are assumed t o be of the same magnitude at a l l The deflections of a constant-stress wing are stations along the wing.

determined from the product of wing configuration and the s t r a i n s pro- duced by the applied stresses. The deflections that would be produced a complete range of stress f o r stainless-steel wings are by creep over shown i n figure 4.

In this figure, stress is plotted against the r a t i o of wing deflection produced by creep t o wing deflection produced by load f o r 17-7 PH stainless steel a t 800° F.

Load deflection i s defined as the s t a t i c deflection of the wing obtained immediately upon application of any stress. A t a stress of 50 ksi, f o r example, the creep deflection of the wing i n 1 hour is equal t o 0.1 of the s t a t i c or load deflection obtained immediately upon application of the stress. I l f this stress is applied f o r approximately 300 hours, the creep deflection increases t o a value equal t o the s t a t i c deflection. A shaded area is indicated f o r the range of creep t o load deflection r a t i o s from 0 . 1 t o 1.0. This area i s assumed t o define the region of i n t e r e s t f o r structures such as air- c r a f t wings. Creep deflections t o the l e f t of the shaded area would be practically negligible; whereas, t o the right, the creep deflections would undoubtedly be considered excessive f o r most s t r u c t u r a l applications.

Creep s t r a i n s that are associated w i t h the range of deflection r a t i o s shown i n figure 4 are indicated i n figure 5.

The solid curves have been reproduced from figure 4.

The dashed curves indicate creep s t r a i n s pro- duced i n the specified t i m e s f o r the range of stresses shown. Ncte that creep s t r a i n s of approximately 0.0002 t o 0.002 are associated w i t h r a t i o s ir 4F '5 These results of creep t o load deflections ranging from 0 . 1 t o 1.0.

apply t o bending deflections of any constant-stress wing regardless of structural configuration because the r a t i o of creep deflection t o load deflection i s determined from the r a t i o of creep s t r a i n t o load s t r a i n .

This method of analysis which is used t o determine the range of creep s t r a i n s that are of i n t e r e s t f o r structures subjected t o bending was applied t o t w o other materials: 2024-T3 aluminum alloy a t 400° F and Inconel X a t 1,350° F. The results f o r the 2024-T3 aluminum alloy are shown i n figure 6, and the results f o r Inconel X are sham i n f i g - ure 7. For 'both materials approximately the same range of values of creep s t r a i n from 0.0002 t o 0.002 was obtained f o r r a t i o s of creep t o load deflections from 0 . 1 t o 1.0.

'IIEMPERATURE RANGES FOR CREEP Consideration w i l l now be given t o the determination of temperature ranges i n which creep w i l l be expected t o influence s t r u c t u r a l design f o r various materials. These temperature ranges are determined by com- paring structural weight required f o r strength w i t h the weight required f o r creep at different temperatures. The r e s u l t s obtained from this analysis f o r stainless s t e e l are presented i n figure 8. The required weight of a tensile member i n arbitrary units i s plotted against tempera-

ture f o r 17-7 PH stainless s t e e l . The s o l i d l i n e indicates the w e i g h t

required f o r strength based on ultimate load after 1,000 hours exposure t o temperature. Ultimate load is assumed t o be 3.75 times the 1 g load.

The dashed curves indicate weight required f o r the three different creep c r i t e r i a f o r 1,000 hours a t 1 g load; namely, creep s t r a i n s of 0.0002 and 0.002 and creep rupture.

The dotted curve f o r 0.0002 creep s t r a i n i n figure 8 indicates that the tensile member can be designed on the basis of strength up t o 6500 F.

Above 6500 F, the weight of the tensile member would increase very rapidly i n order not t o exceed 0.0002 creep s t r a i n . The c r i t e r i o n of 0.002 creep s t r a i n would govern the design above 8250 F. Above 825O F, significant deflections would be expected t o occur i n structures sub- jected t o bending as discussed previously. The region between the curve f o r 0.002 creep s t r a i n and the curve f o r rupture defines the temperature range where creep would be a very i m p o r t a t factor i n s t r u c t u r a l design f o r t h i s material. The region between the two creep-strain l i n e s may be considered t o be the temperature range i n which creep s t r a i n s become perceptible and gradually increase t o a magnitude t h a t produces signif- icant s t r u c t u r a l deformations. It i s of i n t e r e s t t o note t h a t design on the basis of a given creep s t r a i n requires a very large increase i n weight f o r small increases i n temperature. It appears that it w i l l be more feasible t o convert t o a higher strength material than t o add weight 6 : C” in order not to exceed a given value of creep strain. I f other creep and strength criteria are considered, the position of the creep lines is shifted relative to the strength curve; however, the temperature ranges defined by the distance between the various creep lines remain essentially constant.

This method of analysis of weight required for strength and creep to determine temperature ranges in which creep will be a design consid- eration was applied to two other materials which are shown in figure 9 .

The materials considered are 2024-T3 aluminum alloy, 17-7 PH stainless

steel and Inconel X. The solid lines indicate the weight required for strength based on ultimate load. The shaded regions define the tempera- ture range for each material where creep may be an important factor in structural design. The width of the shaded regions for each material was established by determining required weight for creep on the basis of several different creep criteria. These results indicate that creep problems will be restricted to a rather narrow range of temperatures for each material and that creep does not become a design consideration until temperatures are reached where the strength of the material deteriorates rapidly. Note that the weight required for creep increases very rapidly with small increases in temperature for all materials considered. It appears that, whenever a temperature is reached where creep is a design consideration, less structural weight will be required by converting to a higher strength material than by designing for creep with the original material. It is realized that conversion to a higher strength material introduces many new problems such as changes in production methods and consideration of availability and strategic importance of the higher strength material. Because of such factors, it is anticipated that the weight of some structural components will be increased to account for material creep rather than converting to a higher strength material.

CONCLUDING REMARKS The results presented indicate that material creep w i l l influence structural design over a rather narrow range of temperatures for each striictural material. In this temperature range, lifetime or collapse time can be estimated satisfactorily for structural elements by using isochronous stress-strain curves in conjunction with established methods for predicting maximum strength.

I f useful life is detedned by deflec- tions rather than collapse, the simplified analysis of creep deflection of constant-stress wings indicates that creep strains ranging from approximately 0.0002 to 0.002 define the region of interest for struc- . L tures subjected to bending.

p c:,

4L J

REFERl3NCES 1. Libove, Charles: Creep-Buckling Analysis of Rectangular-Section Columns. NACA TN 2956, 1953.

2. Mathauser, Eldon E., and Brooks, William A., Jr.: An Investigation of the Creep Lifetime of 75s-T6 Aluminum-Alloy Columns. NACA TN 3204, 1 9 % .

3. Mathauser, Eldon E., and Deveikis, William D.: Investigation of the Compressive Strength and Creep Lifetime of 2024-Tf, Aluminum-Alloy Plates at Elevated Temperatures. NACA TN 3552, 1956. (Supersedes NACA RM L55Ellb. ) 4. Sanders, J. well, Jr., McComb, Harvey G., Jr., and Schlechte, Floyd R.: A Variational Theorem f o r Creep with Applications to Plates and Columns. NACA TN 4003, 1957. (Prospective NACA paper.)

5. Hoff, N. J., Erickson, Burton, et al.: Creep Bending and Buckling of Thin Circular Cylindrical Shells. PIBAL Rep. No. 355 (Contract Nos. Naw-6392 and PJaw-6447), Polytechnic Inst. Brooklyn, July 1956.

f COMPRESSIVE STRESS-STRAIN CURVES 17-7 PH ST41NLESS STEEL; 800" F /v---- TIME, HR I4O[ I20 / I I O 1,000 STRESS, KSI

---

MATERIAL

- ISOCHRONOUS

0 .002 .004 .006 .008 .010 STRAIN Figure 1 CREEP LIFETIME OF PLATES 17-7 PH STAINLESS STEEL; 800" F - -0 STRESS, KSI - 3 0 4 A.,

6ot . 40

I I I I I I l l 1 I I l l . O L .&I I " ; 5 I O 50 LIFETIME, HR LIFETIME OF UNSTIFFENED CYLINDERS 5052-0 ALUMINUM ALLOY; 500" F

120- c c r = k G { - PREDICTED

000.0 EXPERIMENT r 100 - - BENDING MOMENT, IN-KIPS O L .I .5 I 5 IO LIFETIME, HR RATIO OF CREEP TO LOAD DEFLECTIONS FOR WINGS 17-7 PH STAINLESS STEEL;800" F TIME, HR

.^^ '251

'""I

75.

STRESS, KS I 50.

CREEP DEFLECTION LOAD DEFLECTION Figure 4 CREEP STRAIN IN WINGS 17-7 PH STAINLESS STEEL; 800" F TIME, HR I25 I oc 7 5 STRESS, KS I 5c 2 5 I I I I I 1 1 1 1 I I l l .05 .I .5 I 5 CREEP DEFLECTION LOAD DEFLECTION Figure 5 CREEP STRAIN I N WINGS 2024-T3 ALUMINUM ALLOY; 400" F TIME, HR CREEP STRAlN=O.OI .

Figure 6 CREEP STRAIN IN WINGS INCONEL X;l,35Oo F

70 -

CREEP STRAIN = 0.01 STRESS, KS I -

\ '. 1 , 0 0 0

-

2 0 I I I I 1 1 1 1 I I l l OL .d5' ' I '!I .5 I 5 CREEP DEFLECTION LOAD DEFLECTION Figure 7 WEIGHT FOR CONSTANT TENSILE LOAD 17-7 PH STAINLESS STEEL TENSILE STRENGTH, ULTIMATE LOAD, 1,000 HR EXPOSURE 1 I I I I 1 0 200 400 600 800 1,000 TEMP, O F

Figure 8 ' -405

TEMPERATURE RANGES FOR CREEP 2 . 0 0 1 1.75, 1.50.

WEIGHT R EQUl RED 1.25.

1.00, , "., '-- -.- 'I' CREEP .75- I I I I 0 500 1.000 1,500 TEMP., O F Figure 9 A RELATION BETWEEN STRESS, STRAIN RATE, TIME, AND TEMPEF3lTURE FOR METALS AT ELEVATED T E M P E B A ! l Y J F U 3 S By Elbridge Z. Stowell and George J. Heimerl Langley Aeronautical Laboratory A relation between stress, s t r a i n rate, time, and temperature is suggested t o account f o r the behavior of polycrystalline metals at ele- vated temperatures.

The metal i s assumed t o have the basic properties of e l a s t i c i t y , thermal expansion, and viscosity. An appropriate com- bination of these three properties has been shown t o account f a i r l y well f o r the steady creep rate, time t o creep rupture, stress-strain curves, and rapid-heating curves f o r 7073-6 aluminum alloy. Similar calcula- tions made f o r low-carbon steels show good correlation between ultimate t e n s i l e strength, time f o r creep rupture, and the steady creep rates.

In the case of a complex alloy l i k e Inconel X, fair correlation i s also obtained provided one of the constants i n the relation is permitted a slow variation with temperature.

INTRODUCTION The need f o r knowledge of the behavior of metals a t elevated tem- peratures i s constantly becoming more and more important as f l i g h t speeds increase and as the effects of aerodynamic heating become more pronounced.

Information is needed concerning -

(1) The creep of metals at these elevated temperatures (2) The time at which rupture can be expected i f the creep i s allowed t o continue ( 3 ) The stress-strain characteristics at some particular temperature and s t r a i n r a t e (4) The behaxior of the metal when heated rapidly up t o some high temperature Evidently the job of providing t h i s information would c a l l f o r a great deal of testing, and it would be a useful achievement i f some method of calculation could be found which would simplify the task. Such a method follows from the relation between stress, s t r a i n rate, and temperature proposed i n t h i s paper.

SYMBOLS s t r a i n s t r a i n rate, per hr t time, hr stress, k s i U

E Young ’ s modulus, ks i

l i n e a r expansion coefficient, per 4c

U T temperature, ?K unless otherwise indicated S constant, per hr per OK activation energy f o r creep, c a l per mole AH R gas constant, taken as 2 c a l per mole per ?K constant, k s i I- t i m e t o rupture, hr constants kl’k2 STATEMENT O F THE RELATION

The s t r a i n rate $$ at the absolute temperature T and the stress

U b u may be stated as follows: dT -AH/RT a

+ a - + 2sTe

s inh

,=dt(E) d t

The first term t o t h e r i g h t of the equal sign gives the contribution t o the s t r a i n r a t e due t o a change i n stress a; .E i s Young’s modulus, _.

which is considered t o be known as a function of temperature. The mid- dle term gives the contribution due t o a possible thermal expansion o r contraction; a, the linear expansion coefficient, i s assumed known as a function of the temperature. The last term on the right gives the contribution due t o viscous flow. The exponential term, which describes the usual effects of temperature on viscous materials, contains AE, t h e constant activation energy f o r creep of the material, and R, the gas constant. The remaining constants i n the viscous term are s and bo.

The relation (eq. (1)) holds only f o r temperatures high enough f o r t h i s viscous term t o have an appreciable value, that is, f o r temperatures higher than about one-half the melting point.

Equation (1) m y be integrated i n various ways t o provide informa- t i o n on such properties as steady creep, rupture t i m e , stress-strain relations, and the effects of rapid heating. For example, a t constant

stress and temperature, - da = - dT = 0, and t h e relation (eq. (1)) becomes

a t at

simply the equation f o r steady creep. If the creep i s allowed t o con- tinue without interruption, the material w i l l rupture i n a time T given d€

by the relation T - = Constant. The stress-strain curve a t any con-

a t

stant temperature T i s obtained by setting the s t r a i n r a t e equal t o the known constant t e s t i n g r a t e and then solving t h e resulting equation as a function of the time. And finally, i f the for a (with material i s held under a constant stress and heated rapidly, the resulting s t r a i n is found by integrating the expression with

( a t

with respect t o time.

The d e t a i l s of such applications t o one material, 7075-T6 aluminum alloy, are given i n reference 1.

APPLICATIONS Creep and Rupture Parameters I n recent years, various empirical and semiempirical temperature parameters have been proposed f o r the creep of metals. Two of these parameters may be derived from the relation given by equation (1) when stress a is large enough t o permit replacement of the hyperbolic the sine by the exponential. Under t h i s condition, a = sol$ + log, i + log,

) kg

where k l i s a constant. Thus, i f the s t r e s s i s plotted against the

parameter @ + log, 6 , a single straight l i n e with a slope equal t o bo

RT should be obtained.

is made of t h e relation between creep r a t e k use If, i n addition, and rupture time T 6~ = Constant (ref. 2), then equation (2) may also be as found by Monkman and Grant written as (3) e where k2 i s another constant. Thus, if the s t r e s s i s plotted against AH

the parameter - - log T, a single straight l i n e with a slope equal

RT e t o o0 should be obtained.

I n figure 1, which presents a correlation of creep and rupture data

f o r 7075-T6 clad aluminum alloy, the parameters + log 6 and

RT e

- - AH loge T a r e plotted on the same abscissa scale against s t r e s s as

RT ordinate. The data points, taken from reference 3 , f a l l along two straight l i n e s having the same slope. Since the temperature of 2 1 2 ' F is known t o be too low for equation (1) t o hold, the data points taken a t that temperature do not f a l l on the l i n e s but were included f o r comparison.

Steady Creep Rate Figure 2 shows the steady creep r a t e per hour as a function of stress f o r two clad aluminum alloys: 7075-6 on the l e f t and 2024-T3 on the right. The solid-line curves represent actual data from refer- ence 3 and it is seen t h a t f o r the 7075-T6 alloy the solid-line curves are nearly p a r a l l e l straight lines. The steady-creep l a w given by equa- t i o n (2) requires that such curves be p a r a l l e l straight lines; the dashed-line curves were computed from equation (2) with the use of the The data f o r the 2024-T3 alloy do not form par- constants i n table I.

a l l e l straight lines and f o r t h i s material the relation does not apply.

Stress-Strain Curves Figure 3 shows the stress-strain curves f o r the 7075-6 aluminum alloy at three temperatures and f o r a s t r a i n r a t e of 0.002 per minute.

The dashed- The solid-line curves represent data taken from reference 4.

l i n e curves were computed by using the constants i n table I. The agree- ment i s good at the two higher temperatures and i s .poor a t the lowest temperature, which is below the temperatures a t which the theory can be expected t o hold.

Rapid-Heating Curves Figure 4 shows the s t r a i n s obtained when specimens of 7075-6 alu- minum alloy, held under three constant stresses as indicated, are heated The s l a n t portions of t h e rapidly at widely different temperature rates.

curves give mainly the effect of thermal expansion. The sharp upward The solid- turn at the right of each curve gives the effect of viscosity.

l i n e curves a r e data taken from reference 4, and t h e dashed-line curves are computed by using the constants i n table I. Agreement i s good a t the higher temperatures.

The constants l i s t e d i n table I f o r the different applications t o 7 0 7 5 - 6 aluminum alloy are not quite the same. For a discussion of these small differences, see reference 1.

Low-Carbon Steels I n order t o show how the relation works f o r materials other than aluminum alloys, an attempt w a s made t o check the available data on low- carbon s t e e l s (ref. 5 ) . The s o l i d l i n e s of figure 5 show the variation with temperature of the ultimate t e n s i l e strength, the stress t o give creep rupture i n 100 hours, and the stress t o give a creep rate of LOW6 per hour. The dashed-line curves give the corresponding quantities com- puted by using the constants i n table I.

The agreement i s good, espe- c i a l l y above about 8oOo F.

Inconel X The solid-line curves of figure 6 represent t h e same quantities as i n figure 5 but are f o r the alloy Inconel X; the data are taken from The corresponding dashed-line curves were computed by using reference 6.

the constants i n t a b l e I; note that for t h i s complex alloy the values of a0 vary slowly with the temperature. It is believed that t h i s var- iation r e f l e c t s the microstructural changes which occur i n Inconel X at elevated temperatures. The agreement with the data i s fair and seems t o indicate that the proposed relation w i l l be satisfactory even f o r a complex alloy, provided allowance is made f o r some i n s t a b i l i t y with temperature.

CONCLUDING REMARKS A relation between stress, strain rate, time, and temperature has The relation has been suggested f o r metals at elevated temperatures.

been applied successfully t o steady creep, creep rupture, stress-strain relations, rapid heating, and t e n s i l e strength f o r a f e w materials. The relation makes use of the e l a s t i c i t y , thermal expansion, and viscosity of the metal, and i s an equation of s t a t e i n r a t e form. The relation is inapplicable t o metals which a r e markedly unstable or which undergo aging o r changes i n structure. The metal must be such that its steady creep is describable by the relation i n order that the constants may be deter- mined. With such a metal, however, the relation may be useful i n the prediction of other properties from steady-creep data.

RFFERENCES 1. Stowell, Elbridge Z.: A Phenomenological Relation f o r Metals at Elevated Temperatures. NACA TN 4000, 1957. (Prospective NACA paper.)

2. Monkman, Forest C., and Grant, Nicholas J.: An Empirical Relationship Between Rupture L i f e and Minimum Creep Rate i n Creep-Rupture Tests.

(Presented at Fifty-Ninth Annual Meeting of Paper NO. 72, A.S.T.M.

A.S.T.M., June 17-22, 1956.)

3. Anon.: Strength of Metal Aircraft Elements. ANC-5 B u l l . , Rev. ed., Depts. of A i r Force, Navy, and Commerce, Mar. 1955.

4. Heimerl, George J., and Inge, John E.: Tensile Properties of 7075-T6 and 2024-T3 Aluminum-Alloy Sheet Heated at Uniform Temperature Rates Under Constant Load. NACA TN 3462, 1955.

5. Simmons, Ward F., and Cross, Howard C.: Elevated-Temperature Properties of Carbon Steels. Special Tech. Pub. No. 180, A.S.T.M., 1955.

6. Anon. : Inconel "X" - A High Strength, High Temperature Alloy, Data

and Information. The International Nickel Co., Inc., Dev. and Res.

Div., Jan. 1949.

c as, 6, Metal Application ‘7 cal/mole ‘ 0 , ai at ‘ 9 9 per per OK 7075-T6 clad aluminum alloy 35,800 4.3 All 1.62 X lo6 Steady creep 0.0077 7075-T6 aluminum alloy Stress-strainrelations 34,700 4 . 3 All 1.50 7075-T6 aluminum alloy 34,700 4.3 All Rapid heating 3.60 Low-carbon steels All 7 2 , 0 0 0 2.0 All 9-15 X lo8 0.025 Inconel X A l l 4.9 1,ooO 3,000 X lo8 0.0095 4.9 1,200 4 . 6 1,350 4.1 1,425 3.85 1,450 3.50 1,475 3.a 1,500 2.70 1,550 -

I 2.4 1 , 6 0 0

CORRELATION OF C R E E P AND R U P T U R E DATA e .

FOR 7075-T6 CLAD ALUMINUM ALLOY 0 0 60-

50 -

-RUPTURE

40 -

STRESS, KS' 30- A 375OF

20 -

0 300°F

- 0 212OF

I O I I I I I 25 30 35 40 45 50 0

4 + log, k OR - ffy - loge r

RT Figure 1 STEADY CREEP O F 7075-T6 AND 2024-T3 C L A D ALUMINUM ALLOYS 7 0 7 5 - T 6 /

-

5 0

-

-

STRESS, K S I

-

EXPERIMENT

----

C A L C U LATE D

- -

1 0 STRESS - S T R A I N C U R V E S FOR 7075 - T 6 ALUMINUM ALLOY EXPERIMENT

----

C ALC U LAT ED ,/-- ,0' 2OOOF STRESS, KSI

--- 4 O O O F

0 .002 .004 .006 .008 .OlO S T R A I N RAPID - H E A T I N G CURVES FOR 7 0 7 5 - T 6 ALUMINUM ALLOY AT T H R E E STRESSES TEMP. RATE ,OF/SEC

.020 -

2 96 S T R A I N I I I I 0 200 400 600 800 TEMPERATURE, OF Figure 4 STRENGTH OF LOW-CARBON STEELS

- E X P E R I M E N T A L

C A L C U L A T E D

40 -

STRES KS I

30 -

CREEP RATE I 0 500 1,000 1,500 2,000 TEMPERATURE, OF Figure 5 STRENGTH O F I N C O N E L X F I40 I 2 0 RUPTURE - STRESS,

-

K S ' 60

-

I I 0 1,000 1,200 1,400 1,600 1,800 T E M P E R A T U R E , OF Figure 6 REACTIONS OF MATERIALS I N HIGH-TEMPERATURE AIR FLOWS By Joseph G. Thibodaux, Jr., and Joseph N. Kotanchik Langley Aeronautical Laboratory SUMMARY Ceramic-heated air jets and high-intensity arc-powered jets which are capable of duplicating some of the environmental conditions of hyper- sonic flight up to reentry velocities have been developed and are being operated. Initial tests of structural materials in these facilities at stagnation temperatures of 4,000° F and above indicate that these mate- rials will be ignited, melted, or be severely oxidized. Surface heat inputs due to oxidation can be great enough to cause melting in high- velocity airstreams with stagnation temperatures several hundred degrees below the melting point of the materials. Laboratory experiments indicate that recombination of dissociated atoms on catalytic material surfaces can cause severe heating and greatly increased oxidation rates.

INTRODUCTION In order to meet the current demand for high-temperature data, the National Advisory Cormnittee for Aeronautics is now operating, or is putting into operation, many new high-temperature facilities. In these facilities, attempts are being made to duplicate environmental conditions which might be encountered by hypersonic airplanes and missiles in flying through and in reentering the earth's atmosphere. Current research pro- grams are aimed, first, at furnishing sufficient data to insure the suc- cessful design and operation of hypersonic aircraft and, second, at furthering the understanding of high-temperature phenomena. Of particular interest at this time are reactions between structural materials and high- temperature environments. This paper w i l l briefly describe two types of high-temperature air-jet facilities and discuss results of some materials tests conducted in them.

CERAMTC-HEATED AIR JET Experience with rocket and combustion jets has sham that results were influenced $y jet composition, that is, concentration of oxygen and steam, both of which oxidize most of the conventional aircraft structural materials. In order t o avoid t h i s limitation, ceramic-heated air jets have been designed and put i n t o operation. The general arrangement of t h i s type of f a c i l i t y i s sham i n figure 1. It consists of a cylindrical s t e e l pressure vessel which i s lined w i t h various types of refractories and interlocking ceramic refractory bricks. The central hole is f i l l e d with 3/8-inch-diameter lime-stabilized zirconia pebbles. A burner a t the top supplies hot combustion gases which are drawn downward through the bed. When the required bed temperature and temperature distribution are reached, compressed air i s blown back through the bed and expanded by a water-cooled nozzle.

Operating characteristics of two completed f a c i l i t i e s are as follows : Operating conditions Laboratory m o d e l P i l o t model

0.75 t o 1.00 Jet-exit diameter, in. . . . . . . 4.0

To 100 Stagnation pressure, lb/sq in. . . To 1,600

To 4,000 Stagnation temperature, ? F . . . . To 4,000

Jet velocity, ft/sec . . . . . . .

3,500 t o 5,200 4,300 t o 6,100 Mass flow, lb/sec . . . . . . . . .

0.2 t o 0.5 6 t o 10 G a s composition . . . . . . . . . .

The maximum operating temperature i s now limited t o 4,000° F because the pebble bed begins t o soften and lose strength a t slightly higher tempera- tures. Tests are now i n progress which indicate t h a t the maximum temper- ature may soon be increased t o 5,000° F by the use of thoria bricks and pebbles.

Up t o the present time, materials tests were conducted t o determine if the material reacted w i t h the high temperature, high-velocity airstream, and, i f so, t o w h a t extent the reaction contributed t o the melting or the destruction of the material. These tests consisted of putting m o d e l s of various materials i n t o the j e t and observing t h e i r behavior by means of high-speed color motion pictures. mese pictures were carefully studied t o determine if oxidation or ignition occurred and t o determine the nature and severity of the reaction.

J e t stagnation temperature i s usually higher than the melting point of the materials, and, i n this event, melting would occur even i n the absence of any reaction.

Solid models of various shapes, having a maximum diameter of 1/2 inch, were used i n a l l tests.

Typical shapes were cones with different angles and nose radii, hemisphere cylinders, and flat-face cylinders. I n i t i a l .. n heating rates were greatly influenced by shape as w e l l as by airstream properties. 'Ilests of i d e n t i c a l models of various materials were used Tests of i d e n t i c a l - t o compare the r e l a t i v e behavior of the materials.

materials of various shapes were used t o compare the e f f e c t of shape and heating rate.

Results of tests of typical s t r u c t u r a l materials i n the ceramic- heated air j e t w i l l now be discussed.' Operating conditions f o r the t e s t s are as follows:

Stagnation temperature, OF . . . . . . . . . . . . . . . . . . 4,000

. . . . . . . . . . . . . . Stagnation pressure, lb/sq in. abs

J e t velocity, ft/sec . . . . . . . . . . . . . . . . . . . . . 5,200

Jet Mach nmber . . . . . . . . . . . . . . . . . . . . . . . 2

in. . . . . . . . . . . . . . . . . . . . . 0.8

Jet-exit diameter, Magnesium The magnesium model w a s a s o l i d 20° cone with a 1/32-inch nose radius.

The material being tested formed only the f i r s t 3/8 inch of the cone.

B e remainder of the cone w a s a s t e e l model support which w a s separated from the t e s t specimen by a bakelite insulator. I n the motion pictures, this insulator w i l l be observed t o i g n i t e and burn before the model m e l t s or ignites. This burning of the insulator plays no p a r t i n the behavior of the model and should be disregarded.

This cone-shape model had a maximum i n i t i a l heating r a t e of 2,000 Btu per square foot per second.

The magnesium began melting 0.2 second after entering t h e j e t with no noticeable oxidation or ignition. Melting continued and the m e t a l flowed back f r e e l y and froze on cooler portions of the model support.

Intermittent ignition and combustion appeared i n 0.6 second.

The model w a s completely melted i n 0.9 second. Downstream i n the wake, out of the camera f i e l d , magnesium w a s vaporized and burned vigorously.

Aluminum The aluminum m o d e l was of the sa.he design as the magnesium m o d e l .

The aluminum began melting 0.4 second after entering the jet. Melting w a s not accompanied by noticeable oxidation or ignition. Aluminum flowed freely and froze on the cooler portions of the model support. The model w a s completely melted i n 1.5 seconds. Downstream i n the wake, out of the view of the camera, aluminum ignited and burned i n locations where the model support acted as a flame holder.

' A notion-picture f i l m supplement (L217) has been prepwed and i s available on loan from NACA Headquarters, Washington, D. C.

S t e e l The s t e e l model w a s the same design as the magnesium model. S t e e l began oxidizing immediately after entering t h e j e t as evidenced by dis- coloration a t the t i p . Melting and The m o d e l heated t o incandescence.

simultaneous ignition were noted 0.7 second a f t e r entering the j e t . The reaction rate increased rapidly and completely engulfed the model and model-support surface i n flame. The model w a s completely destroyed i n 3.5 seconds.

Stainless S t e e l The stainless-steel modelwas the same design as the magnesium model.

Stainless steel began heating up w i t h the formation of oxides as evidenced by t i p discoloration. The oxide began t o build up and formed a hard, crusty, adherent deposit a t the t i p . This sxide afforded some protection from further oxidation until subsurface melting began 1.1 seconds after the model entered the j e t . The oxide w a s blown away, new surface w a s exposed, and t h e oxidation process w a s then repeated. Soon, as the model heated up, the reaction became vigorous enough t o cause continuous melting.

Copper The copper m o d e l was the same design as the magnesium model. Copper began t o form a black cupric oxide 0.5 second after entering the jet.

This oxide continued t o form at a relatively slow rate. It w a s very adherent and appeared t o protect the copper from rapid oxidation. I n 2.9 seconds, the cupric oxide began t o decompose t o the red cuprous oxide a t the t i p , and i n 3.0 seconds melting began. The model w a s completely destroyed i n 5 seconds.

Titanium m o d e l w a s a 1/2-inch-diameter hemisphere cylinder.

The titanium I n i t i a l heating r a t e w a s approximately 500 Btu per square foot per second.

The cylindrical model required a much longer time' t o heat than the cone- shape models because of the lower heating rate and t h e larger surface-to- mass r a t i o . The m o d e l began oxidizing 2 seconds after entering the jet.

This oxide formed u n t i l a stable coating protected the model from further oxidation. In approximately 13 seconds, at a temperature approaching the melting point, titanium suddenly burst i n t o a violent reaction which completely destroyed the m o d e l i n approximately 1 second.

Molybdenum The molybdenum model w a s the same design as the magnesium m o d e l except that the rear conical support w a s graphite and no bakelite sepa- r a t o r w a s used. The melting point of molybdenum w a s approximately 600° F above the j e t stagnation temperature. The model entered the j e t and, i n 0.2 second, a black oxide, probably the sesquioxide, w a s formed. In 1.3 seconds, a gray oxide, probably a mixture of the sesquioxide and trioxide, formed. I n 2.5 seconds, a yellow oxide, molybdenum trioxide, formed. All these oxides were v o l a t i l e and condensed out on portions of the model and support which were cooler than the sublimation temperature of the oxide. A s the temperature increased, they a l l vaporized. In 3 . 1 seconds, a vigorous reaction began a t the t i p . I n 3.2 seconds, igni- t i o n occurred and melting began. Vigorous oxidation and burning a t the surface furnished s u f f i c i e n t additional heat input t o cause and sustain melting.

Tungs t e n The tungsten model w a s the same design as the molybdenum m o d e l . The melting point of tungsten w a s approximately 2,000' F above the stream stagnation temperature. Tungsten began t o oxidize 0.5 second a f t e r entering the j e t with the formation of a black oxide, probably t h e dioxide. I n 2.5 seconds, a yellow oxide, probably the trioxide, w a s seen forming and condensing out on the cooler portions of the model sup- port. This oxidation, although not vigorous, w a s steady. The tungsten oxidized with reasonable loss of mass of the m o d e l ; however, oxidation w a s not sufficient t o cause melting or ignition. 'Phe trioxide vaporized or reacted with the graphite model holder as the temperature increased.

!The graphite m o d e l holder w a s oxidized t o a much greater extent than it would have been if it were tested alone; this f a c t indicates t h a t tungsten or one of i t s oxides catalyzed the oxidation of graphite.

Graphite Coated With Flame-Sprayed Zirconia !The zirconia-coated graphite m o d e l w a s a 30° cone with a diameter of 3/4 inch and a nose radius of 1/8 inch.

The model survived 10 seconds of test with no damage.

The t e s t was terminated by f a i l u r e of the support system of the m o d e l .

HIGH-INTENSITY ARC-POWERED JETS Ceramic-heated jets can produce temperatures which m e l t or severely oxidize most conventional s t r u c t u r a l materials.

These temperatures are

4 Z I

considerably less than environmental temperatures which are associated with reentry. It is theoretically impossible to obtain reentry tempera- tures by chemical means, either directly or indirectly. For production of these high temperatures, the Langley Laboratory has been developing jets in which the energy is supplied by a high-intensity electric arc.

Initial operation of these arc-powered jets was conducted with water and liquid oxygen as the jet medium. More recently, they have been successfully operated with liquid and gaseous air as the jet medium.

Operation with air is now being emphasized inasmuch as this medium more nearly reproduces the atmospheric environment at reentry velocities.

An arc-powered jet is shown schematically in figure 2. I t consists of a pressure chamber that houses the arc and the jet medium which is to be heated.

The anode enters the chamber through a hole in the bottom.

The top forms the cathode and a hole in the top forms the nozzle. A high-intensity arc is struck and maintained between the anode and the cathode. Air enters the bottom of the chamber and flaws into the arc chamber through an annular opening around the anode. It is then heated and expanded to high velocity through the nozzle. Power is supplied as indicated. This diagram shows a direct-current arc. 'Ilhree-phase alternating-current arcs have also been operated successfully.

Characteristics of typical arc-powered jets which have been operated at this laboratory are as follows:

Jet-exit diameter, in. . . . . . . . . . . . . . . . . . 0.25 to 1 . 0 0

Power, kw . . . . . . . . . . . . . . . . . . . . . . 60to1,000

Stagnation temperature, + >15,000 . . . . . . . . . . . . . . .

Stagnation pressure, lb/sq in. . . . . . . . . . . . . .

3 to 30

Jet composition . . . . . . . . . . . . . . . . . . Air (dissociated)

Heating rate (hemisphere nose), Btu/ft2-sec . . . . . . 2,200

Temperatures and pressures indicated represent what has been achieved up to the present time and do not represent the maximum capabilities of this type of facility .

Materials tests similar to those conducted in the ceramic-heated air jets have also been run in the high-intensity arc-powered jets. For the purpose of comparing the relative severity of test conditions and behavior of materials in these two jets, results of tests of titanium, molybdenum, and graphite models will be presented. Jet conditions for these tests are as follows: 7 F

Stagnation temperature, OF . . . . . . . . . . . . . . . . . >13,000

Stagnation pressure, lb/sq in. . . . . . . . . . . . . . . . - 10

J e t velocity . . . . . . . . . . . . . . . . . . . . . . . . Subsonic

J e t medium . . . . . . . . . . . . . . . . . . . . . . . . . Air

Jetdia.meter,in. . . . . . . . . . . . . . . . . . . . . . 0,375

Initial heating rate, Btu/ftZ-sec . . . . . . . . . . . 1,000 t o 2,200

T i t a n i u m The titanium model i s a l/;l-inch-diameter flat-face cylinder. A hemisphere-cylinder model with one-half the i n i t i a l heating r a t e with- stood 13 seconds i n the ceramic-heated a i r j e t before ignition occurred.

The model i n the arc-powered a i r j e t ignited i n approximately 0.1 second.

The reaction was violent. Heating rates were extremely high. Examina- t i o n of the model afterward showed l i t t l e penetration of heat i n t o the model and indicates t h a t most of the material was l o s t i n a manner resembling ablation.

Molybdenum The molybdenum model was the same shape as the titanium model.

The molybdenum model having similar i n i t i a l heating r a t e s required 3.1 seconds t o melt i n the ceramic-heated air j e t .

The model i n the arc-powered air j e t began t o react violently i n 2 seconds. Examination of the model a f t e r the t e s t also indicated that material w a s l o s t i n a manner resembling ablation.

Graphite The graphite model w a s a 1/2-inch-diameter hemisphere cylinder.

Graphite w a s relatively undamaged by a 20-second exposure i n the ceramic- heated air j e t . I n the present case, the graphite model suffered l i t t l e damage due t o a 5-second exposure t o the arc-powered a i r j e t . Some material was l o s t because of oxidation or sublimation, although the model was rapidly heated t o incandescence.

The t e s t s i n both j e t s were contrived t o produce rapid model heating so t h a t materials reactions, if present, would begin soon a f t e r the models were introduced i n t o the j e t s . Oxidation and ignition are complex phenomena which depend on many factors and conditions. Some of these are the temperature of both reactants, the thermal properties of react- ants and products, the thermal and xass transport properties of react- ants and products, the kinetics of reaction, the physical properties of reactants and products, and the surface-to-mass r a t i o of the model.

Changes i n the size and shape of models may well a f f e c t some of these properties and conditions. Until a suitable explanation for the inter- relation of these properties and conditions is found, results of these tests should be regarded as qualitative, and should not be applied directly to models of other sizes and shapes.

Both types of jets are being operated as free jets exhausting into the atmosphere.

This type of operation allows reasonable duplication of stagnation condi%ions, and to some extent, velocity. It does not allow duplication of static conditions. Exact duplication of both static and stagnation conditions will require the use of vacuum chambers, diffusers, or auxiliary ejectors.

Both jets may be operated with inert gases, pure gases, and gas mixtures. Use of inert gases would allow determination of heat transfer in the absence of oxidation. Pure and mixed gases may be used to study reactions in controlled environments, and to study the aerothermochemical phenomena.

One such phenomenon, that of enhanced oxidation by oxygen atoms at elevated temperatures, has been studied and reported by Fryburg in refer- ence 1 . Platinum was chosen for this investigation because of its known catalytic activity in promoting recombination of oxygen atoms. Platinum strips were heated and their temperatures were maintained at temperatures of l,OOOo C and above solely by recombination of oxygen atoms at the surface. The rates of oxidation of platinum were measured and found to be directly proportional to the number of atoms striking the surface.

