Flight Flutter Testing Symposium

CONTENTS Page ........................................

Col. F. N. Moyers: Introduction. 1 PART I. THEORY

....................... E. Molla-Christensen: A Theory of Flight Flutter Testing

R. W. Warner: A General Aerodynamic Approach to the Problem of Decaying or Growing Vibrations of Thin, Flexible Wings with Supersonic Leading and Trailing Edges and No Side’Edges .....................................................

G. E. Sanderson, E. A. Bartsch: Damping Measurements in Flight Flutter Tests ........

J. C. Houbolt, A. G. Rainey: On the Prediction of Critical Flutter Conditions from Subcritical Response Data and Some Related Wind-Tunnel Experience. .............

31 E. G. Broadbent: Vector Plotting as an Indication of the Approach to Flutter ...........

.

41 W. H. Reed 1 1 1 : A Flight Investigation of Oscillating Air Forces: Equipment and Technique

PART 11. METHODS AND TECHNIQUES - SECTION I

H. R. Roglin: The Application of Measurement Techniques to Track Flutter Testing . 51

R. H. Stringham Jr., E. J. Lenk: Pulse Techniques in Flight Flutter Testing ...........

E. F. Baird, N. S. Sinder, R. 8. Wittman: Stabilizer Flutter Investigated by Flight Test . . e ..........

C. V. Stahle, W. R. Forlifer: Ground Vibration Testing of Complex Structures G. Kachadourian, R. L. Goldman, D. M. Roha: Flight Flutter Testing the P6M ..........

R. J. Werdes: Transient Flight Flutter Test of a Wing with Tip Tanks ...............

PART I I . METHQDS AND TECHNIQUES - SECTION I1

P. T..Mahaffey: Flight Flutter Testing of the B-58 Airplane ......................

. W. R. Laidlaw, V. L. Beals: The Application of Pulse Excitation to Ground and Flight

L. I. Mirowitz: Transonic Flight Flutter Tests of a Control Surface Using an Impedance C. R. Kutschinski: Flight Testing Air-to-Air Missiles for Flutter . . . . . . . . . . . . . . . . . .

FLIGHT FLUTTER TESTING - PAST AND FUTURE

PART III.

L. A. Tolve: A History of Flight Flutter Testing.. ............................

M. 0. W. Wolfe: A Review of Flight Flutter Testing Techniques in Great Britain ........

...

! I I CONTENTS (cont) Page

PANEL DISCUSSION - FUTURE O F FLIGHT FLUTTER TESTING

.......................................

I. E. Garrick: Research Viewpoint 175 R. Rosenbaum: Future of Flight Flutter Testing in the Field of Civil Certification . . . 179 .............

M. J. Turner: Magnitude and Objectives of Future Flight Flutter Testing 183

W. J. Mykytow: The Flight Flutter Testing Status from a Military Standpoint. . . 187

M. 0 . W. Wolfe: Important Lines of Development for Future Application of Flight ..................................................

Flutter Testing 191 PART IV. ADDENDUM

iv

INTRODUCTION Col. F. N . Moyers - Vice Commander, Air Force Ofice of Scientific Research throughout the free world working in universities, in Mr. Baird, Members of the Symposium: industry, in foundations, and in government research agencies, under approximately 700 research contracts A s co-sponsor of this symposium, the Com- awarded by our organization. We define our program mander and Staff of the A i r Force Office of Scientific as one of exploratory research. It is that research Research are pleased to welcome you. Today's meet- that provides answers to which there have been no ing, the first to treat flutter testing exclusively, has questions. It is research with a view toward adding been arranged by the Aircraft Industries Association to the total of man's knowledge in areas of Air Force Flutter Research Panel and members of the AIA and interest. The product of this research provides AFOSR.

"capabilities" - - capabilities for providing new con-

cepts of weapons systems that may revolutionize the In looking over the agenda of this symposium, a r t and science of aerial warfare.

I feel that it is scientifically very impressive and surely meets the high quality standards established by the AIA in the area of aeromechanics.

Most of the AFOSR research projects a r e con- ducted in universities although industry is certainly We believe that one of the most important jobs not excluded. Hence, a considerable amount of grad- to be done in research and development today is that uate students training results as a secondary benefit of insuring the adequate flow of research information.

of our research program. In view of the general To that end, we consider meetings such as this a shortage of qualified technical personnel, our program positive step in that they provide a vital link in the in this way has long-term advantages to universities, channel of research communication. It is meetings industry, and the government.

such as this that makes it possible to translate usable basic knowledge to the engineer who has the job of During the past 15 years, we have witnessed a applying this knowledge to the more effective hard- remarkable increase in speed, power, altitude, range, ware which we so urgently require in this age of and complexity of aircraft. At low speeds, structures accelerated technology.

were designed with sufficient rigidity to preclude most aeroelastic phenomena. At the higher speeds we en- In speaking of research communication, I would counter today, designers have been faced with a wide like to take this opportunity to say a few words con- variety of problems which a r e Aeroelastic in origin.

cerning our organization, the A i r Force Office of Thermal effects due to kinetic heating have further Scientific Research. We a r e a major activity of the complicated these problems. It would appear that USAF A i r Research and Development Command.

the development of aerodynamic theory has been out- stripped by practice. In many cases, theory is of Our mission is that of fundamental, theoretical, such importance that it is virtually impossible to or experimental investigation to increase man's know- interpret test results without it.

ledge and understanding of the natural world and to recognize the implications of new scientificknowledge In this regard, I would like to give you a few upon weapons systems concepts. Our capability to examples of how AFOSR exploratory research, ini- carry out this mission is represented by scientists perfect fluid flow to the prediction of theaerodynamic tiated in some cases as much as 6 years ago, are forces that act on thin wings and slender bodiesas contributing to the solution of design problemk.

a result of small, unsteady motions in supersonic A simplified aerodynamic theory called the flight. This work is of value both for the further “piston theory” w a s greatly extended in scope by development of the theory and in practical flutter and stability analysis.

Dr. Ashley and his coworkers at MIT. The theory permits a large reduction in the labor required in aeroelastic stability calculations and has been used From these few examples you can see that re- in connection with the design of practically every search is not at a standstill, however, much work re- surfaces, such as the Talos, Nike, Wizard, and in ad- mains to be done. The Air Force of the future is in vance fighters like the F105.

the laboratories of today. It is our job to integrate the results of this fundamental research and insure At CIT, Dr. E. E. Sechler has been studying the greatest possible utilization of the researchprad- the nature of panel flutter at transonic and supersonic uct. It is our objective that this symposium will speeds. Some significant and interesting results have serve to bring the scientist and engineer up to date on been found. At supersonic speeds, within certain old problems, acquaint them with new problems, pro- limits, an increased in the initial deviation from flat- vide an opportunity to exchange ideas and information ness was found to be beneficial to the prevention of on testing procedures, and, in general to promote panel flutter. Dr. Sechler has evolved simplified progress in the field.

analyses for finite ratio panels which could set the boundary limits for design and set standards for wind I would like to thank each of you and your re- tunnel and flight test methods.

spective organizations for participating in this meet- will have a profitable symposium ing. I hope that you Dr. John Miles, UCLA, has completed a com- and an enjoyable stay in Washington.

prehensive monograph on the application of theory of

A THEORY OF FLlGHT FLUTTER T E S T l N G

Erik MoLl@Christensen - California lnstitute of Technology Finally, we shall look at the accuracy of a Abstract flutter prediction, in terms of the precision of the data used in the computation.

Flight flutter testing is considered as a method for finding generalized aerodynamic forces. The co- The Equations of Motion efficients determined from flight flutter tests are used in flutter calculations, using a simple expansion W e assume the wing to be perfectly elastic, and in frequency and Mach number. The e r r o r s in the assume the motion of the wing to be small, such that procedure are discussed, and expressions for the the aerodynamic loads are proportional to some e r r o r in flutter prediction are given. Methods of linear integral-differential transform of the deflec- testing procedure are discussed.

tions.

This integro-differential dependence of airloads INTRODUCTION on deflection is proportiohal to dynamic pressure, but may depend upon flight altitude, and depends upon Mach number and frequency of oscillation.

This paper considers flutter testing and flight flutter testing a part of flutter analysis. Very often The equation of motion can then be written: nowadays, tests which were originally intended as Z ( X , Y ) = 88vzngCir. ~ 1 5 , q 1 { w 2 m f f , q J z ( 6 . 7) + proof tests o r acceptance tests inadvertently became llrea exploration of the unknown. This situation will per- sist until flutter analysis can be used withconfidence, F ( 5 , 7) + i p l 1 2 D I ( f , q; k . M18.fWtng~(6. q; r, s , k , M I to the extent that the accuracy of a flutter prediction Are a can be computed as part of the analysis.

D 2 / r , s; k , M l z f r , sldrdsldfdq Since this situation exists, one might as well where: consider such tests as links in the flutter analysis, Re [ Z h , Y l t ? Z W t l , and squeeze out as much information as possible from the test results, rather than rest content with is the deflection of the wing at (x, y) at time t.

as the say, flutter frequency, speed and Mach number only result of a wind tunnel flutter test, which usually 2nw cannot be repeated using the same model.

is the frequency of vibration.

We shall, therefore, consider the equations of m l r , y l motion on a wing vibrating in an airstream, examine is the mass per unit wing area at (x, y).

which quantities can be measured, which quantities C l X . Y 1 5 . 77, can be found from a simpler test, and attempt to as- is the deflection at (x, y) due to a unit load applied say the accuracy of data obtained from static, ground vibration, flight vibration and flutter tests. at ( 5 . 7').

Re [Fix. y l e f W t ] Mach number M, the combined equation becomes es- pecially simple, and takes on the form: is the force applied to the wing by shakers, or ground supports.

(4) q(& 7 ; r, s, k , M I D z ( r , s, k , Mlz(r, s l d r d s D (C, 7 ; k , M J J J Wz ng is the operator which yields the lift per unit area at

( <, 7 ) divided by the dynamic pressure for a deflec-

tion amplitude distribution z(x, y) at Mach number M where we have included a structural damping term wb

and reduced frequency . with [ d ] asthe matrix of damping coefficients. n is

the test number, so z,, is the deflection amplitude at (x,, Y J in the n'th test, W, is the frequency, and At zero airspeed and frequency, this is the equa- tion for a ground static test, f o r zero airspeed only 1 ' is the dynamic pressure in the n'th test.

( ~ p U 2 J n it is the equation of a ground vibration test, and for zero impressed force, it is the equation for flutter, After having performed a set of N tests, where a flight vibration all but N columns of one of the matrices in Equation while the whole equation describes test. (4) are either measured in the tests o r known from previous tests or analysis, it is possible to compute To be able to use the equation, one must rewrite the unknown columns. As examples, we shall con- it using some kind of approximation. One can use an sider a set of static tests, a set of ground vibration approximation in natural modes, but that seemspoint- tests, a set of flutter tests and a set of flight vibra- tion tests.

less unless they are known precisely. The alternative is to use an approximation in discrete ordinates, or if A set of static tests should obey the equation: one is in a fancy mood, to use station functions, or an approximation in terms of surface stresses.

[z, 1 = [c,3 LF,,I We shall use an approximation in discrete or- which can be inverted to yield: dinates, namely the deflections Z , a t the points ( x u , -1 [c,,] = [z,] [ F u n ] yVJ where v refers to the number ofthe point in some kind of ordered sequence.

-1 where [F,] is Equation 1 then becomes: tZJ = [c,l CrnulQ2 [ H I {ZJ + 1 c , l C H I {FJ +

-

-PJ2 2 [c,] [ q v a ( k , M I 1 {zu} 2) F A is the cofactor of the element F;, in the

transpose of [F,] . The first order e r r o r in

where fv,1 is the matrix corresponding to the [c,] due to e r r o r in the measurement of zpu and linear integro-differential operator which yields the lift distribution. [ H I is a diagonal matrixof integra- [ F , , I can be evaluated a s fbllows: tion weights, it has been lumped with the [ 4 u a ( k , M I ] in the last term on the right hand side.

The equation for flutter states that the determin- {FJ = 0 in order to ob- ant of (2) must vanish for tain a non-trivial solution: D I 1-13 + w ' [ c l [ r n ] [ H I + L P U 2 [ c l [ 9 ( k , M 1 1 I = 0 (3) If the e r r o r s are given in terms of standard

deviations, O F r s and U Z , , the standard deviation

We shall now proceed to write down the equa- in the element cpv is: tions for a set of tests, and to examine the rate of change of flutter speed with changes in the elements = 1 1 X;: u Z : , + 1 1 K " u u ~ p v r s r s rs F r s of the flutter determinant. The latter will enable us The coefficients X F s can be seen to be large to assess the first order e r r o r in the flutter predic- when the determinant IF1 is small, Le. when one of tion due to e r r o r s in wing parameters and aerody- the columns o r rows in the loading matrix is nearly namic coefficients.

a linear combination of the other columns or rows.

The Equation for a Set of Tests The Equation for a Set of Ground Vibration Tests For a set of ground vibration tests, one ob- If one repeats a flight vibration test N times, one obtains N equations like equation (l), which can be written as a single equation. If all these tests are performed at the same reduced frequency k and Equating real parts: Re [ z p 1 = [c,] [H,] [ m l Re bun 1 [mi 1 + [c,,] Re [ F , , I -1 -1 or [ m l = [H,] [c,,] f R e [ z p u l - -1 -1 [ c J R e [F,,lj [ w i l [ R e z , , ] and we see that if the determinants of [c,,] and [zun1 are small, the first order e r r o r s may become large. However, in the flutter equation, [ m ] only occurs in the combination: [c,l [H,I [ m u ] and therefore only this combination is of interest: set of equations may be insufficient to de- -1 -1 This [c,] [ H , ] [ m u ] = (Re [z,] - [c,,] [ReF,]) [ w i l [Rez,,]

termine [ q , J k , M I 1 . However, some of the

q p v ( k . MI are not very important as far as the which shows that these e r r o r s in Izpl and [ F u n ] flutter speed is concerned, the zero order terms in k are really important. The matrix of first order er- can be determined by wind tunnel tests on stationary rors of the left hand side is [A] , where: but deformed wings (tied down), others can again be guessed at, at least, from linearized aerodynamic theory. The purpose of a flight vibration test o r a -1 -1 flutter test is then to determine the remaining aero- + f [ R e z J - [cpul IReF,lJ ( ( A [ w ; l [Rez,,] I dynamic coefficients. Without going into a discussion -1 -1 of which aerodynamic coefficients a r e to be chosenas + [mil A ( [ R e z p l ! I those which neither theory nor wind tunnel static tests The e r r o r will therefore be proportional to the in- can yield, we shall consider the precision obtainable verse square of the determinant of [Rezwu1 ; this in q p , ( k , MI when it is determined from tests.

determinant should be maximized by arranging the test such that the columns of the determinant a r e The term which is most liable to magnify the orthogonal if possible, This means that each test [zpU3

e r r o r s i s the e r r o r s in the inverse of . The

-1 should be performed at a natural frequency.

value of [ z , ] is Equation for a Set of Flight Vibration Tests o r Flutter Tests The information obtainable from a set of flight When differentiating to evaluate the e r r o r , one obtains vibration tests o r flutter tests which cannot be obtained an expression with 1 z I 2 in the denominator. To from tests where there a r e no aerodynamic forces minimize errors, one must try to make 121 as large are, of course, the aerodynamic forces.

as possible, i.e., the columns in [z,I should be as different as possible. Vibration is natural modes Since the aerodynamic coefficients depend upon only will go far towards the accomplishment of pre- Mach number, M, and reduced frequency, k, the tests cision.

must either be performed a t constant M and k, o r one must somehow approximate this dependence.

Errors in Flutter Prediction due to E r r o r s in Struc- tural, Mass and Aerodynamic Parameters a Taylor series ex- One can for example use in k and M about some value pansion of [ q p u f k , M I 1 Before the obtainable precision in experimental of M, Mref. and zero reduced frequency. One obtains: determination of structural, mass and aerodynamic information can be meaningful in terms of resulting [ q p u ( k , M I 1 = accuracy in flutter prediction, we have to analyze the sensitivity of a flutter point to such errors.

ar as (M - M r e f I r k s

+=o 2 s = o [ (- aMr - a k s qp,,(k, M$ k =

r! s!

Flutter occurs whenever the determinant (Eq.

]

(3)) vanishes: M = ‘ r e f D f k , M,-pU2, m l , ... . , m N , d . .... , d,, Instead of expanding in power of (M-Mref), one can 2 expand in powers of (M2-1) for transonic Mach num- q l I ? - - . . . q,4/N. ell>....* C N N ) = o bers and (M2-l)’h for supersonic Mach numbers.

Vary one of the parameters, which we shall call P.

Both the real and imaginary parts of the flutter de- A s an engineering approximation one would only terminant will then change, and k and &pU2 must use the first and zero order terms.

.

is realized that only the practising flutter then be changed to compensate, such as to maintain lined. It the value of the flutter determinant at zero at constant analyst can choose the method of analysis and the tests to be performed, knowing the limitations of his

M. Instead of changing kland $-pu2 , k and M can

facilities and his personnel.

, or p and k can be

be changed, at constant ~ p ~ 2 changed only, at constant M and U.

The method which has been outlined is clearly if some of its elements are used, We shall only consider changes in k and impractical; however, T~ u 2 at constant M. or if nothing else, its viewpoint is adopted, the paper will have accomplished its purpose.

To maintain flutter for a change in P, one must have : Bibliography 1. Molineaux, W. G., The Determination of Aero- dynamic Coefficients from Flutter Test Data, unpublished Ministry of Supply Report, U.K.

Solving for A ( - ; ~ U ~ J and Ak , one obtains: 2 . Mollo-Christensen, E., and Martuccelli, J. R., M = const.

A Study of the FeasibiIity of Experimental De- termination of Aerodynamic Forces for use in Flutter Calculation, M.I.T. Aeroelastic and Struc- tures Research Lab., Technical Reports 66-1, 66-2,66-3, June, 1957.

3. Bisplinghoff, R. L., Ashley, H., and Halfman, R. L., Aeroelasticity, Addison Wesley, Cam- bridge, 1955.

4. Garrick, I . E. and Rubinow, S. I., Flutter and (Akl,,, = Oscillating Air-Force Calculations for an Airfoil in Two-dimensional Supersonic Flow, NACA Re- port 846, 1946.

5. Ashley, H., and Zartarian, G . , Piston Theory-- where the bars denote the complex conjugate and the derivative with respect to k is taken at constant M A New Aerodynamic Tool for the Aeroelastician, and &,2 , and the derivative with respect to 1 2 Jour. Aero. Sci., Vol. 23, No. 12, pp. 1109-1118, --Po 2 2 December, 1956.

is taken at constant k and M.

6. Goland, M., The Flutter of a Uniform Cantilever It is, of course, complicated to evaluate these W-ing, Journal of Applied Mechanics, Vol. 12, derivatives, but it seems to be necessary for finding No. 4, December, 1945.

the sensitivity of a flutter point to parameter changes.

With modern computers it may, however, be possible.

7. Buxton, G. H. L., and Minhmnick, I. T., Expres- sions for the Rates of Change of Critical Flutter A rough knowledge of the precision of a flutter Speeds and Frequencies with Inertial, Aerody- prediction will always be useful; one must keep firmly namics and Elastic Coefficients, BR. A.R.C., in mind, however, that the estimate of precision is in R . and M. 2444, September, 1945.

terms of a given numerical approximation, and can give no information about the remainder term of the 8 . Baker, R. C., Effect of E r r o r s and Changes in numerical approximation.