Oxygen atoms were 400 times more effective in oxidizing platinum than oxygen molecules, thereby indicating that extrapolation of low-temperature- oxidation data obtained in conventional environments to reentry conditions could cause serious errors.

CONCLUDING REMARKS High-temperature air-jet facilities which can duplicate some environ- mental condition of hypersonic flight up to reentry velocities are now being operated.

Tests of materials in high-velocity airstreams at temperatures of 4,000° F and greater indicate that conventional structural materials undergo melting, ignition, .or severe oxidation.

Oxidation and ignition characteristics of materials may be limiting properties rather than strength, creep, or fatigue.

Under certain conditions, recombination of dissociated atoms on catalytic surfaces can cause severe heating and oxidation.

The f a c t t h a t materials undergo oxidation and ignition, and t h a t these reactions can give rise t o large surface heat inputs, suggests the use of caution i n extrapolating law-temgerature heat-transfer data t o reentry conditions.

1. Fryburg, George C.: Enhanced Oxidation of Platinum i n Activated Oxygen. Jour. Chem. Phys., vol. 24, no. 2, Feb. 1956, pp. 175-180.

CERAMIC- HEATED J E T WATER -COOLED N O Z Z L E WATER -COOLED CHAMBER c BURNER ZIRCONIUM OXIDE SPHERES O I L I N L E T BURNER AIR I N L E T INSULATING ZIRCONIA BRICK INSULATING FIREBRICK DENSE ZIRCONIA BRICK CAST INSULATING BRICK DIRECTION OF COMBUST10 PRODUCTS DURING FIRING DIRECTION OF AIR FLOW DURING BLOWDOWN Figure 1 ELECTRIC-ARC AIR JET I ANODE Figure 2 FATIGUE-CRACK PROPAGATION AND RESIDUAL STATIC S'I!RENGTH O F BUILT-UP STRETURES By Herbert F. W d r a t h and Richard E. Whaley Langley Aeronautical Laboratory Fatigue tests were conducted on box beams and tension panels i n order t o study sane of the factors affecting fatigue-crack propagation.

The box beams had essentially the same configuration except for the mode of connecting stringers t o the tension cover. The beams w i t h bonded stringers had the lowest r a t e of crack growth, and beams w i t h riveted and integral stiffeners had successively higher rates of crack growth.

Crack growth w a s slower i n beams w i t h close r i v e t spacing than i n beams w i t h greater r i v e t spacing. The tension panels were a l l of the same general configuration except t h a t the proportions.of cross-sectional areas of skin, stringers, and flanges were varied. Panels w i t h heavy stringers and thin skin had lower rates of crack growth than did panels w i t h heavy skin and light stringers.

Static t e s t s were performed on box beams, on tension panels, and on two types of wings, a l l of which contained fatigue cracks. The com- parison of results with predictions made by a simple theory indicates that t e s t r e s u l t s were affected by a redistribution of loads among the various rmaining elements and by whether cracks terminated at r i v e t holes.

INTRODUCTION During the past several years the idea of "fail-safe" design has become a very popular topic f o r discussion among a i r c r a f t structural designers. Although t h e conditions for calling a given design fail-safe have not been clearly defined, almost a l l engineers concerned agree on several general conditions. F i r s t , the progress of a fatigue crack through a structure must be reasonably slow, preferably i n a readily inspectable location. Second, the structure containing a crack must r e t a i n enough s t a t i c strength t o withstand s m e specified load.

The m e a n s f o r accmplishing these ends involve such factors as the selection of materials w agation and s t a t i c I notch-strength properties, the arrangement of material t o i n h i b i t crack growth, the provision of multiple load paths, and others. The purpose of the present paper is t o review current research which deals w i t h t h e systematic study of sane of these factors and t h e i r application t o the ?

design of structures used i n wings.

CRACK PROPAGATION Box Beams One phase of the study of crack propagation involves fatigue t e s t s of box beams such as those shown i n figure 1. Two general configurations were tested. For the first configuration the tension cover had integral s t i f f e n e r s and was machined f r o m a plate. For the other configuration the stringers and skin were either bonded or riveted. The webs and cam- pression covers on a l l beams were of identical built-up construction f o r simplicity i n construction and analysis. All beams were 20 inches w i d e and 8 f e e t long. Identical beams were constructed in each of the aluminum alloys, 2024 and "Om. The beams were loaded as shown i n figure 1 t o produce t e n s i l e stresses of 13 f 6.5 k s i i n the carry-through bay.

A n oblong hole was made i n the center of the carry-through bay t o i n i t i a t e the crack a t that point. Cracks generally g r e w symmetrically across t h e chord. Although sane of the data have been published previously (ref. 1) , representative r e s u l t s are given i n figure 2.

In figure 2 the percentage of the tension area l o s t by fatigue cracking is plotted as a function of the number of cycles of load applied a f t e r crack i n i t i a t i o n .

The curves a r e f o r beams w i t h integral, riveted, and bonded covers. The material i n each case w a s 7075 aluminum alloy.

The r e s u l t s f o r 2024 aluminum-alloy beams are not shoq, but the same general observations apply except t h a t crack growth i s appreciably slower i n beams made of 2024 aluminum alloy.

A s indicated by the curves, the cracks g r e w l e a s t rapidly i n beams The crack growth w a s confined t o the skin and pro- w i t h bonded covers.

gressed at a reasonable r a t e , probably controlled by support Tram the Measurements of stringer stresses taken a t intervals during stringers.

t h e t e s t indicated that these stresses increased more slowly than stresses i n beams w i t h other types of connections, probably because of the f a c t that the bond between the skin and stringers peeled back as the crack grew across the beam. Since there were no r i v e t holes i n the stringers, no s t r e s s raisers w e r e present, and no stringers failed before the crack had grown completely through the skin.

In riveted covers the stringers were sanewhat more vulnerable t o f a i l u r e because stringer stresses increased more rapidly and s t r e s s r a i s e r s due t o r i v e t holes were present. The l o s s of stringers i n the case of riveted beams contributes t o the more rapid loss of tension material. In the case of the integrally stiffened covers the cracks grew a t t h e f a s t e s t r a t e because no natural barriers t o crack growth were present, These observations indicate t h a t crack propagation is very much a function of the effectiveness of connections between the sheet and stringers. An extension of t h i s work t o beams i n which the r i v e t pitch was varied w a s therefore undertaken, and some of the r e s u l t s of this work are shown in figure 3.

I n figure 3 the curves from f i v e 2 are replotted as solid lines.

N e w curves f o r beams w i t h r i v e t pitches of one-half and of twice the r i v e t pitch used i n the previous beam a r e shown by dotted lines. The symbols represent the stage of the t e s t when one or more stringers had completely failed. Crack growth was slower i n beams w i t h a r i v e t pitch of 3/4 inch than i n those w i t h a r i v e t pitch of 1 ; inches and was much slower than i n beams w i t h a r i v e t pitch of 3 inches. The s t r e s s measurements previously mentioned indicated that stresses i n stringers straddling cracks increased more rapidly i n beams with a r i v e t pitch of 3/4 inch than i n other beams w i t h riveted stringers. This increase i n stresses had two effects: a slow r a t e of crack propagation i n the sheet as indi- cated by the low i n i t i a l slope of t h i s curve, and increased probability of stringer f a i l u r e as indicated by t h e f a c t t h a t i n t h i s beam two stringers f a i l e d after only about 8 percent of the structure had been l o s t by skin cracking. O n the other hand, i n beams w i t h a r i v e t pitch of 3 inches, the stringer s t r e s s increased more slowly and indicated t h a t l e s s support w a s given t o the sheet; consequently, crack growth was very rapid i n the skin. The r e s u l t s of these t e s t s show that the closer the r i v e t pitch, the better t h e resistance t o crack propagation.

Fabrication limitations prevent decreasing the r i v e t pitch further.

Integral construction, which m i g h t appear the same as r i v e t s w i t h a zero pitch, displays rapid crack growth. The reason appears t o be t h a t i n integral construction only one crack needs t o be started, and then that crack grows caupletely through the panel.

Tension Panels Another phase of the investigation of crack propagation involves tension tests of stiffened panels. Sme of the results a r e shown i n The panels tested were 30 inches wide and were composed of figure 4.

a skin, f o u r s t r i n g e r s , and two flanges. The parameters varied were the percentages of the areas of skin, stringers, and flanges as indicated by values listed i n the figure. Two of the configurations had 40 percent of t h e area i n the skin, and one configuration had 80 percent of the + * area i n the skiin. Many current a i r c r a f t have proportions within this range. Repeated tension loads were applied t o produce nominal stresses of 14 & 4.7 ksi. Fatigue cracks were i n i t i a t e d at cutouts w i t h the Although only a few results are available, shapes indicated i n figure 4.

preliminary discussions are of interest.

The heavier stringers i n panels w i t h 40 percent of the area i n the skin appear t o have controlled the r a t e of crack growth more effectively The result than i n the panels with 80 percent of the area in the skin.

i s an appreciably lower r a t e of crack propagation i n panels with lighter gage skin. One configuration had a 3-inch-square cutout which w a s the width of one skin panel. This cutout removed approximately 7 percent of the original net section, and the beginning of the curve f o r t h i s specimen i s plotted a t t h a t value. In this case the growth of fatigue cracks w a s very slow i n the i n i t i a l stages of the t e s t and i l l u s t r a t e d the beneficial e f f e c t of framing members adjacent t o cutouts.

RESIDUAL STATIC STRENG!TH The r e s t of t h i s paper deals w i t h the study of residual s t a t i c strength i n the specimens j u s t described. The r e s u l t s which are pre- liminary i n nature are discussed i n order t o indicate trends. These r e s u l t s are then compared with r e s u l t s of a simple analysis. Static t e s t s of Convair 240 (designated herein as CV-240) and c-46 wings con- taining fatigue cracks a r e also discussed.

Box Beams In figure 5 the ordinate represents the ultimate load producing s t a t i c f a i l u r e of beams w i t h cracks expressed as a percent of the load calculated t o produce f a i l u r e of the tension covers i n uncracked beams.

The abscissa represents the length of the fatigue crack in t h e cover skin.

The symbols represent the r e s u l t s of s t a t i c t e s t s of box beams which were made of 7075 aluminum alloy and which were identical except f o r the fastenings between the skin and stringers. The symbols represent either bonded covers or riveted covers as shown i n figure 5. The dotted l i n e represents the strength of the beam having a skin crack only, w i t h no allowance made f o r s t r e s s concentration K due t o the crack. The s o l i d l i n e s represent predictions made by calculations of the s t a t i c strength of a specimen containing a fatigue crack i n the skin only. The basis of t h i s method is t o compute a stress-concentration factor K , f o r the sheet by the method outlined i n reference 2. The residual s t a t i c strength of a sheet containing a crack was added t o the s t a t i c strength of struc- turalmembers such as stringers and flanges t o produce the values f o r the upper curve. Each of the other curves was ccanputed i n a similar w a y F except that one or more stringers were assumed failed. Each test point is connected by a v e r t i c a l l i n e t o the curve appropriate f o r the number of stringers failed i n the specimen represented.

When the crudeness of the method used is considered, the agreement between predicted strength and actual strength of riveted beams is good.

The beams w i t h a r i v e t pitch of 3/4 inch f a l l farthest below the predicted curves, probably because of the higher stresses carried by stringers.

Evidently the distribution of loads among the remaining members i n the structure m u s t be taken i n t o account i n order t o improve t h e predictions.

The strengths of beams w i t h bonded covers are higher than t h e respective No predicted strengths while other strengths are lower than predicted.

reason for t h i s behavior has been found. One point f e l l above t h e dotted l i n e which represents loss of strength equal t o loss of area. This high strength w a s caused by t h e f a c t t h a t t h e actual material strength w a s higher than the specification values used i n computations. Adjustment of the computation for actual material proportions would a f f e c t a l l the r e s u l t s .

Tension Panels Figure 6 gives results similar t o those i n figure 3 f o r s t a t i c tests of the tension panels w i t h 80 percent of the area i n the skin. In t h i s case the data were somewhat higher than predictions (shown by solid l i n e s i n the figure) made by t h e method previously used. The reason appears t o be t h a t i n these panels the fatigue cracks ended at r i v e t holes.

The computation of the stress-concentration factor should, therefore, equal t o the radius of the r i v e t allow for a radius of curvature p instead of the effective radius at t h e root of a crack. Calculations based on t h i s assumption are indicated by the dashed lines, and t h e t e s t r e s u l t s f a l l below t h e predictions as before.

CV-240 Wings Same CV-240 outer wing panels were subjected t o repeated loading i n order t h a t crack growth m i g h t be studied, and then s t a t i c tests were performed i n order that the residual s t a t i c strength might be determined.

Figure 7 presents the r e s u l t s of three s t a t i c t e s t s of CV-240 wings con- taining fatigue cracks. The p l o t of figure 7 i s similar t o the p l o t s of figures 5 and 6 except that the abscissa is the tension cross-sectional area failed expressed as a percentage of the t o t a l tension cross-sectional area. The dotted l i n e represents reduction in static strength i n t h e same proportion as the reduction i n area. These wings were constructed of 7On aluminum alloy, and the structure w a s somewhat more cmplex than t h a t of the box beams discussed previously. A s before, t h e stress concentra- t i o n w a s computed f o r the skin only. Also, since cracks terminated a t r i v e t holes o r g r e w t o r i v e t holes a t an early stage of t h e s t a t i c test, t h e r i v e t radius w a s used i n the calculations. The cracks i n these winns originated i n t h e rear spar caps and then g r e w across the chord. "he cal- culation w a s , therefore, f o r a sheet w i t h a notch on one side only. The t e s t r e s u l t s f e l l s l i g h t l y below the prediction as before.

C-46 wings The fatigue t e s t s of C-46 wings have been discussed i n references 3 Thirteen wings were s t a t i c tested a f t e r various amounts of t h e and 4.

tension material were failed i n fatigue tests. The r e s u l t s of the s t a t i c tests have been presented i n reference 4.

The results are a l s o shown i n figure 8 i n the same ty-pe of p l o t as w a s used i n figure 7. The predicted curve w a s computed on the assmption t h a t the skin w a s continuous across the chord. The r i v e t radius w a s used i n the calculation f o r the same reason as before.

In s p i t e of the f a c t t h a t a w i d e variety of s t r u c t u r a l members failed during t h e fatigue tests on these specimens, the predicted strengths f e l l i n a very narrow band which is represented i n the figure as a single line. The discrepancy between results and predictions w a s somewhat greater than i n the previous cases. This discrepancy was t o be expected as a result of the much more complicated structure i n the C-46 wings.

Obviously, the redistribution of loads i n t h i s structure w i l l have t o be considered before more accurate predictions can be made.

The apparent large loss of strength w i t h small cracks applies only t o t h e tension surface.

In compression-critical wings, such as the C-46 and CV-240, the loss i n wing strength is very s m a l l u n t i l large cracks a r e present.

CONCLUDING REMARKS Crack-propagation and static-strength tests i n several types of built-up specimens and full-scale wings have been reviewed. The r e s u l t s , t o date, indicate t h a t the rate of crack propagation i s influenced strongly by t h e mode of connecting the skin t o stringers and by the proportions of areas of the skin and stringers. The analysis of residual s t a t i c strength of complex structures indicates the f e a s i b i l i t y of applying simple methods, 'Gut the results are subject t o questions regarding the redistribution of loads, interactions between various members, and such seemingly t r i v i a l considerations as whether or not a crack terminates a t a r i v e t . Much work remains t o be done on these problems. Other configurations designed t o improve both the rate of crack propagation and residual s t a t i c strength should be investigated.

’ l3ERBENCES Landers, Charles B., and 1. Hardrath, Herbert F., Leybold, Herbert A., Hauschild, Louis W: : Fatigue-Crack Propagation i n Aluminum-kloy Box Beams. NACA TN 3856, 1956.

2. McEvily, Arthur J., Jr., I l l g , Walter, and Hardrath, Herbert F.: Static Strength of Aluminum-Allay Specimens Containing Fatigue Cracks. NACA TN 3816, 1956.

3. McGuigan, M. J., Jr., Bryan, D. F., and Whaley, R. E.: Fatigue

Investigation of Full-scale Transport-Airplane Wings - Surmnary

of Constant-Amplitude Tests Through 1953. NACA ”IV 3190, 1934.

Fatigue- 4. Whaley, Richard E., McGuigan, M. J., Jr., and Bryan, D. F.: Results on Full-scale Crack-Propagation and Residual-Static-Strength Transport-Airplane Wings. NACA TN 3847, 1956.

CONFIGURATION OF BOX BEAMS INTEGRAL RIVETED OR BONDED t STRESS 3 13.0 f 6.5 KSI Figure 1 CRACK GROWTH IN BOX BEAMS 7075 ALUMINUM ALLOY AREA f/-RIVETED LOST, % 0 20 40 60 80 100x103 CYCLES AFTER INITIATION OF CRACK

s

CRACK GROWTH IN BOX BEAMS 7075 ALUMINUM ALLOY FAILURE 0 2 STRINGERS

?

I 0 I STRINGER I RIVET I &INTEGRAL PITCH, INCHES AREA LOST, "/.

20 40 60 80 1OOX , 1 0 3 CYCLES AFTER INITIATION OF CRACK Figure 3 CRACK PROPAGATION IN TENSION PANELS 7075 ALUMINUM ALLOY CUTOUT 0 0 SHEET AREA,% ............ 80 40 40 STRINGERS,% ............. I O 30 30 FLANGES, %.................IO 30 30 - AREA LOST,

-

Sb Figure 4 , STATIC STRENGTH OF BOX BEAMS 7 0 7 ' 5 ALUMINUM ALLOY t ULTlMATE LOAD, OF ORIGINAL -3 h

1 0 BONDED

2o 1 h $INPITCH]

o I i I N . PITCH RIVETED

* 3 IN. PITCH

I I I I 1 0 5 1 0 1 5 20 CRACK LENGTH, INCHES Figure 5 STATIC STRENGTH OF TENSION PANELS 7075 ALUMINUM ALLOY ULTIMATE LOAD,% 5 0 OF ORIGINAL 0 1 0 20 30 CRACK LENGTH, INCHES Figure 6 STATIC STRENGTH OF CV-240 WINGS 7075 ALUMINUM ALLOY ULTIMATE "/, OF ORIGINAL 20 40 60 80 100 0 AREA LOST,% Figure 7 STATIC STRENGTH OF C - 4 6 WINGS 2024 CLAD ALUMINUM ALLOY 1 0 0 ULTIMATE LOAD, "/o OF ORIGINAL Figure 8 F SOME ASPECTS OF FAIL-SAFE DESIGN OF PRESSURIZED FUSELAGES By Paul K u h n and Roger W. Peters Langley Aeronautical Laboratory Separate investigations have dealt with the critical crack length of flat sheets or of unstiffened cyliniiers and with the type of rupture experienced by stiffened cylinders. These investigations are correlated, supplemented by new tests, and combined into a uniform scheme for pre- dicting critical crack length and type of rupture in stiffened pressur- ized cylinders.

INTRODUCTION The fail-safe design of pressurized fuselages is a problem that has attracted much attention in the past few years. This paper is a progress report on work in this field and an attempt to correlate several lines of investigation.

net area, sq ini ANET ring area (cross sectional), sq in.

AR stress-concentration factor for ultimate load KU K stress-concentration factor for cylinder u, C-YL ring spacing, in.

load, ks i P r radius of cylinder, in.

skin thickness, in.

t S length of original slit, in.

s

U s t r e s s , k s i U maximum stress, k s i MAX ultimate t e n s i l e stress, k s i UU DEFINITIONS The problem is defined i n a general way by t w o questions: If ini- t i a l damage, such as a fatigue crack, is i n f l i c t e d on a pressurized stiffened shell, how large can the damage be before the pressure causes a rupture of the shell, and w h a t is the nature of the rupture? The only type of i n i t i a l damage which is considered here i s a longitudinal crack o r s l i t of length 6 as shown i n figure 1. (For aluminum alloys, t o which t h i s discussion is confined the difference between a fatigue crack and a f i n e s l i t is negligible. For any specified pressure o r hoop tension, a c r i t i c a l length of crack e x i s t s at which the pressure w i l l rupture the skin. The term "confined rupture" i n t h i s paper w i l l refer t o a rupture which stops a t the nearest rings, as indicated on the sketch a t the l e f t . The term ''unconfined rupture" w i l l refer t o a rupture which extends into adjacent bays, as indicated on the sketch a t the r i g h t . A n unconfined rupture of the skin often results i n fail- ure of the rings and sometimes of t h e stringers.

'SURVEY O F PRFVIOUS INVESTIGATIONS C r i t i c a l Crack Length Figure 2 shows schematically the first two steps in the investiga- t i o n of c r i t i c a l crack length. A t the top i s shown a flat sheet under tension with a central crack of length 6. When the maximum s t r e s s uMAx i n the sheet at the two ends of the crack becomes equal t o the tensile strength of the material, the sheet w i l l t e a r apart. A t t h i s instant, the maximum s t r e s s is equal t o the product of the net-section s t r e s s P / A ~ ~ and a stress-concentration factor G.

has been published i n A method f o r calculating the factor K, reference 1. The calculation involves the stress-strain curve and a size-effect constant which is determined from a tension t e s t on a speci- men with a sharp notch of known radius.

The presence of t h i s size effect i i n problems involving cracks or sharp notches invalidates t h e mechanical l a w of similarity that geometrically similar structures f a i l at' the same s t r e s s and makes it impossible t o draw generalized curves based on dimen- sionless parameters.

The lower sketch i n figure 2 shows a pressurized unstiffened cylinder w i t h a longitudinal crack. The stress-concentration factor f o r such a cylinder is calculated by the formula shown. The quantity Ku i s the stress-concentration f a c t o r calculated f o r the configuration obtained by The term i n parentheses is t h e unwrapping t h e cylinder i n t o a plane.

"curvature correction," which w a s found empirically and applies t o 2024-T3 The experimental basis ahminun alloy as well as 7075-T6 aluminum alloy.

f o r t h e formula may be found i n reference 2.

The importance of t h e curvature correction is shown i n figure 3.

For t h e two aluminum alloys, t h e c r i t i c a l crack length is shown as func- t i o n of the t e n s i l e stress f o r flat sheet and f o r cylinders w i t h a radius

of 15 inches, which is a widely used size representing roughly a 1/4-

scale model of a fuselage. For a l l but very short cracks, the drop i n strength due t o curvature e f f e c t is obviously substantial. Curves of c r i t i c a l crack lengths of unstiffened cylinders corresponding t o t h e curves shown i n figure 3 w i l l be used later as a yardstick o r reference basis f o r stiffened cylinders.

me of Rupture

The i n i t i a l investigation of t h e problem of type of rupture w a s con- ducted on cylinders w i t h r a d i i of 15 o r 24 inches, stiffened by stringers and riveted-on rings. Subjecting these cylinders t o a constant internal pressure and t o repeated torsion loads resulted i n fatigue cracks at 45' t o the cylinder axis.

Figure 4 shows the results of the i n i t i a l investigation on 2024-T3 cylinders. Hoop stress is plotted as the ordinate and ring-reinforcement r a t i o , t h e r a t i o of t h e cross-sectional area of a r i n g t o the area AR of the associated skin 2 t s , i s plotted as t h e abscissa. The dashed line, labeled "theoretical criterion, 'I is based on elemetary considera- tions and gives the area which t h e rings must have t o carry the hoop load if t h e skin i t s e l f cannot carry it because it is cracked or cut.

The c i r c l e s denote confined ruptures, t h e x-marks denote unconfined rup- tests.

tures i n the The s o l i d l i n e , labeled "empirical criterion," i s approximately the upper boundary of the confined ruptures. The ring- size c r i t e r i o n can thus be used as a basis f o r predicting the type of rupture. The data are taken from reference 3, except that the curve showing the empirical c r i t e r i o n is drawn here i n a somewhat more con- servative fashion than i n the reference.

A few t e s t s of the same nature have been made on cylindeis of 7075-T6 material. The number of t e s t s was too small t o establish an empirical criterion f o r ring size, and the method of testing, pressure combined t w i t h cyclic torsion, has been replaced by pressure cycling.

N E W INVESTIGATIONS Presented herewith a r e evaluations of more recent data. The pres- entation is aimed a t answering two questions: (1) What correlation exists between the c r i t i c a l crack length f o r unstiffened cylinders and that f o r stiffened cylinders?

(2) How r e l i a b l e i s the ring-size criterion f o r predicting the nature of the rupture of stiffened cylinders when the cracks a r e longitudinal rather than at 45O, as in the original investigation?

The majority of the tests discussed were actually made t o obtain some preliminary information on the e.ffect of parameters not considered previously, f o r instance, type of rings used. A s a r e s u l t , t h e t e s t s available at t h i s time are inadequate f o r giving definite answers t o the two questions posed, but they do indicate trends.

The t e s t s f a l l i n t o three groups according t o s i z e of cylinder: small cylinders with a radius of 3.6 inches; medium-size ones with a radius of 13 inches; and full-scale ones w i t h a radius of about 70 inches.

A l l were stiffened by stringers and rings or hoops.

The small cylinders had precut slits and were brought t o rupture by increasing t h e pressure steadily.

The crack-length r e s u l t s a r e shown i n figure 5 . The curve, labeled

b, gives the c r i t i c a l crack length of

unstiffened cylinders having the same radius.

The c i r c l e s denote again confined ruptures; the x-marks, unconfined ruptures. Regardless of the type of rupture, a l l the c r i t i c a l crack lengths plot f a i r l y close t o the reference curve, which means that the c r i t i c a l crack lengths of the stiff- ened cylinders i n t h i s group of t e s t s are equal t o those of corresponding unstiffened cylinders.

Figure 6 shows the ring-size criterion plot f o r the same.group of Each t e s t point represents the same specimen as the point a t the t e s t s .

same s t r e s s l e v e l i n figure 5 . The empirical criterion l i n e i s taken from figure 4. A l l ruptures observed are i n agreement with the criterion: unconfined if above the curve, confined if below the curve. The cylinders i n t h i s t e s t group had either rather l i g h t rings or e l s e rather heavy rings; as a r e s u l t t h i s test group does not give a sensitive check on the

i 441

O n the other hand, the f a c t that accuracy of the ring-size criterion.

rather extreme ri s i z e s were used tends t o increase the weight of the evidence regarding c ck length shown i n figure 5 .

\

The next group of t e s t s is on medium-size cylinders (15-inch radius) On these cylinders, the internal pressure w a s cycled of 2024-T3 material.

Figure 7 shows t o grow a fatigue crack, s t a r t i n g from an i n i t i a l s l i t .

The c r i t i c a l crack lengths f o r t h i s group of tests the crack-length plot.

are consistently longer than indicated by the reference curve, the excess The result thus length varying roughly from 40 percent t o 100 percent.

differs markedly from that obtained on the small cylinders.

The Figure 8 is the ring-size plot f o r the medium-size cylinders.

types of f a i l u r e are i n agreement with the prediction, if the prediction f o r the border-line case on the l i n e i s made conservatively. This plot shows only 3 points, and thus no counterparts a r e shown f o r many of the points shown i n figure 7; the missing points a r e discussed i n the following paragraph.

O n the small cylinders, and on the three medium-size cylinders dis- cussed i n the previous paragraph, the rings were riveted continuously t o the skin. O n the other medium-size cylinders, t h e rings were e i t h e r floating, that is, not touching the skin a t a l l , or they were touching the skin, but riveted t o it only a t the intersections with the stringers.

Rings of e i t h e r type are believed t o have l i t t l e if any power t o confine rupture; therefore, the assumption is made t h a t the presence of either type of ring j u s t i f i e s a prediction of unconfined rupture, and conse- quently, it i s unnecessary t o plot the point on the ring-criterion plot i n order t o arrive a t a prediction of the type of rupture. So far, there appears t o be no evidence that the assumption is unduly conservative.

Figure 9 shows the crack-length r e s u l t s f o r medium-size cylinders A l l t h e points plot close t o the reference curve.

of 7075-6. Since the corresponding plot f o r 2024-T3 material ( f i g . 7) showed excess crack lengths ranging from 40 percent t o 100 percent, it may be said that 2024-T3 has a "hidden margin of safety," under some conditions, which appears t o be lacking i n 7075-T6 material.

Figure 10 i s the ring-size plot f o r the 7075-6 cylinders.

Only t h e theoretical criterion is shown, since no empirical criterion is estab- lished, as mentioned previously.

The type of rupture i s as expected i n a l l cases, but the location of the points is such that the empirical c r i - terion s t i l l remains undefined.

Figure 1 1 w i t h data taken from references 4 and 5 shows two t e s t s made by two a i r c r a f t manufacturers on full-scale models of fuselages with a radius of about 70 inches. The c r i t i c a l crack length is j u s t above the reference value f o r specimen A and about 60 percent larger f o r specimen B.

This s c a t t e r suggests a s c a t t e r band somewhat similar t o that obtained on the medium-size cylinders. 8 ' In specimen A, a s a w s l i t had been made through the skin as w e l l as through the r i n g underneath it. With one r i n g thus out of action, the ring-reinforcement r a t i o w a s marginal, which would lead t o the prediction that the rupture w i l l probably be unconfined. For specimen B, an uncon- fined rupture would be predicted because the rings were floating. The symbols indicate that both specimens had unconfined ruptures. It should be noted that both specimens served as s t a r t i n g points i n the Gevelopment of f i n a l designs.

CONCLUDING REMARKS The crack-length criterion and t h e ring-size c r i t e r i o n appear t o offer some promise as tools f o r putting some aspects of fail-safe design on a quantitative basis. The crack-length criterion i n i t s present form states t h a t the c r i t i c a l crack length of a stiffened cylinder is a t least equal t o that of an unstiffened cylinder of the same radius.

The ring- s i z e criterion, which is reasonably w e l l established f o r 2024-T3 aluminum alloy but not f o r 7075-6 aluminum alloy, appears t o permit a prediction whether the rupture w i l l be confined or unconfined when the rings are continuously riveted t o the skin. When the rings are not so riveted ( o r otherwise fastened), the rupture w i l l probably be unconfined.

Much work remains t o be done, however. The conditions under which the c r i t i c a l crack length of the stiffened cylinder can be greater than that of the unstiffened cylinder should be established more f u l l y .

Only s t r a y bits of information a r e available at present on a number of factors, such as effect of stringers, of load-carrying members bridging a crack, and of producing the i n i t i a l damage very rapidly.

-7 I 1. McEvily, Arthur J., Jr., Illg, Walter, and Hardrath, Herbert F.: Static Strength of Aluminum-Alloy Specimens Containing Fatigue Cracks. NACA TN 3816, 1956.

2. Peters, Roger W., and Kuhn, Paul: Bursting Strength of Unstiffened Pressure Cylinders With Slits. NACA TN 3993, 1957.

3. Peters, Roger W., and Dow, Norris F.: Failure Characteristics of Pressurized Stiffened Cylinders. NACA TN 3851, 1956.

4. Sorensen, Arne: Some Design Considerations for Tear-Resistant Air- plane Structures. Preprint No. 618, S.M.F. Fund Preprint, Inst.

Aero. Sci . , Jan. 1956.

5. Spaulding, E. H.: Observations on the Design of Fatigue-Resistant

and 'Fail Safe' Aircraft Structures. Session 8 . Paper 2. Presented at International Conference on Fatigue of Metals sponsored by British Inst. Mech. Eng. and A.S.M.E., Sept. 10-14 (London) & Nov. 28-30 (New York) , 1956.

TYPES OF RUPTURE

d8t

CONFINED RUPTURE UNCONFINED RUPTURE Figure 1 STRENGTH OF CRACKED SPECIMENS K,,CYL = Ku (I + 46#) FOR 2024-T3 AND 7075 -T6 ALUMINUM ALLOY Figure 2 3F CRITICAL CRACK LENGTHS UNSTIFFENED CYLINDERS HOOP STRESS, 2024 -T 3 KSI

\

7075 -T 6

2o t

L r45 2024 -T3 L7075 -T6 I I I I I I I Figure 3 RING-SIZE CRITERION FOR 2 0 2 4 - T 3 r=15 AND 24 IN.; PRESSURE AND TORSION X EMPIRICAL CRITERION

t o<

STRESS, HOOP 2 0 1 /d ’

KSI THEORETICAL CRITERION 0 CONFINED RUPTURE X UNCONFINED RUPTURE 0 -2 .4 .6 RING-REINFORCEMENTRATIO, AR/ltS Figure 4 CRACK LENGTHS FOR 2024-T3 r=3.6 IN.; PRESSURE RISING RUPTURE 0 CONFINED x UNCONFINED 0 I 2 8, INCHES Figure 5 RING-SIZE CRITERION FOR 2024-T3 r = 3.6 IN.; PRESSURE RISING

30 -

X RUPTURE 0 CONFINED X UNCONFINED 0 0 CRITERION I I I 0 .2 . 4 .6 A R / 2 k Figure 6 I CRACK LENGTHS FOR 2024-T3 r=15 IN.; PRESSURE CYCLING 30- RUPTURE 0 CONFINED X UNCONFINED

-

20.

UNSTIFFENED HOOP ' . CYLINDER STRESS, KS I - X I O .

t

I I I I I I

0 2 4 6 8 IO 8, IN.(INCLUDING INITIAL DAMAGE) Figure 7 RING-SIZE CRITERION FOR 2024-T3 r=15 IN.; PRESSURE CYCLING

/ /

/ /

- / - /

/ I I I / I I I Figure 8 CRACK LENGTHS FOR 7075-T6 r = 1 5 IN.; PRESSURE CYCLING 301- RUPTURE 0 CONFINED X UNCONFINED

\

20- HOOP

STRESS, -

KS I

-

IO UNSTIFFENED CYLINDER 0 2 4 6 8 1 0 6, IN. (INCLUDING INITIAL: DAMAGE) Figure 9 RING-SIZE CRITERION FOR 7075 -T6 r = 1 5 IN.; PRESSURE CYCLING / / /

"/

/

STRESS, xx

/ "

KSI

t /

I I , I 0 . 2 .4 . 6 AR/%

449 Figure 10

CRACK LENGTHS FOR 2024-T3 r=70 I N . ; PRESSURE CONSTANT

30 -

-

HOOP

STRESS, -

UNSTIFFENED KSI CYLINDER 0 4 8 1 2 1 6 20 8, INCHES Figure 11 By John B. Gamin Langley Aeronautical Laboratory The importance of the "fail-safe" design concept with regard t o fatigue i n modern airplane structures is evidenced by the great attention which has recently been directed t o t h i s subject. Involved i n t h i s con- cept are a need t o know something of the behavior of a fatigue crack as it s t a r t s and grows i n an airplane component and, i n addition, a need f o r howledge of a b i l i t y t o estimate the fatigue l i f e of the a i r c r a f t structure.

This paper presents r e s u l t s from an experimental investigation of Crack behavior and fatigue l i f e were studied full-scale-airplane fatigue.

loads t o t h e wings during the application of random o r variable-amplitude These w i n g s were the same types of of a C-46 transport-type airplane.

tests reported structures which were used i n constant-amplitude fatigue i n references 1 and 2. The fatigue t e s t s of these wings provide t h e first opportunity t o compare results from full-scale constant-amplitude loadings with those simulating actual f l i g h t .

The loading chosen f o r the variable-amplitude t e s t s was the gust spectrum reported by Rhode and Donely f o r a wide sampling of transport The gust spectrum w a s operations i n the United States. (See ref. 3.)

selected because the loads due t o f l i g h t maneuvers and ground operations were not considered t o play a significant part i n the fatigue l i f e of t h i s airplane.

Figure 1 presents the incremental loading spectrum f o r the C-46.

The ranges of incremental load factor f o r each loading level are shown plotted against the number of loads applied at each level. Loads were applied at the mean of each of the 16 load ranges designated by the circled points. Thus, the lowest value of incremental load w a s 0.225g, representing the range from the threshold value of O.l5g t o 0.30g. The numbers of cycles were established on the basis of a representative f l i g h t distance of 10 million m i l e s . The maximum loading associated with a f l i g h t operation of t h i s duration would., as is indicated by the position of the dashed l i n e i n the figure, be somewhat greater than l i m i t load f o r t h i s airplane.

In order t o apply the loadings i n such a way as t o avoid putting on a l l one s i z e load prior t o any other, the spectrum of figure l w a s divided by 100 which would correspond t o a distance of 100,000 miles or about 500 flying hours under the assumed typical conditions of f l i g h t . The loads which appeared less than 100 times i n the original spectrum would appear only occasionally i n the reduced spectra.

For the purpose of introducing randomness into t h i s method of loading, the actual order of application of the loading steps w a s estab- lished by reference t o a table of random numbers. Such an arrangement has I1 been called a "Sequence. The random arrangements of the loadings i n the reduced spectra f o r the first three sequences are i l l u s t r a t e d i n table I.

The first incremental loading i n the first sequence is the 0.525g load applied 3,510 times; t h i s i s followed by the 0.675g load applied 4 0 6 7 times. The load at 2.475g and a l l other loads i n t h i s sequence which appear with a zero value f o r the number of cycles applied are those loads which occur less than 100 times i n the original LO-million-mile spectrum and thus only appear occasionally i n the 100 sequences. It can be readily seen t h a t the orders of application of the loads i n the 3 sequences shown are different, and it m a y be of i n t e r e s t t o note that none of the 100 sequences were identical with regard t o order of load application t o the specimen. Loading sequences greater than 100 repeated the original order; thus, the 101 sequence w a s the same as the first sequence.

L The fatigue machine used f o r this investigation i s seen i n figure 2.

This machine w a s basically a concentrated-eccentric-mass type of shaker capable of being operated at any frequency up t o 4 cycles per second.