System Parameters on the Flutter Point, S.M.

Thesis, M.I.T., 1956.

In practice, when a flutter point proves very in- sensitive to parameter changes, it should not be al- 9. Crout, P, D., A Short Method of Evaluating De- lowed to cause unalleviated elation, since then it will terminants and Solving Systems of Linear Equa- take a major design change to move the flutter point tions with Real or Complex Coefficients, Trans.

out of the flight envelope of the airplane, for example.

A.I.E.E., voi. 60, pp. 1235-1240,1941.

Conclusion 10. Cramer, H., Mathematical Methods of Statistics, p. 213, Princeton University Press, 1954.

A viewpoint and a method of approach to flight flutter testing and to flutter in general has been out- A GENERAL AERODYNAMIC APPROACH T O THE PROBLEM OF DECAYING O R G R O W I N G VIBRATIONS OF T H I N , FLEXIBLE W I N G S W I T H SUPERSONIC LEADING 6 TRAILING EDGES A N D N O SIDE EDGES R. W . Warner - N A C A , Ames Laboratory, Moffett Field, California Abstract dynamic forcing terms in gust problems. They can also give the aerodynamic terms due to decaying or The type of solution presented in this paper has growing vibrations that occur in the equations of mo- extreme significance for the problem of flight flutter tion for problems of gust response, airplane dynamic testing since the flutter characteristics of a flight stability, and the approach to a flutter boundary. The vehicle could be checked analytically without actually latter application has significance for flight flutter penetrating the flutter region. For such a study in- testing since the flutter characteristics of a flight dicial aerodynamic influence coefficients have several vehicle could be compared with analysis without ac- advantages. The indicial nature of the coefficients tual penetration of the flutter region.

(responses to step function) makes them more readily applicable to decaying or growing motion than sinu- As with Pines and other authors (References 1 soidal coefficients. Inaddition, aerodynamic influence through 4), the present method is based ondividing coefficients can be applied to any plan form (within the wing plan form into a number of discrete areas o r the limitations of the aerodynamic theory) and to any boxes. In each of these areas the downwash is as- mode shape. sumed to be uniform. In this paper a simplified is used to find the pressure at any point on approach For the reasons stated above, indicial aerody- the wing due to the downwash oneacharea in its Mach namic influence coefficients have been evaluatedfrom forecone. A variety of area shapes is permitted. By a thin, flexible wing with super- potential theory for means of these so-called "aerodynamic influence co- sonic leading and trailing edges only. The analysis efficients," arbitrary downwash distributions can be is based on the use of small surface areas in which achieved for various plan forms. The present ap- the downwash is assumed uniform. Within this lim- proach differs from the earlier methods primarily itation, the results are exact except for the restric- in its use of indicial aerodynamic influence coeffi- tion of linearized theory. The a r e a s a r e not restricted cients. The adjective "indicial" means that the uni- either to square boxes or Mach boxes. A given area form downwash is applied suddenly to the area and may be any rectangle o r square which may or may maintained constant thereafter. The principal ad- area can not be cut by the Mach forecone, and any vantage of the indicial function is that it is a single be used anywhere in the forecone without loss of function of time which can be superposed to give accuracy .

pressure for arbitrary time-dependent downwash. If sinusoidal functions were used to produce such down- wash, both their real and imaginary pa& would have to be superposed.

INTRODUCTION The Indicia1 Aerodynamic Influence Coefficient for The purpose of this paper is to describe a the Fundamental Area feasible method for calculation of the aerodynamic forces due to arbitrary time-dependent downwash on In Figure 1, a general plan form with super-, sonic edges is outlined in dotted lines, with the flow flexible wings. Such aerodynamic forces have several pa:sing over it a t velocity V. A grid of small areas important applications. They can provde the aero- GENERAL SUPERSONIC-EDGED PLAN FORM WITH relative to the point (x, y), and these coordinates are SUPERIMPOSED GRID prominent in the results which follow.

The exact indicial aerodynamic influence coef- a fundamental area have been found ficients for such

by linearized theory. The result for< 5 L, where

x M M is the free-stream Mach number, is presented in M l t l

Figure 3 a s the quantity { -) in the right-hand

kr column, with corresponding time zones indicated in the left-hand column. In Figure 3, A P(t) is the indicial pressure difference between the upper and lower sur- faces of the wing at point (x, y), considered positive when it acts upward; W is the amount of uniform in- dicial downwash due to wing motion o r gust velocity, positive downward; c is the speed of sound in the un- disturbed medium; t is time. is the density of the Figure 1. General Supersonic-Edged Plan Form with

undisturbed fluid; and 1 is Y E . One point to be

Superimposed Grid noted in Figure 3 is the elementary nature of the of uniform downwash is shown with solid lines and

functions. It should also be stated that if 2' 2

x' M' gives rise to a serrated leading edge in the approx- then the first two time zones are replaced by a single imation. The portions of those areas which can affect W(tJ the pressure at a typical point (x, y) lie within the

time zone for which (-1 is zero; and the other

W Mach forecone from that point and a r e shown shaded two zones a r e unaffected.

in Figure 1. Examples of these so-called "Mach forecone" areas are the polygons with three, four, five, l NDl CIAL AERODYNAMIC INFLUENCE COEFFICIENT and six sides, as numbered in Figure 1.

FOR FUNDAMENTAL AREA IF y'/x'S I/M It has been found that aerodynamic influence TIME Z O N E S VALUES OF coefficients for all the various polygons can be de- rived from the coefficient formula for a so-called "fundamental area" of uniform downwash. The fun- damental area used herein consists of that portion of a representative quadrant in the plane of the wing (see Figure 2) which lies between the origin of the quadrant and one forward Mach line from (x, y). Thus the fundamental area is the shaded triangle in Figure 2. The point (x, y), where pressure is found, is taken to be in the plane of the wing and the triangle. The x', y' coordinates shown in Figure 2 are used only to locate the right-angle corner of the fundamental area ct.m t J F U N D A M E N T A L A R E A Figure 3. Indicial Aerodynamic Influence Coefficient for Fundamental Area If y'/x' = 1/M Application of the Indicial Aerodynamic Influence Coefficient for the Fundamental Area The present calculations a r e based on applica- tion of the indicial aerodynamic influence coefficient for the fundamental area. The Mach box grid, such as that shown in Figure 4 for M = 1.6, is used. For this grid, introduced by Ta Li (References 2 and 3), the dimensions are A normal to the stream and ;3A parallel to the stream. The pressure is evaluated at the centroid of each box as, for example, at the Hence, apex of the Mach forecone shown in Figure 4.

all Mach forecone areas of uniform downwash are triangles, like 10 and 47, o r rectangles, like 14 and Figure 2. Fundamental Area 39. As can be seen, the portion of the plan form TYPICAL MACH BOX GRID the black triangle in step I of Figure 5. In a process FOR GENERAL SUPERSONIC-EDGED P L A N FORM of superposition, one then subtracts the coefficients for the shaded triangle in step 1 1 and the shaded tri- angle in step 1 1 1 as indicated by the minus signs and the braces in Figure 5. One thenadds the shaded tri- angle in step IV because this coefficient was sub- tracted twice, once each in steps I1 and 111. These steps leave only the coefficient for the black rectangle of step IV, which is the lower half of area 14; and this result is doubled to account for the upper half. Since all the fundamental areas used in these examples have

5 < &, the coefficient formula of Figure 3 is used

without modification. It is essential, however, to modify the coefficient in the manner previously de-

scribedwhen xt Y ' > M' 1

The indicial influence coefficients for the four Figure 4. Typical Mach Box Grid for General Super- Mach forecone areas shown shaded in Figure 4 a r e sonic-Edged Plan Form plotted in Figure 6 against a dimensionless time, c_t The upper curve gives the pressure difference shown in Figure 4 has a rather general shape. The A ' x ' and y' axes, which define the right-angle corners a t the apex of the Mach forecone in Figure 4 due to of fundamental areas, originate at the point where uniform indicial downwash on Mach forecone area pressure is sought.

10. This is the only curve having a non-zero initial time zone since 10 is the only area containing the Although the fundamental area shown in Figure point a t which pressure is found. The other three 2 can be applied to more complicated Mach forecone curves define the pressure differences at that point 4, its application to areas than a r e shown in Figure due to Mach forecone areas 4'7,14, and 39 as indicated areas such as 10, 4'7, 14, and 39 is representative.

in Figure 6. The principal point to be noted is the The pressure difference at the Mach forecone apex segmented nature of the curves.

due to uniform indicial downwash on Mach forecone 9h If the transverse motion of the centroid of each area 10 is found by substituting x' = -

, y' = 0 into

basic-grid box were considered to be a degree of the coefficient formula of Figure 3 to account for the freedom in the equations of motion, results such as lower half of 10 in Figure 4 and doubling the result those shown here would have to be used in the Duhamel to account for the upper half. For the triangular superposition integral for the analysis of decaying o r (or fundamental) area 4 ' 7 , it is only necessary to sub- growing oscillations. The form of this integral, the qPh 7h large number of degrees of freedom required, and

stitute the values x' = - , y' = -for the single

2 2 the irregular time histories of the indicial coefficients right-angle corner. For Mach forecone area 14 (see would cause extreme difficulties in high-speed ma- Figures 4 and 5) one starts with the coefficient for chine computation. If an analog machine were used, DEVELOPMENT OF THE COEFFICIENT FOR AREA 14 TYPICAL INDICIAL AERODYNAMIC INFLUENCE COEFFICIENTS 4 - 2 - -- AREA 1 - 2 - -4 -

1 ,/ STEPID v STEP1

[P I I 1 I I I 8 8 /" / -6..