The wing attached t o a central portion of the a s e l a g e can be seen inverted and mounted between two large supporting structures near the center of the picture. The eccentric weights can be seen under the wing tip; t h e gearbox and drive shafting are under the wing; and the necessasy controls and cycle-measuring equipment were located centrally near the main support structures. Loads were applied dynamically up to incremental values of t1 g. Those loads above t h i s level were applied s t a t i c a l l y by means of the hydraulic ram located directly over the eccentric weights. A l l loads applied during the t e s t s were monitored by either i n t e r n a l structural s t r a i n gages or external load-measuring dynamameters which are located rams.

on top of the loading This program has, up t o the present time, performed variable-amplitude t e s t s on three complete wings, each camposed of one center section and two outer panels. A t o t a l of 46 cracks have been observed, of which one crack on each of the s i x outer panels grew t o such s i z e as t o indicate imminent f a i l u r e of the wing. lifetimes accumulated by these wings Actual f i n a l ranged between l a and 219 sequences of load corresponding t o assumed f l i g h t times of from 62,000 t o 114,000 f l i g h t hours.

Three subjects appear of i n t e r e s t from the results of these variable the area of fatigue crack initiation, the r a t e of growth amplitude t e s t s : ion of fatigue damage i n the e .

o r propagation of the crac structure during variable r

4s2

I With regard t o crack initiation, it w a s noted t h a t fatigue cracks which grew t o f i n a l f a i l u r e i n the variable-amplitude t e s t s i n i t i a t e d i n areas where cracks i n i t i a t e d only during the high-level constant- amplitude loadings. In other words, the serious cracks found under the random t e s t conditions did not occur at the loadings which might be considered representative of that for greatest damage i n the constant- a constant-level fatigue t e s t at the l e v e l of level tests. Therefore, greatest fatigue damage might not reveal the proper area of crack i n i t i - ation which would be of i n t e r e s t t o operational inspection crews.

Crack-growth information i s shown i n figure 3 . The abscissa scale i s the percentage of f i n a l l i f e f o r the specimen. This scale was chosen f o r convenience i n displaying the results f o r specimens which were sub- jected t o different values of constant-amplitude loading as w e l l as those subjected t o random loadings. This w i l l be clear when it i s realized that the specimen tested a t a constant alternating load level of f l g sustained only 100,000 cycles of load, while the variable-amplitude ’ specimens accumulated about 10,000,000 cycles of load before f i n a l f a i l - ure. The dashed curves show crack growth f o r two representative constant- amplitude specimens tested at a low and a high value of alternating load, and the solid curves show results f o r two representative variable= amplitude specimens. All curves appear t o exhibit a characteristic shape denoting slow growth of the crack from i n i t i a t i o n a t about one-third t o one-half of the f i n a l l i f e u n t i l about 95 percent of the l i f e had been spent, a f t e r which there w a s a very rapid growth of the crack u n t i l the entire specimen failed. This rapid growth i n i t i a t e d at a point where the crack had approached a value between 5 and 10 percent of the t o t a l tension material. The appearance of the step shown i n the two upper curves at about 70 percent of the l i f e i s associated with the f a i l u r e of a f a i r l y heavy element of the structure. This f a i l u r e characteristic appears t o be associated w i t h a particular configuration and might not be generally applicable t o other structures. It would seem, however, from these results, t h a t crack growth under variable-amplitude loading conditions is, i n general, like crack growth under the constant-amplitude loadings.

An assessment of the amount of fatigue damage which an airplane wing might accumulate during the variable-amplitude loadings of f l i g h t may be determined i n several ways. The cumulative-damage criterion, usually attributed t o Miner, has been selected f o r a first comparison.

(See

r e f . 4. ) Since t h i s damage criterion is based on an endurance curve

from constant level testing and since such a curve w a s available from previous t e s t s on an identical structure, having the same load distribu- tion and corresponding load ranges, it w a s f e l t t h a t this damage criterion might give an excellent prediction of l i f e f o r both crack i n i t i a t i o n and f o r f i n a l f a i l u r e of the w i n g .

Figures 4 and 5 show the agreement obtained f o r the six outer wing A bar graph i s used panels tested under variable-amplitude loadings.

The standard of camparison t o show the r e l a t i v e l i f e of these panels.

is the l i f e calculated from the r e s u l t s of the constant-level tests.

Figure 4 shows the r e l a t i v e l i f e u n t i l i n i t i a t i o n of the crack which grew and figure 5 shows the relative l i f e u n t i l f i n a l t o f a i l each specimen, failure. The calculated l i f e f o r crack i n i t i a t i o n w a s 17.4 sequences o r about 8,700 flight hours while the calculated l i f e t o f i n a l f a i l u r e w a s 37 sequences o r about 18,500 hours. It can be seen i n figure 4 t h a t t h e average actual l i f e t o crack i n i t i a t i o n i s about 35 times the pre- dicted l i f e w i t h a spread of about 5 t o 1. Similar comparisons f o r a l l the 46 cracks which i n i t i a t e d i n these wings would show that the average l i f e would have been about 4& times the predicted l i f e , while the overall 33 t o 1. The e a r l i e s t crack which occurred i n any spread would be about of the wings w a s found t o occur at about one-third of the l i f e predicted by the cumulative-damage criterion.

Figure 5 shows that the actual f i n a l l i f e of these specimens w a s about four times t h a t predicted by t h i s damage c r i t e r i o n and that the spread i n the f i n a l failure values is slightly less than 2 t o 1. It would appear from t h i s that an estimation of a f i n i t e l i f e either t o crack i n i t i a t i o n o r f i n a l f a i l u r e by the cumulative-damage method based on constant-level fatigue-test r e s u l t s would be uncertain.

w a s performed on these data Another method of analyzing fatigue l i f e f o r camparison purposes. This method, h o w n as the "intersect" method, makes use of the summation curve f o r the spectrum loading i n condunction w i t h the appropriate endurance curves from the constant-level tests.

These r e s u l t s f o r the same specimens are shown i n figures 6 and 7.

I n figure 6, the difference between predicted l i f e and measured l i f e has a value of about 2 while the spread, been reduced t o as would be expected, as f o r the cumulative-damage method.

remains the same I n the case f o r 7, differences of about 2 t o 1 are seen as f i n a l f a i l u r e shown i n figure were noted i n the case f o r crack i n i t i a t i o n by t h i s method; here again the spread i s the same as f o r the cumulative-damage method.

Although the intersect method indicates closer values of l i f e prediction than the cumulative-damage method., there appears t o be l i t t l e advantage of one method over the other because of the influence of spread i n the data, particularly i n the crack-initiation case.

The significance of any particular value of estimated l i f e by either method. would appear t o be questionable; however, t h i s would be the case i n any attempt t o use the r e s u l t s from one o r several constant-level fatigue tests t o predict the endurance of a similar component subjected t o the variable loads of actual f l i g h t .

I The apparent increase i n l i f e of the c-46 wings as indicated by the absolute values of both methods might be explained by the application of the higher loads of the spectrum. It is noted t h a t these larger loads were of such amagnitude as t o cause a considerable increase i n Life as indicated by r e s u l t s from constant-level t e s t s on Meteor 4 tailplanes Whether o r not t h i s reported by Raithby and Longson i n reference.5.

is not known.

effect fully accounts f o r the increase i n l i f e noted here it appears t h a t a constant-amplitude fatigue t e s t might I n summary, not reveal the area wherein a crack would i n i t i a t e t o cause failure of a structure subjected t o the variable loadings of f l i g h t ; crack propa- gation behavior based on the f i n a l l i f e of the specimen appears t o be s i m i l a r under both constant-- and variable-amplitude loadings j and, finally, the assessment of fatigue damage by either the cumulative damage method or the intersect method appears questionable when based only on constant- level f atigue-test results.

REFERENCES 1 . McGuigan, M. J., Jr., Bryan, D. F., and Whaley, R. E.: Fatigue Inves-

tigation of Full-scale Transport-Airplane Wings - Summary of

Constant-Amplitude Tests Through 1953. NACA TN 3190, 19%.

2. Mhaley, Richard E., McGuigan, M. J., Jr., and Bryan, D. F . : Fatigue- Crack-Propagation and Residual-Static-Strength Results on Full-scale Transport-Airplane Wings. NACA TN 3847, 1956.

3. mode, Richard V., and Donely, Phillip: Frequency of Occurrence of Atmospheric Gusts and of Related Loads on Airplane Structures.

NACA W R L-121, 1944.

(Formerly NACA ARR LkI21. ) 4. Miner, Milton A.: Cumulative Damage i n Fatigue. Jour. Appl. Mech., vol. 12, no. 3, Sept. 1945, pp. A-159 - A-164.

5. Raithby, K. D., and Longson, Jennifer: Some Fatigue Characteristics of a Two Spar Light Alloy Structure (Meteor 4 Tailplane).

Rep.

No. Structures 195, British R.A.E., Jan. 1956.

TABLE I . - ORDER OF LOADING

Second sequence Third sequence F i r s t sequence Sycles Cycles b a d , L h Cycles Load, An Load, An 0 0.225 0.525 3,510 1.725 39,3= 0 0 1.125 2 1 2 475 2.175 1.425 1 0 .825 1.875 236 1.425 1 2.029 0 2,325 675 1,067 1.275 5 2.475 0 1 2.025 1.575 975 73 1.125 1 975 73 1.875 1 0 1.575 2 475 9 525 3,510 0 15,444 1 1.725 375 1.575 6 .225 0 1.275 39,312 2.325 0 .825 2.175 675 1,067 235 1.125 525 3,510 675 1,067 1 0 1.425 975 73 1.725 2.025 0 .825 235 1.275 5 0 0 ,225 59,312 2.325 2.175 15,444 1 15,444 375 1.875 375 ‘7 I C-46 LOAD SPECTRUM 1O7MlLES O F FLIGHT 2.7 2.4 LIMIT LOAD

__------

2. I I .a INCREMENTAL LOAD FACTOR, LOAD VALUES All 1.2 .9 .6 .3 THRESI +OLD 100 1 0 1 102 103 104 105 106 to7 CYCLES Figure 1 C- 46 VARIABLE-AMPLITUDE FATIGUE MACHINE L-57-479.1 Figure 2 FATIGUE -CRACK PROPAGATION VARIABLE AMPLITUDE - CONSTANT AMPLITUDE

------ An = 0.35

---

An = 1.00 TENSION 30 AREA FAILED, % 20 IO 0 20 40 60 80 I O 0 LIFE TO FINAL FAILURE, % Figure 3 DAMAGE EVALUATION CUMULATIVE DAMAGE METHOD ; CRACK INITIATION I I 5 I I ~I SPECIMEN NUMBER

v- AVERAGE

I I 0 I 2 3 4 5 6 7 Figure 4 4 A&.

s

DAMAGE EVALUATION CUMULATIVE DAMAGE METHOD ; FINAL FAILURE AVERAGE LIFE SPECIMEN NUMBER I I f I I I f I I I I l l f I 1 1 0 I 2 3 4 5 6 7 ACTUAL RELATIVE LIFE, CALCULATED Figure 5 DAMAGE EVALUATION INTERSECT METHOD j CRACK INITIATION

5 I

SPECIMEN 4 PAVERAGE

I

NUMBER I Figure 6 \-.

I DAMAGE EVALUATION INTERSECT METHOD ; FINAL FAILURE AVERAGE LIFE ACTUAL RELATIVE LIFE, CALCULATED Figure 7 STUDIES OF S T R U C T U R A L FAILURE ACOUSTIC LOADING

- -

By Robert W. Hess, Robert W. Fralich, and Harvey H. Hubbard Langley Aeronautical Laboratory Some discussion of t h e acoustic fatigue problem of a i r c r a f t struc- tures i s given along with data pertaining t o the acoustic inputs from some powerplants i n common use. Comparisons a r e given f o r r e s u l t s of some fatigue tests of flat panels and cantilever beams exposed t o both random- and discrete-type inputs. I n t h i s regard it appears that both the s t r e s s l e v e l of the test and the type of model a r e significant; hence, no generalization can be mde a t t h i s time. With regard t o increasing the fatigue l i f e , it w a s noted that increased stiffening of a panel due t o curvature and pressure d i f f e r e n t i a l is particularly beneficial.

INTRODUCTION It is well-known that fatigue damage can occur t o a i r c r a f t struc- tures which a r e exposed t o intense acoustic pressure loads.

Damage usually occurs i n t h e secondary structure of the a i r c r a f t as a result of a large number of relatively small loads applied at the r a t e of sev- eral hundred loading cycles per second. This paper presents information pertaining particularly t o the problem of exposure t o random noise such as that encountered from turbojets, r a m jets, rocket engines, and aero- dynamic boundary layers.

Some of the phenomena involved in t h i s problem can be discussed with the a i d of the block diagram of t a b l e I. L e t us first direct our atten- t i o n t o the blocks themselves. The acoustic inputs are i n the form of fluctuating pressures on the exposed surface of the structure. They impose loads that tend t o vibrate the surface. Depending on i t s struc- tural characteristics, such as geometry and method of construction, the w i l l have a certain dynamic response. This dynamic response surface influences t h e s t r e s s patterns i n the structure which, i n turn, deter- mine the fatigue l i f e .

Analyses have been published (refs. 1 and 2) wherein the phenomena denoted as A i n table I were made use of t o calculate stresses on a simple panel. A knowledge of the noise spectra a t an arbitrary point and the dynamic response t o a uniform load have made it possible t o cal- culate, by spectral techniques, t h e stresses at an arbitrary point on the panel. For more complex structures or inputs o r both, t h i s approach may not be sufficient and it may thus be necessary t o use the quantities denoted as B i n table I f o r the stress analyses. For instance, a knowledge of t h e correlation functions of the acoustic input and the complex dynamic influence coefficients of a panel surface might make it possible t o calculate the s t r e s s distribution over t h e surface.

Thus, it i s seen that the blocks i n table I each represent rather complex phenomena. Detailed analyses of a l l parts of t h i s problem would involve considerable e f f o r t and a r e beyond the scope of t h i s paper. The rest of t h i s paper w i l l deal mainly w i t h the fatigue l i f e of structures exposed t o noise and, i n particular, w i l l compare results of random and discrete frequency fatigue testing. The other parts of the problem are discussed only b r i e f l y .

SYMBOLS nozzle diameter a x i a l distance measured from nozzle e x i t plane power spectral density of noise input mechanical impedance of panel power spectrum of stress i n panel INPUTS ACOUSTIC The ingredient of t h i s problem which differentiates it from other fatigue problems i s the nature of the input function. This can be described b r i e f l y w i t h the aid of figure 1. Shown here are the acoustic inputs f o r various powerplants i n common use. The data shown are t h e noise pressure loads on a surface p a r a l l e l t o the thrust axis of the engine and four e x i t diameters distant from it. (Free space measure- ments were increased by 3 decibels t o adjust them t o conditions at the surface of the w a l l . ) Both the noise pressure levels i n decibels and t h e equivalent noise pressures i n pounds per square foot are given on the v e r t i c a l scale as a function of distance f r o m t h e e x i t nozzle of t the engine. Surface pressure data are given f o r two turbojet engines and one rocket engine. It should be noted t h a t the numbers associated w i t h the coded legend are the pounds of thrust developed by the engine per square foot of nozzle e x i t area. The short s o l i d turbojet curve applies t o t h e J34-WE-22 turbojet engine whereas t h e curve of long dashes applies t o the 557-P-3 engine f o r which free-space data are given i n reference 3 . These two curves i l l u s t r a t e t h e growing severity of t h e problem as the engine performance increases because of t h e increased engine pressure r a t i o . The curve of long-short dashes applies t o a World War I1 rocket engine. It is seen that these pressures are of t h e order of 10 decibels higher than those f o r the 557 turbojet engine.

For rocket engines operating a t higher pressure r a t i o s , there i s some evidence t h a t the acoustic pressure would also tend t o be higher. A l l these engines generate intense noise i n the range of frequencies that is detrimental t o a i r c r a f t structures. For t h e type of random spectra generated by these engines, fatigue damage can occur at overall levels of t h e order of 1 4 0 decibels or higher. The amount of damage incurred a t any given level, of course, is a function of the (1) detail design of t h e structure, (2) t h e length of exposure t o t h e noise, and, also, ( 3 ) t h e spectrum of t h e noise.

DYNAMTC RESPONSE The importance of t h e noise spectrum with r e l a t i o n t o the dynamic response of a given structure i s i l l u s t r a t e d by the diagrams of figure 2.

Conditions a r e defined f o r t e s t s of flat panels exposed t o discrete f r e - quency noise from a s i r e n and t o random noise from a j e t .

The input spectra of figure 2 are related t o the s t r e s s spectra by t h e panel admittance. It can be seen that the noise from the s i r e n w a s contained largely i n the fundamental frequency, t h e harmonics being f e w i n number and r e l a t i v e l y weak. For these t e s t s the s i r e n was tuned u n t i l t h e fundamental frequency coincided w i t h t h e first natural mode of the panel. As a result nearly a l l t h e energy accepted by the panel i s i n its first mode. A panel being excited by t h e broad-band spectrum of the j e t , on t h e other hand, responds i n some degree t o a l l frequencies.

It can be seen from an inspection of the figure that a panel w i l l accept essentially a l l t h e energy available from t h e siren whereas a large p a r t of the energy available from the j e t is not accepted. For these p a r t i c u l a r tests, the stress developed by a discrete-type excita- t i o n would be expected t o be greater a t a given overall noise pressure.

FATIGUE LIFE .

Effects of Overall Noise Level Some fatigue r e s u l t s obtained f o r panels exposed t o both of these Fatigue l i f e as a function of types of input are given i n figure 3 .

the overall noise l e v e l is shown f o r an O.032-inch gage flat panel 1 1 inches by 1.3 inches mounted over a rectangular cutout i n a r i g i d w a s attached by small round head b o l t s tightened t o frame. The panel This configuration w a s chosen f o r the reason a predetermined torque.

that it f a c i l i t a t e d assembly and disassembly of models while stress con- centrations similar t o those i n a riveted structure were retained. For the solid points which represent fatigue data obtained w i t h the siren, the curve has been sketched i n through the available points t o indicate a general trend of the data. Fatigue l i f e i s very strongly dependent on the level of noise excitation, since it varies from under a minute t o several hours i n the noise-level range of t h e t e s t s .

Attention is called particularly t o the open points which are data obtained w i t h the j e t . These data f a l l generally t o the right of the curve i n figure 3 ; thus, a longer fatigue l i f e i s indicated. This d i f - ference i n fatigue l i f e is due i n part t o the f a c t that the panel has a higher root-mean-square s t r e s s l e v e l when excited by the s i r e n for a given overall noise l e v e l than when excited by the air jet.

Effects of Method of Mounting During the discrete frequency tests w i t h these simple panels, t h e opportunity w a s taken t o change the manner of mounting t o evaluate pos- sible effects on fatigue l i f e . These mounting configurations are shown schematically i n figure 4 along with some of the test results i n bar graph form. For a l l the mountings, t h e gage and s i z e of panel were con- s t a n t and the input noise levels were also constant. The basic configu- ration A is the same as that f o r which data w e r e presented i n figure 3.

Failures i n the skin panel occurred first near the b o l t heads and the average fatigue l i f e $or t h i s configuration i s used as a reference i n the figure.

Configuration B i s t h e same as configuration A except that a layer of bonding material is placed between the panel and the r i g i d frame.

During testing, the panel first peeled away from the bonding and then f a i l u r e i n the skin occurred near the bolt heads. This configuration lasted on the average about 50 percent longer than configuration A.

A n attempt w a s made t o eliminate peeling by bonding both sides and clamping t h e panel between two r i g i d surfaces as i n configuration C.

I n this case failure occurred at the edge of the frame and the average - model lasted twice as lon

4e:. 4

. -.

.

b 0 , . & 0 ) . 0 .

.

. . . .

m . I I I .

I n order t o study the effects of curvature some panel models were rolled t o an 8-foot radius and were fastened f o r t e s t i n g t o a curved r i g i d frame as indicated i n configuration D. Failures were i n i t i a t e d This condition resulted near the b o l t heads as i n configurations A and B.

i n an average l i f e about 15 times as long as f o r configuration A even though the frequency of the stress cycles increased by about 50 percept.

A further increase of fatigue l i f e was obtained by leaving t h e edges of T h i s latter scheme the frame sharp instead of rounding as i n the figure.

instead of a t the caused t h e failures t o occur at t h e edge of the frame bolt head; by so doing t h e fatigue l i f e was doubled as indicated by the bar of dashed lines. Configuration E i s the same as configuration D except that tests were made w i t h a pressure d i f f e r e n t i a l of 6 pounds per square inch across t h e panel. This high internal pressure caused t h e first panel frequency t o nearly treble and the fatigue l i f e w a s greatly increased as shown, i n s p i t e of t h e much faster rate of application of stress cycles.

A s a matter of i n t e r e s t a 0.064-inch-gage panel was t e s t e d i n a con- figuration similar t o configuration A f o r comparison. It w a s found that doubling the gage thickness of t h e panel increased i t s fatigue l i f e t o about twenty times that of configuration A. This finding w a s confirmed i n both the jet and s i r e n tests.

A Limited number of other tests have been made on larger and more complex panels. I n a l l cases failures came first i n the s t i f f e n e r ele- ments; thus, the importance of detail design of t h e panel supporting structure is emphasized. It w a s also noted that crack growth w a s mark- edly more rapid i n bonded structures than i n riveted structures.

Comparison of Random and Discrete Frequency Tests F l a t panels.- The rest of t h e paper w i l l deal w i t h comparisons of fatigue l i f e under discrete and random loading a t the same root-mean- square (RMS) s t r e s s levels. The r e s u l t s of flat-panel tests are given i n figure 5. Time t o failure i n hours is shown f o r various root-mean- square stress levels f o r an 0.032-inch-gage panel. The s o l i d points were obtained by means of discrete frequency excitation from a siren whereas t h e open points were obtained with random excitation from an air jet. The curve is a least-square curve through t h e s o l i d points.

It can be seen that at a given root-mean-square stress level, failure occurs i n a shorter time when the panels are excited by the random jet noise. The f a c t that the random noise of the jet i s more destructive may r e s u l t f r o m t h e f a c t that some o f t h e peak stress responses are sev- eral times as great f o r a given root-mean-square value'as they are f o r the constant-level s i r e n tests. This phenomenon is particularly notice- able a t t h e lower stress levels where the differences i n fatigue l i f e tend t o be t h e greatest and the panel damping i s r e l a t i v e l y low. A t

a # "<$

higher stress levels the panel damping i s greater and the differences i n fatigue l i f e tend t o be smaller.

Cantilever beams.- Similar fatigue t e s t s have been made f o r notched cantilever beams at various stress levels f o r both random- and discrete- type inputs. A schematic diagram of the model along with some of the test r e s u l t s are i l l u s t r a t e d i n figure 6.

Here again the time t o failure i n hours is shown at various root- mean-square stress levels f o r t h e beams tested i n bending. The speci-

mens were 3 inches long, 1 inch wide, and 1/4 inch deep with 3/16-inch

notches located 1/2 inch from the root. The open points were obtained by means of an amplified tape recording of jet noise fed i n t o a shaker attached t o the t i p . The solid points were obtained by applying a sinus- oidal load at the t i p i n a Sonntag bending fatigue machine. There is a tendency i n these t e s t s also f o r the random load t o be relatively less destructive a t the higher s t r e s s levels and more destructive a t the lower s t r e s s levels than the sinusoidal load. For the data of figures 5 and 6 the strain-gage locations were arbitrary and hence the root-mean- square stresses shown i n figures 5 and 6 are not necessarily comparable.

A theoretical prediction of the time t o failure f o r the random loading is given by the s o l i d curve. This theory is essentially one given by Miles (ref. 1) and is based on Miner's rule of l i n e a r accumur l a t i o n of damage. It can be seen that t h i s theoretical curve fits the data f a i r l y well at low stress levels but is very conservative at the higher stress levels.

CONCLUDING R E M A R K S The problem of acoustic fatigue of a i r c r a f t structures has been discussed with particular emphasis on a comparison of t h e fatigue l i f e due t o discrete- and random-type loadings. I n t h i s regard it appears that both the stress l e v e l of t h e t e s t and the type of model are signif- icant; hence, no generalizations can be made at t h i s time. With regard t o increasing the fatigue l i f e , it w a s noted that increased stiffening of a panel due t o curvature and pressure d i f f e r e n t i a l is particularly beneficial.

REFEBENCES 1. Miles, John W.: O n Structural Fatigue Under Random Loading. Jour.

Aero. Sci., vol. 21, no. 11, Nov. 1954, pp. 753-762.

2. Lassiter, Leslie W., Hess, Robert W., and Hubbard, FIarvey H.: An Exper- imental Study of t h e Response of Simple Panels t o Intense Acoustic Loading.

Jour. Aero. Sci., vol. 24, no. 1, Jan. 1957, pp. 19-24, 80.

3 . Howes, Walton L., and Mull, Harold R.: Near Noise Field of a Jet- Engine Exhaust. I - Sound Pressures. NACA TN 3763, 1956.

-1 . .

.

1..

I .

TABLE I ACOUSTIC FATIGUE PROBLEM A. NOISE SPECTRUM AT ARBITRARY POINT ACOUSTIC INPUTS B. CORRELATIONS A. DYNAMIC RESPONSE TO UNIFORM LOAD STRUCTURAL CHARACTER1 STlCS B. DY NAM I C IN F WENCE COE FF IC I E NTS (COMPLEX ) A. STRESS AT ARBITRARY POINT STRESS 8. STRESS DISTRIBUTION OVER SURFACE -..

ACOUSTIC INPUTS

THRUST, AIRCRAFT SURFACE-’ T

LB/SQ FT

I c - x 41d

TURBOJET

--- c

- 2,600

-- 3,800

ROCKET / --- 25,000 ,/’\,,-\-/ I I60 - 40 OVERALL NOISE

j

NOISE c PRESSURE, /--- LEVEL, / LB/SQ FT \

/ i

DECIBELS 150 , I I3

-

/ / f I 1 4 0 - : 4 -4 0 4 8 1 2 1 6 20 AXIAL DISTANCE, x/d Figure 1 INPUT AND RESPONSE CHARACTERISTICS SlREN AIR JET

SPECTRUM INPUT @N~u)l 7

SPECTRUM @$d FREQUENCY FREQUENCY 156 - Y m GAGE 0 8 o O o : *...**'

&*& \ : . e '

- \

'x x " ? B B a O OVERALL NOISE

- am ..'C,.... a&&l %""

o+ LEVEL, DffiIBEW

'-. M

- . - h 0

- 0 LABORATORY AIR JET

, .--SIREN Figure 3 RELATIVE FATIGUE LIFE PANEL GAGE AND SIZE CONSTANT 0.032" ----_---------

3 _ _ _ _ _ _ _ _ _ _ _ 130

DIFFERENTIAL PRESSURE=6 P S I RELATIVE TIME TO FAILURE FATIGUE OF FLAT PANELS 0 AIR JET

0 - SIREN

12,000 8,000 RMS STRESS, P S I t 4,000 0 .01 .I I I O TIME TO FAILURE, HOURS Figure 5 FATIGUE OF NOTCHED CANTILEVER BEAMS FUNDAMENTAL FREQUENCY, 1 1 9 CPS 0 JET NOSE LOAD 0 SINUSOIDAL LOAD

- THEORY

20,000 Q 0 RMS STRESS, PSI I0,OOO

I I I I L I

0 .01 .I I IO 100 TIME TO FAILURE, HOURS Figure 6

FLUTTER AND

BUFFETING

* e 'IIIE USE OF WIND TUNNELS TO PREDICT FLIGHT BUFFET LOADS By Don D. Davis, Jr., and Wilbur B. Huston Langley Aeronautic a1 Laboratory Methods and techniques developed f o r the study of buffeting by use of wind-tunnel models are described. Requirements on model damping and frequency characteristics, the model support system, and the e f f e c t s of wind-tunnel turbulence on buffet tests are outlined. The results are sham of a recent comparison of buffet loads measured on a research air- plane w i t h t h i n unswept wings and on two different models of the airplane i n two different wind tunnels.

INTRODUCTION One objective of buffet research has been t o learn how t o predict flight buffet loads from wind-tunnelmeasurements. A method f o r meeting t h i s objective i s described i n reference 1. Bending-moment measurements were made w i t h e l e c t r i c a l s t r a i n gages mounted near the wing root.

By combining knowledge from two different f i e l d s , those of s t r u c t u r a l beam theory and s t a t i s t i c a l analysis, an equation w a s derived f o r predicting f l i g h t bending moments from the buffet measurements on the model. Results were presented f o r two specific cases, and they were encouraging.

Additional experience has been gained, since the publication of reference 1, with regard t o test techniques and modelrequirements. The the present paper i s t o discuss these factors.

primary purpose of SYMBOLS average chord first-mode generalized lift-curve slope f o r damping component of aerodynamic force due t o wing vibration Mach number velocity

angle of attack #7?

a air density P root-mean-square value of bending moment due t o buffet UM aerodynamic input parameter; parer spectral density, a t % , 1 first-mode resonant frequency, of generalized normal- force coefficient f o r first-mode vibration circular frequency Subscript : MAX maximum DISCUSSION Model Damping Requirement One requirement f o r a buffet model concerns the damping of the buffet vibration. The question that arises is whether the damping i s

aerodynamic, structural, or some combination of the two. mis question

can be answered, i n a given case, by studying the variation of buffet bending moment w i t h air density as is done i n figure 1. I n order t o f a c i l i t a t e comparison between different tests, the density values f o r a particular test have been normalized i n figure 1 b y dividing by the maximum density f o r that test. Similarly, the bending moments f o r 'a particular test have been normalized by dividing by the bending moment a t the maximum density. The bending moment i s herein defined as the root-mean-square value of the vibratory part of the wing-root bending moment; the static bending moment has been removed from the data.

If the damping i s structural, the damping coefficient w i l l be con- s t a n t and the bending moment w i l l be directly proportional t o the exciting force and thus t o the air density. This variation i s shown by the dashed l i n e i n figure 1.

If the damping is aerodynamic, on the other hand, the damping coef- f i c i e n t and the exciting force w i l l both be directly proportional t o the density. By the methods of power spectral analysis, the root-mean-square bending momer;t is found t o be proportional t o the square root of the (See ref. 2.)

density. This variation i s shown by the solid l i n e i n figure 1.

Flight-test data indicate that the damping of the buffet vibration i s primarily aerodynamic. (S ) I n order t o i l l u s t r a t e t h i s point, some flight r e s u l t h circular symbols i n . 0 *.

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o m .

. .

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figure 1.

Such r e s u l t s l e d t o the assumption of aerodynamic damping i n developing the equation of reference 1 f o r scaling buffet bending moments from wind-tunnel models t o full-scale airplanes. The equation i s applic- able, therefore, only when the damping i s primarily aerodynamic f o r the model as w e l l as f o r the airplane.

In order t o determine whether the damping of models actually is aerodynamic, bending-moment data f o r three ordinary force-test models are plotted i n figure 1. Model 1 i s suitable f o r buffet loads tests because the damping i s primarily aerodynamic. For models 2 and 3 , on the other hand, the damping i s largely structural; thus, the scaling equations of reference 1 d o not apply t o these m o d e l s . The model data shown i n figure 1 represent two extremes, and anything between these extremes is possible.

If the model is tested i n a variable-density wind tunnel, a p l o t l i k e figure 1 provides a means f o r learning, a f t e r the t e s t i s finished, whether the model w a s suitable f o r buffet loads tests. It would be better, of course, t o know t h i s before making the test. As a guide f o r t h a t purpose, the following procedure i s suggested. With tabulated f l u t t e r coefficients, make a rough estimate of the aerodynamic damping.

In order t o approximate the structural damping, measure the damping of the wing i n a s t i l l - a i r vibration test. If the measured s t r u c t u r a l damping i s as l o w as 1/10 of the estimated aerodynamic damping, the model w i l l probably be satisfactory. Experience i n transonic tunnels operating a t atmospheric stagnation pressure has shown t h a t solid m e t a l wings are generally satisfactory if the wing-fuselage j o i n t s me t i g h t l y clamped. Difficulty has been experienced when insufficient j o i n t f i x i t y resulted i n high s t r u c t u r a l damping and when tests w e r e run a t such l o w dynamic pressures that the aerodynamic damping w a s too low.

Model Frequency Requirements Another requirement for the buffet m o d e l i s that the vibratory mode shape and reduced resonant frequency be the same as those f o r the airplane.

O f these two quantities, simulation of the resonant frequency probably is the more important. The power spectral density of the wing-root bending moment i s plotted as a function of the reduced frequency i n figure 2 f o r an airplane and for a 0.075-scale model of the airplane a t the same Mach nmiber. The vibration of the airplane wing i s concentrated i n the first symnetrical bending mode. This i s also the case f o r the model; further- more, the reduced resonant frequency f o r the m c d e l i s about the same as that f o r the airplane. This comparison i s interesting because the model has a standard solid-metal force-test wing. I n the design of t h i s model, there was no consideration whatever given t o the resonant frequencies of the wing and yet frequency simulation of the first symmetrical bending mode w a s obtained. This seems t o be a normal characteristic of solid- n e t a l models of fighter-t east i n the absence of external stores); thus, the simulation of wing resonant frequency f o r such airplanes presents no serious model design problems.

I n the case of the tail, however, the situation i s very different.

The power spectral density of the bending moment a t the root of a hori- zontal s t a b i l i z e r i s plotted as a function of the reduced frequency i n figure 3 f o r an airplane and for a 0.25-scale model of the airplane.

Again there w a s no attempt i n the model design t o simulate the frequency characteristics of the airplane. For the airplane, the most prominent mode i s associated with fuselage torsion but t h i s mode i s hardly v i s i b l e on the model, presumably because the model fuselage i s more r i g i d than t h a t of the airplane. Note also that, f o r the model, the frequencies of the various vibration modes are very different from those f o r the airplane. B u f f e t bending moments measured on t h i s model s t a b i l i z e r would probably bear l i t t l e relation t o those measured on the airplane.

It appears then that, although force-test models are usually satisfactory f o r the study of wing buffet loads, the scaling of t a i l buffet loads w i l l require models specially designed f o r t h a t purpose.

Support System The vibration modes of the model may be influenced by the support system. Figure 4 shows power spectrums obtained with two different types of model supports. The spectrum a t the l e f t i s f o r a floor-mounted that w a s tested i n the A m e s semispan model 12-foot pressure tunnel. The predominant mode i s first symmetrical bending as it w a s i n the case of the airplane wing i n figure 2. The spectrum on the r i g h t i s f o r a sting- mounted full-span model.

Two new modes are evident i n t h i s spectrum.

The antisymmetrical bending mode i s actually a wing mode but the other new mode i s essentially a rigid-body r o l l i n g vibration due t o the tor- sional f l e x i b i l i t y of the s t i n g support. This mode has no counterpart i n f l i g h t and therefore should be eliminated before an attempt i s made t o calculate f l i g h t bending moments.

A t present, there are three methods of eliminating the mode due t o The first method i s t o determine the power spectrum the s t i n g support.

and then subtract the response i n t h i s mode. The second method, which i s the same i n principle but less costly i n practice, is t o remove the s t i n g mode with an e l e c t r i c a l filter either a t the t i m e the data are taken or later. For some combinations of model and s t i n g supports, the natural frequency of the s t i n g mode is so close t o t h a t of the symmetrical bending mode t h a t these two methods are not applicable. When these methods cannot be used, the third method can be used. The s t i n g torsion response can be canceled by placing bending-moment gages on both wings and summing the outputs electrically. The dashed l i n e i n the p l o t a t t h e r i g h t of figure 4 shows a spectrum t h a t w a s obtained by t h i s method.

Note, however, t h a t not only the sting torsion mode but also the anti- symmetrical wing mode i s eliminated. The elimination of this antisym- metrical mode would be undesirable i n a case where this mode contributed a large part of the t o t a l wing-root bending moment. Fortunately, however, the contribution of modes higher than the first-symmetrical bending mode i s small for the fighter airplanes f o r which flight spectra are available.

Wind-Tunnel Turbulence Experience has shown t h a t wind-tunnel turbulence sometimes compli- cates the r e s u l t s of buffet t e s t s . An example i s i l l u s t r a t e d i n f i g - ure 5. The ordinate for the curves i n this figure is a parameter t h a t i s proportional t o the root-mean-square value of the wing-root bending moment. The numerator i s associated w i t h the input force t h a t causes the wing t o buffet and the denominator w i t h the damping force t h a t This parameter i s plotted limits the amplitude of the buffet vibration.

as a function of the angle of attack f o r three different Mach numbers.

A t a Mach number of 0.4, the f l a t portion of the curve at low angles of attack i s the response due t o wind-tunnel turbulence. The point where the curve r i s e s steeply i s considered t o be the buffet boundary. A t Mach numbers of 0.7 and 0.85, the response t o turbulence is much higher.

This increase has two effects. First, the turbulence tends t o obsc&e the buffet boundary, as is the case at a Mach number of 0.7. In addi- tion, the bending moments are higher because of the contribution of the wind-tunnel turbulence. The manner i n which the turbulence and buffet inputs add t o give the t o t a l is not yet completely understood. Any correction of the measured t o t a l f o r the effects of turbulence depends upon the frequency distribution of t h i s input and on the degree of corre- lation between the t w o inputs, factors t h a t have not yet been determined.

A subtraction process i s indicated schematically on t h e curve f o r a Mach number of 0.85 where the buffet response i s considered t o be only the p a r t labeled "buffeting." Note t h a t the r e s u l t s i n figure 5 t h a t were chosen for purposes of i l l u s t r a t i o n are f o r a particularly bad case.

The effects of turbulence are not always s o severe as shown here. O n the other hand, it i s important t o realize that because the wing i s a resonant system with very l i t t l e damping, a small exciting force due t o turbulence may cause a sizable response.

For buffet t e s t s , the important quantity is not the overallturbu- lence l e v e l i n the wind tunnel but rather the power spectral density of the turbulence a t the resonant frequency of the wing. There i s l i t t l e information available on the turbulence spectra of various wind tunnels i n the frequency range of i n t e r e s t here. Wind-tunnel turbulence has been investigated rather extensively i n connection with studies of boundary-layer transition. The frequencies of i n t e r e s t f o r boundary- layer transition, however, are much higher than the buffet frequencies.

- - c i c . . 0 . .*

. * s ... * ? . . .

. . 7 . 1 a - - - -

At the present time, therefore, the best way to learn whether a given tunnel is suitable for buffet tests probably is to make such a test.