0 1 . 2 3 4 6 7 8 9 1 0

E l 5

Figure 6. Typical Indicia1 Aerodynamic Influence Figure 5. Development of the Coefficient for Area 14 Coefficients it would be essential to approximate these coefficients It should be noted that the number of chordwise boxes at the maximum chord, namely eight, coin- by a different set of exponentials for each of their cides with the minimum number recommended by segments. Although the exponential approximation Zartarian (Reference 5) for oscillatory functions. As would also facilitate digital computation, the use of he states, more boxes would be required ifthe chord- a digital machine for such calculations would still wise deformation shape had more than one half-wave.

require an extremely large memory. However, these indicial aerodynamic influence coefficients can be The generalized indicial force found for the used relatively easily to evaluate generalized indicial forces. With these forces, relatively few degrees delta wing just described is CL ’ that is, lift due to q ’ of freedom are required. In addition, a generalized indicial pitching velocity, q, about the apex. In Figure indicial force is likely to be sufficiently smooth to 8 the lift is nondimensionalized in the usual fashion, be subject to approximation by one set of exponentials and q is nondimensionalized with respect to the flow over its entire time history.

speed V, and the maximum chord co. In the present approximation, the uniform downwash on each boxdue To determine the feasibility of applying indicial to q is evaluated at the centroid of each box except coefficients to the calculation of generalized indicial for the trailing-edge boxes, where the trailing edge forces, a simple rigid-body example, for which exact is the reference for downwash as well as pressure.

are known, will be presented.

theoretical results The time is made dimensionless in this case by the Consider a rigid, supersonic-edged delta wing at a flow speed V and the maximum chord co.

Mach number of 1.2. The wing is shown in Figure 7 with dashed lines and has aleading-edge sweepof 24”.

L I F T DUE TO INDICIAL PITCHING OF A The sweep has no bearing on the exact result for the SUPERSONIC-EDGED DELTA WING ABOUT ITS A P E X delta wing but does influence the selection of boxes in the approximation. The wing is covered with 96 4.0 Mach boxes for M = 1.2, the box length normal to the stream being A and that parallel to the stream being 3.6 - for the trailing-edge boxes and P A for the rest, -EXACT RESULT OF LOMAX, ET AL.

3.2 as indicated in Figure 7. The uniform pressure as-

_ _ _ _

RESULT DERIVED FROM INDICIAL sumed over the trailing-edge boxes is evaluated a t CL; AERODYNAMIC INFLUENCE COEFFICIENTS the trailing edge. For any pair of supersonic lead-

2.8 _ _ EXPONENTIAL APPROXIMATION TO

ing edges, the placing of the apex on the leading edge RESULT FROM COEFFICIENTS vt of the foremost box in the Mach box system has the C L d = 4 0 8 5 + 0 6 7 3 e - 3 6 0 $ - 2 5 0 0 e - 0 9 4 G 2.4 principal advantage of minimizing the extent to which the boxes carry assumed constant pressure across I I I I I I I the apex Mach lines, where the pressure distribution 2.0 I 2 3,,,4 5 6 7 changes rapidly. Such an arrangement also alternates - CO the carry-over o f high pressure difference and low Figure 8. Lift Due to Indicia1 Pitching of a Supersonic- pressure difference, as with boxes 71 and 70, re- Edged Delta Wing About Its Apex spectively, in Figure 7. The rule of thumb for dis- carding boxes along the leading edges is simply that boxes conforming to the pattern of the basic grid a r e 8 contains three curves: the exact the- Figure included only if their centroids lie on the plan form oretical result taken from Reference 6, the curve of the delta wing.

derived from the indicial aerodynamic influence co- efficients, and an exponential approximation based on SUPERSONIC-EDGED DELTA WING points taken from the curve determined by the influ- WITH MACH BOX GRID FOR M.1.2 ence coefficients. The irregularities in the curve derived from the coefficients a r e the result of using a finite number of boxes. The exponential approxi- mation is in e r r o r relative to the exact result by a maximum of nearly 2 percent.

The question arises as to whether such a good exponential curve fitting could have been accom- plished if the exact result had not been known in ad- a large part of the curve-fitting vance. Fortunately, procedure is quite general and does not require spe- cific knowledge of the exact result. The first step is to select from the function determined by the indicial coefficients a set of points upon which the exponential approximation is to be based. In the Figure 7. Supersonic-Edged Delta Wing with Mach present case, the points chosen were those whose Box Grid for M = 1.2 abscissas lie halfway between the peaks of the ser- wc rated curve in Figure 8, with the valley nearest time duced frequency, 2, for which the necessary tabu- 2v will be dis- zero excluded. (The initial time zone lated functions a r e generally available. The exact Vt

cussed later.) In addition, the initial (- = 0 ) and

results for CL q(rea1) '

based on an CO

and c~ q(imag), '

steady-state ( cg vt - - 6) points of the serrated curve

integral evaluated in reference 8 in terms of functions

tabulated in Reference 9, a r e plotted against - a 0 in

were used. The valley points were chosen, rather than peak or mean values, because one would expert 2v Figure 9. The results of introducing the exponential the exact function to be smaller than the function based approximation of Figure 8 in the Duhamel integraland on the coefficients even if the exact function were not specializing for sinusoidal motion a r e also shown in known. This results from the fact that the total area Figure 9. The maximum percentage discrepancy be- of the boxes is approximately 1 percent greater than tween the approximate and the exact results occurs the actual delta-wing area. Furthermore, the evalua- a 0 tion of the downwash right at the trailing edge gives

at the very small values of CL '

q(imag) near - =

2v somewhat too high a uniform downwash over the half 2.0. Elsewhere, the largest e r r o r s a r e around 3 per- a procedure for the boxes on the trailing edge. Such cent, which is considered quite good.

selection of points upon which to base the exponential approximation in all but the earliest time region would COMPARISON OF EXACT AND APPROXIMATE be expected to apply to more complicated plan forms SINUSOIDAL RESULTS and mode shapes.

CL&?EAL, CL;(IMAO, EXACT The second step in the exponential curve fitting APPROXIMATE is the application of judgment as to the nature of the indicial function in the earliest time region. This

3 4 \

step is aided by the general knowledge that all the various supersonic indicial functions calculated for specific plan forms and mode shapes in References 6 and 7 have one o r more inflection p i n t s near time - -1.0 zero. However, some of the functions have one point of inflection without a dip, and some have two points of inflection with a dip. Thus the rejection of the

2.0 -

first valley in the serrated curve of Figure 8 and the subsequent selection of the exponential approximation I l l I I I I I I I I 0 0.2 0.4 0.6 0.8 1 . 0 I2 1.4 1.6 1.8 2.0 with only an indistinguishable dip, essentially at time zero, required knowledge of the exact result for the present case. For more general indicial functions, Figure 9. Comparison of Exact and Approximate then, the decision as to whether to ignore the dip may Sinusoidal Results give rise to an e r r o r as large as 10 perceht in the earliest time region. This potential e r r o r can be reduced, of course, by developing usable points closer CONCLUSION to time zero. The principal means of doing this is the use of a larger number of boxes, whichwould improve accuracy over the entire time span.

In view of the foregoing results and discussion, it appears that the application of generalized indicial Once the points to approximate have been se- forces, derived from indicial aerodynamic influence lected and the behavior near time zero has been es- coefficients, to the problem of predicting decay rates timated, the third step is the actual exponential ap- in flight flutter testing will be feasible.

proximation. Two exponentials and a constant term a r e used for the example in Figure 8. The constant REFERENCES term is the steady-state value derived from the in- dicial coefficients. It can be adjusted according to 1 . Pines, Samuel, Dugundji, John, and Neuringer, the relative areas of the boxes and the actual wing if desired. One of the exponentials is adjusted to fit Joseph: Aerodynamic Flutter Derivatives for a Flexible Wing with Supersonic and Subsonic Edges.

at the higher values of the points to be approximated Jour. Aero. Sci., vol. 22, no. 10, Oct. 1955, pp.

time. The other exponential, having a larger ex- 693-700. (See also Pines, S., and Dugundji, J.: ponent, is used to match the desired properties near Aerodynamic Flutter Derivatives of a Flexible time zero and damp out at larger times. Such a pro- Wing with Supersonic Edges.

cedure will probably suffice for more general indicial Aircraft Ind. Assoc.

ATC Rep. No. ARTC-7, Feb. 15, 1954.

functions than that of Figure 8. Pines, S . , and Dugundji, J.: Application of Aerodynamic Flutter Derivatives to Flexible Wings with Super- As a check on the adequacy of the particular sonic and Subsonic Edges. Republic Aviation Corp.

exponential approximation in Figure 8, a frequency Rep. E-SAF-2, Apr. 1954) response is computed over the limited range of re- 2. Li, Ta C. H.: Aerodynamic Influence Coefficients efficients. WADC Tech. Rep. 56-97, Part 11, for an Oscillating Finite Thin Wing. Chance Vought ASTIA Doc. No. AD 110592, Feb. 1956.

Aircraft, Inc., CVA Rep. No. 9513, Aug. 23, 1954.

6. Lomax, Harvard, Heaslet, Max. A., Fuller, Frank- lyn B., and Sluder, Lorna: Two- and Three- 3 . Li, TA: Aerodynamic Influence Coefficients for an Oscillating Finite Thin Wing in Supersonic Dimensional Unsteady Lift Problems in High-speed Flow. Jour. Aero. Sci., vol. 23, no. 7, July 1956, Flight. NACA Rep. 1077, 1952. (Supersedes NACA pp. 613-622. T N ' s 2256, 2387, and 2403) 4 . Voss, H. M., 7. Lomax, Harvard, Fuller, Franklyn, B., and Sluder, Zartarian, G., and Hsu, P. T.: Ap- plication of Numerical Integration Techniques to Loma: Generalized Indicia1 Forces on Deform- the Low-Aspect-Ratio Flutter Problem in Sub- ing Rectangular Wings in Supersonic Flight. NACA sonic and Supersonic Flows. M.I.T. Aeroelastic Rep. 1230, 1955. (Supersedes NACA TN 3286) and Structures Research Laboratory Technical Re- port 52-3, Contract NOa(s) 53-564-c for Bureau 8. Tobak, Murray: On the Minimization of Airplane of Aeronautics, USN, Oct. 1954. Responses to Random Gusts. NACA TN 3290,1957.

Tabulation of the f h Functions 5 . Zartarian, Garabed: Theoretical Studies on the 9. Huckel, Vera: Prediction of Unsteady Supersonic Airloads on Which Occur in the Aerodynamic Theory of Oscil- Elastic Wings. Part 2 . Rules for Application of lating Wings in Supersonic Flow. NACA TN 3606, Oscillatory Supersonic Aerodynamic Influence Co- 1956.

IN-FLIGHT DAMPING MEASUREMENT G. E. Sanderson, E. A. Bartsch - Lockheed Aircraft Corp., Burbank, Calif orqzia only possible with derived data. But even an indirect Abstract comparison is very useful in order to insure that the This paper describes a new testing technique data from analysis are reliable. Before flight test, the various structural modes of an airplane are de- which can be applied in determining the damping co- terminedin a ground shake test where only structural efficient of the critical vibration modes of anairplane damping is present. During flight, additional aerody- in flight. The damping coefficient can be determined in several different ways from the same datausing namic forces are present which vary with speed and different features of a modified response curve which altitude. They affect the frequency and damping of the implies the possibility of checking one value against modes.

the other.

In flight vibration tests, the various modes of The method introduces the effect of sweep vibration have to be excited by means of some con- rate in the driving system. This effect on the fre- trollable source of energy and the variation of the quency response curve of the critical vibratign mode response with speed and altitude has to be measured.

and its various characteristics are used in the deter- mination of damping coefficient. A theoretical exam- The method of excitation and the methodof eval- ination is made of these characteristics for single uation of the response curves a r e closely related.

degree of freedom systems. There are different types of exciters: Mechanical exciter with a rotating single out- of-balance weight or with a pair of out-of- INTRODUCTION balance weights coupled with each other in this way that one component of the force*is can- celled. The balance weight can be preloaded by a spring in order to obtain a desired function The main objective of flight flutter tests is to demonstrate that an airplane is flutter safe in its de- of the exciting force versus frequency.

signed range of speed and altitude. An airplane can be considered as flutter safe if all structural vibra- Aerodynamic exciter can be any flap in the free tion modes exceed a minimum requirement in damp- airstream placed in the proper position, e.g.

any control surface or additional flaps. The ing. The minimum requirement is a matter of ex- perience and may be agreed upon between airframe real force or moment of excitation cannot be manufacturer and customer. A certain safety margin determined due to the interaction between ex- from the critical speed must be observed. The air- citer and airplane. This type of exciter may plane cannot be flown and tested at the critical speed be mandatory if no place for a mechanical ex- unless artificial damping of predictable magnitude citer is available.

can be applied. This is one reason why flight test data cannot be immediately compared with data from By using a small explosive charge suitably lo- flutter analysis which mainly deals with the critical cated it is possible to excite transient response speed o r zero damping condition. A comparison is in all the various modes of vibration.

the input The mechanical and the aerodynamic exciters frequencies compared with the magnitude of allow the application of sinusoidal input function with which is contained in the integral. In this case the step by step variable frequency. The response func- frequency response curve will be in e r r o r at these tion is the so-called "frequency response curve". frequencies.

The test procedure is to excite the system at a fixed and constant frequency until a steady-state amplitude The determination of damping coefficient from is achieved. This procedure has to be repeated for transient response data must be approached withcare.

each frequency and each flight condition. It is ex- It is difficult to determine that no other input forcing tremely time-consuming especially when the fre- function has been applied during the time the deter- quency interval has to be chosen very small in case mination is being made. Further confusion can arise of a response function with a high maximum re- if the energy put into one mode is transferred slowly sponse and a steep slope of the response function.

to some more complex mode. This can give rise to apparent rapid decays and high damping simply due to Both exciters can also be used for application unfortunate choice of either the locationordirectionof of a variable input frequency. The input frequency forcing function.

function versus time may be described by a poly- nomial. The simplest polynomial is the straight line.

The decay of the free oscillation is also very It implies a new variable, the slope of the straight sensitive to random input. If the damping of the sys- line o r the "sweep rate" of the frequency variation.

tem is low, a very small impulse is necessary to The sweep rate can be made proportional to the fre- quency, but this method does not give more informa- excite the system and vary the amplitude of the re- sponse. Also the presence of other structural modes tion (Applied by H. G. S . Peacock, Gloster Aircraft and even the motion of the rigid airplane make the Co., Reference 1 ) .

evaluation of the decay quite questionable.

Any variation of the input frequency makes the response function dependent on the time. We may While, as stated earlier, the purpose of inflight call it a "time response curve" in order to distin- w a s to gain information about the vibration testing guish it from the "frequency response curve" obtained damping characteristics of the various modes of inter- by applying a constant input frequency.

est, several other ground rules were used to arrive at the procedure to be described more fully.

The method with variable frequency excitation requires considerably less time than the method with constant driving frequency. The entire frequency These ground rules were: range of interest can be covered in one sweep up and down for each flight condition.

(1) That the method requires a s small a time as possible to gather the data. This is to The excitation with a short sharp impulse gives relieve the problems of very high speed a transient response function followed by a decay. It low altitude testing.

is theoretically possible to excite transient response in all the various modes of vibration.

(2) The method requires an absolute minimum of rework to the airplane. The surfaces in Common to all response functions obtained in question in one case were all blind struc- flight test is the superimposition of the response to tures, very thin and were not amenable to random input which tends to mask the response curve.

additional weight without danger of adding It is impossible in flight test to avoid the random in- a new unknown problem.

put. The different response functions are more or less sensitive with respect to random input. Especi- (3) I f possible, the method should not require ally sensitive is the transient response to a sharp an absolute value of input force since this impulse. The frequency spectrum of a sharp impulse covers theoretically a wide range of input frequencies would nearly always present a more diffi- which can be viewed as the sum of sinusoidal waves. cult problem.

Therefore, the response of a linear system to a tran- sient input can be viewed as its response to the sum of (4) The methoddidnot necessarily require a firm theoretical foundation, preferably it should sinusoidal waves contained in the transient input. The procedure for converting transient data from the time have.

to the frequency domain is based on the use of the Fourier integral. It has to be taken separately for (5) The method should be fairly simple to apply the input and output function. This method requires so that the flight program would not be steady state condition in some finite time which is unduly impeded by lack of information.

quite difficult to obtain in flight test.

(6) The method should arrive at least a rea- The frequency spectrum of the random input sonable prediction as to the safety for the is not contained in the integral of the input a flutter which next several steps in approaching function may have a pretty high magnitude at certain boundary.

The argument of the forcing function on the Response to Variable Frequency Input right side is a quadratic function of time. The first derivative of the argument with respect to time is Before discussing the testing technique with a the input frequency.

variable frequency input function, we need some in- formation about the effect of the sweep rate on the 2 r f i = m + 2mlt response.

where m = input frequency at t = 0 in radians Existing references indicate neglect of the ef- per second fect of the sweep rate o r assume constant correction.

It can be shown that this assumption is misleading and m = rate of change of input frequency, in cases of low damping which we are mostly con- called "sweep rate", in radians per cerned with.

second squared Some information we get from Frank M. Lewis' Setting m l = 0, we get the classical case of constant report about "Vibration During Acceleration Through input frequency. In all cases m i 7 0 we may set the a Critical Speed" (Reference 2). We extended this

initial frequency m, = 0 and in cases m i < 0 we may

We will work to the method covered in the paper.

set rno = 2p.

now discuss the response of a linear single degree of freedom system to a forcing function of variable Figure 1 shows the frequency response curve frequency with constant sweep rate. The case of obtained by applying a constant frequency forcing constant driving frequency is included as boundary function (ml = 0) compared with two response curves case with zero sweep rate.

to variable frequency excitation.

The damping coef- ficient in all three cases is Y = 0.1. The response For better understanding of the curves the curves for m i # 0 are "pseudo frequency response symbols used may be explained. The differential curves", because the frequency depends on the time.

equation for a single degree of freedom system with variable frequency excitation and with unit input can

The first curve ( m i = 0) depends only on the

be expressed as: Y and the input frequency. Some features damping

of the curve depend only on Y . The maximum re-

2 2 sponse - the amplitude ratio R - is proportional

y + 2 ny + p y = sin (mot + mlt ) 1/ Y for small damping. The proportionality factor is the ratio of the maximum response to the response at zero input frequency (static condition). The static where: response is difficult to measure in flight test. An- - - ,response for unit input Y other feature of the response curve is the width of the response peak a t 0.707R. It is well known that the - - system frequency in radians per p = 2nf width at this response (3 db down point) is equal to second

the damping Y . W e know that the maximum response

occurs at the frequency ratio "one", if the damping system frequency in cycles per is small, and that the maximum response shifts to f O second lower frequency ratios if the damping is high.

input frequency at t = 0 in ra- mO dians per second RESPONSE AMPLITUDE OF A SINGLE DEGREE OF FREEDOM SYSTEM VS. FREQUENCY 2ml = 2 n f ' - - rate of change of input frequency

I LCONSTA FREQUENCY l

in radians per second squared rate of change of input frequency in cycles per second squared dimensionless rate of change of input frequency, c a l l e d "sweep rate" 2n y =- damping coefficient P variable input frequency in cycles I I I 1 f i per second 0 0.5 I .o 1.5 2 .o

INPUT FREQ. / SYSTEM FREQ. - fi/fo

input frequency at maximum re- Figure 1. Response Amplitude of a Single Degree of sponse in cycles per second Freedom System Versus Frequency In case of variable frequency excitation we have PHASE ANGLE OF A SINGLE DEGREE OF one additional new variable in the input frequency FREEDOM SYSTEM VS. FREQUENCY function, the slope of the frequency function, called the "sweep rate" f' o r (dimensionless). The sweep rate causes a delay in the response. In case of increasing frequency the maximum response occurs at higher frequency and in case of decreasing fre- quency at lower frequency. The maximum response is in both cases lower than in the case of zero sweep rate, because the excited system has not enough time to build up higher amplitudes.