The effect of turbulence on buffet measurements is not a problem for the wind tunnels only. On occasion, turbulence has interfered with buffet tests of both rocket-propelled free-flight models and airplanes.

In these cases, the solution to the problem is to avoid atmospheric turbulence when making buffet tests.

Instrumentation With regard to instrumentation, tape recordings of the wing strain- gage output have been particularly useful. Power spectrums are obtained by recording the strain-gage output on magnetic tape and later analyzing

the tape records (ref. 4 ) . Root-mean-square bending-moment values can

be obtained from the tape record or they can be obtained at the time of the test by means of a thermocouple meter, which is sensitive to the mean-square value of a random electrical current. The Ames Aeronautical Laboratory has developed an instrument that measures the peak buffet loads in successive 10-second intervals over a period of several minutes.

The instrument is basically a condenser charged through a diode that conducts current only during a peak that is higher than any previous peak. Thus, the charge on the condenser is a measure of the highest peak. Either peak or root-mean-square measurements can be used to study buffeting. The measured peak values in the tests at the Ames laboratory were two to four times higher than the root-mean-square values and thus were about what would be expected for a Gaussian random process.

Additional Results Bearing on Validity of !Theory The experimental technique that is discussed in this paper is based on the assumption that buffeting is essentially a Gaussian random process and that the response of the wing can be treated as the linear response of a lightly damped single-degree-of-freedom elastic system. A recent analysis of flight-test data (ref. 5) has shown that wing buffet loads do indeed exhibit the characteristics of a Gaussian random process. For a representative stall maneuver, the loads are normally distributed, and the probability that a load peak will exceed a given level is in agree- For a repre- ment with the theoretical results obtained in reference 6 .

sentative pull-up into buffeting in the shock regime, the buffet intensity appears to vary linearly with penetration beyond the buffet boundary.

The loads under maneuvering conditions are therefore not stationary and By means of a simple linear transformation, how- are thus non-Gaussian.

ever, the buffet loads in maneuvering flight can be treated as a Gaussian process.

r .

w .* .* ..

. . ..

I .

e m . 8 * . . -, I 8.

Another r e s u l t of theoretical i n t e r e s t has been established by an analysis (unpublished) of parer spectrums of wing bending moments It w a s found t h a t the relationship of the a wind tunnel.

obtained i n maximum value of the spectrum, the band width of the spectrum a t the 1/2-parer points, and the integrated mean-square bending moment i s the same f o r the wing during buffeting as f o r a lightly damped linear single- degree-of-freedom system. This result is important not only as v e r i f i - cation of a basic assumption but also because it implies that the magni- tude of the wing damping forces can be evaluated, a t l e a s t i n principle, from the parer spectrum.

Comparison of Flight and Wind-Tunnel Results Wing-root bending moments during buffet have been measured i n flight on a thin, unswept wing, research airplane (X-1E). They have also been measured on two models of different s i z e s i n two different wind tunnels. The wind-tunnel results have been scaled up t o f l i g h t conditions by using the equation presented i n reference 1. The values obtained are compared with the flight bending moments i n figure 6. When the f a c t that buffeting i s inherently a random process i s considered, the agreement between flight and wind-tunnel results shown i n t h i s f i g - ure i s regarded as satisfactory. Apparently, flight buffet loads can be estimated from wind-tunnel results, a t least f o r simple wings. It follows from t h i s r e s u l t that wind tunnels can a l s o be used t o study the e f f e c t of airplane modifications on the buffet loads.

CONCLUDING REMARKS A description has been given of recent developments i n the appli- cation of a method f o r predicting f l t t buffet loads from wind-tunnel

modelmeasurements. Model requiremen !? s have been outlined f o r proper

scaling of the damping characteristics and vibration frequencies.

These requirements appear t o be easily met f o r wing loads, but special care w i l l be needed i n the construction of models f o r the study of t a i l loads.

‘The influence of the m o d e l support system and of the turbulence the wind tunnel on test results has been discussed, and the l e v e l i n instrumentation f o r wind-tunnel studies has been described. A comparison has been made of the wing buffet loads on a research airplane with t h i n that were measured on two models of the air- unswept wings and the loads plane b u i l t t o different scales and tested i n different wind tunnels.

The comparison indicates t h a t flight wing loads can be estimated from wind-tunnel results; thus, wind tunnels could also be used t o study the effects of airplane modifications on buffet loads.

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...

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REFERENCES 1. Huston, Wilber B., Rainey, A. Gerald, and Baker, !Thomas F.: A Study of the Correlation Between Flight and Wind-Tunnel Buffeting Loads.

NACA RM L55El6b, 1955.

2. Liepmann, E. W.: Parameters f o r U s e i n Buffeting Flight Tests.

Rep. No. SM-14631, Douglas Aircraft Co., Inc., Jan. 3, 1953.

3. Huston, Wilber B., and Skopinski, T. H. : Measurement and Analysis NACA of Wing and T a i l Buffeting Loads on a Fighter Airplane.

Rep. 1219, 1955. (Supersedes NACA TN 3080.)

4. Smith, Francis B.: Analog Equipment f o r Processing Randomly Fluc- tuating D a t a . Aero. Eng. Rev., vol. 14, no. 5, M a y 1955, pp. 113-119.

5. Huston, Wilber B., and Skopinski, T. H. : Probability and Frequency Characteristics of Some Flight B u f f e t Loads. NACA T N 3733, 1956.

6. Rice, S. 0.: Mathematical Analysis of Random Noise. Pts. I and 11.

B e l l Syst. Tech. Jour., vol. X X I I I , no. 3, July 1944, pp. 282-332; Pts. I11 and IV, vol. XXIV, no. 1, Jan. 1945, pp. 46-136.

DAMRNG AERODYNAMIC OR STRUCTURAL I AERODYNAMIC .5 a M (P) 0 AIRPLANE ffM (PMAX) 0 MODEL I 0 MODEL 2

/

A MODEL 3 STRUCTURAL

A DAMPING

(rMaP) .I L l I I I 0 . I .2 .5 I PPMAX Figure 1 MODEL DESIGN SI MULATlON OF WING NATURAL FREQUENCY AIRPLANE SYMMETRICAL BENDING P O W E R SPECTRAL

DENSITY , 0.075-SCALE MODEL

BENDING 0 .2 4 .6 .0 REDUCED FREQUENCY ,- Figure 2 5 . .' - .,.

MODEL DESIGN DISSIMILARITY OF TAIL NATURAL FREQUENCIES AIRPLANE I TORSION STABILIZER BENDING BENDING POWER I J SPECTRAL 0 DENSITY

I

r STABILIZER

BENDING FUSELAGE SUPPORT SYSTEM EFFECT ON MODEL BUFFET MODES

-

RIGHT WING

----

SUMMATION FLOOR- MOUNTED STING-MOUNTED SEMISPAN MODEL FULL-SPAN MODEL FIRST BENDING SECOND FREQUENCY FREQUENCY

4s2 Figure 4

h -4 J TURBULENCE COMPLICATES BUFFET TESTS 1 2 XIO-3

r

M = 0.4 I V ( % ) F M = 0.7 M = 0.85 BUFFETING TURBULENCE 0 4 8 1 2 1 6 0 4 8 1 2 1 6 a,cm . Q, DEG Figure 5 BUFFET LOAD FLIGHT AND WIND-TUNNEL COMPARISON FOR X-IE FLIGHT 30 xi03 0 0.25- SCALE MODEL

0 0.075 - SCALE MODEL

M -0.7

25 c

20 1

U BUFFET 0 BENDING 15

-

M m O . 8 U

YE? 0.0, . 0

0 0

-

1 0 0 0 0 0 5 - .

I I - I I

-

a, DEG Figure 6 . .b ..

.. .. . .

. . . I . ... 8

ON BUFFETING EFFECTS O F WING AND FUSELAGE MODIFICATIONS B. Sutton and J. Walter Lautenberger, Jr.

By Fred Ames Aeronautical Laboratory INTRODUCTION The performance of many high-speed a i r c r a f t has been adversely affected by shock-induced separation encountered at moderate l i f t coef- f i c i e n t s a t high subsonic speeds. This phenomenon i s usually evidenced by severe decreases i n longitudinal s t a b i l i t y , large increases i n drag, and heavy buffeting. Much research has been directed toward the a l l e - viation of the s t a b i l i t y and drag difficulties, but l i t t l e i s known about the effects on buffeting of such s t a b i l i t y and d r a g "fixes" as wing fences, wing leading- and trailing-edge modifications, and fuselage indentations. This paper presents some results of investigations i n the Langley 8-foot transonic pressure tunnel and i n the Ames 12-foot pressure tunnel t o obtain an indication of the effects of these devices on buffeting .

DISCUSSION The t e s t s i n the 8-foot tunnel were conducted with a model of a modified delta-wing airplane and some typical r e s u l t s of the t e s t s i n Fluctuating wing bending moments t h i s tunnel are shown i n figure 1.

measured a t the wing root of the model were reduced t o show the rela- t i v e buffeting input due t o the aerodynamics of several model configu- rations. The apparent buffeting input a t low l i f t coefficients i s believed t o be due t o wind-tunnel turbulence. Test data are shown f o r a Mach number of 0.97, which corresponds t o a f l i g h t speed a t which buffeting is c r i t i c a l .

Figure 1 shows one-half of the sting-mounted full-span model used f o r the investigation. The heavy solid l i n e i s the outline of the basic configuration. The buffet inputs of the wing as a function of the lift coefficient are shown i n t h i s figure. When conical camber was added t o the leading edge of the wing, the buffet intensity at the higher l i f t coefficients w a s reduced considerably. By further adding a swept t r a i l i n g edge t o the wing and a bump t o the body i n order t o improve the area dis- tribution of the airplane, the buffet intensity was s t i l l further reduced.

These modifications, which were designed t o improve the airplane perform- ance, thus were quite effective also i n reducing the buffet loads at transonic speeds.

e..

..e 4 P The investigation in the 12-foot tunnel was made with a wing- fuselage-tail combination having a relatively thick sweptback wing with a high aspect ratio. This combination was typical of transport and bomber airplanes designed for long-range flight at high subsonic speeds.

Reference 1 describes the semispan-model technique and the instrumenta- tion eqloyed in the investigation of buffeting in the 12-foot tunnel.

Figures 2 and 3 illustrate the semispan-model setup and the model con- figurations used in this wind tunnel, respectively. Included in the investigation were studies of the effect of wing fences, a leading-edge extension, and a fuselage indentation of the Kuchemann type. The wing used in this investigation was twisted and cambered and had NACA 6 4 ~ - series thickness distributions. A strain-gage bridge was mounted at the wing root to measure fluctuations of wing bending moment due to buf- feting. The bridge output was fed into an electronic recorder-analyzer.

This apparatus permitted the convenient recording and rapid analysis of data samples corresponding to several thousand fluctuations of bending moment and provided the maximum peak intensities as well as the usually measured root-mean-square intensities (refs. 2 and 3 ) of the fluctuating wing bending moments.

It has not been possible to deduce from the buffet outputs meas- ured in the 12-foot tunnel the buffet inputs due to the model aerody- namics as was the case with the results obtained in the 8-foot tunnel.

Instead, the measured fluctuating bending moments have been converted to approximate values of fluctuating normal-force coefficient mN.

Because the dynamic characteristics of the model were essentially con- stant for the various configurations tested, these results do indicate relative buffeting .

The effects of wing fences and a leading-edge extension on the buf- feting of the wing-fuselage-tail combination are shown in figures 4 and

5 . Figure 4 shows the variation of X N , ~ with lift coefficient at

a Mach number of 0.86, and figure 5 shows boundaries of lift coefficient and Mach number for heavy buffeting.

The intensity chosen for heavy buffeting, A C N , ~ = W.08, is strictly arbitrary and is intended only to indicate buffeting of rela- tively heavy degree. The boundaries shown were determined from maximum buffet intensities; however, boundaries from comparable root-mean-square intensities were very similar. The test results indiEated that, at most Mach numbers, the wing fences generally reduced the erratic variation of buffet intensity with increasing lift coefficient and reduced buffet intensities at moderate and high lift coefficients. The wing leading- 4 and 5 ) was relatively ineffective as a means of edge extension (figs.

reducing buffeting and, for some test conditions, increased buffeting.

Figure 5 also shows that the fences greatly reduced the adverse effects

The combination was also of increasing Mach number on heavy buffeting.

tested with a fuselage indentation which was designed to reduce the wing-fuselage interference effects. These results are not shown but they indicate that the fuselage indentation reduced buffeting for some test conditions; however, these effects were small compared with the improvements derived from the use of wing fences.

The lift coefficients for drag divergence and for pitching-moment- curve inflection or pitch-up are considered important design parameters in analyzing the static longitudinal characteristics of airplanes. These

parameters are compared in figure 6 with boundaries of Mach number and

lift coefficient for light buffeting and the previously described bound- aries for heavy buffeting. The intensity selected for light buffeting, A C N , ~ = C0.02, approximates the boundary for buffet onset. At the higher Mach numbers, the lift coefficients for drag divergence are close to the boundaries for buffet onset for both the model with and without wing fences. However, heavy buffeting was indicated at lift coefficients considerably lower than those for pitch-up. This is significant, inas- much as the occurrence of heavy buffeting at these comparatively low lift coefficients indicates that the usable range of lift coefficients is probably much less than the lift-coefficient range for stability.

Wing fences did much to lessen this difference, but heavy buffeting was still indicated at lift coefficients which were appreciably lower than those for pitch-up.

SuMMeRY OF RESULTS The results of these investigations may be swmnarized as follows: 1 . Many modifications intended to improve drag and stability char- acteristics are also effective buffet alleviators.

2. For a model of a modified delta-wing airplane, a conically cam- bered leading edge, a swept trailing edge, and body bumps to improve area distribution all reduced buffeting.

3 . For sweptback wings having high aspect ratios, fences were a To a much lesser degree, very effective means of reducing buffeting.

a Kuchemann fuselage indentation also reduced buffeting. A wing leading- edge extension was ineffective as a means of alleviating buffeting and, for some test conditions, increased the buffeting.

4. At high subsonic speeds for sweptback wings having high aspect ratios, the lift-coefficient boundaries for buffeting onset are close to the lift-coefficient boundaries for drag divergence; however, heavy buffeting at these speeds usually occurred at lift coefficients which were considerably lower than the lift coefficients for pitch-up.

I REFERENCES 1. Davis, Don D., Jr., and Huston, Wilber B.: The Use of Wind Tunnels To Predict Buff e t Loads.

(Prospective NACA paper. ) 2 . Polentz, Perry P., Page, W i l l i a m A., and Levy, Lionel L., Jr.: The Unsteady Normal-Force Characteristics of Selected NACA Profiles at High Subsonic Mach Numbers. NACA RM A33CO2, 1933.

3 . Huston, Wilber B., Rainey, A. Gerald, and Baker, Thomas F. : A Study of the Correlation Between Flight and Wind-Tunnel Buffeting Loads.

NACA RM LZE16b, 1953.

EFFECTS OF MODIFICATIONS M-0.95 v; o BASIC MODEL 0 L.E. CAMBER 0 L.E. CAMBER + SWEPT T.E. t FUSELAGE BUMP BUFFET INPUT A m 0 “ 0 ” -2 0 .2 .4 .6 .8 GL Figure 1 GENERAL ARRANGEMENT BASIC FUSELAGE ----- INDENTED FUSELAGE 54.61 ‘I TUNNEL FLOOR Figure 2

* ” 488

WING VARIABLES A= 4 0 ' A = 7.0 / TYPICAL FENCE CATIANC FENCES ACN, MAX 0 .2 .4 .6 .8 I .o CL Figure 4 3G EFFECTS OF WING MODIFICATIONS ACN, MAX 20.08

-

1 . 0

J- +FENCES

. 8 - - . 6 CL - \ . 4

*2 t

L L I I I I 0 . 6 . 7 .8 .9 1 . 0 M Figure 5 COMPARISON OF BUFFET BOUNDARIES WITH STATIC LONGlTUDlNAL PARAMETERS ' 1 . 0 .8 .6 GL (LIGHT BUFFET) - .4

-

.2

1 FENCES OFF '\ FENCES ON -\

I I I I I L I I I I 1 0 . 6 .7 .8 .9 I .o . 6 .7 .8 .9 1 . 0 M M 0 .

TH!IORETICAL AND EXPERIMENTAL INVESTIGATIONS OF DELTA-WING VIBRATIONS By Edwin T. Kruszewski, Eldon .E. Kordes, and Deene J. Weidman Langley Aeronautical Laboratory SUMMARY The results of some theoretical and experimental investigations of delta-wing vibrations are discussed.

Nodal-line patterns and frequencies of a 45' built-up thin-skin delta-wing specimen obtained experimentally are compared with those cal-

culated by two analytical methods - the idealized-structure type of

method as described by Levy and EL limited-deformation type of method proposed by Stein and Sanders. It is shown that when the effects of transverse shear are included into the Levy approach the agreement between calculated and experimental frequencies is exceptionally good.

Experimental nodal-line patterns and frequencies for a 60° thick- skin delta wing are also shown.

INTRODUCTION The prediction of the vibrational characteristics of aircraft struc- tures is a problem of importance to the designer of high-speed aircraft.

As was discuksed in reference 1, methods of predicting modes and fre- quencies for the large-apect-ratio box-beam type of structure are very successful. However, for low-aspect-ratio or delta wings, the problem is still of particular concern because of the analytical difficulties involved in predicting their stiffness characteristics.

An experimental investigation of the modes and frequencies of two large-scale built-up delta-wing specimens has recently been completed.

The results of this experimental investigation are being used to evalu- ate theoretical methods of deflectional analysis. This paper will deal with the findings of this evaluation.

.

.. .

DISCUSSION One of the delta-wing specimens used i n the experimental investiga- t i o n is shown i n figure 1. It i s a built-up large-scale 45' delta with a span of 18 f e e t 8 inches, a midchord of 8 feet, and a uniform carry- through section of 2 f e e t 8 inches. The wing is uniform i n depth i n the chordwise direction but varies i n depth in the spanwise direction from

5-i- 1 inches a t the carry-through section t o 1 2 inches at the t i p . The

covers are made up of a t h i n sheet stiffened by spanwise stringers. I n order t o f a c i l i t a t e construction, the stringers w e r e placed on the out- side of the covers. The internal construction consisted of four spanwise spars and a bent leading-edge spar with l i g h t streamwise r i b s spaced a t close intervals. A detailed description of the s t i f f n e s s properties and weight distribution of the specimen is given i n reference 2.

A general view of the vibration test setup i s shown i n figure 2.

The delta wing i s hung v e r t i c a l l y by flexible a i r c r a f t cables from the gallows shown i n the figure. The specimen w a s vibrated i n the horizon- t a l direction so t h a t the wing could be considered t o be essentially free-free. The vibrations were produced by four electromagnetic shakers (three of which can be seen i n f i g . 2). The mode shapes were obtained from pickups mounted at the intersection of t h e spars and r i b s while the node-line locations were determined with a portable probe pickup.

A t o t a l of 10 natural modes of vibration was established, f i v e symmetrical and f i v e antisymmetrical, with frequencies ranging from 43 t o 216 cycles per second. Detailed descriptions of the vibration tests a r e given i n reference 2.

I n recent years a variety of methods of load deflectional analysis f o r low-aspect-ratio and d e l t a wings has been proposed. (See, f o r exam- ple, r e f s . 3 t o 6.) Two of these methods have been used f o r calculating the modes and frequencies of t h i s specimen.

One w a s described by Levy i n reference 3 and the other w a s developed by Stein and Sanders i n ref- erence 4. Although both of these methods were discussed i n d e t a i l i n references 3 and 4, a recapitulation i s thought t o be worthwhile. Both of the methods are an influence-coefficient type of procedure; that is, the vibrational problem i s set up through the use of s t a t i c influence coefficients and the i n e r t i a l characteristics of the structure. Further- more, both methods neglect the effects of transverse shear.

The essential features of t h e two methods a r e shown schematically i n figure 3 . The Levy method deals with a simplified structure but allows arbitrary deflections of that structure. On the other hand, the Stein-Sanders method analyzes the actual structure but r e s t r i c t s the allowable deflection shape.

c 63- hd4 3 the actual Consider first the Levy method. A s shown i n figure and torque wing is idealized i n t o a system of interconnecting beams boxes. A l l the spanwise normal-stress-carrying material of the covers, both sheet and stringers, i s concentrated i n t o t h e spars of t h e ideal- ized wing while a l l the chordwise normal-stress-carrying material i s concentrated into the ribs. The shear-carrying capacity of the cover sheets i s accounted f o r by torsion boxes i n the spar-rib c e l l s .

The s t i f f n e s s influence coefficients f o r each component part of the idealized structure, t h a t is, the spars, ribs, and torsion boxes, are superimposed t o yield the s t i f f n e s s influence coefficients of the com- p l e t e structure. The f l e x i b i l i t y influence coefficients are then obtained directly by inversion. Note that because of the nature of t h e idealiza- t i o n used, the Levy method i s intended t o be applied primarily t o thin- skin structures, such as the particular 4 5 O delta-wing specimen used i n the experimental investigation.

The Stein-Sanders method deals w i t h the deflections of the neutral surface of the actual w i n g . It i s assumed that the chordwise variation of the deflection w is parabolic and can be expressed i n t h e form shown

i n figure 3 . I n t h i s case Id,, gl, and g2 give the spanwise variation

of the deflection, slope, and chordwise curvature at t h e t r a i l i n g edge.

Since the effects of transverse shear are neglected, t h e distortions of the various elements i n the wing can be expressed .in terms of the 6 ' s .

Further by taking a number of stations along the wing and by going through a straightforward calculation, at the various the v a h e s of the 6 ' s stations can be expressed i n terms of the loading at those stations.

Since the Stein-Sanders method deals w i t h the a c t u a l structure, it should handle a thick-skin wing as well as a thin-skin w i n g . However, the r e s t r i c t i o n t o parabolic deflections i n the chordwise direction may lead t o serious errors unless the center section i s very stiff against chordwise bending.

The comparisons of t h e r e s u l t s of these two theoretical solutions and those obtained from the experimental investigation are shown i n

figure 4. I n t h i s figure the nodal-line patterns and frequencies a r e

shown for the first f i v e symmetrical modes.

A s can be seen, the nodal-line patterns from the Stein-Sanders method agree quite w e l l with the ones obtained experimentally. The frequency agreement, however, is poor; t h e errors ranging from 7 per- cent i n the first mode t o 38 percent i n the f i f t h mode. On the other hand, the frequency agreement i n the Levy method is much better. The largest error i n the first four modes (which occurs i n the t h i r d mode) i s only 7 1 percent while the error i n the f i f t h mode i s 20 percent.

Some of the errors in the Stein-Sanders method are undoubtedly due to the assumption of parabolic chordwise deformation. This particular specimen had no extra chordwise stiffening in the center of the wing, such as would be furnished by a fuselage, for example. On the other hand, as previously noted, the Levy approach should be applicable to this specimen because of its relatively thin covers. Therefore, it is not too surprising that the Levy method gives better results.

Although the Levy method does give better results, the results are still somewhat unsatisfactory, especially for the fifth mode. For this reason, an investigation of the influence of transverse shear, which was neglected in the preceding calculations, was undertaken. This investi- gation dealt solely with the Levy method for which an approximate cor- rection for transverse shear could be made with little additional labor.

The effects of the shear deformations of the webs were simply included in the stiffness-coefficient calculations of the individual spars and ribs, but the torsion-box coefficients were left unchanged.

The results from this recalculation are presented in table I which summarizes the frequencies obtained by the different methods for the first five symmetrical modes. The frequencies as obtained experimentally are tabulated in the first row. The corresponding frequencies as calcu- lated by the Stein-Sanders method and by the Levy method without shear are shown in the second and third rows, respectively. Shown in the fourth row are the results from the Levy method with the effects of trans- verse shear included. The frequencies shown in the last row will be dis- cussed a little later in the paper. A s can be seen, the frequencies cal- culated by the Levy method with shear are in excellent agreement with the experimental frequencies. The largest error, which occurred in the fourth mode, being siightly less than 4 percent. Furthermore, a comparison of the frequencies in the third and fourth rows shows that the effects of transverse shear can be appreciable; the largest effect being in the fifth mode where the inclusion of transverse shear causes an 18-percent reduc- tion in the calculated frequency. The effects of transverse shear on the calculated nodal-line patterns were slight. The changes that did occur, however, tended to improve the comparison between theory and experiment.

Although only the symmetrical modes of vibration have been discussed, the antisymmetrical results indicate the same conclusions; that is, the Levy method predicts the modes and frequencies of thin wings with thin skins such as the 45' delta wing tested with more accuracy than the Stein- Sanders method and, secondly, the effects of transverse shear, which can be appreciable, are easily and accurately incorporated into the Levy method.

Now to digress a little, consider the frequencies shown in the last row of table I, which were calculated from influence coefficients deter- mined experimentally. These resulss are of interest because a popular e I i . e method of obtaining frequencies is t o measure influence coefficients either on a model or a full-scale structure and then t o use these coef- f i c i e n t s i n a vibrational analysis. For the delta-wing specimen, t h i s However, particular method yields r e s u l t s which are a l s o very good.

it must be remembered that the influence coefficients were measured on the actual wing; therefore, no errors due t o modeling a r e involved.

The advantage of the purely analytical method i n the design stage i s obvious.

An investigation of the vibrational characteristics of another delta-wing specimen of entirely different type of construction is being carried out. Although the calculations are not complete, the eqerimen- t a l information obtained should be of interest. A sketch of t h i s speci- men i s shown i n figure 5. It i s a built-up 60° d e l t a wing with a span of 8 feet and a midchord of 7 f e e t 4 inches. A chordwise cross section of the wing is shown i n the figure. The covers are plates with integral waffle-like stiffening and are fastened t o relatively l i g h t spars and r i b s .

The sketches of the experimental nodal lines of t h e 60° d e l t a wing f o r the first s i x modes ( 3 symmetrical and 3 antisymmetrical) are shown i n figure 6. The corresponding natural frequencies are noted at the bottom of each sketch. The frequencies range from 82.5 cycles per sec- ond i n the first mode (first antisymmetrical) t o 207.9 cycles per sec- ond i n the s i x t h mode ( t h i r d antisymmetrical). Only s i x modes of vibra- t i o n were obtained due t o excessive panel vibrations of the covers. It i s also believed that these panel vibrations could be p a r t l y responsible f o r the asymmetry of the nodal-line patterns.

The specimen is representative of thick-skin construction and thus w i l l furnish an acid t e s t f o r the Levy method. Although calculations have not been made, it is believed that the Levy method w i t h correction f o r transverse shear w i l l not predict the frequencies of the 60° d e l t a as w e l l as it predicted the frequencies of the 45' delta wing. The wing principal source of error i n the Levy method is t h e neglect of the influ- ence of the Poisson's r a t i o effect on the interaction of the chordwise and spanwise stresses. This effect, which i s important i n thick-skin wings, cannot be readily included into the Levy approach.

CONCLUSIONS Comparisons of experimental and calculated modes and frequencies of a delta-wing specimen have shown that the idealized-structure type of method as proposed by Levy gives excellent r e s u l t s f o r thin-skin wings provided that corrections are made f o r the effects of transverse shear.

The limitied deformation type of met-hod proposed by Stein and Sanders i s apparently inapplicable t o low-aspect-ratio wings when the center sec- t i o n is not very stiff against chordwise bending.

REFERENCES 1. Hedgepeth, John M . : Summary of Recent Theoretical and Experimental Work On Box-Beam Vibrations. NACA RM L55EOga, 1955.

2. Kordes, Eldon E., Kruszewski, Edwin T., and Weidman, Deene J.: Experi- mental Influence Coefficients and Vibration Modes of a Built-Up 45O Delta-Wing Specimen. NACA TN 3999, 1957. (Prospective NACA paper.)

3 . Levy, Samuel: Structural Analysis and Influence Coefficients f o r Delta W i n g s . Jour. Aero. Sci., vol. 20, no. 7, July 1953, pp. 449-454.

4. Stein, Manuel, and Sanders, J. Lyell, Jr.: A Method f o r Deflection * Analysis of Thin Low-Aspect-Ratio Wings. NACA TN 3640, 1956.

5 . Schuerch, H. U., and Freelin, J. R . : Structural Analysis of a D e l t a Rep. No. zs-182, Convair, Wing Structure by Elastic Coefficients.

May 5 , 1953.

6. Williams, D.: Recent Developments i n the Structural Approach t o Aero- e l a s t i c Problems. Jour. R.A.S., vol. 58, June 1954, pp. 403-428.

TABLE I COMPARISON OF EXPERIMENTAL AND CALCULATED FREQUENCIES

Frequency, cps, for -

Frequency determined by -

1 s t I 2 d I 3d I 4th I 5th

mode mode mode mode mode 88.8 122.8 164.2 Experiment . . . . . . . . . . . . . .

43.3 179 7

Stein-Sanders method . . . . . . . . . 46.4

150.0 202.0 248.0 105.3 Levy method (without shear) . . . . .

132.0 172.0 44.6 216.0 94.7

88.9 120.1 158.0 Levy method (with shear) . . . . . . . k2.8

Experimental influence coefficient . . 43.1

83.0 118.0 146.0 172.0

-

45" DELTA - W I N G SPECIMEN RIBS

- {SPARS

STRINGERS Figure 1 VIBRATION-TEST SETUP OF DELTA-WING SPECIMEN L-88071 Figure 2 T H E O R E T I C A L APPROACHES CONSIDERED

L E V Y STEIN - SANDERS

NODE LINES AND FREQUENCIES FOR 45" DELTA WING z d MODE 1st MODE

-EXPERIMENTAL A (43.3)

- EXP E R I MEN TAL (8 8.8)

----LEVY (44.6) 3 d MODE ---- LEVY (94.7)

---STEIN - SANDERS (105.3) ---STEIN - SANDERS (46.4)

--____

.\. _ - _ . I

- EXPERIMENTAL (122.8) _--- LEVY (132) 5 th MODE 4 t h ---STEIN-SANDERS (150)

A

I , ; _... '\ '

- EXPERIMENTAL(I64.2) -EX PER I M ENTAL ( I 79.7)

--__ LEVY (172) ----LEVY (216) ---STEIN -SANDERS ( 2 4 8 ) STEIN -SANDERS (202) 60" DELTA - W I N G SPECIMEN

t=i

6 "

I 8' 0" I

NODE LINES AND FREQUENCIES OF 60" DELTA WING 1st MODE

A 90.6 CPS

2 d MODE 3 d MODE

A 102.3 CPS A 171.2 CPS

(a) SYMMETRICAL.

1st MODE

A 8 2 . 5 CPS

?id MODE &.,

A 207.9 CPS

143.1 CPS (b) ANTISYMMETRIGAL.

Figure 6

50%

OSCILLATING AIR FORCES AND A PRESENTATION OF SOME FLU'ITER CALCULATIONS By Charles E. Watkins, Donald S. Woolston, and Herbert J. Cunningham Langley Aeronautical Laboratory INTRODUCTION This paper is made up in two parts: the first part being a summary of the present status with regard to the calculation of aerodynamic forces necessary in aeroelastic problems, such as flutter; the second part being a presentation of some recent results of flutter calculations that are compared with experimentally determined results.

SYMBOLS A aspect ratio XtY;S,rl Cartesian coordinates cp velocity potential f ,Fn functions of 5 and q

an constant coefficients

density P M Mach number u) circular frequency circular frequency of first and second vibration modes, 9 J U 2 respectively

v velocity

root chord k

frequency parameter, -

2v amplitude of downwash velocity lift distribution kernel function region of integration amplitude of lift coefficient associated with translatory oscillations amplitude of lift coefficient associated with pitching oscillations amplitude of lift coefficient associated with parabolic chordwise camber oscillations amplitude of lift coefficient associated with parabolic bending oscillations amplitude of moment coefficient associated with transla- tory oscillations amplitude of moment coefficient associated with pitching oscillations phase angle associated with lift due to translatory oscillations phase angle associated with lift due to pitching oscillations phase angle associated with lift due to parabolic chord- wise camber oscillations phase angle associated with lift due to parabolic bending oscillations phase angle associated with moment due to translatory oscillations phase angle associated with moment due to pitching os c illat i ons

5;:3

- . 1 -

*I * * * a * L a.

. * a - - s t i f f n e s s parameter I sweep A trailing-edge sweep AERODYNAMIC FORCES A n aeroelastic problem involves an e l a s t i c structure, such as an A airplane wing or control surface, on which aerodynamic forces a c t .

solution t o such a problem might imply a determination of the deformation that the structure undergoes because of aerodynamic loading or it might imply a determination of conditions under which the structure can vibrate or f l u t t e r i n an undamped mode of oscillation.

The aerodynamic forces referred t o herein a r e not the forces required t o sustain f l i g h t but are superimposed forces generated by deformations o r oscillations that the structure undergoes. This means that air forces and s t r u c t u r a l deformations a r e mutually dependent; that is, the air forces depend on the structural deformations and the structural deforma- tions, i n turn, depend on the air forces. Hence, i n order t o solve an aeroelastic problem, it must first be put i n some form whereby the inter- action between deformations and air forces can be accounted for. This can be done by various considerations, depending, of course, on the prob- lem a t hand.

With f l u t t e r problems the most comon and perhaps most practical way of relating structural deformations and air forces is by resorting t o a so-called modal analysis. This analysis involves an assumption that f l u t - t e r modes of vibration can be s a t i s f a c t o r i l y represented by a superposi- t i o n of a few known supplementary modes, f o r example, modes of t h e type i l l u s t r a t e d i n figure 1. The mode shapes used f o r t h i s i l l u s t r a t i o n a r e the first three natural modes of a tapered configuration that can be seen i n outline i n figure 1. They were determined experimentially by a photo- graphic process and can be seen t o involve considerable camber o r curva- ture i n both the chordwise and spanwise directions.

Before the aerodynamic forces necessary i n t h i s modal approach f o r solving f l u t t e r problems a r e discussed, perhaps a few words regarding i t s applicability a r e i n order. This approach has proved t o be very satisfactory f o r wings or configurations that are so constructed that they behave as simple beams. However, the behavior of thin, low-aspect- r a t i o wings of many current and future airplanes is more l i k e that of a plate than of a beam. With configurations that behave as plates, a modal approach f o r solving f l u t t e r problems becomes somewhat precarious because of the d i f f i c u l t y involved i n choosing mode shapes t h a t w i l l unite satis- The most logical modes t o choose a r e f a c t o r i l y t o yield a f l u t t e r mode.

if available, of the configuration under con- the f r e e vibration modes, sideration. But even with these modes, it appears necessary t o e q l o y considerably more modes f o r plate-like structures than f o r beam-like structures.

The aerodynamic forces necessary i n a modal approach a r e the forces associated with each chosen supplementary mode. It is of interest t o note that the l i t e r a t u r e on unsteady aerodynamics deals mainly with t h i s form of forces, although f o r the most part t h i s l i t e r a t u r e pertains t o special plan forms and very simple mode shapes. I n recent years, how- ever, considerable advancement has been made i n calculating aerodynamic forces f o r arbitrary plan forms and mode shapes f o r both subsonic and supersonic speeds. These advancements w i l l be discussed momentarily but first it is of interest t o review b r i e f l y the pertinent plan forms and give some indication as t o methods by which the aerodynamics f o r unsteady wings has developed. The plan forms for which oscillatory aerodynamic forces are known, roughly i n order of development, are as follows: I. Wings of i n f i n i t e aspect r a t i o (a) Velocity potential (b) Indicial functions 11. Wings of vanishingly small aspect r a t i o (a) Velocity potential 111. Circular p l a t e i n incompressible flow (a) Pressure potential I V . Finite wings for which flow normal t o a l l edges i s supersonic (a) Velocity potential (b) I n d i c i a l functions

( c ) Simple piston theory /k = - 1 W c r - <<

(z M 2 V

V. Rectangular and arrowhead plan forms i n supersonic flow (a) Velocity potential expanded i n powers of frequency V I . Wings of any plan form (a) L i f t distribution (1) Box method (2) Kernel function method These w i l l be dealt with very b r i e f l y i n t h i s paper. A good li ogr aphy and accounting of developments can be found i n reference 1.

The first item i s the wing of infinite aspect r a t i o . The velocity potential, and hence the forces and moments, f o r t h i s wing undergoing harmonic translation and pitching oscillations is now known f o r the com- plete Mach number range. I n the past the theoretical aerodynamics of f l u t t e r has been based mainly on t h i s two-dimensional theory. This theory has been employed i n various strip-analysis methods and has been found t o be very useful, particularly f o r high-aspect-ratio wings with beam-like behavior. I n addition t o the velocity potential f o r the i n f i n i t e wing, the i n d i c i a l response functions associated with sudden v e r t i c a l and pitching motions are numerically known. These functions have applica- tions i n certain types of analog studies of f l u t t e r problems. They also have useful applications i n such problems as determination of an air- plane's response t o gust.

The second plan form l i s t e d is a wing of vanishingly small aspect r a t i o . Results f o r t h i s case are based on the assumption that a l l the forces a r i s e from crossflows and that the t r a i l i n g edge has no influence on the nature of the aerodynamic forces that a c t upon the wing. These results are of academic i n t e r e s t i n that they correspond t o the one extreme, A = 0; whereas the two-dimensional r e s u l t s correspond t o the other extreme, A = m .

a consideration of a Results f o r the circular p l a t e are based on pressure or acceleration potential. Aerodynamic coefficients associated with a few simple modes f o r t h i s configuration have been tabulated. Cor- responding r e s u l t s f o r other modes can, without very'great difficulty, be obtained. It i s not proposed that such r e s u l t s would ever be very use- f u l i n actual f l u t t e r studies, but they can be very useful i n assessing other approximate procedures f o r obtaining aerodynamic forces.

The fourth plan form considered i s a wing f o r which flow normal t o a l l edges is supersonic. This case stands somewhat alone, because the velocity potential i s known, a t l e a s t i n the form of a surface integral, f o r any given mode shape. In addition t o t h i s , i n d i c i a l functions cor- responding t o instantaneous v e r t i c a l and pitching displacements f o r such plan forms are explicitly known. I n order t o obtain the distribution of forces associated with the integral representation of the velocity poten- t i a l , it i s generally necessary t o resort t o approximate procedures f o r handling surface integrals. I n t h i s regard an approximation that applies when the Mach number i s large and the reduced frequency i s low has come t o be known as "piston theory" and has created eonsiderable interest i n the past f e w months.