Figure 2 shows how the maximum response and the frequency at the maximum response depend on the damping Y of the excited system and onthe sweep rate of the input function. The up or down going lines are lines of constant sweep rate. In the INPUT FREQUENCY 1 SYSTEM FREQUENCY fi/lo middle is the line for zero sweep rate (classical Figure 3. Phase Angle of a Single Degree of Freedom case), on the right for positive, and on the left for System Versus Frequency negative sweep rates. The lines going from the left the right are lines of constant damping Y . The rate. The phase angle at the maximum response to higher the sweep rate is,the higher is the effect on shifts to higher values for increasing frequency and the maximum response and the frequency shift at to lower values for decreasing frequency.

maximum response. This dependency allows us to pick up more information from the response curves The slope of the phase angle curve at the maxi- to variable input frequency then from the classical mum response is lower than that for zerosweep rate.

response curve. Applying a positive and a negative The maximum slope which occurs somewhat later is sweep rate of same magnitude in two test runs under nearly the same as that for zero sweep rate. Figure 4 shows the phase angle at the maximum response same conditions, we can measure a total frequency shift which depends on the damping Y and the sweep vs. frequency for different damping values Y , rate iiil.

Also here we and different sweep rates ml.

can state that the effect of the sweep rate is increas- Before we discuss the crossplottings along the ing with decreasing Y and that the shift of the phase lines of constant damping and constant sweep rate, angle is opposite for positive and negative sweep let's look a t the phase angle of the response for the rates. The magnitude of the total phase angle shift same three cases. Figure 3 . shows the phase angle can again be utilized in determining the damping.

vs. frequency. From the classical case (mi = 0) The following figures a r e crossplottings of the we know that the phase angle starts with zero degree different features vs. sweep rate E1 and vs. damp- at frequency ratio "one" and approaches 180" for very ing Y .

high frequencies. The slope of the phase angle at the is proportional 1,' Y for small maximum response In Figure 5, we see the maximum reponseR vs.

damping. The phase angle of the response to vari-

sweep rate for different Y . The effect of the

able frequency input is also affected by the sweep PHASE ANGLE Q: AT M A X I M U M RESPONSE MAXIMUM RESPONSE R VS. FREQUENCY VS. FREQUENCY -. .

0.8 0.9 I .o 1 . 1 I .2 0.90 0.95 1.00 1.05 1 . 1 0 FREQ. OF MAX. RESPONSE f SYSTEM FREQ. fmffo FREQ. OF MAX. RESPONSE f SYSTEM FREQ. -tm/fo Figure 4 . Phase Angle at Maximum Response Figure 2. Maximum Response Versus Frequency Versus Frequency 7 the frequency shift of sweep rate is very little in case of high damping Y , In the following Figure but remarkable in case of low damping. In all cases the maximum response is plotted vs. sweep rate. The but zero sweep rate we get afinite maximum response, maximum response shifts to higher frequencies in case of increasing frequency and to lower frequencies even for Y = 0.

for decreasing frequency. The frequency shift is re- markable and well measurable in case of low damping.

MAXIMUM RESPONSE R VS.

This plotting is very useful in determining the fre- SWEEP RATE 103fii, quency and the damping of the excited system. In 1 0 0 1 \ I I I I order to get a well measurable frequency shift it is advisable to apply a positive and a negative sweep

so

rate of same magnitude under the same flight condi- tion. The frequency shift is independent on the mag- nitude’ of the input function; it depends only on the damping and the sweep rate. Therefore, the damping IO can be determined directly without knowledge of the real input function and the magnification factor.

a FREQUENCY SHIFT OF MAXIMUM RESPQUSE - fm VS. SWEEP RATE IO%,

I I I I

1.2 0 1 2 3 4 lo3 8 , Figure 5. Maximum Response Versus Sweep Rate I 1 This finding is very important for practical * E121 0 flight flutter tests. The method with variable fre- quency excitation applied with caution is not more dangerous than a straight flight with always present random excitation, 09 The next plotting (Figure 6) is more suitable for practical application. It shows the maximum 0.8 response vs. damping for different sweep rates. Us- Figure 7 . Frequency Shift of Maximum ing the maximum response for determining the damp- Response Versus Sweep Rate ing coefficient Y a preliminary study of the pro- portionality or magnification factor is necessary. It Crossplottings of the frequency shift vs damping can be assumed as a first approximation that this Y for different sweep rates are presented in Figure 8.

factor is constant in a certain speed and altitude range.

It shows the effect of the sweep rate and the damping on the frequency shift.

FREQUENCY SHIFT OF MAXIMUM RESPONSE VS. DAMPING i j 1.21 I I I 1 h I I a P

=I

0 . 9 I I I I 0 . 8 1 I I I I 0 0. I 0.3 0.4 0 (XI 0.2 0.3 0.4

d O** ‘II

Figure 8. Frequency Shift of Maximum Figure 6. Maximum Response Versus Damping Response Versus Damping The next plotting (Figure 9) is very convenient WIDTH O F THE RESPONSE CURVE W for a quick estimation of the damping from the total AT 0.707 R VS. DAMPING 7 frequency shift between the positive and negative 0.5 I I I I sweep rate of the same magnitude. All three plottings of the frequency shift indicate that the accuracy of 0.4 is better in case of low damping than of high reading damping.

0.3 IFFERENCE OF FREQ. SHIFT OF M A X . RESPONSE I

& VS DAMPING$ FOR POS. & NEG. SWEEP RATE

0.2

0 . 3 1 I I I I

0. I 0.2 0 0. I 0.2 0.3 0.4

S I 2

d

a

Figure 11. Width of the Response Curve at 0. I 0.707R Versus Damping PHASE ANGLE CC AT MAXIMUM RESPONSE

vs. SWEEP RATE 1 0 3 ~ ~

0 0. I 0.2 0.3 0.4 I 80° I \

d

INCREASING FREQUENCY Figure 9. Difference of Frequency Shift of Maximum Response Versus Damping for Positive and Negative Sweep Rate Another feature of the response function which can be used for direct reading of the damping coef- ficient without knowledge of the input function is the width of the response curve at 0.707R (Figures 10 and 11). The width w = 7 for the classical case of zero sweep rate mi = 0 and small damping. The I I effect of the sweep rate on the width w is quite re- 0 I 2 3 4 5 markable at low damping. Neglecting the effect of 10~6, the sweep rate can be dangerous.

WIDTH OF THE RESPONSE CURVE W Figure 12. Phase Angle at Maximum Response AT 0.707 R VS. SWEEP RATE IO3%, Versus Sweep Rate 0.51

1 '8 ~ 0 . 4

maximum response, but the character of the curves 0.4 I is quite similar to those in Figure 7.

0.3 The crossplotting of the phase angle vs. damping (Figure 13) can be compared with the plotting (Figure 5 = 8): frequency shift vs. damping. The phase angle 0.2 shift in case of low damping is remarkable.

0. I The difference of the phase angle at max- imum response for positive and negative sweep rate is shown in the next Figure 14. This plotting is useful for a quick estimation of the damping.

0 I 2 3 4 103 iil, Finally, lets take a look at the increment of the Figure 10. Width of the Response Curve at phase angle at maximum response. In Figure 15 the 0.707R Versus Sweep Rate slope of the phase angle a' is plottedvs. sweep rate.

Figure 12 represents the crossplotting of the These curves .look quite similar to those in Figure 5, phase angle at maximum response a vs. sweep rate.

maximum response vs. sweep rate. The plotting of The phase angle is more sensitive with respect to the slope a' vs. damping (Figre 16) is similar to variation of the input frequency than the frequency a t Figure 6.

INCREMENT OF PHASE ANGLE AT MAXIMUM PHASE ANGLE CC AT M A X ~ M U M RESPONSE

RESPONSE a'vs. DAMPING 7

VS. DAMPING '8

5,000 3,000 VI

; 1 , 0 0 0

n 500

I I I I I

IOOL I I I I 0 01 0 2 0.3 0.4 0 0. I 0.3 0.4 d Figure 16. Increment of Phase Angle at Maximum Figure 13. Phase Angle at Maximum Response Response Versus Damping Versus Damping The phase angle and the slope of the phase angle a r e pretty sensitive with respect to any random input.

PHASE ANGLE DIFFERENCE AOC AT M A X . RESPONSE Therefore, the data obtained from the phase angle

VS. DAMPING d FOR POS. & NEG. SWEEP RATE

curve a r e less reliable than those obtained from the response curve. Some experience is required in judg- ing how to weigh each of thefeatures. The possibility to use quite a number of the features of the response curve for determining the damping coefficient pro- vides the opportunity of checking.

Summarizing, we can say that the new variable, the sweep rate, causes more variation in the response curve. The evaluation seems to be more difficult at first sight, but with the knowledge of the dependence on damping and sweep rate of the different, features we can determine the damping in different ways. We can pick up more information from the response to variable input frequency than from the frequency re-

d

sponse curve for zero sweep rate (El = o).

Figure 14. Phase Angle Difference at Maximum Response Versus Damping for Positive and Negative Sweep Rate DISCUSSION INCREMENT OF PHASE ANGLE AT MAXIMUM RESPONSE CC'VS. SWEEP RATE IO3%, A theoretical study on a single degree of freedom system showed that the response to a forcing function of variable frequency with constant rate of frequency I I I change depends on the sweep rate and the damping of the system. The sweep rate causes a diminution of the maximum response and a frequency shift of the maximum response to higher or lower input frequen- cies. Also, the phase angle between output and input at function and the slope of the phase angle function .JV I 40 the maximum response vary with the sweep rate. The width of the response curve is another feature which 200 ' varies with the sweep rate. The variation of all the IO0 features just mentioned is of such a magnitude, 0 1 2 3 4 especially in case of small system damping, that it io3 iii, cannot be neglected. It can rather be an aid in deter- mining the damping coefficient of the system if the Figure 15. Increment of Phase Angle at Maximum sweep rate is properly chosen and kept constant in Response Versus Sweep Rate the frequency range of interest.