Large values of Mach number M and low values of frequency parame- t e r k imply small values of the r a t i o k/M. When t h i s r a t i o is small enough, the velocity potential f o r t h i s case can be explicitly expressed i n a simple limiting form rather than as a surface integral. The forces obtained a t a given point from such a limiting form depend solely on the motion of the structure a t that point. Hence, each point of the surface can be imagined t o behave as a s m a l l independent piston; thus, the name "piston theory." The word "simple" i s used here t o distinguish results, which are s t r i c t l y linear, that are obtained from t h i s limiting process that are a l s o known as piston from more elaborate second-order r e s u l t s theory. For example, see the results of Hayes and Lighthill ( r e f . 1) .

The main concern here i s the subsonic and low supersonic speed range wherein there i s no basis f o r piston theory.

Item V i n the l i s t pertains t o rectangular- and arrow-type plan forms. The velocity potential corresponding t o f a i r l y simple mode shapes f o r these plan forms can be derived i n the form of a power series i n terms of the frequency of oscillation. This procedure and certain appli- cations thereof have been published f o r several years now. It i s men- tioned a t t h i s time f o r two reasons: F i r s t , because of some significant derivations and applications that have recently been made and are dis- cussed l a t e r i n t h i s paper and second, because r e s u l t s of the expansion procedure are used as a yardstick by which other l e s s r e s t r i c t e d approxi- mate procedures t h a t a r e about t o be discussed can be evaluated.

I t e m V I i n the l i s t pertains t o arbitrary plan forms. It i s f o r such plan forms that aerodynamic information has been c r i t i c a l l y lacking f o r a long time. It is also f o r these plan forms that significant advancements have recently been made. The advancements referred t o are not based on new principles. The general methods on which they are based have been known f o r some time, but there has been a drawback t o t h e i r application because of the enormous amount of calculation involved.

With the high-capacity computing equipment t h a t is now available, how- ever, t h i s phase of the work becomes simply a task of systemization.

Such systemizations are being accomplished, and it appears that a point w i l l soon be reached where the aerodynamics of linearized theory can be completely exploited.

The ''box method" as used herein pertains only t o wings with a l l supersonic edges. Basically, it is a method f o r numerically handling t o a given certain surface integrals t o which the forces corresponding mode can be reduced. The form of these integrals is shown i n the fol- lowing express ion : The function f i n the integral is related t o a mode of oscillation and i s known. The function Cp i s the potential f o r a source and is, of course, known. The region of integration S ' is indicated by shaded areas i n the sketches i n figure 2. This method w a s named by Pines and others at Republic Aviation Company, who proposed a procedure termed "box method" f o r obtaining generalized forces on flexible wings. A s originally proposed, the wing plan form i s replaced by a rectangular grid as indicated i n the sketch a t the l e f t i n figure 2. The leading edge is made jagged as shown. The integrations, i n t h i s original t r e a t - ment, were effected by expanding integrands and approximating a term- by-term integration over the portion of each l i t t l e box or rectangle that can a f f e c t the force a t a given point x,y. When high-capacity computing equipment, such as an IBM 650 or higher capacity machine, i s used very l i t t l e i s actually gained i n computing time by approximating or by approximating the integrands. Therefore, t h i s pro- the plan form cedure has been programed f o r calculating forces f o r wings with super- a way that the sonic edges without expanding the integrands and i n such plan form is completely accounted for, as indicated i n the sketch a t the right i n figure 2. The leading edge is not broken as i n the sketch at the l e f t . The present program i s f o r an IBM 650 machine and has been a comparison with results f o r simple mode shapes cal- tested by making culated by the frequency expansion method. The two s e t s of results agree very satisfactorily. The program w i l l probably be converted t o an IBM 704 machine i n the near future.

The kernel-function approach w i l l now be considered. This method applies t o e i t h e r subsonic or supersonic speeds and i s perfectly general with regard t o plan form and frequency. It involves approximating solu- tions t o an integral equation, namely, I n t h i s equation w(x,y) i s the known amplitude of downwash or the nor- m a l velocity of points (x,y) of a wing; p is the f l u i d density; L(6,q) i s the unknown l i f t distribution acting on the wing; and K(x,y;(,v;M,cu) i s the known kernel function of the integral equation. The region of integration S t extends over the portion of the wing that can affect the induced normal velocity o r downwash a t a given point (x,y).

For subsonic speeds S ' extends over the e n t i r e wing surface but f o r super- sonic speeds it depends on Mach number. The region of integration f o r a triangular plan form and one particular supersonic speed and f o r a l l subsonic speeds is i l l u s t r a t e d i n figure 3 .

The procedure f o r approximating solutions t o t h e integral equation is t o assume that the lift can be represented by a series of functions that are known except f o r certain constant coefficients. A general form of expression f o r the l i f t and the resulting downwash equation a r e indi- cated i n the following equation:

a

I n t h i s equation represents unknown constants and the functions Fn are known expressions chosen t o be combined s o as t o represent the l i f t distribution L( g , q) . Hence, when the coefficients are determined, an approximate expression f o r the l i f t i s known. In making a choice of Fn, one must be guided by certain conditions that must be the functions s a t i s f i e d along the wing edges and the r e s u l t s f o r the few cases f o r which the l i f t distribution is known.

I n order t o determine the coefficients

an, a system of linear alge-

braic equations i n which these quantities are the only unknowns can be

N + 1 points a t which t o s a t i s f y t h e known down- obtained by choosing

wash. The coefficients of % i n t h i s system of equations however involve complicated surface integrals. These integrals, which must be evaluated t o make t h e equations explicit, have t o be handled by numeri- c a l methods and, because of strong singularities involved i n the kernel function, the evaluations require special procedures. This i s espe- c i a l l y true i n the neighborhood of the s t r i p , shown darkened i n f i g - ure 4, extending ahead of the point at which t h e downwash i s being satisfied. Furthermore, the tremendous task of computations involved i n evaluating the integrals make t h e task feasible only with the use of high-capacity computing equipment.

What makes t h e number of computations so great i s the kernel func- tion. It has t o be evaluated many times i n t h e process of determining the l i f t f o r one s e t of conditions and it is of such a nature that it can be evaluated quickly only by automatic high-speed equipment. I n an e f f o r t t o accelerate development and uses of t h i s kernel function approach f o r treating aerodynamic problems, the A i r Research and Development Command i s sponsoring a tabulation of the kernel function f o r a f e w Mach numbers ( M = 0.6, 0.8, and 1.0). This tabulation, which is now about complete, is being made a t the Harvard University Computation Laboratory.

These tables w i l l have many uses but there now exist computing machines that are capable of handling the complete aerodynamic problem, including generation of the kernel function as it i s needed, so t h a t searching f o r these values i n voluminous tables i s not necessary.

With regard t o evaluating the surface integrals involved i n the kernel-function approach, several procedures have been considered.

Runyan and Woolston ( r e f . 2) have developed a method of t r e a t i n g the case f o r subsonic speeds by a procedure similar t o that of Falkner (ref. 3) f o r treating steady f i n i t e wings. Although t h i s procedure appears t o give satisfactory results, it is not readily adaptable for systematically programing f o r machine calculation. Furthermore, there supersonic.

is no basis f o r its application when the speed is Nelson and Diederich ( r e f . 4) have developed a method f o r subsoiiic involves dividing the wing i n t o many small elements i n each speeds that of which the downwash i s s a t i s f i e d a t the center of area. The lift i n the elements bounded by the wing edges i s represented by functions that have the proper behavior as the edge is approached. I n a l l other ele- ments the l i f t i s represented by simple polynomials. Integrations are effected over each individual element. (See r e f . 4.)

Recently, a method somewhat l i k e that of Multhopp ( r e f . 5 ) f o r treating steady wings has been developed and programed f o r machine cal- culation at the Langley laboratory. It applies i n principle t o both since the kernel function d i f f e r s subsonic and supersonic speeds but, f o r subsonic and supersonic speeds, a separate program i s required f o r the two speed regimes. I n order t o describe t h i s procedure briefly, the machine i s instructed t o calculate the spanwise distance over which the integrations extend and then t o divide t h i s distance i n t o a specified number of intervals. Numerical integrating formulas a r e then applied along chordwise sections a t each subdivision. Results of the chordwise integrations are then employed i n the spanwise integrating formulas t o complete the integrations. These integrations are simple and straight- forward except i n the QeighborhGod of singularities. I n these neighbor- hoods, use of limiting forms and special formulas make it very easy t o overcome t h e d i f f i c u l t i e s .

This setup f o r subsonic speeds has j u s t recently been programed f o r an IBM 704 machine. Although the program i s j u s t being tested, t h i s machine requires less than ll minutes per control point t o calculate the forces associated with f i v e vibration modes f o r a given frequency value and Mach number. This means that, f o r 9 control points, which should be sufficient i n most cases, t h e IBM 704 machine w i l l require l e s s than 15 minutes running time per frequency value and Mach number t o calculate the forces associated with f i v e different vibration modes.

The supersonic case has been recently programed f o r an IBM 650 machine and t h i s machine requires about s i x t y t i m e s as much time as the IBM 704 t o make the corresponding calculations.

That is, it takes the IBM 650 machine about 15-hours running t i m e per frequency value and Machnumber t o calculate the forces based on 9 control points f o r f i v e different vibration m o d e s . The program f o r the supersonic case w i l l be converted t o the IBM 704 machine i n the near future and it is estimated t h a t it w i l l require less time on t h i s machine than the subsonic case does.

I n order t o give some indication as t o w h a t might be expected with regard t o accuracy of r e s u l t s calculated by this kernel function proce- dure, some comparisons a r e made f o r supersonic speeds by this method w i t h r e s u l t s calculated by the frequency-expansion procedure f o r a tri- angular wing. I n reference 6 the expansion procedure is applied t o mch w i n g s deforming according t o a general quadratic equation. The deforma- tions considered f o r comparison are shown i n figure 4. They include v e r t i c a l translation and pitching of t h e wing considered as rigid, i l l u s - trated by section AA; a parabolic chordwise camber mode, i l l u s t r a t e d by section AA; and a parabolic bending mode, i l l u s t r a t e d by section BB. The

particular plan form considered is a 6 0 ' d e l t a wing. The reduced fre-

quency parameter i s 3/8 or 0.375 and t h e Mach number is 2. "his i s the Mach number condition f o r which t h e flow normal t o edges swept 6 0 ' is sonic.

Amplitudes of the forces and associated phase angles have been cal- culated by the two methods. R e s u l t s f o r the r i g i d modes a r e shown i n figures 5 and 6. The magnitudes of lift and moment as well as phase angle are seen t o be i n very good agreement. Results f o r the camber and bending modes a r e shown i n figure 7. The amplitudes a r e seen t o be in almost per- f e c t agreement, and the phase angles a r e i n fair agreement. There i s thus a good indication that t h e kernel-function procedure as programed i s sound.

Furthermore, there seems t o be no reason why it would not give as good r e s u l t s f o r subsonic speed as these results indicate it does f o r super- sonic speed. It therefore appears that there i s a sound and feasible way of determining t h e linearized aerodynamic forces f o r any given plan form, mode shape, Mach number, and frequency. It is further pointed out that, by considering t h e mode shape i n the form of a matrix of deflection func- tions, the kernel-function procedure can be handled so as t o yield aero- dynamic influence coefficients useful i n a d i r e c t attack on the eigen- value problem f o r the f l u t t e r mode.

SOME EXAMPUS OF FLUTTEB CALCULATIONS Consideration is now given t o a few f l u t t e r calculations. The con- figuration f o r which results are first presented is a model of a 4 5 O delta "he wing plan form wing. Results f o r t h i s model are shown i n figure 8.

is shown i n sketch at the r i g h t of the figure. The modal lines corre- sponding t o t h e first four natural modes of the model are shown.

The nec- essary information regarding mode shapes f o r this p a r t i c u l a r model were obtained by fixing a s m a l l mirror a t 24 different points on the surface and recording the t r a c e of a reflected l i g h t G O U T C ~ as t h e wing w a s forced t o vibrate at a natural frequency. Unfortunately, only four modes were measured. The model w a s f l u t t e r tested i n the Langley 8-foot transonic pressure tunnel and experienced f l u t t e r at a Mach number of 0.85 and a density corresponding t o an a l t i t u d e of about 33,000 f e e t .

I 51%

Aerodynamic forces appropriate for t h i s plan form and its mode shapes were determined by t h e kernel-function method and f l u t t e r cal- culations have been made f o r several a l t i t u d e conditions employing first three and then four modes. Results of the three-mode analyses are indi- cated by squares and r e s u l t s f o r t h e four-mode analyses, by c i r c l e s .

The four-mode r e s u l t s may be noted t o be within about 10 percent of t h e measured f l u t t e r speed. Although the r e s u l t s appear t o have almost con- verged, it would be desirable t o include additional modes t o see t h e effect that they might have on the calculated r e s u l t s .

The next r e s u l t s are f o r t h e all-supersonic edge case. Cunningham ( r e f . 7) has recently employed t h e velocity-potential expansion proce- dure t o develop aerodynamic forces associated with r o l l i n g and s y m e t r i c flapping modes f o r arrowhead wings with all-supersonic edges. The moti- vation f o r these derivations w a s that the r e s u l t s were needed f o r ana- lyzing the f l u t t e r of some all-movable control surface models t e s t e d i n t h e Langley 9-inch by 18-inch supersonic f l u t t e r tunnel.

From observation and measurement of t h e node l i n e s of t h e natural modes, it w a s noted that the models had essentially a l l t h e i r f l e x i b i l i t y concentrated i n the supporting shaft. Two coupled modes were used i n the analyses, and each coupled mode involved components of v e r t i c a l t r a n s - lation, pitching, and flapping. The amount of each component could be determined by the location of the node l i n e s because t h e control surface w a s essentially rigid.

A sample result of the analysis i s shown i n figure 9. This is f o r an all-movable 45' d e l t a plan form with i t s supporting axis at 55.4 per- cent of the root chord. The Mach number i s 1.6. The v e r t i c a l coordinate f o r t h e figure is a s t i f f n e s s parameter cpl/2V where cr i s root chord, V is t h e airspeed, and 'ol i s t h e frequency of t h e first natu- ral mode. The horizontal coordinate i s t h e r a t i o of t h e frequencies of t h e first and second natural modes. The calculated f l u t t e r boundary is a smooth curve with a large peak near a frequency r a t i o of 1. The f l u t - ter region is below the curve and t h e peak indicates that more and more s t i f f n e s s i s required t o prevent f l u t t e r as the first and second fre- quencies approach one another.

Two experimental points are shown. The open point is a no-flutter point and t h e dark point denotes that f l u t t e r occurred a f t e r the shaft had been weakened by a certain amount. The c r i t i c a l f l u t t e r speed should then f a l l between the two points. The theory is on t h e conservative side f o r both points and agrees very w e l l with experiment. Similar r e s u l t s were obtained f o r several other arrowhead wings f o r M = 1.6 and these are shown i n figure 10. The plan forms are identified by leading-edge sweep and trailing-edge sweep. Sweepback is positive. Location of t h e supporting axis is given i n percent root chord. I n the upper left-hand corner of figure 10 are results f o r the same configuration as t h a t j u s t discussed i n figure 9 but with the pitch axis moved rearward t o the 63.3 percent root chord. I n the upper right-hand corner are r e s u l t s f o r a wing with the leading edge swept back 450 and the t r a i l i n g edge swept forward 13O. I n the lower left-hand corner are r e s u l t s f o r a 50' delta wing and i n the lower right-hand corner a r e results f o r t h i s 5 0 ' wing with t h e t r a i l i n g edge swept back 15O. The theory is seen t o be consistently conservative and t o give results that a r e i n reasonable agreement with the experimental data.

CONCLUDING RFMARKS Several approaches t o the determination of the aerodynamic forces on oscillating wings have been b r i e f l y considered.

These approaches take into account the actual plan form under consideration and the spe- c i f i c modes of oscillation. The few f l u t t e r calculations t h a t have been discussed indicate that, when sufficient structural modes along with appropriate aerodynamic forces are taken into account, a reason- able correlation between theory and experiment can be obtained. It is emphasized that the kernel-function approach discussed is a highly ver- s a t i l e procedure and is currently being systematically programed f o r a high-speed calculator f o r both subsonic and supersonic speeds. Results obtained thus far indicate that, a t l e a s t where linear theory i s appli- cable, it should be a very powerful aid t o the f l u t t e r analyst.

REFERENCES 1. Garrick, I. E.: Nonsteady Wing Characteristics. Aerodynamic Compo- nents of Aircraft at High Speeds. Vol. VI1 of High Speed Aerody- namics and Jet Propulsion, sec. F, A. F. Donovan and H. R. Lawrence, eds., Princeton Univ. Press, 1957, pp. 658-793.

2. Rmyan, Harry L., and Woolston, Donald S.: Method for Calculating the Aerodynamic Loading on an Oscillating Finite Wing in Subsonic and Sonic Flow. NACA TN 3694, 1956.

3. Falkner, V. M.: The Calculation of Aerodynamic Loading on Surfaces of Any Shape.

R. & M. No. 1910, British A.R.C., Aug. 1943.

4. Nelson, H. C., and Diederich, F. W.: A Numerical Integration Method for Calculating Pressure Distributions on Wings of Arbitrary Plan Form Deforming Harmonically in Subsonic Flow. (Prospective NACA paper. ) 5. Multhopp, H.: Methods for Calculating the Lift Distribution of Wings (Subsonic Lifting Surface .Theory). Rep. No. Aero. 2353, British R.A.E., Jan. 1950.

6. Watkins, Charles E., and Berman, Julian H. : Velocity Potential and

Air Forces Associated With a Triangular Wing in Supersonic Flow, With Subsonic Leading Edges, and Deforming Harmonically According to a General Quadratic Equation. NACA TN 3009, 1953.

7. Cunningham, H. J.: Lift and Moment on Thin Arrowhead Wings With

Supersonic Edges Oscillating in Symmetric Flapping and Roll and Application to the Flutter of All-Movable Control Surfaces. (Pro- spective NACA paper. ) .

MODES OF VIBRATION FOR A FLEXIBLE WING Figure 1 SCHEME OF CALCULATION B Y BOX M E T H O D SUPERSONIC E D G E S 2 Figure SCHEME OF C A L C U L A T I O N B Y K E R N E L FUNCTION METHOD S U P E R S O N I C S U B S O N I C Figure 3 SOME DEFLECTION MODES TREATED BY FREQUENCY EXPANSION METHOD DEFLECTION VERTICAL PITCHING PARABOLIC MODES: TRANS X 2 Y2 Figure 4

SECTION LIFT AND PHASE ANGLES FOR TRANSLATION AND PITCH ABOUT MIDCHORD M=2; b0.375

1.2 r

- EXPANSlON

o KERNEL

‘cz’h‘ -*b . 4

0 .5 I 0 .5 I I C l , al DEG -I 0 0 .5 1 0 .5 I SPAN SPAN Figure 5 SECTION MOMENTS AND PHASE ANGLES FOR TRANSLATION AND PITCH ABOUT MIDCHORD M=2; k.0.375

- EXPANSION

o KERNEL

, % . d . 2 5 ~ +g::;L

IClqal ‘.2p7) .8 .”.-

-50 0 5 I 0 b I SPAN SPAN Figure 6

SECTION LIFT AND PHASE ANGLES FOR PARABOLIC MODES M = 2; k = 0.375 -EXPANSION 0 KERNEL

DEG , 80 L

u 0 .5 I 0 .5 I

loo r

-

0 .5 I 0 .5 I SPAN SPAN Figure 7 CALCULATED AND EXPERIMENTAL FLUTTER SPEED OF A DELTA WING M=0.85 - 1,000 MODE - 2

- \ -

FLUTTER 6oo 800 SPEED, Fps 400- EXPEWMENT 0 4 8 1 2 1 6 ~ 1 0 ~ DENSITY, S L U W FT Figure 8

. . C ' c

..C ..

' > * 3 . . . e 1 .

D 0 . . . , 45" DELTA ALL-MOVABLE CONTROL PITCH AXIS AT 55.4% ROOT CHORD; M.1.6 .

v 7 ~ r EXPERIMENT NEAREST NO-FLUTTER FLUTTER 0 I FREQUENCY RATIO, 01/02 FLUTTER RESULTS FOR SOME ARROWHEAD ALL - MOVABLE CONTROL SURFACES M = 1.6 A = 45" A = 45" e 7 0 [ - ATE = 0 0 A [ A T E = - ! ~ ~ PITCH AXIS AT 65.3% ROOT CHOR 55.8% ROOT CHOR .35 STIFFNESS

PARAMETER, "

PITCH AXIS AT 69.4% ROOT CH I 0 I O FREQUENCY RATIO, W l / W 2 Figure 10 4 d .

b 4 0 .

. .

- . I ..

OG FLUTTER AT VERY HIGH SPEEDS By Harry L. Runyan and Homer G. Morgan Langley Aeronautical Laboratory SUMMARY This paper is concerned with a discussion of some of the problems of flutter and aeroelasticity that are or may be important at high speeds.

Various theoretical procedures for treating high Mach number flutter are reviewed. Application of two of these methods, namely, the Van Dyke method and piston-theory method, is made to a specific example and com- pared with linear two- and three-dimensional results. It is shown that the effects of thickness and airfoil shape are destabilizing as compared with linear theory at high Mach number. In order to demonstrate the validity of these large predicted effects, experimental flutter results are shown f o r two rectangular wings at Mach numbers of 6.86 and 3 . The results of nonlinear piston-theory calculations were in good agreement with experiment, whereas the results of using two- and three-dimensional linear theory were not.

In addition, some results demonstrating the importance of including camber modes in a flutter analysis are shown, as well as a discussion of one case of flutter due to aerodynamic heating.

INTRODUCTION This paper is concerned with some problems of flutter and aero- elasticity at very high flight speeds. For this purpose high speeds will be defined as starting in the Mach number range of 2.5 to 3 .

Some of the problems which are or may be important at high speeds

are discussed according to the forces in the aeroelastic problem - aero-

dynamic, structural, and inertial. Under the aerodynamic part are: (a) Nonlinear effect of airfoil shape, thickness, and angle of attack: There appears to be a very large effect of these factors on the flutter speed, which is discussed subsequently.

(b) Effect of shocks: Information is lacking and constitutes an area requiring research effort.

52.3

c

, . - I

(c) Boundary layer and viscous effects: Here again information i s lacking, (of course, even i n the low speed case),but, with t h e thick boundary layers encountered a t high-speed flight, t h e dynamics of the boundary layer could become important, particularly, interactions of the boundary layer w i t h shocks.

(d) Plan form: Some of t h e new plan forms having sweep angles of t h e order of 7 5 O w i l l pose special problems with respect t o unsteady aerowamics, and there arises the d i f f i c u l t problem of studying and developing theories t h a t w i l l take i n t o account t h e e f f e c t of both air- f o i l shape and aspect r a t i o .

(e) Controls: Controls have always been a source of trouble f o r 10 t o 20, the type I n the Mach number range of t h e f l u t t e r analysts.

But from of control that w i l l prove t o be satisfactory i s not known.

past experience, whatever type of aerodynamic control, if any, i s found t o be satisfactory, it w i l l probably constitute a f l u t t e r problem.

Structures required f o r high-speed flight present another. area of d i f f i c u l t y . Some of t h e problems are: ( a ) Aerodynamic heating: An example of aerodynamic heating r e l a t i n g t o f l u t t e r i s b r i e f l y discussed.

(b) Panels and heat shields: For t h e flat-bottomed highly heated flight, it appears t h a t t h e a i r c r a f t now envisioned f o r high-speed f l u t t e r of panels and heat shields w i l l be a very real problem.

Under high-temperature conditions, buckling w i l l probably occur and w i l l require nonlinear treatment.

(c) Plan form: For wings of high aspect r a t i o , the distortions of t h e w i n g involved mainly a twisting and bending of t h e wing, so t h a t the elementary concepts of "beamology" could be used.

However, the low- aspect-ratio wings now being considered behave more l i k e plates and involve a large amount of chordwise deflection.

is the t h i r d type of force i n the aeroelastic prob- I n e r t i a l force The a i r c r a f t s t r u c t u r a l weight i s decreasing i n comparison with l e m .

Conse- the weight of the fuel, particularly with regard t o missiles.

quently, such nonlinear problems as f u e l sloshing and swirl are becoming exceedingly important.

Three of these problems w i l l be discussed: t h e e f f e c t of a i r f o i l shape, s t r u c t u r a l plan form, and aerodynamic heating.

, . a - - -

a ... < * m .

* * ( a m a ~ a a , * a a - _ _ - .*.

A aspect r a t i o a speed of sound b half chord, in.

P - Po

pressure coefficient, C P moment of i n e r t i a about e l a s t i c axis IU M Mach number

lb - se c

m mass of wing per u n i t of span length, in.

pressure a t point x,y P pressure i n undisturbed stream P O dynamic pressure

radius of gyration, ru2 = Ia

rU mb2 t thickness r a t i o W v e r t i c a l induced velocity or downwash

v

stream velocity, f t /sec Cartesian coordinates X, Y U angle of attack specific heat r a t i o Y bending frequency, radians/sec 9-l torsional frequency, radians /sec “h; first bending frequency, radians/sec m

mass r a t i o , -

Fr npb2 P f l u i d density cp velocity potential Subscripts: L l i n e a r NL nonlinear ANALYTICAL METHODS This section i s concerned with a brief description of the theoretical methods available for high Mach number studies. The complete nonlinear p a r t i a l d i f f e r e n t i a l equations f o r the potential and the pressure coeffi- cient are shown by ‘ p L + ‘ p N L = o and can be broken down i n t o a l i n e a r part plus a nonlinear part.

The linear solution now i n general use is obtained from equations (1) and (2) by s e t t i n g the nonlinear p a r t equal t o zero, as given by c q = o ( 3 ) cp = Cp,L and then solving the equations with suitable boundary conditions.

Several approximate methods are available for obtaining nonlinear solutions. The first of these i s the solution of Van ‘Dyke ( r e f . 1) .

H e first eliminated the third-order terms from these two nonlinear equations ( t h i s procedure, i n effect, eliminates the effect of f i n i t e shocks) and then inserted the solution f o r the l i n e a r equation ( 3 ) i n the nonlinear part of equation (1). This procedure resulted i n a l i n e a r p a r t i a l differ- e n t i a l equation plus a known function as

. .-

B . 8 m i ) ~ , ,’ $ 8 . . m 1 ) . 8 r . , L .

.*.

By a laborious technique, Van Dyke then solved these equations f o r the pressure on specific a i r f o i l s .

Another nonlinear method i s the so-called piston theory. T h i s pro- cedure w a s originally suggested by Hayes ( r e f . 2), w a s used by L i g h t h i l l (ref. 3 ) t o check the r e s u l t s of Van Dyke a t high Mach number, and later w a s elaborated on and applied t o the f l u t t e r problem by Ashley and

Zartarian ( r e f . 4) . The advantage of piston theory i s i t s u t t e r s i m -

p l i c i t y as compared with other theories. The pressure coefficient i s easily derived on the basis of a piston moving i n a one-dimensional channel. The expression f o r t h e pressure coefficient i s given i n

cp = 2kk) + ($2 + y+l 12 M ( $ + . . 1

where w i s the instantaneous v e r t i c a l velocity of a point on the wing, and V i s the stream velocity. Note that, as M i s increased, the first term would become l e s s important, and the higher order nonlinear terms would begin t o take an added importance.

i s use of the Newtonian concept.

Another method I n t h i s procedure it i s assumed t h a t the flow striking the exposed surface i s compressed t o a very t h i n boundary layer and the force exerted on the a i r f o i l i s due t o the component of momentum perpendicular t o the surface. The resulting pressure coefficient 1 2 w*,4 + . .

cP = 2/(!)2 - 3 (7, was obtained by expanding cos2 M. For a curved surface or an oscillating

v

surface, additional terms due t o centrifugal force could be added. Note t h a t the first t e r m i s missing as compared with piston theory and the coefficient of the squared t e r m has a factor of 1 as compared with 0.6 f o r 7 = 1.4. Later, use w i l l be made of the Van Dyke and piston-theory solution.

APPLICATION TO SPECIFIC MAMPLES Some applications and comparisons of the various theories are given.

I n figure 1 are shown the r e s u l t s of calculating the f l u t t e r of a rectan- gular wing of panel aspect r a t i o 1.5 throughout the Mach number range of 1 . 3 t o 10. The a i r f o i l section w a s 63 series, tapering from 4 percent Four theories have been used: a t the r o o t t o 3 percent at the t i p .

linear two-dimensional theory, linear three-dimensional theory, nonlinear

52%

piston theory, and Van Dyke theory. The r e s u l t s are plotted against the

s t i f f n e s s - a l t i t u d e parameter, 6. The f l u t t e r region i s below the

curves. Constant-altitude l i n e s are horizontal and constant-dynamic- pressure l i n e s are radial l i n e s emanating from the origin. There are four points of i n t e r e s t i n this plot. F i r s t , the large difference between the l i n e a r theories and t h e two theories which include the e f f e c t of thickness a t the higher Mach numbers. This effect i s primarily due t o a forward s h i f t i n the center of pressure due t o a i r f o i l shape whereas the center of pressure f o r t h e two-dimensional l i n e a r theory i s fixed a t the 70-percent chord and t h e forward s h i f t of the center of pressure i n as much forward movement as the t h e three-dimensional t i p does not predict nonlinear theories. Another point i s the agreement of the more compli- cated Van Dyke theory with the simpler and more readily used piston theory a t t h e higher Mach number. A t h i r d point of i n t e r e s t i s the cross It has usually over of the two- and three-dimensional theory a t M = 1.6.

been assumed that inclusion of t h e three-dimensional e f f e c t s i s a This relieving e f f e c t when compared w i t h the two-dimensional theory.

is usually t r u e a t the lower Mach numbers but it is not necessarily t r u e a t the high Mach numbers. A fourth point i s that the e f f e c t of a i r f o i l shape and thickness i s destabilizing. For instance, at an a l t i t u d e cor- a value of the ordinate of 3.3, nonlinear theory indicates responding t o t h a t f l u t t e r would be experienced at a Mach number of 5 , whereas the l i n e a r theory would predict the a i r f o i l t o be f l u t t e r free.

2 i s shown the calculated e f f e c t of thickness and a i r f o i l I n figure obtained by using nonlinear piston theory.

shape on f l u t t e r a t M = 10 The stiffness-altitude parameter i s shown plotted against the r a t i o of bending t o torsion frequency. The f l u t t e r region is below t h e curve.

Curves are presented f o r a flat plate, a 4-percent wedge, and a 4-percent biconvex a i r f o i l . L e t us focus our attention on the curves f o r the f l a t p l a t e or zero-thickness a i r f o i l and t h e biconvex a i r f o i l . For low- frequency r a t i o , the zero-thickness a i r f o i l gives no f l u t t e r solution whereas the biconvex a i r f o i l shows a d e f i n i t e f l u t t e r solution. A s the frequency r a t i o i s increased, however, the curves tend t o approach each oh

other and a t - = 1.2 they actually cross. That is, the e f f e c t of

% thickness i s destabilizing f o r low values of the frequency r a t i o and s t a b i l i z i n g for high values, a t least f o r t h i s case. that t h e wedge Note has a shape similar t o the f l a t p l a t e except it i s s l i g h t l y destabilizing.

I n figures 1 and 2 are shown some r a t h e r large and disturbing e f f e c t s of thickness and a i r f o i l shape i n reducing the f l u t t e r speed. The ques- t i o n is then "are these large effects, i n f a c t , true." I n an attempt t h i s t o answer question two wings have been f l u t t e r e d a t high speed. The frequency r a t i o selected f o r these wings w a s deliberately chosen so that as w i d e a spread as possible between the zero-thickness and t h e thickness solution could be obtained. For these cases the frequency r a t i o was , I

52.5

i approximately 0.35. Although the parameters f o r figure 2 are not t h e same as those f o r the experiment, the trends are t h e same and at a fre- quency r a t i o of about 0.35 there i s quite a difference between the zero- thickness and the thickness cases.

COMPARISON O F MPERIMENTAL AND T€BORECICAL RESULTS F l u t t e r a t Mach Numbers of 6.86 and 3.0 Results f o r two rectangular wings are shown i n figures 3 and 4, One i s an 11-percent double- each having a panel aspect r a t i o of 0.8.

The properties wedge section and t h e other i s a 4-percent f l a t wing.

of these wings are given i n the following table: 11-percent wedge 4-percent p l a t e b . . . . . . . . .

2 -55 2 -57 m . . . . . . . . . 0.0001276 O.OOOl.27

o .269

ra2 . . . . . . . . 0.251

xo . . . . . . . . 0.467 0.46

. . . . . . . . 0.0745

0 -0545

. . . . . . . . 110 .g 106

'"tL . . . . . . . .

V a t M = 3 . 0 . . . 2,110 2,120

V a t M = 6 . 8 6 . . .

3,255 3,290 .

(The torsion mode f o r both wings w a s taken as unity across the span.

The bending mode f o r the 11-percent wing w a s taken as f h = 0.23 + 0 . 1 9 2 5 ~

and f o r the 4-percent w i n g as f h = 0.335 + 0 . 1 8 6 ~ where x varies

fYom 0 t o 4 inch&.) The wings were very r i g i d and were mounted on f l e x i b l e shafts so that, i n effect, they corresponded t o all-movable controls. The results are again plotted as the stiffness-altitude parameter against Mach number. The experimental results are shown as solid points and were obtained a t Mach numbers of 6.86 and 3 i n the Langley 11-inch hypersonic tunnel and t h e Langley 9- by 18-inch super- sonic flutter tunnel, respectively. Let us examine first the double wedge. The solid l i n e is the r e s u l t of using nonlinear piston theory and fairly good agreement is indicated with t h e experiment. The two- dimensional, zero-thickness method gave no solution. The three- dimensional l i n e a r case indicated a f l u t t e r - f r e e wing a t a Mach number of 6.86 but gave a solution a t a lower Mach number as indicated. For the &-percent plate, simi&r - @ s t o n theory and experiment was obtained. Again, two-dimensional zero thickness gave no solution and indicated the wing t o be f l u t t e r free; whereas, inclusion of the three-dimensional t i p effect gave a solution as indicated. The value

of reduced frequency k f o r the M = 6.86 t e s t was - and a first-order

theory i n frequency such as the piston theory should be satisfactory.

Thus, it appears that the detrimental effect of thickness on f l u t t e r as predicted by piston theory i s i n f a c t t r u e and that nonlinear theories must be used a t the high flight speeds. One interesting f a c t i s that l i n e s drawn through the experimental points intersect the origin; thus a constant "q" f l u t t e r variation is indicated.

F l u t t e r of Delta Wings N o w l e t us turn our attention t o some f l u t t e r calculations of t w o low-aspect-ratio cantilever wings. In figure 5 the stiffness-altitude coefficient has been plotted against Mach number for 45' and 6 0 ' delta wings. The wings were flat plates with beveled leading and t r a i l i n g edges.

The circular points a r e the experimental r e s u l t s from reference 5 and the s o l i d and dashed l i n e s are analytical result-s. Piston theory w a s used f o r the aerodynamic input.

A modal type of analyses which was based on experimentally measured mode shapes was used. Since these modes had a large amount of deflection i n t h e chord direction, it did not seem.that the deflection curves could be approximated by the usual procedure of bending and twisting of a straight l i n e . Hence, analytical curves were f i t t e d t o the experimental deflection curves a t each of 10 spanwise stations f o r use i n the analysis. The r e s u l t s are shown by solid l i n e s and show f a i r l y good agreement with experiment. I n order t o assess the e f f e c t of chordwise deflection, the camber was a r b i t r a r i l y eliminated from each mode and then recalculated. The results are shown by the dashed l i n e s . For the 600 wing, the curve w a s shifted over t o the nonconservative side, whereas f o r the 4 5 O wing a very wide divergence i s found. Thus the importance of including the camber deflection i n the analysis of a low-aspect-ratio w i n g i s demonstrated.

/

F l u t t e r Due t o Aerodynamic Heating Another well-known problem of high speed is the e f f e c t of aero- dynamic heating. With regard t o f l u t t e r , the main e f f e c t of aerodynamic heating i s t o cause a loss i n torsional stiffness, particularly during transient conditions. A s o l i d duralumin wing has been tested a t a Mach number of 2 i n the preflight j e t of the Langley P i l o t l e s s Aircraft Research Station a t Wallops Island, Va. Two runs were made, a cold run during which the.wing did not f l u t t e r and a hot run during which the wing fluttered. This phenomena can be explained with the aid of figure 1. These i .

L 527

L G calculations apply t o t h i s heated wing. I n the cold condition the value of the stiffness-altitude parameter at a Mach number of 2 i s 3.07 and is well i n the stable region. During the fast start of the tunnel, the leading and t r a i l i n g edges heated up much more r a p i d l y t h a n the thicker center section; t h i s condition causes a momentary loss i n torsional stiff- ness. Thus the torsional frequency was reduced; t h e stiffness-altitude parameter i s correspondingly reduced and would follow a v e r t i c a l l i n e t o an intersection of the f l u t t e r curve. Calculations of the l o s s i n t o r - sional s t i f f n e s s have been made and show a reduction i n the torsional fre- quency by 50 percent which i s sufficient t o intersect the f l u t t e r region.

Thus, f l u t t e r which has been induced by aerodynamic heating, at least f o r a simple solid wing, can be calculated.

CONCLUDPNG REMARKS New f l u t t e r and aeroelastic problems w i l l appear a, high f l i g h t speeds. Configurations dictated by high-speed requirements will probably also exhibit new problems i n the lower speed ranges. An essential fea- For ture of many of these problems is t h e i r inherent nonlinearity.

accurate f l u t t e r prediction, inclusion of these nonlinearities, such as i s a necessity.

the effect of a i r f o i l thickness and shape, REFEREXCES 1. Van Dyke, Milton D.: Supersonic Flow Past Oscillating Airfoils NACA Rep. 1183, 19%. Including Nonlinear Thickness Effects.