A new flight testing technique can be based on input frequency, as shown in Figure 18, for increasing the comparison of the measured response curve with and decreasing frequency. Most information used in a system with one degree of the response curve of determining the damping coefficient can be picked up freedom. The different features of the response from these response functions: the maximum re- function which depend on the sweep rate of the input sponse, the frequency shift of the maximum response, function and the damping of the system allow the and the width of the response curve.

The sweep rate determination of the damping coefficient. Apractically is taken from the frequency functionversus time. The l/R is agood f reciprocal of the maximum response

= . - = lies in the range

convenient sweep rate indication of the damping, it increases with increasing 4 7 f O of 0.0005 to 0.0015. The sweepratehas to be constant damping and decreases with decreasing damping. The in order to avoid additional response to variation of damping coefficient determined by comparison of the the sweep rate. The determination of the damping measured response curve with the response curve of coefficient from the different features provides the a system with one degree of freedom is plotted in possibility of checking one value against the other. Figure 19 versus Mach number for constant altitude.

AMPLITUDE RATIO VS. INPUT FREQUENCY A BEAC study was made on a three degree of freedom system with one predominant mode of small

3000 I

I I I I I I

damping. was kept The amplitude of the input force constant and the varying frequency was controlled by hand. Figure 17 shows a comparison of the frequency shift of the maximum response of the three degree of freedom system with that of a single degree of freedom system. The frequency shift curves plotted versus rate of change of input frequency show fairly good agreement.

FREQ. SHIFT OF M A X . RESPONSE VS. SWEEP RATE 103iii, F R O M 3-DEGREE O F F R E E D O M BEAC STUDY f i in C.P.S.

I I Figure 18. Amplitude Ratio: Fin Root TorWion Moment per Degree Yaw Damper Deflection 2 1 - 0 Versus Yaw Damper Frequency 1.0

DAMPING d VS. MACH NUMBER

1 . 1 STEEL FIN - ALT. l0,OOO FT.

FIN ROOT B E N D I N G FIN ROOT TORSION 0 . 3 I .o 0.2 10~6, 1 0 ~ 1 5 , Figure 17. Frequency Shift of Maximum Responses \o Versus Sweep Rate from 3-Degree of Freedom 0. I BEAC Study Flight Test Results C We applied the new testing technique success- 0.9 1 . 0 1.1 1.2 1.3 fully on the F-104A and other airplanes. Here are a M M few results. The tests indicated that there were no Figure 19. Damping Coefficient Versus Mach Number satisfactory means of determining the exact input forcing function. Only an indirect input function could be applied through the yaw damper. So the yaw damper The tests were repeated at different altitudes. The deflection was used as an indication of the input minimum damping picked up from these plottings is function. The bending and torsion moment at the fin now plotted versus altitude. Figures 20 and 21 show root was used as output. Any other measured and the minimum damping versus altitude for the F-104A recorded quantity which is closely related to the fin with aluminum and steel skin respectively. The structural mode of interest can be considered as an altitude for zero damping can be found by extrapolation.

output.

22 shows a comparison of the flight test re- Figure sults with the analytical and wind tunnel results. A The time response function, output amplitude fairly good agreement can be stated.

divided by the input amplitude, canbe replottedversus COMPARISON OF .125 ALUMINUM

MINIMUM DAMPING 8 VS. ALTITUDE

0.125 IN. ALUM. FIN FIN ROOT TORSION FIN ROOT BENDING o 0.1 0 . 2 0 . 3 o 0.1 a2 a3

d d

Figure 22. Comparison of Flight Test Results with Figure 20. Minimum Damping Versus Altitude the Analytical and Wind Tunnel Results for Aluminum Fin

MINIMUM DAMPING d VS. ALTITUDE

This was a brief survey about the application of STEEL FIN the testing technique with variable input frequency in FIN ROOT TORSION FIN ROOT BENDING flight flutter tests because of the limited time avail- able.

REFERENCES I . H. 6. S. Peasock, "Flight Flutter Tests on the Gloster Javelin".

2. Frank M. Lewis, Vibration During Acceleration Through a Critical Speed".

Figure 21. Minimum Damping Versus Altitude for Steel Fin O N THE PREDICTION OF CRITICAL FLUTTER CONDlTIONS FROM SUBCRITICAL RESPONSE D A T A A N D SOME RELATED W I N D - T U N N E L EXPERIENCE /. C. Houbolt and A . G. Rainey - N A C A , Langley Laboratory, Langley Field, Virginia Abstract ocity enters. Actually, the work started whenwe were considering the application of ideas suggested by Methods of interpreting response measurements Professor Moll$- Christensen. The p r e s e n t work which could be amenable to flight flutter testing pro- evolved a s a special consideration, and we thought it cedures a r e being studied analytically and in the wind to be of enough interest to merit separate attention.

tunnel. One suggested scheme, which requires evalu- ation, is an iterative technique in which derivatives In the first part of the paper an elementary but obtained from subcritical response data are used to rational analysis is given to show how the response indicate the approach to flutter. This paper considers of a wing system might be expected to depend on air a simplification of this procedure by examining the density, for both the cases of sinusoidal and random manner in which a single characteristic of the sub- force input. A theoretical model illustrating the critical response behaves in relation to variations of to the flutter condition is technique of extrapolation the density or dynamic pressure in the approach to then considered. Then, in the second part of the paper, flutter. The use of this single parameter scheme is attention is focused on the experimental testing of the examined for random excitation as well as for sin- approach by application to some wind-tunnel studies.

usoidal forcing. The feasibility of the method is illustrated by several examples and the relative merits of random and sinusoidal excitation are discussed.

ANALYTICAL TREATMENT INTRODUCTION Derivation of Extrapolation Equations Let u s consider an aeroelastic system which is In this paper certain new slants are given on the being excited into motion by either a sinusoidal shaker prediction of critical flutter condition from subcritical response data. Specifically, the technique considered or a sinusoidal gust, and then proceed to investigate herein deals with the manner in which the forced how the amplitude of the response, such as deflection, response behavior of an aeroelastic system varies is dependent on the density of the air flow. To do this, air density, while velocity is being introduce the equation governing the motion of the with changes in held essentially fixed. The impression is not to be system as follows given that density considerations are necessarily new, but rather the point of view is held that a further examination of density effects may lead to a simple index which may be useful in the prediction of flutter.

The motivation stemsfrom the fact that density appears where the equation may be interpreted either in dif- in a rather clean-cut fashion in the equations for ferential operator form or in matrix notation. The flutter, in contrast to the complex way in which vel- operator D on the left hand side converts the surface deflection w into the total surface loading composed By inverting this equation and at the same time sep- of the inertia, aerodynamic, and applied loadings on arating the effects of the shaker and gust terms, we the right hand side. The operator DL is complex and arrive at the final twoequations whichindicate how the is a function of Mach number and reduced frequency, amplitude of wing deflection varies with density and when operating onthe deflection, leads to the aero- dynamic loading; the shaker force Fs (considered to shaker only (?a) be distributed over a small area to give an intensity) P Fg are treated together for and the gust loading convenience, and will be separated later. It is re- marked that the sinusoidal gust condition is introduced

because this condition yields a necessary part - the

transfer function - of the solution for response when

random inputs are involved; the density p is shown These two equations suggest the basic linear extra- as an ingredient of the gust loading so as specifically polation procedure of this paper. Thus, assume that to keep the density in an explicit sense throughout in-flight measurements of response are made accord- the analysis.

ing to the following plan: we fly at a velocity near the expected flutter speed (or at a velocity for which we We now choose to make an approximate solution want to prove the aircraft safe), but take care to first of equation (l), since our essential result is arrived fly at a high altitude where the density is low. Then, at rather quickly, and will leave a more rigorous, repeat the tests at successively lower altitudes. Then, but lengthier, treatment which leads to the same re- for tests utilizing a sinusoidal shaker input, we might sult to an appendix. The approximate solution is of expect a plot of the reciprocal of the amplitude versus the Galerkin type and is made by assuming that the density to form a straight line, which when extra- deflection is expressed in terms of the modal shape which occurs at flutter, thus polated to 1 - = o yields the density that ought to pro-

a1 1 1

duce flutter. For the caseof agust i n p u t , m i s plotted w = a w (2) I f

against ; for an expected linear relationship. In the

actual testing in a random force input environment, the where a1 is a coefficient to be determined and wf is output spectrum of response will be found. But since the flutter deflection shape which satisfies the equation this spectrum is proportional to the square of the frequency response function for sinusoidal gust input,

m = mw + pf v f 2 ~ ~ wf (3)

we see that the reciprocal of the square root of the f f f f output spectrum should be plotted against-, to arrive P which is simply equation (1) with the forcing terms at a condition consistent with that indicated by equation suppressed. Substitute equation (2) into (l), use equa- (7b).

tion (3), multiply by wf and integrate over the wing surface; the result leads to the following solution for In applying equations (7a) and (?b), it is implied that the frequency of flutter is known. This is, of a1 so; therefore the procedure to follow is to course, not Qs + P Q g observe the amplitude -density behavior at several (4) al = frequencies until it becomes clear from the frequency m2 - w 2 M + pf vf2Af - P : A response plots what frequency is emerging as the f flutter frequency.

where Qs and Qg are in the nature of generalized Example of Calculated Results forces

Q~ = J wfFsdS, Qg = f W F dS As a test of the possible range of applicability

f g of equations (?a) and (?b), response calculations were made for a rectangular cantilever wing, and inter- and preted in accordance with these equations. The re- " sponse analysis was limited to two degrees of freedom, M = Jmw &dS, A = J w D w dS, A = rwfDLwfdS (5) f f f L f f one bending and one torsion, and employed the aero- dynamic coefficients for M = 0.8 in a strip fashion.