(Supersedes NACA TN 2982.)

2. Hayes, Wallace D.: O n Hypersonic Similitude. Quarterly Appl. Math., vol. V, no. 1, Apr. 1947; pp. 105-106.

Oscillating Airfoils a t High Mach Number. Jour.

3. Lighthill, M. J.: Aero. Sci., vol. 20, no. 6, June 1953, pp. 402-406.

Piston Theory - A New Aero-

4 . Ashley, Holt, and Zartarian, Garabed: Jour. Aero. Sci., vol. 23, dynamic Tool f o r the Aeroelastician.

no. 12, Dec. 1956, pp. 1109-1118.

5 . Tuovila, W . J . , and McCarty, John Locke: m e r i m e n t a l F l u t t e r

Results f o r Cantilever-Wing Models a t Mach Numbers up t o 3.0.

NACA RM L55El1, 1955.

F Y FLUTTER FOR VARIOUS AERODYNAMIC THEORIES 4 - bw,& a 3 .

2 .

I - FLUTTER REGION I I I I 1 v 0 2 4 6 8 1 0 M Figure 1 CALCULATED EFFECT OF AIRFOIL SHAPE

-_----

4 O / o BfCONVEX I I I I I 0 .4 .0 1 . 2 I .6 2 .o Wh / w a FLUTTER OF A DOUBLE WEDGE WING AT HIGH SPEED E.A.=46.7%; c.G.=49.4% i A z 0 . 8

--=zzm-

t = 11% 6- - 4 - PISTON THEORY ( t = 1 1 % )

-

a 2 -

EXPERIMENT -? [-;DIMEN. ( t = 0 )

-

--_ 2-DIMEN. ( t = 0 )

---_

-

I I t r --,I I FLUTTER OF A THIN WING AT HIGH SPEED E.A. = 46 O i ' o ; C.G. - 5 0 % ; A = 0.8 t = 4 O/O EXPERIMENT

-7

I I I / I

I I I I

2 3 4 5 6 7 0 I M Figure 4 '. " .

FLUTTER OF DELTA WINGS 2.c 60° I .5 I .c

bwlfi a

0 A /'

0 EXPERIMENT .5 '

-

WITH CAMBER /

- --- :FLUTTER

WITHOUT CAMBER

' REGION

-

0 I 2 3 f 3 M .... . ...

-anarr . . . .

FWTTER OF WINGS WITH AND WITHOUT EXTEXNAL STORE3 AT TRANSONIC AND SUPERSONIC SPEEDS By Laurence K . Iaftin, Jr., and William T . Lauten, Jr.

Langley Aeronautical Laboratory INTRODUCTION Much of the available experimental information on wing flutter at transonic and supersonic speeds deals with plain wings of moderate aspect ratio and taper ratio. In the present paper, some aspects of the flutter behavior at transonic and supersonic speeds of delta wings and highly tapered swept wings, and of wings with mass balance and external stores w i l l be discussed. The Mach number range to be considered is from 0 . 8 to 3.0. The majority of the material to be presented was obtained recently, is rather fragmentary, and should be regarded as suggestive of possible leads or hints rather than as a basis for forming broad conclu- sions or design rules. Trends for the plain wings will be discussed first and then some results for wings with mass balance and stores will be presented.

A aspect ratio a speed of sound, ft/sec b streamwise root semichord, ft C streamwise chord, ft Mach number M dynamic pressure, lb/sq ft dynamic pressure at flutter of wing without'stores or bodies, lb/sq ft dynamic pressure at flutter of wing with stores or bodies, s, lb/sq ft , . * , . e * .

e.

..I L A angle of sweep, deg A taper ratio nondimensional density parameter (ratio of mass of exposed v semispan wing to mass of air contained in the frustum of a cone whose upper and lower base diameters are equal to strewise tip and root chords) frequency of predominantly torsion mode, radians/sec % uncoupled store pitching frequency, radians/sec

cue

RESULTS AND DISCUSSION Plain-Wing Results The flutter trends to be discussed for wings without stores or balance weights are shown in figure 1 . This is a plot of the stiffness- altitude parameter baufi Gainst Mach number. The flutter region is a the region below the curve. Constant altitude is indicated by a hori- zontal line, constant dynamic pressure by a straight line through the origin. An increase in altitude for a gi-renwing corresponds to an increase in the stiffness-altitude parameter. Wends are presented for a 6 0 ° delta wing, a 45’ swept wing with a taper ratio of 0 . 2 and, for comparison, a 4 5 O swept wing with a taper ratio of 0 . 6 . The plan forms of the wings are indicated by the sketches on the left. The curves shown are based on data obtained in the 26-inch Langley transonic blowdown tunnel at Mach numbers from 0 . 8 to 1.4 and in the Langley 9- by 18-inch supersonic flutter tunnel from 1.3 to 3.0. The trends shown in this figure are thought to be particularly interesting in that the configura- tions investigated at transonic and supersonic Mach numbers are nearly the same and an acceptable basis for evaluating the relative severity of the flutter problem at transonic and supersonic Mach numbers is thus provided, at least for the plan forms considered. & e trends show the existence of a critical flutter region mound Mach number 1 . 0 , after which the three wings are flutter-free at altitudes equal to or greater than that necessary to avoid flutter at transonic speeds, until the Mach number reaches values of the order of 2.0. No especial significance should necessarily be attached to the Mach number around 2 . 0 , at which value the stiffness-altitude parameter becomes equal to the critical value around Mach number 1.0, except insofar as the particular configura- tions considered in the figure are concerned. Investigations at both transonic and supersonic Mach numbers indicate that the values of the stiffness-altitude parameter corresponding to flutter can be al+,eredby I

j i 533

3 . 0 . .

1 . 3 .

changes in wing plan form, center-of-gravity position, and perhaps other parameters. The trends of this figure, however, emphasize the necessity for careful consideration of the flutter boundaries at both transonic and supersonic speeds on any new high-speed aircraft.

An interesting detailed feature of the results shown in figure 1 is the behavior of the highly tapered wings at Mach nurdbers around 1 . 0 .

In contrast to the results for the wing with taper ratio of 0 . 6 , the value of the stiffness-altitude parameter for the highly tapered wings is seen to drop suddenly to a larer value aad then increase .slowly as the Mach number is increased.

Thus, a large stable region for these two wings is indicated at Mach nuuibers somewhat in excess of 1 . 0 . The sudden decrease in stiffness-altitude parameter has been found to accompany an increase in flutter frequency by a factor of approximately 2, with the wing fluttering at about the natural torsional frequency. This change in flutter mode is felt to be of interest because the nature of a ''fix" required to suppress flutter may be different for the different flutter modes. Tne combination of parameters responsible for the favorable decrease in the stiffness-altitude parameter with the accompanying increase in the flutter frequency is not understood; therefore, the range of application of the results cannot be assessed at this time.

Effects of Mass Balance The results of some recent studies at transonic speeds of the effects of mass balance will now be discussed. The wing plan form employed was the same 4 5 ' swept wing with taper ratio of 0.2 discussed in figure 1 .

The configuratims investigated are shown at the top of figure 2 . The shaded areas shown at the leading edge represent the two positions of balance mass for which experiments were made. Balance masses of 6 and 12 percent of the wing mass were attached at each position and in each configuration the mass extended over 25 percent of the span.

The results obtained from the four mass-balance configurations are sham in the bottom part of the figure. These results are plotted in the form of dynamic pres- sure required for flutter against Mach nurdber.

The area above the curve is the flutter region. B e solid line represents data taken from figure 1 for the wing without balance. The dashed line is a fairing of data taken for all balance conditions since no significant difference existed between the data for the four configurations. The results show that in the crit- ical flutter range between Mach numbers of 0.9 and 1.05, where the very pronounced peaks in stiffness-altitude parameter were evident in figure 1 , the leading-edge balance mass increased the d y & c pressure required for flutter by as much as 1 0 0 percent. The hatched area labeled "no flutter" indicates that flutter could not be obtained beyond Mach num- ber 1.1for azzy of the mass-balance configurations up to the maximum dynamic pressure employed in the investigation. Obviously, substantial improvements in the transonic flutter chasacteristics of this wing can be obtained by the use of mass balance. In t h i s connection, it is per- haps of some i n t e r e s t t o point out t h a t an increase of approximately 100 percent i n the plain-wing torsional stiffness would be required i n order t o achieve the effect produced by the addition of 6 percent of the wing weight as a mass balance. The f a c t t h a t decreasing the amount of balance mass by a factor of 2 , t h a t is, f r o m 12 percent t o 6 percent wing mass, had no effect on the improvement shown leads t o the question of j u s t how l i t t l e mass balance could be used i n order t o obtain a cer- t a i n desired increase i n dynamic pressure f o r f l u t t e r . There is no general criterion f o r the optimum amount and position of the,balance mass and each case w i l l probably have t o be a subject f o r individual study.

Wings With External Stores I n contrast t o the work j u s t discussed on distributed mass, some exploratory studies have been made a t Mach numbers from 0.8 t o 1.3 on the effect on f l u t t e r of concentrated masses i n the form of external stores. This work was aimed a t gaining some insight i n t o the nature of the problems encountered, and, if possible, w h a t properties of the store might be significant t o the f l u t t e r problem. Three configurations studied a t transonic speeds are shown i n figure 3. !be wing was swept back 45O, had no taper, and had an aspect r a t i o of 4.0. The three stores employed were of the underslung type mounted on pylons, and had an aero- dynamic shape consistent with current transonic design practice. The Stores A and B were nearly identical, stores are labeled as A, B, Elnd C.

except f o r a change i n center-of-gravity position, and had a weight of about 70 percent of the wing weight-. Store C w a s 40 percent heavier (approximately equal t o the wing weight). The center of gravity of store A was located a t the 38-percent-chord point a t midsemispan and the center of gravity of store B was at the 12-percent-chord point, also at the midsemispan. The center of gravity of store C w a s 25 percent ahead of the leading edge at about 80 percent of the semispan.

The experimental results f o r the various store configurations are sham i n figure 4 i n which the r a t i o of the dynamic pressure at f l u t t e r of the wing w i t h stores t o t h a t of the wing without stores i s plotted against Mach number. No significant difference was found i n the results f o r stores A and B, and the solid l i n e i n this figure represents a f a i r i n g of both s e t s of data. It may be seen t h a t the dynamic pressure f o r f l u t t e r of the wing w i t h stores A and B l i e s between 70 and 80 percent of t h a t f o r the plain wing i n the range of Mach number from 0.8 t o about 1.3. The dashed l i n e indicates the results obtained from the t e s t s of configura- t i o n C. As can be seen, the dynamic pressure for f l u t t e r a t M = 0.95 has been increased from about 75 percent t o about 90 percent of that f o r the wing without stores as a result of t h i s change i n the weight positionj outside the Mach number range of 0.88 t o 1.05, the. dynamic pressure required f o r f l u t t e r is larger f o r the wing w i t h the store than f o r the + .

wing without the store.

!G The f a c t that forward movement of the store center of gravity had no effect on the results obtained f o r stores A and B i s perhaps not too surprising when consideration i s given t o the nddal patterns for t h e two store configurations. It may be seen in figure 5 that the s h i f t i n the center of gravity makes only a small change i n the location of the nodal pattern and the uncoupled frequencies would not be expected t o be much different. In regard t o configuration C, it w a s assumed that a large forward movement of the predominantly torsion node l i n e might, as previous investigators have suggested, be indicative of a favorable coupling e f f e c t w i t h a corresponding increase i n the dynamic pressure of f l u t t e r . Consequently, a vibration survey w a s made w i t h the store located i n numerous spanwise and chordwise positions. Configuration C w a s found t o give the type of node l i n e desired and yielded an increase i n t h e f l u t t e r dynamic pressure. Any differences i n the e f f e c t s of the aero- dynamic forces and moments of the store on the f l u t t e r condition as the store w a s moved from the location of A and B t o C were assumed t o be of second-order importance. The results shown i n this figure indicate that, j u s t as i s the case at lower speeds, the addition of stores should not necessarily cause a serious f l u t t e r problem at transonic speeds and may perhaps be employed as a m e a n s f o r alleviating the problem.

A short exploratory study has also been made at transonic speeds of the effects of the introduction of f l e x i b i l i t y i n t o the store mount s o as t o give a pitching degree of freedom. lPle configuration and some of the results obtained are shown i n figure 6. The same untapered wing used i n connection with figures 4 and 5 w a s employed i n these studies. A schematic diagram of the s t o r e mount i s shown a t the right of the figure.

The store w a s mounted close t o the'under surface of the wing and w a s connected t o the wing by a spring i n such a manner that the store w a s essentially r i g i d i n yaw and side bending but had f l e x i b i l i t y i n pitch.

The spanwise position of the store w a s chosen t o correspond approximately t o the plain-wing second bending node l i n e which w a s at about 75 percent of the semispan. 'phe store mass w a s about the same as that of the plain semispan wing. The center of gravity w a s located a t 3 l p e r c e n t of the wing chord. The data shown are i n the form of the r a t i o of the dynamic pressure required f o r f l u t t e r f o r the wing w i t h s t o r e t o t h a t f o r the wing without store, plotted against the r a t i o of the uncoupled store pitching frequency t o the uncoupled torsion frequency % of the plain wing. The highest value of this r a t i o shown here represents about as near a r i g i d condition as could be obtained. The circled points represent values of the frequency r a t i o f o r which data w e r e obtained.

The results are f o r a Mach number of approximately 0.85. The trend of the data indicates a definite optimum value of the pitch f l e x i b i l i t y .

For the particular configuration studied, the optimum value of the r a t i o of pitching frequency t o torsion frequency w a s about 0.6, w i t h reductions i n the dynamic pressure required f o r f l u t t e r accompanying e i t h e r increases or decreases i n the f l e x i b i l i t y of the s t o r e mount. The results sham i n t h i s figure indicate the possibility of lessening the f l u t t e r problem w i t h stores a t transonic speeds b i l i t y i n the store mount.

5%

m e 0 2 , 0 . e .

a .

e . e e - 1 0 ..

.. . - - .

Studies of the effects of external bodies on f l u t t e r a t supersonic 9- speeds are being carried out i n the Langley by 18-inch supersonic - f l u t t e r tunnel. The plan forms f o r w h i c h these studies are being made Some of the results f o r the 600 d e l t a include those shown i n figure 1.

wing and the 4 5 O swept wing with taper r a t i o of 0.2 w i l l be presented.

The configurations investigated on the d e l t a wing are shown i n figure 7.

The symbols indicate the I 2 positions of the body center of gravity f o r which tests were made. The positions were -25, 0, 25, and 50 percent of the wing chord. The spanwise positions were 1/4, 1/2, and 3/4 of the bodies are indicated by the outline semispan. The size and shape of the drawings at the 50-percent-semispan station. The mass of the body w a s slightly more than one-half of the wing semispan &ass. In all cases the at the 50-percent-semispan body was equal i n length t o the wing chord position and had a fineness r a t i o of 10. The shape of the body was rather crude; however, the slope of the l i f t and moment curves on a body of such high fineness r a t i o i s relatively small and i s not affected t o any great extent by detailed changes i n the shape. It w a s therefore assumed t h a t the shape of the bodies was relatively unimportant i n determining the f l u t t e r characteristics. A f e w t e s t s with bodies of cleaner aerodynamic shape have indicated that t h i s assumption i s valid.

The e f f e c t of the center-of-gravity location on the f l u t t e r character- i s t i c s of the 600 d e l t a wings i s shown for Mach numbers 1.3 and 2.0 i n figures 8 and 9, respectively. The ordinate i s again the r a t i o of dynamic pressure necessary f o r f l u t t e r with body attached t o t h a t necessary f o r f l u t t e r w i t h the plain wing. is the fraction of the semispan.

The abscissa The c i r c l e s indicate the center of-gravity ahead of the leading edge, the squares indicate the leading-edge center-of-gravity position, the diamonds indicate the 25-percent-chord position, and the triangles indicate the 50-percent-chord position. The open points indicate that no f l u t t e r was obtained f o r these body locations up t o the maximum dynamic pressure possible i n the tunnel. Points above the solid l i n e a t a value of qs/Q of 1 indicate an increase i n the dynamic pressure required f o r f l u t t e r resulting from i n s t a l l a t i o n of the external body. Large increases i n the dynamic pressure required f o r f l u t t e r are seen t o accompany many body locations a t Mach numbers of both 1.3 and 2.0. Although the r e s u l t s are not completely consistent, the far-forward, 3/4-semispan position of the center of gravity appears t o be the most favorable.

The configurations investigated on the 45' swept wing with the taper r a t i o of 0.2 are shown i n figure 10.

The chordwise center-of-gravity locations were the same as for the 60° delta wing but the spanwise posi- tions were a t l/3, 2/3, and f u l l semispan. 'he e f f e c t of the i n s t a l l a t i o n of the bodies on the f l u t t e r characteristics of the 45O sweptback wing is shown i n figures 1 1 and 12 f o r Mach numbers of 1.3 and 2.0, respec- tively. %e ordinate and abscissa are the same as f o r the d e l t a wing.

As the case of the 60° d e l t a wing, large increases i n the dynamic pressure required f o r f l u t t e r are seen t o be associated with most of the ,* .* o + .

body installations. The far-forward position of the center of gravity seems t o cause the greatest increase i n the dynamic pressure f o r f l u t t e r .

The most favorable spanwise position would appear t o be near the 2/3-semispan position, particularly a t the higher Mach number. A t f i r s t glance, t h i s may appear t o contradict the results obtained on the d e l t a wing but on the delta wing the outermost position w a s only 3/4 semispan.

The improvements shown i n figures 8, 9, 11, and 12 t o accompany the installation of external bodies on the d e l t a and sweptback wings indicate that the increase i n the stiffness-altitude parameter notedlin figure 1 for the plain wings a t the higher Mach numbers may be alleviated by the considered location of an external body.

CONCLUDING REMARKS The trends which have been presented emphasize the necessity f o r careful consideration of wing f l u t t e r boundaries at both transonic and supersonic speeds on any new high-speed a i r c r a f t . The use of mass balance would seem t o hold promise as a means f o r lessening the wing f l u t t e r problem. Large external bodies need not cause severe penalties from the f l u t t e r point of view and, i n fact, hold promise as a possible m e a n s for alleviating the f l u t t e r problem a t both transonic and supersonic Mach numbers.

EFFECT OF MACH NUMBER NO FLUTTER

-L

A A x

-

60° A WING -- 45O 4 .2

-\ ----

45O 4 .6

- n

FLUTTER I I I 0 I 2 3 M Figure 1 EFFECT OF MASS BALANCE BALANCE MASS 6 AND 1 2 " L o OF WING MASS q,LB/SQ FT M i*.

STORE CONFIGURATIONS A = 4 5 O ; A=4.0 ; Xz1.0

1 AIRSTREAM

Figure 3 EFFECT OF STORES A=45': Az4.0; X=i.O

P - A AND B

1 I I I I I 0 .8 I ,o 1 2 1.4 M Figure 4 WING TORSIONAL NODE LINES A=45O; A=4.0; X=I.O FAIRSTREAM Figure 5 EFFECT OF STORE-MOUNT FLEXIBILITY M = 0.85 I I I I 0 4 .0 I .2 I .6 we

FREQUENCY RATIO, -

W a Figure 6

I 5 4 3 2

60° DELTA P L A N FORM SHOWING C.G. LOCATION OF EXTERNAL BODIES -25% C 0 O/O c ~ 25% C 50% C Figure 7 E F F E C T O F C.G. S H I F T OF E X T E R N A L BODIES M.1.3 i A = 6 O o I C.G., To C A ;

/ 4 NO FLUTTER

.5 I I I I ‘/4 ‘/2 3/4 I FRACTION OF SEMISPAN Figure 8 EFFECT OF C.G. SHIFT OF EXTERNAL BODIES M = 2 . 0 $ A = 6 0 ° C.G.,%C 0 -25 m o

+ 25

/ 1 0 / \NO FLUTTER /

.5 L

I i I I I 0 I /4 112 314 I FRACTION OF SEMISPAN 45O SWEPT PLAN FORM SHOWING C.G. LOCATION OF EXTERNAL BODIES Figure 10 e .e 3 e 13G EFFECT OF C.G. SHIFT OF EXTERNAL BODIES M.1.3 j A = 4 5 O C.G. ,% C -25 m o

+ 25

2 . 0 A. 50 1 . 0 ' .5L I 1 I J 0 ' / 3 5 I FRACTION OF SEMISPAN Figure ll EFFECT OF C.G. SHIFT OF EXTERNAL BODIES M z 2 . 0 ; A=45O I I I 1 0 1 1 3 2/3 I FRACTION OF SEMISPAN Figure 12 0 0 0 8 0 .

.. A 0 0

AERODYNAMICS O F OSCILLATING CONTROL SURFACES

- A T TRANSONIC SPEEDS

By Robert F. Thompson and Sherman A. Clevenson Langley Aeronautical Laboratory SUMMARY Oscillating flap-type and all-movable controls a r e discussed w i t h particular emphasis on the aerodynamic forces and moments a t transonic speeds. Hinge-moment r e s u l t s from recent wind-tunnel and rocket-powered- model t e s t s are summarized f o r trailing-edge flap-type controls t o i l l u s - t r a t e the effects of control hinge-line position and p r o f i l e shape on one-degree-of-freedom f l u t t e r of t h i s type of control. From a wind- tunnel investigation of a model considered representative of an a l l - movable control, the aerodynamic effects due t o rigid-body-oscillation modes i n r o l l and i n pitch are presented.

The general magnitudes of the unstable aerodynamic damping moments f o r the flap-type controls tested a r e pre,sented. No significant benefits toward alleviating the unstable aerodynamic damping i n the control rota- tionalmode at transonic speeds were obtained f o r a wide range of hinge- l i n e positions tested.

O f three control profile modifications tested, only a "wedge" modification t o a 35-percent-overhang balanced control gave significant improvements i n "buzz" s t a b i l i t y . This wedge control gave stable aerodynamic damping i n the control rotational mode up t o the maximum speed tested. However, the stable damping and improvement i n f l u t t e r characteristics were limited t o oscillation amplitudes l e s s than about 3 O .

For an all-movable control, the oscillating aerodynamic derivatives which define the separate effects of rigid-body pitch and rigid-body r o l l have been presented through the transonic speed range. The aerodynamic w i n g f o r t h i s low-aspect-ratio all-movable control was stable at a l l conditions tested.

INTRODUCTION Oscillating aerodynamic forces and moments are needed i n analyzing the dynamic or f l u t t e r characteristics of any airplane component.

"hese aerodynamic values cannot be accurately computed f o r the mixed-flow conditions at transonic speeds, and there is a current need f o r experi- mental data. The purpose of t h i s paper is t o summarize some recent t e s t s on o s c i l l a t i n g flap-type and all-movable controls, wherein t h e aerodynamic effects at transonic speeds have been measured. Flap-type controls are discussed first, and results pertain primarily t o one- degree-of-freedon f l u t t e r o r "buzz." Then, t h e aerodynamic e f f e c t s due t o rigid-body modes i n p i t c h and i n r o l l are presented f o r an all-movable control.

SYMBOLS flap-type-control chord, distance from hinge l i n e t o t r a i l i n g edge of control (see f i g . 2), f t flap-type-control balance chord, distance from hinge l i n e forward t o leading eQe of control (see f i g . 2), f t root chord of all-movable control, f t t o t a l control chord at midspan of control,

cb + ca, f t

reduced frequency of all-movable-control pitch o s c i l l a -

ka

tion, 2v reduced frequency of flap-type-control oscillation, 2v reduced frequency of all-movable-control r o l l o s c i l l a - Wr

tion, -

2v M free -stream Mach number M' area moment of flap-type-control area rearward of and about t h e hinge line, cu f t free-stream dynamic pressure, lb/sq f't S semispan area of all-movable control, sq f t free-stream velocity, f t / s e c V c flap-type-control hinge-moment coefficient, ‘ h Hinge moment 2M‘q Model lift lift coefficient, cL (4s rolling-moment coefficient (fig. 7 ) , Model rolling moment about roll axis Cr

qs -

pitching-moment coefficient (fig . 7 ) , ‘ m Model pitching moment about pitch axis amplitude of all-movable-control pitch oscillation, U radians except as noted amplitude of f lap-type-control oscillation, measured in plane perpendicular to hinge line, radians except as noted amplitude of all-movable-control roll oscillation,

#

radians except as noted 0 angular frequency of oscillation, radians/sec

derivative with respect to 6, a, or # as noted

6 C ,

derivative with respect to -

2v &Cr

derivative with respect to -

2v

derivative with respect to &

2v Subscript : derivative obtained from an oscillation u) DISCUSSION OF RESULTS Flap-Type Controls The aerodynamic hinge moment existing on the oscillating flap-type controls discussed herein i s represented i n complex notation by the relationship Resultant hinge moment - -

C + i k C

h6,U %;Lo a ' q 6

where ch represents an aerodynamic spring -moment derivative pro -

8 9 0 portional t o the component of the t o t a l aerodynamic moment i n phase with control position. The product k C is an aerodynamic damping param- %,a e t e r , proportional t o the component of the t o t a l aerodynamic moment i n phase with control r o t a t i o n a l velocity, and contributes the damping.

represents an aerodynamic viscous-damping derivative.

The p a r t %,0 Theoretical considerations.- Theoretical values f o r control aerody- namic damping a r e shown i n figure 1. These two-dimensional-flow r e s u l t s were obtained from references 1 t o 3 and a r e presented t o provide a frame- work f o r evaluating $he experimental flap-type-control data. Theoretical damping derivatives are plotted against Mach number f o r a 30-percent- chord flap-type control hinged at the leading edge.

The dotted portion of the l i n e s is an arbitrary f a i r i n g between the subsonic and supersonic theories, and the Mach number variation indicated is i n general agree- ment with experiment. Theory shows the aerodynamic damping t o be unstable f o r some values of reduced frequency at Mach numbers from about 0.9 t o 1.5. I n this region, control-surface f l u t t e r can occur unless sufficient nonaerodynamic damping i s present i n the control system t o provide damping moments greater than the unstable aerodynamic moments. The subsonic and supersonic damping derivatives are f a i r l y independent of Mach number and reduced frequency. However, large effects a r e indicated at transonic speeds, and the idealized theory indicates stable damping f o r reduced frequencies representing very high oscillating frequencies.

Experimental damping r e s u l t s t o date (refs. 4 t o ll) have a l l been i n the frequency range where theory indicates instability, and these experimental data show unstable damping i n the control rotational mode at transonic speeds.

The magnitudes indicated by test and theory are often i n poor agreement, but this is not surprising considering the mixed-flow conditions which e x i s t at transonic speeds and the possible influence from nonpotential sources. Based on these results, a fundamental approach i n alleviating control-surface "buzz" would be t o provide enough nonaerodynamic damping i n the control system t o overcome t h e unstable aerodynamic effects. This approach generally necessitates the addition of some type of a r t i f i c i a l damping t o the control system, f o r example, the type provided by a hydraulic damper. This addition can often lead t o mechanical complexi- t i e s , especially when such factors as control f r e e piay a r e considered; and it would be desirable t o s t a b i l i z e the control aerodynamic danrping by some change i n geometric characteristics provided overall control efficiency can be maintained.

Control hinge position and profile shape a r e known t o have large effects on s t a t i c hinge moments, and some of t h e i r effects on dynamic hinge moments have recently been determined i n the hope that stable con- t r o l aerodynamic damping at transonic speeds can be achieved.

Effects of hinge position.- Studies of the effects of control hinge position and profile shape were made i n t h e Langley high-speed 7- by 10-foot tunnel with the wing-control configuration shown i n figure 2 ( r e f s . 7 and 8). These t e s t s were at a Reynolds number of about 2 x 106 based on the wing mean aerodynamic chord. Model plan form w a s held con- stant and the t o t a l control chord w a s 30 percent of the wing chord. The range of test conditions covered is indicated i n figure 2. From figure 1 it can be seen t h a t the test frequencies a r e i n a range where two- dimensional-flow theory indicates unstable aerodynamic damping at tran- sonic speeds f o r a 30-percent-chord control hinged at the leading edge.

This paper first presents the effects of hinge-line position, as indicated by results f o r the three conventional control profiles shown' i n figure 2, and then summarizes the effects of the profile modifications indicated.

The hinge l i n e i s located by the r a t i o of t h e balance chord cb t o the chord of the control rearward of the hinge l i n e ca, and 20-, 35-, and 100-percent-overhang balanced controls were tested.

I n figure 3 the effects of hinge position on the control aerodynamic damping are surmnarized. These data are presented f o r a reduced frequency of 0.10 and an angle of attack of 0 ' ; i n general, the variations i n angle of attack and reduced frequency covered i n these t e s t s had small e f f e c t s on the control hinge-moment results. A free-oscillation t e s t technique was used and the damping derivative is plotted against oscillation anrpli- tude f o r representative t e s t Mach numbers i n figure 3(a) with the complete Mach number variation shown i n figure 3(b) f o r l o w oscillation amplitudes.

Positive values of C indicate unstable aerodynamic damping. The % , a f l u t t e r o r buzz associated with the unstable damping shown f o r t h i s model w a s a self-excited oscillation and b u i l t up i n amplitude u n t i l the aero- dynamic energy fed into the control system over a complete cycle was belanced by the energy dissipated due t o s t r u c t u r a l and f r i c t i o n a l damping.

Steady-state f l u t t e r points f o r the t e s t control system a r e indicated by t h e circular symbols i n figure 3(a). The damping derivative f o r the 20- and 35-percent-overhang balanced controls at subsonic speed was stable

and f a i r l y constant t o oscillation amplitudes of about loo. Damping for

the LOO-percent-overhang balanced control was nonlinear with amplitude a t t h i s speed and unstable at the higher oscillation amplitudes.

I n this subsonic Mach number, order t o i n i t i a t e the model f l u t t e r shown f o r it was necessary t o displace i n i t i a l l y t h e control t o some intermediate amplitude and suddenly release it. This i n s t a b i l i t y at a low Mach num- ber i s believed t o be closely related t o a s t a l l - f l u t t e r type of phe- nomenon. Increasing the Mach number into the transonic speed range caused the control aerodynamic damping t o become unstable f o r all hinge positions tested. For the 100-percent-overhang balanced control there w a s first a large stable increase i n damping with increasing Mach number before the damping became unstable. Model f l u t t e r a t these transonic speeds w a s i n i t i a t e d by random tunnel disturbances, and the f l u t t e r amplitude was markedly decreased a t sonic speed w i t h the hinge located at the control midchord. The damping a t transonic speeds was nonlinear with amplitude f o r all hinge positions and indicated the influence of nonpotential effects which r e s t r i c t the application of any potential theory.

Shown i n figure 4 are recent control aerodynamic damping r e s u l t s obtained from a free-flight rocket-powered-model test by the Langley P i l o t l e s s Aircraft Research Division. These data were obtained by a free-oscillation t e s t technique similar t o that described i n reference 10.

T e s t Reynolds number, based on the wing mean aerodynamic chord, varied 6 6

from 2 x 10 t o 13 x 10 . The delta-wing configuration is i l l u s t r a t e d

and the trailing-edge flap-type control w a s hinged s l i g h t l y rearward of t h e control midchord. The experimental damping derivative evaluated f o r an oscillation amplitude of 1 . 8 ' is shown f o r Mach numbers from about 0.5 t o 1.9, and the test reduced frequency varied as indicated through the Mach number range. For this midchord hinge position, there was a large increase i n stable damping at high subsonic speeds and unstable aerodynamic damping i n the transonic bhch nuuiber region, with the damping again becoming stable at the higher t e s t supersonic speeds. These aero- dynamic damping trends w i t h Mach number, measured i n f r e e f l i g h t , are i n agreement w i t h the theoretical and wind-tunnel results presented. Based on the data shown i n figures 3 and 4, reasonable hinge positions do not offer much promise i n alleviating the unstable damping i n the control r o t a t i o n a l mode at transonic speeds.

The e f f e c t s of hinge position and Mach number on the control i n phase or s t i f f n e s s derivative for the wind-tunnel model a r e presented Derivatives obtained from dynamic and s t a t i c t e s t s a r e i n figure 5 .

compared t o i l l u s t r a t e the effects of oscillating the control.

Positive values of t h i s derivative indicate overbalanced or s t a t i c a l l y unstable The balancing effect of s h i f t i n g the hinge l i n e rearward hinge moments.

is shown, and the midchord hinge position overbalances the control through- out the speed range tested. The oscillating spring moments a r e approxi- mately equal t o the s t a t i c values f o r the 20- and 35-percent-overhang balanced controls, and the differences shown f o r the 100-percent-overhang 4G balanced control can be attributed to the larger deflection range over which it was necessary to evaluate the stiffness derivative for the dynamic tests. This agreement indicates that, for a wide range of hinge positions, static hinge moments can be used to predict accurately the frequency of control buzz.

Effects of profile shape.- The profile modif2cations studied in the 2. For the 20-percent- wind-tunnel investigation are illustrated in figure overhang balanced control the thickness at the trailing edge was made equal to the hinge-line thickness, and the portion of the control for- ward of the hinge was not altered. Results for the oscillating hinge moments for this control were similar to the results for the original profile with the aerodynamic damping still unstable at transonic speeds.

This modification caused a slight beneficial shift in the level of unsta- ble damping and an increase in the aerodynamic spring stiffness; however, the flutter characteristics of the model were not appreciably improved.

(See ref. 7 . ) On the 35-percent-overhang balanced control two profile changes were made. For the lower modification shown, the rear half of the con- ventional control chord was replaced by a thin "splitter" plate over essentially the full span of the control. This control was similar to some controls tested in a flight investigation by North American Aviation, Inc. (For example, see ref. 12.) In the present tunnel tests, the oscillating hinge-moment and flutter results measured for this splitter- plate control did not show any significant differences relative to the original profile, and the aerodynamic damping indicated about the same level of instability at Mach numbers from about 0.92 to 1.01, the maxi- 12 a trailing-edge splitter plate com- mum speed tested. In reference bined with a slight thickening of the forward portion of the control has given qualitative indication of improved buzz stability. Direct com- parison of the model and flight results is not feasible since the aero- dynamic damping was not measured in flight, and there are appreciable geometric differences between the configurations.

The "wedge" modification to the 35-percent-overhang balanced con- trol did give some beneficial effects on control damping. The trailing- edge thickness was a little more than twice the thickness tested on the modified 20-percent-overhang balanced control. The leading and trailing edges were connected by a straight line which resulted in an increase in the hinge-line thickness relative to the original profile.

Damping results for the wedge control are shown in figure 6 and are compared The aerodynamic damping , with the damping of the conventional profile.

of the wedge control was stable at low oscillation amplitudes for the complete-test speed range. However, at transonic speeds, stability is confined to oscillation amplitudes less than about 3 ' .

Damping for the wedge control is unstable for amplitudes greater than about 3'; if the model wedge control is manually displaced t o these unstable anrplitudes and released, it would f l u t t e r w i t h characteristics very similar t o those i n the response of the conventional control.

All-Movable Control The model used t o measure some oscillating aerodynamic derivatives at transonic speeds f o r conditions of particular application t o all- movable cdntrols is shown i n figure 7. These tests were made i n the Langley 2- by 2-foot transonic f l u t t e r research tunnel at Reynolds numbers, based on the control mean aerodynamic chord, from 1.4 x 106 t o 3.6 x 106.

The rigid-body degrees of freedom i n pitch and r o l l t o be considered are The pitch axis passes through the midchord at the root i l l u s t r a t e d .

and the leading edge at the t i p . The r o l l axis was a r b i t r a r i l y chosen inboard of the model root, and the pitch and r o l l motion together with t h e angles describing the modes are i l l u s t r a t e d . Nomenclature similar t o that used i n discussing the flap-type controls is a l s o used f o r t h i s all-movable control with the resultant aerodynamic forces and moments reduced t o derivatives that are either i n o r out of phase with the motion. The aerodynamic forces and moments existing on the oscillating model are represented i n complex notation f o r pitching motion as Resultant lift -

- cL,,(I, + +c%,u

Resultant pitching moment = k,, + ikcm.

=,os

qs - a

and f o r r o l l i n g motion as Resultant r o l l i n g moment L i f t and pitching-moment derivatives are presented f o r t h e pitching motion, and the damping due t o r o l l is shown f o r the r o l l i n g oscillation.

These experimental data have not yet been compared with existing tbree- dimensional-flow theory ( r e f s . 13 and 14).

L i f t components due t o pitch oscillation of the model are shown i n ' figure 8, and these data were evaluated f o r a forced-oscillation a n r p l i - tude of about 3 ' t o each side of Oo angle of attack. The l i f t i n phase with the motion is shown on the l e f t and t h e out-of-phase component is shown on the right. D a t a were measured f o r a Mach nuztiber range from 0.6 t o 1.2, and the curves represent values f o r various reduced frequencies.

For a constant reduced frequency, the in-phase derivative increases with Mach numbers from 0.6 t o 1.0 and decreases w i t h Mach numbers from 1.0 t o 1.2. The out-of-phase derivative decreases with increasing Mach num- bers from 0.6 t o 1.0 and changes sign from positive t o negative near a Mach number of 1.0. Increasing the reduced frequency decreases the in-phase component of the t o t a l lift at a l l t e s t speeds and causes a positive increment i n the magnitude of the out-of-phase component.

Although it is not presented herein, experimental data have shown that the rolling moments due t o pitch oscillation follow the same trends as those shown herein f o r the l i f t .

I n figure 9 the pitch-damping parameter due t o pitch oscillation of the control i s plotted as a function of reduced frequency and Mach These aerodynamic data were evaluated from the free-oscillation number.

response of the control following removal of the forcing function at an For additional information on t h e oscillation amplitude of about 3 O .

The aerodynamic viscous- t e s t technique used, see references 15 and 16.

w i n g derivative was essentially linear f o r amplitudes from 0 ' t o 3'.

The damping moments were stable throughout the complete Mach number range from 0.6 t o 1.2, and there was a tendency f o r the damping parameter t o become more stable up t o M = 1.0 and then decrease. The damping increased as the reduced frequency was increased. For conditions roughly approximating those of the present t e s t s , two-dimensional-flow theory (refs. 2 and 3 ) indicates unstable values f o r t h i s parameter a t tran- sonic speeds.

However, three-dimensional-flow theory ( r e f s . 13 and 14) indicates a rather large stabilizing effect a t these speeds due t o aspect r a t i o ; therefore, these experimental results showing stable damping appear t o be i n reasonable agreement w i t h existing theory.

Figure 10 shows the roll-damping parameter due t o r o l l oscillation of the control as a function of reduced frequency and Mach number.

These data were evaluated from the free-oscillation response of the control following r o l l oscillations up t o amplitudes $ of about 3'. The r o l l - damping moments were stable throughout the speed range tested, and the damping tends t o become more stable as the t e s t Mach number i s increased.

Increasing the reduced frequency a l s o increases the stable damping-in- r o l l parameter.

CONCLUDING REMARKS The aerodynamic forces and moments acting on oscillating flap-type and all-movable control surfaces at transonic speeds have been summarized.

The discussion on flap-type controls has b r i e f l y reviewed w h a t could be considered t h e fundamental approach i n alleviating one-degree-of-freedom f l u t t e r of t h i s type of control, namely, incorporating sufficient non- aerodynamic damping i n the control system t o overcome the unstable aerodynamic moments. Experimental results were presented which estab- l i s h the general magnitude of the unstable aerodynamic moments f o r the t e s t models. However, it i s desirable t o have a control configuration with inherent aerodynamic s t a b i l i t y ; therefore, the aerodynamic e f f e c t s of control hinge-line position and some p r o f i l e modifications were Based on these results, no significant benefits i n control studied.

aerodynamic damping were obtained f o r a wide range of hinge positions.

O f three control p r o f i l e modifications tested, only a "wedge" modifica- t i o n t o a 33-percent-overhang balanced control gave significant improve- ments i n "buzz" s t a b i l i t y . This wedge control gave stable aerodynamic damping i n the control rotational mode up t o the maximum speed tested.

However, the stable damping and improvement i n f l u t t e r characteristics were limited t o oscillation amplitudes l e s s than about 3'.

For an all-movable control, the oscillating aerodynamic derivatives which define the separate effects of rigid-body pitch and rigid-body The aero- r o l l have been presented through the transonic speed range.

dynamic damping f o r t h i s all-movable control w a s stable at a l l condi- tions tested.

1 1 REFERENCES

1. An n.: Tables of Aerodynamic Coefficients f - an os illating Wing-

Flap System in a Subsonic Compressible Flow. Rep. F.151, Mationaal Luchtvaartlaboratorium, Amsterdam, M a y 1954.

2. Nelson, Herbert C., and Berman, Julian H . : Calculations on the Forces and Moments for an Oscillating Wing-Aileron Combination in Two- Dimensional Potential Flow at Sonic Speed. NACA Rep. 1128, 1953.

(Supersedes NACA TN 2590.)

Garrick, 1. E., and Rubinow, S. I. : Flutter and Oscillating Air-Force 3.

Calculations for an Airfoil in a Two-Dimensional Supersonic Flow.

NACA Rep. 846, 1946. (Supersedes NACA TN 1158.)

4. Reese, David E., Jr.: An Experimental Investigation at Subsonic and Supersonic Speeds of the Torsional Damping Characteristics of a Constant-Chord Control Surface of an Aspect Ratio 2 Triangular Wing.

NACA RM A53D27, 1953.

Martin, Dennis J., Thompson, Robert F., and Martz, C. William: Explor- 5.

atory Investigation of the Moments on Oscillating Control Surfaces at Transonic Speeds. NACA RM L55E31b, 1955.

6 .

Reese, David E., Jr., and Carlson, William C. A.: An Experimental Investigation of the Hinge-Moment Characteristics of a Constant- Chord Control Surface Oscillating at High Frequency. NACA RM A55J24, 1955 * Thompson, Robert F . , and Moseley, William C., Jr.: Oscillating Hinge 7.

Moments and Flutter Characteristics of a Flap-Type Control Surface on a 4-Percent-Thick Unswept Wing With Low Aspect Ratio at Trarnsonic Speeds. NACA RM L55KJ-7, 1956.

a. Thompson, Robert F., and Moseley, William C., Jr.: Effect of Hinge- Line Position on the Oscillating Hinge Moments and Flutter Charac- teristics of a Flap-Type Control at Transonic Speeds.

NACA RM L57C11, 1957. (NACA prospective paper. ) Tuovila, W. J., and Hess, Robert W.: Aerodynamic Damping at Mach 9.

Numbers of 1.3 and 1.6 of a Control Surface on a Two-Dimensional Wing by the Free-Oscillation Method. NACA RM L56A26a, 1956.

10. Martz, C. William: Experhental Hinge Moments on Freely Oscillating Flap-Type Control Surfaces. NACA RM ~56~20, 1956.

e. 0 . a , , a - - 11. Clevenson, Sherman A.: Some Wind-Tunnel Experiments on Single- Degree-of-Freedom F l u t t e r of Ailerons i n t h e High Subsonic Speed Range. NACA TN 3687, 1956. (Supersedes NACA RM L ~ E Q ~ . ) 12. Anon.: Flight T e s t Progress Report No. 23 f o r Period Ending 7 October 1953 f o r Model FJ-4 Airplanes. Rep. No. NA 54H-374-23 (Contract NOa( s) 54-323), North American Aviation, Inc . , Oct . 20, 13. Nelson, Herbert C., Rainey, Ruby A . , and Watkins, Charles E.: L i f t and Moment Coefficients Expanded t o the Seventh Power of Frequency f o r Oscillating Rectangular Wings i n Supersonic Flow and Applied t o a Specific F l u t t e r Problem. NACA “I 3076, 1954.

14. Runyan, Harry L., and Woolston, Donald S.: Method f o r Calculating t h e Aerodynamic Loading on an Oscillating F i n i t e Wing i n Subsonic and Sonic Flow. NACA TN 3694, 1956.

15. Clevenson, Sherman A., and Widmayer, Edward, Jr.: Experimental Measurements of Forces and Moments on a Two-Dimensional Oscillating Wing A t Subsonic Speeds. NACA TN 3686, 1956. (Supersedes NACA RM LgK28a.)

16. WiWyer, Edward, Jr., Clevenson, Sherman A . , and Leadbetter, Sumner A . : Some Measurements of Aerodynamic Forces and Moments at Subsonic a Rectangular Wing of Aspect Ratio 2 Oscillating About Speeds on t h e Midchord. NACA RM L53F19, 1953.

THEORETICAL CONTROL DAMPING TWO -DIMENSIONAL T H E O R Y 1 5 1 0 C hi,, -5 I I 1 I 0 -5 1 . 0 1.5 2 .o M Figure 1 FLAP -TYPE CONTROL MODEL WIND -TUNNEL TESTS MODEL PARAMETERS ASPECT RATIO 1.8 TAPER RATIO 0.74 NACA 6 4 A 0 0 4 SCOPE O F TESTS 0.6TO 1 . 0 1 ANGLE O F ATTACK 0 ° A N D 6 ' REDUCED FREQUENCY 0.06 TO 0.13 Figure 2

*

EFFECT OF HINGE POSITION ON CONTROL DAMPING k=O.lOi a = O 0 I I 0 - 0 - I 1 0 C h8 ,w - 5 0 STEADY- STATE FLUTTER -10 AMPLITUDE EFFECT OF HINGE POSITION ON CONTROL DAMPING kZO.10; Q = O O ; 8 = O 0 1 0 Cb/ca I

- 0.20

D( , I 0.35 I

\ I

1 . 0 0 -15 I I I I I -25 Lk . 7 .8 .9 1.0 1.1 M EFFECT OF MACH NUMBER ON CONTROL DAMPING ROCKET-MODEL TEST;8=+1.8"; a!=O" k = Oilo 96 9 4 chbyw-/ -10 I DLi M Figure 4 EFFECT OF HINGE POSITION ON CONTROL STIFFNESS k . 0 . 1 0 ) Q = O o

- DY N AMlG

0 STATIC C cb/ca hs,, 2 -D- I 1.00 I I A v -0- .35 UNDERBALAN C ED

I ( -

I 20

-2 1 " .c; .1, - n c '

I .a .9 1.0 M EFFECT OF WEDGE PROFILE ON CONTROL DAMPING k=O.IO ; a=O" I a - I chs,w -5 o STEADY STATE FLUTTER AM PLlTUDE - I 0 0 5 IO 1 5 0 5 1 0 1 5 28 ,DEG +S,DEG Figure 6 A L L -MOVABLE CONTROL SURFACE RIGID-BODY DEGREES OF FREEDOM PANEL ASPECT RATIO = 1.25 TAPER RATIO =0.283 NACA 6 5 A 0 0 5 a

T

i t 560

Figure 7 .

EFFECT OF MACH NUMBER ON LIFT COMPONENTS DUE TO PITCH OSCILLATION k 3 - C L a p 2 - I - M M Figure 8 EFFECT OF MACH NUMBER ON PITCH-DAMPING COMPONENT DUE TO PITCH OSCILLATION . 3 k 0.10 .I I5 .I 5 k Cmb,w -3 .I75 - . 6 - :9 L I I I I I I I I I 0 .4 .'5 -6 . 7 .8 .9 1 . 0 1.1 1.2 M Figure 9 EFFECT OF MACH NUMBER ON ROLL-DAMPING COMPONENT DUE TO ROLL OSCILLATION 0.5 k -0.5-0.10 .I I5

.*O \

-2.0- -2.5- I I I

04 . 6 .f .k -6 1 . 0 1.1 1.2

M Figure 10 STATUS O F FLUTTER O F FLAT AND CURVED PANELS By Robert W. Leonard and John M. Hedgepeth Langley Aeronautical Laboratory SUMMARY Representative r e s u l t s are presented t o show the current status of the panel f l u t t e r problem. The discussion includes f l a t panels with and without midplane stresses, buckled panels, and both unstiffened and stiffened i n f i n i t e l y long circular cylinders.

INllRODUCTION The f l u t t e r of the skin panels of supersonic airplanes and missiles has aroused considerable i n t e r e s t i n recent years. Numerous investiga- tions (refs. 1 t o 27) have determined that panel f l u t t e r may govern the design of a t l e a s t very t h i n panels such as those used i n fairings and i n radiation shielding. Representative results of some of these inves- tigations, which tend t o i l l u s t r a t e the current status of the problem, are presented i n t h i s report. 'Ihe discussion i s divided roughly i n t o three parts: F i r s t , the f l u t t e r of flat panels; second, the f l u t t e r of panels stressed beyond the bucMing load; and third, the f l u t t e r of thin-walled circular cylinders.

SYMBOLS a panel dimension i n chordwise direction b panel dimension i n spanwise direction Et3 D panel s t i f f n e s s , * * a b e 1 , , - - e - E Young's modulus i,j,m,p integers M Mach number n integer, number of circumferential waves around the cylinder chordwise midplane load per unit spanwise length px spanwise midplane load per u n i t chordwise length pY % dynamic pressure P R = J PX cylinder radius thickness panel deflection chordwise coordinate spanwise coordinate zqa3 dynamic-pressure parameter,

&?y- D

Poisson's r a t i o (taken equal t o l / 3 throughout) mth mode of uniform clamped-clamped beam of unit length 5 dimensionless coordinate

a4 a4

V 4 = a 7 + 2 + -

b X ax2ay* ay4 FLAT PANELS 1 I t o the present time, the largest research e , , x t has been devoted Typical analytical results for f l a t t o theoretical study of f l a t panels.

panels are shown i n figures 1 and 2.

The results i n figure 1 apply t o panels of i n f i n i t e aspect r a t i o , t h a t is, panels which extend t o i n f i n i t y i n the spanwise direction and, hence, behave structurally l i k e a beam. Figure 2 contains r e s u l t s for a panel with f i n i t e aspect ratio. Both plots give the panel thickness t/a 'necessary t o prevent f l u t t e r , a t various Mach numbers, of r a t i o s t e e l panels a t sea level. The results are r e s t r i c t e d t o panels which are unstressed; t h a t i s , they have no midplane tension or compression.

I n both figure 1 and figure 2, the dashed curves a t low supersonic Mach numbers are two-mode results based on the use of unsteady linearized air forces. (See r e f s . 8, 10, and 20.) The solid curves a t high Mach numbers are two-mode r e s u l t s obtained by using much simpler "static" air forces i n which no account i s taken of unsteady effects. (See refs. 22 Experience has shown that, f o r the high Mach numbers, the and 26.)

s t a t i c approximation yields results i n close agreement with those yielded by more refined theories. The smooth merging of the dashed and solid lines f o r each configuration i l l u s t r a t e s t h i s close agreement.

In figure 1, curves are shown for three different configurations: an array of panels continuous over equally spaced supports, a single panel with pinned ends, and a single panel with clamped ends. The general effect of panel boundary conditions may be seen from the relative posi- tions of the curves a t high Mach numbers. The most c r i t i c a l configwa- tion, requiring thicker panels t o prevent f l u t t e r , i s the array of panels on equally spaced supports.

The effect of aspect r a t i o on required panel thickness i s shown i n figure 2. In t h i s case, both curves are f o r a single panel w i t h pinned edges. The upper curve applies t o an i n f i n i t e span panel and i s the same as the middle curve of figure 1 . The lower curve applies t o a square panel. As would be expected, reducing the aspect r a t i o from i n f i n i t y t o one reduces the required thickness.

It should be pointed out t h a t the moderate reduction i n thickness r a t i o a t high Mach numbers i s due primarily t o the structural effects of aspect ratio. (See ref. 26.) De aerodynamic effect i s less than 2 per- cent throughout the range of the solid curves. Thus, the use of aero- dynamic s t r i p theory would give accurate boundaries f o r the square p l a t e f o r these high Mach numbers.

The situation is apparently different for the low Mach numbers.

In addition to the moderate structural effect, there is now a large aerodynamic effect of aspect ratio and a resulting large reduction in thickness in changing from the infinite-aspect-ratio panel to the square It is interesting to note that, although the low supersonic Mach panel.

number range appears to be critical for infinite-aspect-ratio panels, this may not be the case for the simply supported square panel for which the results show a steady increase in thickness with increase of Mach number.

It should be pointed out that the dashed curves at the low Mach numbers in figures 1 and 2 are based on a rather limited number of cal- culations and this region has not yet been carefully explored. It is known, however, that structural damping is fairly effective in reducing the large thicknesses required for infinite-aspect-ratio panels. (See ref. 10.)

It is also worthwhile to note that a small amount of experimental data has been reported at Mach numbers of 1.3 and 1.56 for clamped panels which behave like the infinite-aspect-ratio panel. (See refs. 6 and 13.)

The data are not shown in figure lbecause they apply to a different altitude and material. When compared with calculations made on the same basis, experiment and theory agree at Mach number 1 . 5 6 . At Mach num- ber 1 . 3 , the deta show a n increase of thickness but not the large increase predicted by the theory. The difference may be due in part to structural damping.

So far, only panels with no midplane stress have been considered.

However, the effect of midplane tension or compression stresses on the required thickness of flat panels has been investigated and is found to be important (ref. 2 6 ) . This effect is illustrated by the results shown in figure 3 .

Figure 3 is a plot of a modified-thiclmess-ratio parameter

( { C l q ' 3 t containing both panel and air properties, against a

D s X chordwise compression parameter

. The coefficient of

(Buckling Px)pv=o J the thickness ratio contains the Mach number My Young's modulus E, and the dynamic pressure and allows the application of the plotted q results to all Mach numbers above about 1.5.

The compression parameter, which specifies stress in'the chordwise direction, is the ratio of chordwise compression Px to the buckling value of chordwise stress which corresponds to zero stress in the spanwise direction. Positive values of this parameter indicate chordwise compression and negative values imply tension. Curves are shown for two pinned-edge panels with aspect ratios of 0.5 and 1 .

I It m u s t be remembered that the calculations apply t o f l a t panels only. Hence, the curves i n figure 3 are valid only up t o the chordwise load which results i n buckling. If the midplane stress i n the spanwise direction i s zero, the curves are therefore valid, by definition, only up t o t h e compression pasmeter equal t o one. If tension i s applied t o the panel i n the spanwise direction, the chordwise load necessary t o cause buckling is raised; the curves would then be valid t o a higher , value of the compression parameter. Spanwise compression would have the opposite effect. It should be noted that this is the only influence of spanwise stress on the f l u t t e r boundaries of f l a t panels. (See r e f . 26.)

The influence of chordwise s t r e s s i s sham by the variation of the curves themselves. Note especially that, f o r each aspect r a t i o , there i s a c r i t i c a l value of chordwise compression f o r which the theory requires very large thicknesses t o prevent flutter. In r e a l panels, the required thickness i n this range i s dependent on the amount of s t r u c t u r a l damping.

However, it i s apparent that these c r i t i c a l combinations of aspect r a t i o and chordwise compression should be avoided i n design.

The mode shapes of f l u t t e r of f l a t panels have an interesting feature t h a t i s i l l u s t r a t e d i n figure 4. Calculated chordwise variations of ty-p- i c a l flutter-mode shapes are shown f o r panels with both pinned and clamped edges. Note t h a t the motion is con- The air flow i s from l e f t t o right.

centrated toward the rear of the panel f o r both panels. This " t a i l - wagging" type of motion i s characteristic of the observed motion i n actual instances of panel f l u t t e r .

Consideration w i l l now be given t o the f l u t t e r of panels which have been buckled by heating or by the application of midplane loads. Buckled panels have been treated i n a number of t h e o r e t i c a l investigations, most of which are confined t o panels of i n f i n i t e aspect r a t i o . (See refs. 1, In addition, a f e w experimental studies have 2, 3, 9, 1 1 , 23, and 26 .)

been made. (See refs. 13, 16, and 2 3 . ) The e f f e c t of buckling may be seen from the results i n figure 5.

is plotted against Mach number f o r The required thickness r a t i o t/a s t e e l panels of i n f i n i t e span i n air at sea level. Curves are s h m at high Mach nmbers f o r both pinned and clamped panels.

The upper pair of curves (fig. 5 ) are calculated boundaries which apply t o buckled panels of i n f i n i t e span without regard t o buckle depth. They result frcan closed- form solutions based on the so-called "transtability" concept.

(See ref. 1.) The lower pair of curves (fig. 5 ) are the corresponding results f o r f l a t panels. Note that the buckled panels require much larger thick- nesses t o prevent f l u t t e r than do the unbuckled panels.

\ i o , . 0

0 O C 0 0 0 0 0 , - - -

c Experimental r e s u l t s f o r clamped buckled panels are also shown i n figure 5. With the exception of the point a t M = 2.18, these r e s u l t s were taken from reference 16. (They have been corrected t o apply t o M = 2.18, which was obtained inde- s t e e l a t sea level.) The point a t pendently (ref. 23), appears t o confirm the other experimental results.

The dashed theoretical curve f o r clamped buckled panels d i f f e r s on the conservative side by about I 2 percent.

In references 13 and 16, some experimental r e s u l t s were presented f o r a group of clamped rectangular panels buckled by heating. These r e s u l t s are rep_eated i n figure 6.

Figure 6 i s constructed w i t h modified-thickness-ratio parameters for both the ordinate and abscissa. One thickness r a t i o is based on the chord and the other, on the span. The data are applicable t o a l l Mach numbers greater than about 1 . 3 . The construction of the plot i s such that data f o r panels of a given aspect r a t i o f a l l on a r a d i a l l i n e from the origin. The aspect r a t i o s and orientation of the t e s t panels are shown by the small figures a t the outer ends of the !radial lines. I n each case, node l i n e s are shown t o i l l u s t r a t e the observed buckle pat- terns. The distance outward from the origin of the plot i s a measure of the panel thickness. Solid points designate panels t h a t f l u t t e r e d and open points indicate t h a t no f l u t t e r was observed.

An attempt has been made t o calculate a theoretical f l u t t e r boundary f o r t h i s particular group of panels buckled by heating. Because the midplane stresses i n the t e s t panels had not been measured, it was neces- sary t o estimate these stresses from the observed buckle patterns.

Some d e t a i l s of t h i s calculation are given i n the appendix.

The solid curve i s the resulting approximate boundary. The curve has been shown dashed on the lower right because the calculation i s a two-mode approximation which must be considered unreliable for the very low-aspect-ratio panels.

The agreement i n figure 6 between the theoretical boundary and the experimental data encourages the viewpoint t h a t successful analyses of rectangular buckled panels are possible. O f particular i n t e r e s t is the finding that, as i n the case of f l a t rectangular panels, there are c r i t - i c a l combinations of aspect r a t i o and s t r e s s f o r which even thick panels can f l u t t e r . One such c r i t i c a l point occurs i n the calculated boundary near an aspect r a t i o of 0.5. Perhaps t h i s explains why the t e s t panels with an aspect r a t i o of 0.5 were more prone t o f l u t t e r than the other t e s t panels were.

It must be pointed out t h a t the theoretical boundary is very sensi- t i v e t o the type of buckling load, especially f o r aspect r a t i o s between 0.5 and 2.

Consequently, t h i s boundary applies only t o the particular series of t e s t s shown.

It should be emphasized t h a t this boundary i s not intended t o be a universal. f l u t t e r boundary f o r finite-aspect-ratio buckled panels. In f a c t , no such universal boundary exists.

CIRCULAR CYLINDERS One other configuration which has received some preliminary atten- t i o n i s the i n f i n i t e l y long thin-walled circular cylinder with a x i a l flow over i t s outer surface. (See refs. 14, 21, and 27.) Typical results, f o r empty steel cylinders, are shown i n figure 7.

The ordinate i n figure 7 i s the r a t i o of w a l l thickness t o cylinder radius t/r and the abscissa i s the Mach number. The curves are theo- r e t i c a l f l u t t e r boundaries which apply t o unstiffened i n f i n i t e l y long cylinders. The solid curves are boundaries t h a t r e s u l t when there i s no static-pressure d i f f e r e n t i a l across the w a l l ; the dashed curves, on the other hand, correspond t o the existence of enough i n t e r n a l pressure t o cause a circwnferential tension near the ultimate.

It w i l l be noted t h a t the required w a l l thicknesses of unstiffened i n f i n i t e l y long cylinders increase rapidly w i t h increase i n Mach number and very quickly reach prohibitive values, even at very high altitudes.

Internal pressure i s seen t o produce only small percentage reductions i n these large thicknesses. Furthermore, it has been pointed out i n reference 27 t h a t negligible benefit can be expected i f internal damping i s taken i n t o account.

O n the other hand, an effect t h a t shows promise of reducing the thicknesses t o reasonable values i s the e f f e c t of f i n i t e length. For the purpose of i l l u s t r a t i n g t h i s effect, an approximate calculation has been m a d e f o r a s t e e l cylinder with r i g i d ring-stiffeners spaced a radius apart. The calculation i s based on equation (42) of reference 21with the a i r forces replaced, f o r simplicity, by their plane s t a t i c approxi- mation. This simplification imposes the requirements t h a t the Mach number M be large and t h a t M 2 >> 2 where n i s the nu-ber of f u l l a 2n waves around the circumference of the cylinder (corresponding t o the maximum required thickness f o r the prevention of f l u t t e r ) and a i s the distance between stiffeners. The resulting thickness r a t i o required t o prevent f l u t t e r at M = 6 of the stiffened s t e e l cylinder a t an a l t i t u d e of 35,000 f e e t with no i n t e r n a l pressure i s shown by the small c i r c l e i n figure 7. This r e s u l t i s only approximate because the above conditions are only approximately s a t i s f i e d (maximum t / R corresponds t o n = 26).

However, it has the correct order of magnitude. Furthermore, i n contrast t o the extremely large thickness r a t i o s predicted at M = 6 f o r the unstiffened i n f i n i t e l y long cylinder, the r e s u l t f o r the stiffened cyl- inder has a reasonable order of magnitude. Thus, the large thicknesses predicted by analyses of i n f i n i t e l y long unstiffened cylinders apparently do not apply t o practical configurations of f i n i t e length.

e e 0 . .. e. . , . - - -

i 1 6 C O N C D I N G REMARKS It may be stated that much progress has been made i n the solution and understanding of the panel f l u t t e r problem. Although, i n general, panel f l u t t e r i s of concern only i n the design of very t h i n panels, there be c r i t i c a l combinations of panel aspect r a t i o and midplane appear t o stress f o r which even very thick panels may f l u t t e r . It should be there i s a need f o r more work on certain phases of the emphasized t h a t I n particular, there i s a need f o r further con- panel f l u t t e r problem.

sideration of cylinders of finite length and f o r more experimental results f o r assessing the validity of theoretical analyses.

..a *.

APPENDIX TRANSTABILITY ANAIYSIS OF THE FLUTPER OF EUCKLFD m C W G U L A R PANEW W I T R CULMPED EDGES The application of the "transtability" concept (ref. 1 ) to rectan- gulm buckled panels with pinned edges is discussed in reference 2 6 .

The corresponding results, for clamped panels, are presented in this appendix.

The transtability problem is governed by the plate equation

DV w + PXwn + PYwn +

where w is the panel deflection and the subscripts denote differentia- tion, and by the proper boundary conditions.

The assumption is made that the panel deflection shape is adequately represented in the chordwise direction by a linear combination of the first two modes of a uniform clamped-clamped beam and in the spanwise direction by a single mode, the pth mode. Then, by the Galerkin method, the condition for the existence of a nontrivial solution is found to be where

The function e ' , ( k ) is the nth mode for a beam of unit length. The

the integrals I$) are given conveniently in refer- beam modes and ences 28 and 29.

As pointed out in reference 26, the critical value of the dynamic- pressure parameter A depends on the midplane loads Px and Py applied to the panel at the boundaries or induced by heating a panel with fixed

boundaries. Let Py = RPx. Substituting % and % from equations (3)

into equation (2) yields a quadratic equation for the buckling loads Px corresponding to given values of R and A. As A increases from zero, the buckling loads approach each other until at the critical "transtability" value of A they coalesce and disappear. This condition is given by the vanishing of the discriminant of the quadratic and yields the result Ill Calculations have been made of the quantities: and for a series of test panels buckled by heating. m e integer p, speci- fying the number of half-waves in the spanwise direction, was taken as the number of spanwise half-waves in the observed buckle patterns.

! 5";'Z

i Furthermore, since the actual loads i n the test panels had not been

measured, the r a t i o R = py - w a s estimated from the buckle patterns

P X with the aid of figure 5 of reference 30. Specifically, f o r each aspect ratio, the average longitudinal buckling load corresponding t o the number of observed spanwise or chordwise half-waves w a s used along with t h e corresponding transverse load.

For an aspect r a t i o of 1, it w a s assumed t h a t R = 1 (Px = Py). The resulting calculated boundary i s shown i n figure 6 along with the t e s t results.

0 . . .* 0 . e . . . . . . e 0 . . *

* - , , a - - - - REFERFNCES 1 . Isaacs, R. P.: Transtability Flutter of Supersonic Aircraft Panels.

U. S. Air Force Project RAND P-101, The Rand Corp., July 1 , 1949.

2 . Hayes, W.: A Buckled Plate in a Supersonic Stream. Rep. No. AL-1029, North American Aviation, Inc., May 1 0 , 1950.

3. Miles, John W.: Dynamic Chordwise Stability at Supersonic Speeds.

Rep. No. AL-1140, North American Aviation, Inc., Oct. 1 8 , 1950.

4. Shen, S. F.: Non-Stationary Aerodynamics of a Two-Dimensional Bump in a Uniform Stream and Its Effect on the Vibration Characteristics of an Elastic Panel. M.I.T. Tech. Rep. (Contract No. N5ori-07833, NR 064~59)~ k y 1952.

5. Shen, S. F.: Flutter of a Two-Dimensional Simply-Supported Uniform Panel in a Supersonic Stream. Contract No. N5oriLO7833, Office of Naval Res., Dept. Aero. Eng., M.I.T., Aug. 6 , 1932.

6. Sylvester, Maurice A., and Baker, John E . : Some Experimental Studies of Panel Flutter at Mach Number 1.3. (Supersedes NACA TN 3914, 1957.

NACA RM ~52116.)

7 . Goland, Martin, and Luke, Yudell L.: An Exact Solution for Two- Dimensional Linear Panel Flutter at Supersonic Speeds. Jour. Aero.

Sei. (Readers' Forum), vol. 21, no. 4, Apr. 1954, pp. 275-276.

8. Hedgepeth, John' M . , Budiansky, Bernard, and Leonard, Robert W. : Analysis of Flutter in Compressible Flow of a Panel on Many Supports.

Jour. Aero. Sci., vol. 21, no. 7 , July 1954, pp. 475-486.

9. Fung, Y. C. : The Static Stability of a Two-Dimensional Curved Panel in a Supersonic Flow, With An Application to Panel Flutter.

Jour.

Aero. Sci., vol. 2 1 ; , no. 8, Aug. 199, pp. 556-565.

10. Nelson, Herbert C., and Cunningham, Herbert J.: llheoretical Investi- gation of Flutter of Two-Dimensional Flat Panels With One Surface Exposed to Supersonic Potential Flow. NACA Rep. 1280, 1956.

(Supersedes NACA TN 3465.)

1 1 . Fung, Y. C.: The Flutter of a Buckled Plate in Supersonic Flow.

GAZCIT Rep. No. OSR-TN-55-237, July 1955.

12. Eisley, 5. G.: The Flutter of Simply Supported Rectangular Plates in a Supersonic Flow. QSR-TN-55-236, GUCIT, July 1955.

7G and Cunningham, Herbert J.: 13. Sylvester, Maurice A . , Nelson, Herbert C . , Experimental and Theoretical Studies of Panel Flutter at Mach Numbers 1.2 to 3.0.

NACA RM L5'jEl8b, 1955.

1 4 . Miles, John W.: Supersonic Flutter of a Cylindrical Shell. The Ramo-Wooldridge Corp., Guided Mssile Res. Div.

I . General Theory. Rep. No. AM 5-2, Aug. 19, 1955.

1 1 . Pressurization and Internal Fluid Effects. Rep. No. AM 5-ll, Nov. 14, 1955.

111. Aeolotropic Shell. Rep. No. AM 5-l2, Dec. 2 , 1955.

IV. Effects of Non-Uniform Steady Flow. Rep. No. AM 5-16,

Dee. 7, 19559

15. Shen, S. F.: Remarks on "An Exact Solution for Two-Dimensional Idnear Panel Flutter at Supersonic Speeds." Jour. Aero. Sci.

(Readers' Forum), vol. 22, no. 9, Sept. 1955, pp. 636-657.

1 6 . Sylvester, Maurice A.: Experimental Studies of Flutter of Buckled Rectangular Panels at Mach Numbers From 1.2 to 3.0 Including Effects of Pressure Differential and of Panel Width-Length Ratio.

NACA RM ~55130, 1957.

17. Luke, Yudell L . , St. John, Andrew, and Goland, Martin: An Exact Solution for Two-Dimensional Linear Panel Flutter at Supersonic Speeds. WADC Tech. Note 56-460 (Contract No. AF 3 3 ( 616) -2897), Midwest Res. Inst., Mar. 15, 1956.

18. Luke, Yudell L., St. John, A. D . , and Gross, Betty: Panel Flutter at Supersonic Speeds. Third Quarterly Progress Rep. (Contract No. AF 3 3 ( 6 1 6 ) - 2 8 9 7 ) , Midwest Res. Inst., Appl. Phys. Div., w. 29, 1956.

19. Luke, Yudell L., St. John, A. D., and Gross, EWtty: Panel Flutter at Supersonic Speeds. Fourth Quarterly Progress Rep. (Contract No. AF 3 3 ( 6 1 6 ) - 2 8 9 7 ) , Midwest Res. Inst., Appl. Phys. Div., M ~ Y 29, 1956.

20. Luke, Yudell L., and St. John, A. D . : Panel Flutter at Supersonic Speeds. Fifth Quarterly Progress Rep. (Contract No. AF 3 3 ( 6 1 6 ) - 2 8 9 7 ) , Midwest Res. Inst., Appl. Phys. Div., Oct. 31, 1956.

21. Ieonard, Robert W., and Hedgepeth, John M . : On Panel Flutter and Divergence of Infinitely Long Unstiffened and Ring-Stiffened Thin- Walled Circular Cylinders.

NACA TN 3638, 1956.

22. Hedgepeth, John M . : On the Flutter of Panels at High Mach Numbers.

Jour. Aero. Sci. (Readers' Forum), vol. 23, no. 6, June 1956, pp. 609-610.

23. Eisley, J. G.: The F l u t t e r of a Two-Dimensional Buckled P l a t e With Clamped Edges i n a Supersonic Flow. OSR-m-56-296, GALCIT, July 1956.

24. Miles, John W.: O n the Aerodynamic I n s t a b i l i t y of Thin Panels.

Jour. Aero. Sci., vol. 23, no. 8, Aug. 1956, pp. 771-780.

25. Ashley, Holt, and Zartarian, Garabed: Piston Theory - A New Aero-

dynamic Tool f o r the Aeroelastician. Jour. Aero. Sci., vol. 23, no. 12, BC. 1956, pp. 1109-1-1.3.8.

26. Hedgepeth, John M.: F l u t t e r of Rectangular Simply Supported Panels a t High Supersonic Speeds. Preprint No. 713, S.M.F. Fund Paper, Inst. Aero. Sci., Inc., Jan. 28-31, 1957.

27. Miles, John W.: Supersonic Flutter of a Cylindrical Shell. Jour.

Aero. Sci., vol. 24, no. 2, Feb. 1957, pp. 107-118.

28. Young, Dana, and Felgar, Robert P., Jr. : Tables of Characteristic Functions Representing Normal Modes of Vibration of a Beam. Univ.

of Texas, Pub. No. 4913, Eng. R e s . Ser. No. 44, Bur. Eng. R e s . , July 1 , 1949.

29. Felgar, Robert P., Jr.: Formulas for Integrals Containing Character- i s t i c Functions of a Vibrating Beam. C i r . No. 14, B u r . Eng. R e s . , Univ. of Texas, 1950.

30. Libove, Charles, and Stein, Manuel: Charts f o r C r i t i c a l Combinations of Longitudinal and Transverse Direct Stress f o r F l a t Rectangular Plates. NACA WR L-224, 1946. (Formerly NACA ARR L6AO5.)

e REQUIRED THICKNESS OF INFINITE -ASPECT-RATIO UNSTRESSED STEEL PANELS AT SEA LEVEL 7 STATIC A I R FORCES

----

UNSTEADY AIR FORCES I I I I 2 3 4 5 M Figure 1 EFFECT OF ASPECT RATIO ON REQUIRED THICKNESS OF UNSTRESSED SIMPLY -SUPPORTED STEEL PANELS AT SEA LEVEL .015- I I I I

n

I

1.7

I I I .010- I I I I t - I a I I I I I - .005 I I

'--

c--

- STATIC AIR FORCES

----

UNSTEADY AIR FORCES I I I I 2 3 4 5 M E F F E C T OF M I D P L A N E S T R E S S ON F L U T T E R OF UNBUCKLED PANELS M > 1.5 1.25- - 1.00 - .75 t

-

a - - .25 I I I

0' -i 0 I 2

PX (BUCKLING P X ) ~ -o Y - TYPICAL FLUTTER - M O D E SHAPES PINNED CLAMPED L E A D I N G EDGE T R A I L I N G EDGE Figure 4 EFFECT OF BUCKLING ON REQUIRED THICKNESS OF I N F I N I T E - ASPECT-RATIO S T E E L PANELS AT SEA L E V E L -OI5r PINNED EDGES

I - -----

CLAMPED EDGES O CLAMPED EDGES EXPERIMENT

.OlO c

.ED

0 0 ------------- I BUCKL

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ }FLAT 00 0

M REQUIRED THICKNESSES OF A SERIES OF TEST PANELS BUCKLED BY HEATING 0 FLUTTER 0 NO FLUTTER .8 .6 I -

' ) 3 q +

.4 .2 0 . 2 .4 . 6 .8 1 . 0 1.2 Figure 6 REQUIRED THICKNESS OF INFINITELY LONG STEEL CYLINDERS .020- .015- NO INTERNAL PRESSURE MAX. INTERNAL PRESSURE

q

35,000 FT NO INTERNAL PRESSURE I 1 5 6 M Figure 7 ... b I .. .

\ L - ’ FLUTTER AND DIVERGENCE OF RECTANGULAR WINGS OF VERY LOW ASPECT RATIO By Robert W. Fralich, John M. Hedgepeth, and W. J. Tuovila Langley Aeronautical Laboratory SUMMARY Slender-body aerodynamic theory is used in conjunction with thin- plate theom in the flutter analysis of low-aspect-ratio rectangular wings of constant thickness when chordwise variations of deflections are considered.

The spanwise variation of deflection is given by a parabola, and the chordwise variation is allowed complete freedom. The results show the variation of flutter speed and mode shape with aspect ratio. Comparisons are made with results obtained by approximating the chordwise deflection shape by the first few terms of a power series.

Comparisons with some preliminary experimental results are also included.

INTRODUCTION The prediction of flutter of wing and tail surfaces of very low aspect ratio is a problem of some concern to aircraft designers. The difficulties in the flutter analysis of such surfaces are mainly con- nected with the presence of large amounts of chordwise curvature in the flutter mode. It is of interest to investigate the complexity of the chordwise deflection shape at flutter and to determine to what degree of accuracy the chordwise deflection must be represented in order to obtain good results. This paper is concerned with the flutter behavior, both theoretical and experimental, of the simple low-aspect-ratio con- figuration shown in figure 1. The analysis is similar to that of ref- erence 1, which treated the static divergence behavior of the same configuration.

SYMBOLS coordinate system (see fig. 1) wing deflection, positive in z-direction free-stream velocity wing thickness wing chord wing semispan time chordwise deflection shape pv2 .

dynanic pressure, -

E Young's modulus of elasticity free-stream density of fluid P density of material period of oscillation Mach number perturbation-velocity potential s3

h flutter-speed parameter, z(1 - p2)$ -

4 t3 K flutter-frequency parameter, u) mass-ratio parameter, S p s E 2 h t Poisson's ratio (taken as 1/3 in all computations) CL

D plate stifmess in bending, Et3/12(l - p2)

U) flutter frequency THEDREZICAL APPROACH The configuration analyzed in this paper consists of a rectangular plate of constant thickness from a rigid wall. (See fig. 1.)

r

I 582

This plate may be thought of as representing one-half of a wing with a chord c and a semispan The plate is located in a fluid flow with s.

The deflection shape of such a low-aspect- a free-stream velocity V.

ratio plate can be expected to vary in a much more complicated manner in the chordwise direction than in the spanwise direction. For this reason the deflection w is assumed to vary as w(x,y,'r) = y2F(x,T), where the spanwise deflection is given by a simple parabola and the chordwise variation F of the deflection is an arbitrary function of the chordwise coordinate x and time 7 . The distortions of the plate The aerodynamic are found through the use of ordinary thin-plate theory.

loadings are found most simply by using slender-body aerodynamic theory.

In this theory streamwise perturbations are neglected in comparison with perturbations in the crossflow direction. The use of this approximate aerodynamic theory simplifies the aeroelastic problem to the extent that an exact solution is possible. A brief description of the analysis and the resulting equations are given in the appendix.

RESULTS AND DISCUSSION Some results are given by the boundaries shown in figure 2. The

ordinate is the dynamic-pressure parameter *, in which q is the

(*/SI3 dynamic pressure, is Young's modulus of elasticity for the plate, E and t/s is the ratio of thickness to semispan. The abscissa is the ratio of chord to semispan c/s. The variation of the dynamic-pressure parameter for flutter with the ratio of chord to semispan is dependent upon

the mass-ratio parameter E in which is the ratio of air density

R t l t Qm to plate density. The flutter boundaries are given for two values of mass-ratio parameter; the region above a particular boundary is unstable while that below is stable. Also shown is the result for static diver- gence obtained from reference 1. This result, which is, of course, independent of the mass ratio, is indicated by a single curve.

Note that divergence is less critical than flutter for these particular mass ratios. Note also that, for the higher mass ratio, the flutter boundary consists of a series of loops approaching a constant value of dynamic- pressure parameter. The lower curve also has these characteristics; how- ever, the loops are so elongated in this case that only one can be seen in this figure.

The kind of flutter mode shapes obtained fromthe analysis is shown in figure 3 . The top set of curves shows the components of tip deflection which are in phase and out of phase with the maximum leading- edge deflection for a value of corresponding to the tick mark on c/s the bottom of the first loop on the flutter boundary in figure 2. The t i p deflection i s given when the leading edge has i t s maximum amplitude and a t one-quarter of a period later when the leading edge has zero deflection. The bottom set of curves gives the components of mode shape f o r a value of c/s given by the t i c k mark on t h e second loop of t h e f l u t t e r boundary of figure 2. The e f f e c t of increasing the chord i s t o add more waves t o the mode shape.

I n the r e s u l t s discussed so far, t h e chordwise variations of deflec- tions were allowed complete freedom and an exact solution w a s possible.

I n a p r a c t i c a l case, an exact solution would not be feasible, and some s o r t of approximation of t h e chordwise deflection shape would be nec- essary. Some f l u t t e r boundaries obtained by approximating the chord- w i s e deflections by t h e first few terms of a power series are shown i n figure 4. The dashed curve gives the results f o r parabolic deformations, and the long-and-short-dashed curve gives the results f o r cubic deforma- Both approxi- tions. The exact boundary i s a l s o shown f o r comparison.

mations y i e l d good results f o r the lower values of c/s. The cubic approximation is almost exact. For longer chords, however, both approxi- mations y i e l d poor r e s u l t s . Apparently, i n order t o analyze the f l u t t e r behavior of wings i n t h i s range, higher order terms i n t h e deflection shape must be used.

It can be seen from figure 2 t h a t f o r each value of mass r a t i o a limiting value of the dynamic-pressure parameter can be obtained by con- sidering t h e values a t the bottom of the loops as the chord becomes large. The variation of t h i s limiting value w i t h mass r a t i o i s shown i n figure 5 . The r e s u l t s obtained so far indicate that t h i s curve gives a conservative estimate of the f l u t t e r speed f o r t h i n rectangular plates of very l o w aspect r a t i o . It should be noted that the f l u t t e r speed i s less than the divergence speed and seems t o approach it asymptotically f o r high mass r a t i o .

Several preliminary tests of some low-aspect-ratio plates a t super- sonic Mach numbers have been run i n the Langley 9- by 18-inch supersonic f l u t t e r tunnel. The The r e s u l t s of these tests are shown i n figure 6.

f l u t t e r speed of t h e various models i s shown as a r a t i o of experimental f l u t t e r speed t o calculated f l u t t e r speed, where t h e calculated f l u t t e r speed w a s obtained from the curve i n figure 5 . T h i s r a t i o i s plotted against the r a t i o of chord t o semispan. The agreement between theory and experiment is f a i r l y good i n view of t h e approximations inherent i n the theory and of the preliminary nature of the tests.

During t h e tests the f l u t t e r modes were observed, and it w a s noted that t h e specimens w i t h the larger r a t i o s of chord t o semispan had t h e more complicated mode shapes as i s predicted by theory.

.

CONCLUDING REMARKS The f l u t t e r analysis of low-aspect-ratio rectangular p l a t e s indi- cates t h a t the flutter-mode shape has an increasing number of waves i n as the aspect r a t i o is reduced; approximating the chordwise direction the chordwise deflection shape by parabolic or cubic curves yields f l u t - t e r speeds i n fair agreement with those of the more exact theory, pro- vided that the aspect r a t i o i s not too l o w . The cubic curve gives some- what b e t t e r r e s u l t s . For lower aspect r a t i o s , higher order approximations must be used. Experimental data indicate that the f l u t t e r speed and the type of mode shape yielded by the theory are i n fair agreement with results.

experimental

APPENDIX AmLYSIS In the application of slender-body aerodynamic theory to the present unsteady-flow problem, terms containing time derivatives in the velocity- potential equation for linearized flow axe neglected in addition to those containing streamwise x-derivatives. The velocity-potential equation thus reduces to Laplace's equation in the crossflow plane. The boundary conditions on velocity and the pressure-potential relations are taken to be the same as those ordinarily used in unsteady linearized aerodynamic theory.

The potential cp and the aerodynamic loads resulting f'romthe given deformation shape are calculated in a manner similar to that used in reference 1 for the static-divergence problem.

The principle of minimum potential energy is used to derive the in a man- differential equation of equilibrium for the function F(x,T) ner analogous to that used in reference 1. Solution yields an eigen- value equation which relates the flutter speed to the properties of the plate and the surrounding air:

Dl cos + E1 cosh cosh + F1 sinh sinh 9) +

L

i ( D 2 sin + E5! U sinh cosh E + 2 cosh % sinh E j

S P S where -.-..

I -

(A3 + hB7) 12A3 - ( 47* + a2 + P2> A J , ] +

I , , 0 . .. .*

0 0 . I , a * .

F 1 = (A3 + AB3)[2u2P2A4 - (4y2 + u2 + P2)A3] +

u2p2(A4 - A) [+ - ( 4r2 + a2 + P2)A4]

D2 = -( A1B2 - A2B1)

+ 8a1 - 8A + - 2(r2 - h )

in which

= 20 (1 - 1.1)A + (Y 2 - A) (2. - y 1 2 j " " )

B2 3

IF 5€h

- 20 (1 - p)A + 1 0 (1 - p ) r 2 + h2 - -- - m o (1 - p ) ( l - 21.1)

A3 - 9

3 3

472 *

A4 = 1 0 (1 - p) + r2

- 10

CI. - Y 2

B3 - 3

In equation (l), u and p can be either r e a l or imaginary quantities.

Solution by t r i a l yields the curves given i n figure 2.

The divergence boundary obtained from reference 1 can also be obtained from t h e present analysis by s e t t i n g the flutter-frequency parameter K equal t o zero.

Mode Shapes The flutter-mode shapes shown i n figure 3 can be obtained from the following equation, whe the component i n phase and

- 9

the imaginary part, the component out of phase with the max- leading- edge deflection: X

im2 5 + C3e a 3 5 + C4e im4 Q

Cleiml = + C2e

f ( x ) =

c1 + c2 + c3 + c4

where

- i ( m l + m 4 ) 4j

+

(5 - %)(a2 - m42)%.3'

C

(5 - ml)(a2 - % 2 2 ) ~ 13 e -i(%+%) 5 +

(ml - 9) (9 - m32)A12e

i n which

m l = 7 + ij3

m ; ! = y - i $

m3 = -7 + ia

m4 = -7 - ia

Approximate Solutions The approximahe analysis used parallels the analysis f o r divergence presented i n reference 1. Cubic approximation of the chordwise varia- t i o n of deflection r e s u l t s i n the following complex determinant: G N v II

& f

+ &It-

@

*

I cu I M v L 2 L . I 81- + I I +

A

N v

No1 -

+ t 1 2 REFERENCE 1. Hedgepeth, John M . , and Waner, Paul G., Jr.: Analysis of Static Aeroelastic Behavior of Low-Aspect-Ratio Rectangular Wings. NACA !JD 3958, 1957.

CANTILEVER PLATE OF VERY LOW ASPECT RATIO Figure 1 FLUTTER AND STATIC DIVERGENCE BOUNDARIES DIVERGENCE

‘r

c/s Figure 2 FLUTTER MODE SHAPES IN-PHASE (T"0) I I I I I I I 0 I 2 3 4 5 6 x/s, DISTANCE IN SEMISPANS Figure 3 FLUTTER BOUNDARIES OBTAINED FROM APPROXIMATE DEFLECTION FUNCTIONS

-

1 . 0 p s .00636 P , t = - \ .8 .6 (t/s) 3

-

.4 EXACT

----- PARABOLIC OEFORMATION

- --- CUBIC DEFORMATION

.2 I I I I I 2 4 6 8 1 0 CIS Figure 4 ENVELOPE VALUES OF CRITICAL DYNAMIC-PRESSURE PARAMETER I I I I I I .02 .03 .04 .05 .06 .01 PS

-

Pm+ Figure 5 1.2- H - H ' 1.0 F ( 2 r '

-

0 .

.0 VEXP VCnLC .6 M .4

} ALUMINUM

0 1.64 .2

l.3 } STEEL

H 1.64 I I I I I I I 0 I 2 3 4 5 6 c/s Figure 6 FLUTTER EXPlKtMENTS W I T H VARIOUS CONTROL CONFIGURATIONS By Robert W . Boswinkle, Jr., and Homer G. Morgan Langley Aeronautical Laboratory SUMMARY The f l u t t e r characteristics of various control-surface configurations have been under study a t the Langley Aeronautical Laboratory. Presented herein i s a compilation of some of the more pertinent results. Most of the models studied were dynamically and e l a s t i c a l l y scaled frm proposed a i r c r a f t . The f l u t t e r investigations w e r e made i n various f a c i l i t i e s over both the transonic and supersonic speed ranges. Configurations tested included a wing with t i p ailerons, all-movable elevators, v e r t i c a l tails with trailing-edge rudders, and a T-tail.

INTRODUCTION A large portion of the f l u t t e r problems which plague modern aircraft is associated with control systems. No r e a l l y reliable analytical method i s available f o r designing controls i n the transonic zone. Such a variety of configurations arise that an overall trend study of characteristics is impractical. i s t o investigate experimentally the various The alternative specific configurations as they arise. Much of the work on controls a t the Langley Aeronautical Laboratory has been of this type.

The Langley Laboratory has worked with various organizations on control-surface f l u t t e r problems of new a i r c r a f t . The work has included transonic and supersonic f l u t t e r t e s t s of models. Most of the models used were both dynamically and e l a s t i c a l l y scaled from the prototype a i r c r a f t .

Some of the more pertinent results of these investigations w i l l be pre- sented. The controls t o be discussed are shown as configurations A t o H i n figure 1. They include a wing with t i p ailerons, two all-movable controls, four v e r t i c a l tails with trailing-edge rudders, and a T - t a i l .

SYMBOLS a speed of sound, ft/sec b root half chord, f t g s t r u c t u r a l damping coefficient M Mach number dynamic pressure, lb/sq f t

v free-stream velocity, f t / s e c

Mass of wing P = Mass of air contained i n truncated cone determined by wing LUf f l u t t e r frequency, radians/sec bending frequency, radians/sec

torsional frequency , radians /sec

a , control-surface rotational frequency, radianslsec p i t c h frequency of all-movable control, radians/sec LUe W 1 first coupled frequency, radians/sec DISCUSSION

Configuration A - Wing With Tip Ailerons

Configuration A w a s a wing of arrowhead plan form, shown i n f i g - The leading ure 1, w i t h trailing-edge flaps and all-moving t i p ailerons.

edge of the wing was swept back 5 5 ' and the t r a i l i n g edge w a s swept for- ward 10'. The aileron w a s about 20 percent of the exposed wing area and i t s hinge l i n e w a s swept back about 4.5'. The hinge l i n e w a s located a t 56 percent of the aileron root chord (where the aileron root chord is the chord which contains the innermost parting l i n e ) . The a i r f o i l w a s 3 per- cent thick. The wing w a s cantilever mounted a t the root. The t r a i l i n g - edge f l a p s had a fixed rotational stiffness. Flutter points were obtained for different values of simulated aileron actuator stiffness.

The r e s u l t s are shown i n figure 2, plotted as the stiffness-altitude Increases i n a l t i t u d e correspond t o parameter against Mach number.

increases i n the value of the stiffness-altitude parameter. I n this type figure, constant a l t i t u d e occurs as a horizontal line, and constant- dynamic-pressure curves are s t r a i g h t lines through the origin. In f i g - ure 2, the frequency i n the stiffness-altitude parameter i s the torsion frequency of the wing. The actuator s t i f f n e s s i s the actual value divided by the original value.

Data f o r the original value of actuator s t i f f n e s s are shown on the l e f t side of figure 2. The no-flutter points correspond t o about sea- level conditions. The mode of f l u t t e r which occurred a t a Mach number of about 0.9 w a s predominantly bending and torsion of the w i n g , whereas the f l u t t e r mode a t supersonic Mach numbers w a s predominantly aileron rotation.

These f l u t t e r points w e r e considered t o be too close t o the air- plane f l i g h t regime and an improvement i n the conditions w a s sought by increasing the actuator s t i f f n e s s t o three times the original s t i f f n e s s .

This increased actuator s t i f f n e s s w a s s t i l l a feasible value. The data obtained with the stiffer actuator are shown by the squares on the r i g h t side of figure 2. The no-flutter points a t supersonic speeds so obtained were a t lower altitudes than the f l u t t e r points previously obtained with the lower actuator s t i f f n e s s . No-flutter points were also obtained a t supersonic speeds w i t h an i n f i n i t e actuator stiffness. I n f i n i t e actuator stiffness w a s simulated by gluing the aileron t o the wing so no r e l a t i v e motion could take place. It i s interesting t o note, however, that, even with i n f i n i t e actuator stiffness, bending-torsion-type f l u t t e r w a s s t i l l obtained near a Mach number of 0.9 and occurred a t about the same a l t i - tude as f o r the lowest value of actuator s t i f f n e s s .

Increasing the actuator s t i f f n e s s w a s one way t o increase the aileron rotation frequency; another way w a s t o reduce the moment of i n e r t i a of th? aileron. Since there was considerable windup of the ailerons, a large reduction i n effective moment of i n e r t i a w a s possible by cutting off the t i p s of the ailerons. Accordingly, the t i p s were cut off along the dashed lines shown i n figure 1. Removal of these t i p s gave beneficial results a t supersonic speeds but again l e f t the subsonic f l u t t e r region essentially unaffected.

Increasing the actuator stiffness o r cutting off the aileron t i p s reduced the a l t i t u d e a t which the aileron-rotation-type f l u t t e r occurred a t supersonic speeds. These changes had no e f f e c t on the bending-torsion- type f l u t t e r obtained a t subsonic speeds.

Configuration B - All-Movable Stabilizer

Configuration B, as sham i n figure 1, w a s an all-movable s t a b i l i z e r .

The model had an aspect r a t i o of 3.3, a taper r a t i o of 0.42, 3 5 ' sweepback of the quarter-chord line, a i r f o i l sections tapering from 6 percent thick a t the root t o 4 percent a t the t i p , a rounded t i p , and a p i t c h axis a t 78.9 percent of the center-line chord. T e s t s were made a t a constant value of s t a b i l i z e r t w i s t s t i f f n e s s and r a t i o of bending frequency t o tor- sion frequency. The pitching frequency of the s t a b i l i z e r on its spindle w a s the main test variable.

These t e s t r e s u l t s are shown i n figure 3 where the stiffness-altitude parameter is shown as a function of Mach number f o r various values of the The frequency i n the r a t i o of bending frequency t o pitch frequency.

stiffness-altitude parameter is the torsion frequency of the s t a b i l i z e r .

The lower curve i s f o r a frequency r a t i o of 0.50. A s the Mach number is increased, the f l u t t e r boundary shifts t o higher altitudes. This Mach number e f f e c t becomes more pronounced as the frequency r a t i o is increased as shown by the slopes of the curves f o r frequency r a t i o s of toward 1.0, 0.62, 0.77, and 0.94.

The e f f e c t of frequency r a t i o a t a Mach number of 0.8 is shown i n figure 4. The flutter-speed coefficient V/bcDa is plotted as a function of frequency r a t i o f o r a given value of mass-density r a t i o . It should be noted that on this p l o t the f l u t t e r side of the boundary is above the The experimental data are shown as a s o l i d curve, cross-plotted curve.

from the previous figure. The other two curves are calculated results and three using two-dimensional incompressible aerodynamic coefficients uncoupled modes. The calculations were made a t a fixed value of the r a t i o of bending frequency t o torsion frequency, % / u + , , = 0.303. The lower dashed-line curves assume zero structural damping coefficient and the upper dashed-line curves use a structural damping coefficient i n each of the three modes equal t o the measured values. This calculation again shows the importance of damping on f l u t t e r speeds a t frequency r a t i o s near 1. The trend a t frequency r a t i o s below 1 appears t o be predicted and the calculations are on the conservative side of the boundary. The calculations predict a favorable jump i n f l u t t e r speed as the frequency r a t i o is increased above 1 although experimental data were not obtained a t large enough frequency r a t i o s f o r verification.

For frequency r a t i o s 1, these calculations indicate that the f l u t t e r speed increases above almost d i r e c t l y w i t h the torsion frequency. Changes i n r a t i o of bending frequency t o pitch frequency would have practically no e f f e c t on the f l u t t e r speed.

However, a t frequency r a t i o s between about 0.3 and 0.8, increases i n torsion frequency may not result i n proportionate increases i n f l u t t e r speed.

The f l u t t e r speed i n this region varies i n a much more complicated manner. For example, notice that an increase i n torsion fre- quency wa w h i l e holding the r a t i o of bending frequency t o torsion f r e - quency constant would require increases i n %, the bending frequency.

This, i n turn,,would increase the r a t i o of bending frequency t o p i t c h frequency and lower the flutter-speed coefficient. A more complete dis- cussion of t h i s behavior is given i n reference 1.

Configuration C - All-Movable Stabilizer

Configuration C y shown i n figure 1, i s a s t a t i c a l l y balanced a l l - movable s t a b i l i z e r . The control w a s spindle mounted with the rotation axis a t 46 percent of the root chord. Its semispan aspect r a t i o w a s 1.56, leading-edge sweepback w a s 20°, the t r a i l i n g edge w a s swept f o r - ward 24O, and the thickness r a t i o w a s 5 percent. Torsion frequency O f the surface w a s very high, so that the predominant control-surface modes were pitch about the spindle axis and bending. Studies were made a t various values of the r a t i o of bending frequency t o pitch frequency.

The results are shown i n figure 5 , with stiffness-altitude parameter plotted as a function of Mach number. The frequency i n the s t i f f n e s s - altitude parameter i s the rotation frequency of the s t a b i l i z e r . The upper curve is the f l u t t e r boundary established f o r an uncoupled bending- pitch frequency r a t i o of 1.02. When the frequency r a t i o w a s increased t o 1.41 or decreased t o 0.92, favorable shifts i n the f l u t t e r boundary were obtained. For the higher frequency ratios the f l u t t e r mode involved both bending and torsion, whereas f o r the lowest frequency r a t i o the f l u t t e r mode involved primarily bending. "hese tests demonstrate that a change i n frequency r a t i o which moves the frequency r a t i o away from 1 is bene- f i c i a l and requires less s t i f f n e s s t o avoid f l u t t e r .

Mass balancing is a common method f o r increasing the f l u t t e r speed of controls. Such a method w a s studied f o r t h i s case. The results a r e The plain-wing data f o r a frequency r a t i o of 1.02 are shown i n figure 6.

repeated from the previous figure. Also shown is the f l u t t e r boundary a heavy leading edge w a s added t o the same configuration on obtained when the outboard 50 percent of the control, as shown by the sketch i n figure 6.

The added weight w a s about 7 percent of the plain-wing weight. The f r e - quency r a t i o ,of the modified model dropped t o 0.95. Adding the weight is seen t o be beneficial so that less s t i f f n e s s i s required t o prevent f l u t - ter. However, the increase i n f l u t t e r speed may be due t o the change i n frequency r a t i o as w e l l as the center-of-gravity s h i f t .

Calculations have been made f o r comparison with the experimental data obtained with the plain wing a t frequency r a t i o s of 1.02 and 1.41.

The calculated and experimental results are compared i n figure 7.

Experimental f l u t t e r points are shaded symbols and experimental no- f l u t t e r points are open symbols.

The calculated results are shown as the curves. These calculations used the first two measured coupled modes of the system. Zero structural damping w a s assumed and the aero- dynamic forces were obtained from piston theory (ref. 2) including the e f f e c t of a i r f o i l thickness.

The calculated f l u t t e r boundary f o r a frequency r a t i o of 1.02 i s seen t o be i n excellent agreement with the experimental data over the

Mach number range investigated - 1.5 t o 2.8. The agreement i s not s o

good f o r a frequency r a t i o of 1.41. For this case, the calculated curve passes through experimental no-flutter points a t Mach numbers of 1.6 and 2.0 and so predict more s t i f f n e s s than necessary. Not enough s t i f f n e s s is predicted a t a Mach number of 2.2. These two examples give some indication of the r e l i a b i l i t y of l o w supersonic flutter-speed calcula- tions using piston theory. For one case, agreement between experiment and calculations is good and i n the other case, not s o good.

Configurations D and E - Vertical Tails With

Trailing-Edge Rudders Configurations D and E, sham i n figure 1, were swept v e r t i c a l tails with unbalanced trailing-edge rudders. Studies were made i n two different f a c i l i t i e s t o obtain the f l u t t e r boundary f o r each configura- t i o n at both transonic and supersonic speeds. The models were canti- lever mounted and had fairings t o keep them out of the tunnel boundary layer.

The models were f l a t plates that w e r e tapered i n thickness along t a i l D the span. Both models had 60° sweptback leading edges. Vertical Its rudder had a panel aspect r a t i o of 0.72 and a taper r a t i o of 0.43.

hinge l i n e w a s swept back 43' and its rudder w a s 24 percent of the exposed surface area. tail E had a panel aspect r a t i o of 0.77 Vertical and a taper r a t i o of 0.48, based on a plan form without a rounded t i p .

Its rudder hinge l i n e had 5 0 ' of sweepback and i t s rudder w a s about 36 percent of the exposed surface.

The results f o r configuration D are presented i n figure 8, where the stiffness-altitude parameter is plotted as a function of Mach number.

The frequency appearing i n the stiffness-altitude parameter is the rota- t i o n frequency of the rudder.

This model w a s cantilever mounted along its e n t i r e root chord. These controls had a r a t i o of first bending frequency t o rudder-rotational frequency of about 0.4. Also shown i n figure 8 is the f l u t t e r frequency referred t o the control rotation frequency.

A t a Mach number of about 1.2, an abrupt increase i n stiff- ness is required t o prevent f l u t t e r . A t the same Mach number the f l u t t e r frequency a l s o changes abruptly. A t lower Mach numbers, the f l u t t e r fre- quency is less than the rudder-rotation frequency, whereas a t higher Mach numbers the f l u t t e r frequency i s greater than the rudder-rotation fre- change i n f l u t t e r frequency is associated with a change i n quency. This the f l u t t e r mode. Previously, f l u t t e r mode changes i n w i n g s without con- t r o l s have been observed t o produce more stable configurations i n the transonic region. I n the present case, however, the change is toward a less stable system.

9 shows the results f o r configuration E wherein the plan form Figure w a s cantilevered from a stub. In this case, the r a t i o of first-bending frequency t o rudder-rotation frequency is about 0.3. Again, the figure shows both the stiffness-altitude parameter and r a t i o of f l u t t e r frequency t o rudder-rotation frequency as functions of Mach number. The f l u t t e r frequency again suggests a change i n the f l u t t e r mode past a Mach number is gradual as Mach number increases and not abrupt as of 1 but the change f o r configuration D. Also, no destablizing jump or discontinuity i n If the stiffness-altitude parameter occurs as Mach number increases.

a flutter-mode change does occur, the shift is gradual and produces no detrimental effects.

For v e r t i c a l tail D, a destablizing jump w a s found i n the f l u t t e r boundary a t low supersonic speeds, whereas none w a s obtained f o r v e r t i - c a l t a i l E. A very different type of f l u t t e r boundary w a s obtained f o r somewhat similar v e r t i c a l tails with rudders. However, f o r both con- t r o l s , if the surface were designed with j u s t enough s t i f f n e s s t o avoid f l u t t e r a t transonic Mach numbers, a new f l u t t e r region would be encountered a t the same a l t i t u d e a t a Mach number of about 2.5. This

again shows the existence of two c r i t i c a l f l u t t e r regions - transonic

A complete description and discussion of the tests on and supersonic.

these two v e r t i c a l tails w i l l be found i n reference 3.

Configurations F and G - Vertical Tails With

Trailing-Edge Rudders Configurations F and G, shown i n figure 1, were swept v e r t i c a l tails with s t a t i c a l l y balanced trailing-edge rudders. S t a t i c balancing w a s accomplished w i t h overhanging-balance weights located a t the top of the rudders. Vertical tail F had an aspect r a t i o of 1.33, taper r a t i o of 0.44, and i t s rudder w a s about 24 percent of the exposed surface area.

Vertical t a i l G had an aspect r a t i o of 1.58, a taper r a t i o of 0.40, and a Both con- rudder which w a s about 20 percent of the exposed surface area.

figurations had 45' sweep a t the quarter-chord line, 2g0 sweep on their rudder hinge l i n e s and tapered i n thickness from about 6 percent a t the 4 percent a t the t i p . The models w e r e cantilever mounted root t o about a t the root.

The results f o r v e r t i c a l t a i l F are presented i n figure 10. The frequency appearing i n the stiffness-altitude parameter is the torsion frequency of the f i n . Fin properties remained essentially unchanged during the test, w h i l e the actuator and rudder twist stiffnesses w e r e varied. The actuator and twist stiffnesses shown i n the figure have been divided by the values of the stiffnesses f o r the original configuration.

The f l u t t e r points obtained w i t h the original v e r t i c a l t a i l are indicated by the circles. This f l u t t e r boundary f e l l within the airplane f l i g h t I n an attempt t o study the nature of this f l u t t e r , a new system regime.

w a s tried wherein the rudder twist s t i f f n e s s w a s increased t o 1 . 3 t i m e s the original value w h i l e actuator s t i f f n e s s w a s reduced t o 0.8 of i t s The squares show where f l u t t e r w a s obtained with the changed value.

They show that the cbange w a s quite detrimental t o the stiffnesses.

f l u t t e r boundary; that is, with a stiffer rudder and a weaker actuator the f l u t t e r boundary shifted t o higher altitudes. The coupled frequency ‘up/uu = 0.33 and spectrum of the two models remained about the same: qJwu = 0.22.

were made with viscous dampers on the original rudder Some t e s t s i n an attempt t o eliminate the f l u t t e r from the f l i g h t envelope of the The dampers were mounted a t about midspan on the rudder.

airplane.

Flutter w a s s t i l l obtained when the damping produced by the dampers w a s 60 percent of c r i t i c a l . The f l u t t e r was eliminated when the damping w a s 120 percent of c r i t i c a l . The damping values quoted here are based on an Since these assumptions yield i n e l a s t i c rudder and back-up structure.

high values of c r i t i c a l damping, the damping actually obtained w a s prob- ably somewhat less than the stated value.

The c i r c l e s f o r the original v e r t i c a l t a i l are repeated as c i r c l e s again i n figure 11where dynamic pressure is shown as a function of Mach For this p l o t the f l u t t e r side of the boundary i s above the number.

curve. Also shown i n this figure are three no-flutter points and a f l u t - t e r point obtained w i t h v e r t i c a l tail G which had a longer and s t i f f e r f i n than vertical t a i l F. As indicated i n the figure, the rudder actuator and t w i s t s t i f f n e s s f o r v e r t i c a l t a i l G were a l s o s o m e w h a t greater than f o r

v e r t i c a l t a i l F, although u”n/% and up/% were about the same. These

results indicate that the f l u t t e r boundary f o r v e r t i c a l t a i l G would be a t substantially higher dynamic pressures than f o r v e r t i c a l t a i l F. Haw- ever, the one f l u t t e r point f o r v e r t i c a l t a i l G w a s s t i l l considered t o be too close t o the airplane f l i g h t regime. An adequate f l u t t e r boundary The dampers pro- appeared t o be obtained when viscous dampers were used.

duced about 15 percent of c r i t i c a l damping.

An additional test w a s made without dampers but w i t h the f i n t i p cut off along the dashed l i n e indicated i n figure 1.

With the f i n t i p cut off, v e r t i c a l tail G had about %he same plan form as v e r t i c a l t a i l F but the frequency r a t i o s w e r e reduced t o cop/ua = 0.25 and d% = 0.18.

The one f l u t t e r point obtained w i t h the f i n t i p cut off, shown i n f i g - ure 11, reveals a large increase i n dynamic pressure required t o f l u t t e r this t a i l compared with v e r t i c a l tail F.

This increase i n dynamic pres- sure required t o f l u t t e r the clipped configuration G over that required f o r configuration F can be attributed t o increases i n the s t i f f n e s s of the f i n , actuator, and rudder. The rudder t w i s t s t i f f n e s s w a s 2.8 t i m e s that of the original configuration and the actuator s t i f f n e s s w a s 1.5 times that of the original configuration.

Studies of v e r t i c a l tails F and G i n the transonic speed range have shown that their f l u t t e r boundaries are sensitive t o changes i n the rudder twist s t i f f n e s s and rudder actuator stiffness. Flutter could be eliminated by using viscous dampers, but the amount of damping required varied greatly between the two configurations.

s -

Configuration H - T - t a i l

Configuration H, shown i n figure 1, i s a T - t a i l which did not have any movable control surfaces. The torsion and side f l e x i b i l i t i e s of the fuselage were simulated i n the t a i l mounts. The f i n had an aspect r a t i o of 1.0, a taper r a t i o of 0.56, and 45' sweepback of the quarter-chord line. The s t a b i l i z e r had an aspect r a t i o of 1.8, a taper r a t i o of 0.43, and 40' sweepback of the quarter-chord l i n e . The r a t i o of cantilevered w a s about 0.55.

f i n bending t o f i n torsion frequencies The r e s u l t s of the f l u t t e r investigation are shown i n figure 12.

Stiffness-altitude parameter is plotted as a function of Mach number and the frequency appearing i n the parameter is the torsion frequency of the f i n . The original s t a b i l i z e r had 1-5' of positive dihedral and the f l u t - ter points obtained with t h i s configuration are indicated by the c i r c l e s .

Models with zero s t a b i l i z e r dihedral were also investigated and the f l u t t e r points obtained w i t h this configuration are indicated by the squares. The results indicate that l e s s f i n s t i f f n e s s i s required f o r zero s t a b i l i z e r dihedral and so s t a b i l i z e r dihedral is indicated t o be detrimental .

The detrimental e f f e c t of s t a b i l i z e r dihedral can be explained as a yawing wing.

qualitatively by considering the s t a b i l i z e r When the f i n t w i s t s , the s t a b i l i z e r yaws. As a result of dihedral this yaw motion produces a rolling moment on the s t a b i l i z e r so that f i n t w i s t r e s u l t s i n f i n bending.

Simple Models of All-Movable Controls I n addition t o the previously discussed scaled models, some simple models of all-movable controls have been investigated a t low supersonic

speeds. As figure 13 shows, they had arrowhead plan forms - a 45' delta

and one with a 45O sweptback leading edge and a 15' sweptforward t r a i l i n g edge. The models w e r e f l a t plates with beveled edges and were supported by a shaft mounted i n a bearing. The f l e x i b i l i t y w a s primarily i n the shaft so that the control surface experienced only rigid-body torsion, flapping, and translation. The r a t i o s of first coupled frequency t o second coupled frequency varied from about 0.3 t o about 0.7.

The r e s u l t s are presented as the stiffness-altitude parameter plotted The frequency i n against rotation-axis position i n percent of root chord.

the stiffness-altitude parameter is the first coupled frequency of the system. The trend shown a t a Mach number of 1.2 for both surfaces pro- duces a more stable configuration as the rotation axis i s moved forward.

The two f l u t t e r points obtained a t a Mach number of 1.6 indicate that, f o r rearward rotation axes, more stiffness i s required t o prevent f l u t t e r as the Mach number increases. However, the s t i f f n e s s required a t a Mach number of 1.6 rapidly decreases as the rotation axis is moved forward s o that, a t the axis location shown i n the figure, the controls were stable This means the a t a zero value of the stiffness-altitude parameter.

controls were f l u t t e r f r e e when unrestrained i n rotation and when f r e e t o f l o a t . Thus, these r e s u l t s show that movement o f ’ t h e axis location forward w a s beneficial on these plan forms a t low supersonic Mach numbers.

CONCLUDING REMARKS A compilation of f l u t t e r experiments w i t - , various control conf-gura- tions a t transonic and supersonic speeds has been presented. Some trends on specific configurations are indicated and improvements i n f l u t t e r characteristics f o r various cases a r e shown. It would be risky t o d r a w general conclusions from these results, but the discussion should be of value.

1. Land, Norman S., and Abbott, Frank T., Jr.: Transonic Flutter Inves- tigation of an All-Movable Horizontal T a i l f o r a Fighter Airplane.

NACA R M ~ 5 6 ~ 0 6 , 1957.

2. Ashley, H o l t , and Zartarian, Garabed: Piston Theory - A N e w Aerody-

Tool f o r the Aeroelastician. Jour. Aero. Sci., vol. 23, namic no. 12, ~ e c . 1956, pp. ~ 0 9 - ~ 1 8 .

3 . Hanson, Perry W., and Rainey, A . Gerald: Experimental Investigation and Supersonic Flutter Characteristics of the Upper of the Transonic and Lower Vertical Tails of an Air-to-Ground Missile. (Prospective NACA paper. ) TEST CONFIGURATIONS A B / C D E F G H Figure 1 TEST CONFIGURATION A WING WITH TIP AILERONS NO ACTUATOR FLUTTER FLUTTER STIFFNESS 0 0 I .o 0 3.0 A A a0 6 6 STABLE

bwa a f ! ! )

/A o m & &

-d4[ 2 8% ooP FLUTTER :j A A

L - L - 0 .6 I .o 1.4 0 .6 I .o 1.4 M M Figure 2 TEST CONFIGURATION B ALL-MOVABLE STABILIZER .50

'r

A .94 0 .6 .7 .8 .9 1.0 1.1 1.2 1.3 M TEST CONFIGURATION B ALL-MOVABLE STABILIZER

-----

O }CALCULATED

---

gEXP 41- FLUTTER 0 .5 I .o I .5 2.0 Wh/ Y Figure 4

i;cr

TEST CONFIGURATION C ALL-MOVABLE STABILIZER 1.4 I 8 D 0.9 I A A Q D I I t 0 LO 1.5 2.0 2.5 3.0 M Figure 5 TEST CONFIGURATION C ALL-MOVABLE STABILIZER I O ( " h P 8 1.02 .95 HEAVY L.E.

'k l l , 0 1.5 2 . 0 2.5 3 . 0 M Figure 6 TEST CONFIGURATION C ALL-MOVABLE STABILIZER FLUTTER FL?&ER wh/w8 1.02 A CALCULATED 6 - a 4 - e - 2 - CALCULATED I I I I I 0 L I .5 1 . 0 1.5 2.0 2.5 3.0 M Figure 7 TEST CONFIGURATION D VERTICAL TAIL WITH T.E. RUDDER 4.0 r I .2 1 . 0 Wf ~ 0 .5 1 . 0 I .5 2 . 0 2.5 3.0 M Figure 8 TEST CONFIGURATION E VERTICAL TAIL WITH T . E . RUDDER FLUTTER I I I I I I I 0 .5 I .o 1 . 5 2.0 2.5 3 . 0 M C TEST CONFIGURATION F VERTICAL TAIL WITH TE. RUDDER STIFFNESS ACTUATOR TWIST

5-0 r

I .o I .o .8 1.3

-4 bw a 45

I

4 .O L I I I I I 0 1.0 1.1 1.2 M Figure 10 TEST CONFIGURATIONS F AND G VERTICAL TAILS WITH T.E. RUDDER STIFFNESS NO CONFIG. FLUTTER FLUTTER ACTUATOR TWIST F 0 I .o I .o G m 0 I .5 2.8

4#000 r

FIN TIP REMOVED-

-

-

q,LB/SQ F T 3,000 Figure 1 1 TEST CONFIGURATION H T - T A I L DIHEDRAL 0 1 5 O 8 O o

-

I .o

-

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-

-

. 6 F L U T T E R c 0 .6 .7 .8 .9 LO 1 . 1 1.2 1.3 All

1 G I 1 Figure 1 2 c

FLUTTER OF TWO ALL-MOVABLE CONTROLS NO FLUTTER FLUTTER

5 r . o w

+

4 - 3 -

34 a

2 - FLUTTER M = 1.6

0 ' t , I & I I I I

4 .5 .6 . 7 ROTATION AXIS, % ROOT CHORD NACA - Langley Field, Va.

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