In general, all of these generalized coefficients are The frequency response functions obtained for ampli- complex. At a velocity and frequency equal to the tude of torsional displacement at the wing tip are values at flutter but at a subcritical value for density, shown in Figure 1, where the curves at the left are the value of a1 is particularly significant and is for a sinusoidal gust input, whereas the curves at the right are for a sinusoidal shaker input located at the Qs + P Qg tip and at 10 percent chord position. The parameter p is a ratio of structural mass to air mass, and = v 2A (pf - pl f f

FREQUENCY RESPONSE

S I N US01 DAL

RANDOM I

P

I St

TOR.

BEND.

[I" I

REL

- I t l O 0 i

AMP

- I I

0 200 400 0 200 400

FREQ, w

F i g u e 1. Frequency Response Figure 2. Extrapolation of the curves to-- 0 indi- therefore may be regarded as inversely proportional 14- to air density. It is seen that as the air density cates a flutter density ( ~ = 89) which agrees identi- increases ( p decreasing) an ever growing and sharper cally with that given by a conventional flutter analysis.

peak develops at a frequency of 158 cps, thus suggest- The very pronounced range of linearity is also to be ing a frequency of flutter.

noted; in fact, using only the data at densities of 45 and 75 percent of-the flutter density would give a Application of equations (7) to the amplitude flutter prediction erring by only a few percent. It is values at this frequency gives the curves shown in

EXTRAPOLAION TECHNIQUE

RANDOM SINUS01DAL

I I I I I 1

Y

0 40 80 120 160 200 240

MASS RATIO p, Figure 2. Extrapolation Technique significant to note also that the data point correspond- unimportant in these instances, and this is actually 45 percent of critical density condition is what the experiment shows. Thus, any flight investi- ing to the gation should keep this possibility in mind.

not a major peak in the frequency response curve for this density. Thus, subcritical response data which have not yet indicated peaks may still be useful.

The single data point anddashedcurve shownfor densities above the critical value are shown simply a s EXPERIMENTAL RESULTS a matter of interest to indicate that the theoretical response calculations based on sinusoidal conditions The previous section concerned the analytical show a branch above the flutter condition a s well as background which has formed a guide to some wind- below.

tunnel. experiments discussed in this section.

The main conclusion to be drawn from this example is that the present technique for predicting The linear extrapolation technique has been flutter appears quite promising. In the secondpart of examined experimentally for six cases involving ran- dom excitation and for one case of sinusoidal excita- the paper we shall see how well it works when applied tion. These various cases are illustrated in Figure to wind-tunnel studies.

3, where a typical flutter boundary is used to illustrate Before looking at the experimental results, we the manner in which the flutter condition was ap- might make a few comments on the general applica- proached, Geometric properties of the four semi- bility of the density extrapolation technique. A s with span, cantilever mounted models are listed in Table other flutter extrapolation techniques, there will un- I. Model A was used to obtain three sets of sub- doubtedly be cases where this scheme breaks down. critical response data - Case I and Case 1 1 at two different stagnation pressures, but increasing velocity, One possible example is that associated with wing and Case I I I at constant velocity but increasing systems which are capable of a single degree of density. Models B and C were tested at constant stag- freedom type flutter. Interestingly enoilgh, equation can be used to demonstrate why. Up to now we nation pressure and increasing velocity. Model Dwas (7) equipped with an electro-hydraulic shaker housed in a have tacitly assumed that unbounded response (al- 0 3 ) occurs when pf - P becomes zero. It, of course, tip tank. This model was examined for two cases - also is possible for the response to become infinite Case I, random excitation at constant stagnation pres- when A vanishes, and this may occur either in a sure, and Case 11, sinusoidal excitation at constant classical way for attached flow, o r what is more velocity. In all of the cases examined the type of flutter encountered was classical bending torsion likely, when the flow becomes separated, such as in is involving the coupling of well separated modes.

stall flutter. The equation indicates that density TYPICAL FLUTTER BOUNDARY SHOWING MANNER OF APPROACH FOR VARIOUS CASES DYNAMIC PRESSURE

f / / m '

CASE I I L

I I I I I I

C .2 .4 . 6 .8 1 . 0 1.2

MACH NUMBER Figure 3. Typical Flutter Boundary Showing Manner of Approach for Various Cases TABLE I GEOMETRIC PROPERTIES O F MODELS TESTED Aspect Taper Sweep Airfoil Model Ratio Ratio at 1/4 C Section

---

A 5 1.0 0" 6 percent Cir- cular Arc B 6 1.0 45" Flat Plate C 3 1/7 45" NACA 65A004 D 3 1.0 0" NACA 65A010 Random Excitation response. These results are illustrated in Figure 4 where the regponse magnitudes are shownasfunctions The subcritical response data for Models A, B, of the ratio of the dynamic pressure at flutter to the and C were obtained by recording the output of re- dynamic pressure associated with each point.

sistance wire strain gage bridges mounted near the It should be pointed out that this form of pre- root of the model, while the model was responding to the normal turbulence in the wind-tunnel airstream. sentation is not identical to that suggested by the The response data were recorded on magnetic tape analysis. Some of the experiments were completed using frequency modulation amplifiers (ref. 1). After before the analysis was available, and the form of completing the tunnel runs, thirty-second samples of presentation chosen was such that all of the experi- the tape records were analyzed using analog data ments would be consistent within themselves. For reduction equipment described in reference 1. The example, the velocity squared term has been combined peak values in the power spectra of strain response with the density to form the dynamic pressure. This were operated on to yield numbers proportional to is a necessary step in that some of the experiments the reciprocal of the absolute magnitude of the strain involved an approach to the flutter condition primarily

EXTRAPOLATION TO FLUTTER CONDITION FROM RANDOM EXCITATION

('%I" GAGES)

1 . 0 1 . 4 1.8 1 . 0 1 . 4 1 . 8 2.2 1 . 0 1 . 4 1 . 8 2.2

I

-

E

0 CASE E L

- I I I I I I

1 . 0 1 . 4 1 . 8 2.2

1 1 0 1 . 4 1 . 8

' FLUTTER

Figure 4. Extrapolation to Flutter Condition from Random Excitation through increases in velocity. These variations in shown in Figure 5. The data in the left hand part of velocity require the statement of additional qualifi- the figure were obtained in the same manner a s the cations to those already mentioned if one is to expect data of the previous figure except that the angular a linear extrapolation of the response data. Perhaps motion of the tip of the model was deduced from the the most important of these additional assumptions combined output of two linear accelerometers mounted is that near the flutter condition, the air forces in the tip tank.

associated with flutter do not vary rapidly with the reduced frequency and Mach number. The data shown in the right hand part of Figure 5 were obtained by measuring the amplitude of re- An idea of the usefulness of these extrapolation sponse at the two accelerometer stations due to a methods can be gained by examining Figure 4. A sinusoidal applied force. The amplitudes were meas- reasonable degree of linearity of the response data is ured after the shaker had been tuned to the frequency indicated for all of the cases, when the dynamic pres- of maximum response which, in this case, appeared to sure is within about 20 percent of the critical value be associated with the torsional mode. Although some and the extrapolation gives a good indication of the response due to turbulence was present during the flutter condition. The least encouraging results were shaker tests, the phase sensitive instrumentationused obtained for Model B which was poorly instrumented. effectively eliminated its effects.

The strain gage bridges were mounted very near the It is noted that both sets of response data indi- root and were about equally sensitive to bending or torsional motions. The response data for the other cate an equally good extrapolation to the flutter con- cases were taken from strain gages arranged such dition. If it is assumed that random excitation and that they were sensitive primarily to torsional strains. sinusoidal excitation will yield equally adequate extra- It might be mentioned that the results shown for the polation results, the question of relative cost o r dif - ficulty of the two methods is of interest. It was third case of Model A indicate a linear relation to lower values of dynamic pressure than most of the mentioned earlier that six cases of random excitation other cases. This result may be associated with a s opposed to one case of sinusoidal excitation have the constant velocity method of obtaining the response been examined. In the wind tunnel, at least, it is data in this case. believed that this six-to-one ratio is a fair estimate of the relative difficulty of the two methods. This is due, primarily, to the fact that the turbulence is always Sinusoidal Excitation available while the shaker must be constructed and In order to gain some insight regarding the installed. Although turbulence also exists in the relative merits of sinusoidal excitation as opposed to atmosphere, the problem of finding it during a flight test and determining enough of its properties to permit random excitation, two cases have been examined for a model equipped with an electro-hydraulic shaker its use might improve the relative attractiveness of a contained in a tip tank (Model D). These results are sinusoidal shaker a s a source of excitation.

COMPARISON OF EXTRAPOLATION FROM RANDOM IAND SINUSOIDAL EXCITATION RANDOM SINUSOIDAL

I .o 1 . 4 1 . 8 2.2 0 .4 .8 1 . 2

q FLUTTER q FLUTTER Figure 5. Comparison of Extrapolation from Random and Sib. ,Ida1 Excitation

APPENDIX We may now proceed to solve equation (1) by expressing the deflection by the following series ex- pansion involving wn The Response-Density Relationship A more rigorous development of equation (7) can w = a w + a w + a w + . . .

(A5) 1 1 2 2 3 3 be made along the following lines. Introduce the two equations where the %'s are unknown coefficients to be deter- 2 2 (D - w m)w = p v DLw (Ala) mined. Substitute into equation (l), use equation (A2a), multiply by Zm, integrate over the surface and then apply equation (A4); the result is an independent solu- 2 2 (D - w m)z = p v D 'z ( A W tion for an as follows L where the first is simply the statementofflutter, i.e., equation (1) with forcing terms suppressed, and the is what we shall term the transposed mate of second

equation (Ala). For fixed v and w , these equations

may be regarded as eigenvalue statements of p ; they Now, if W , v, and P , are chosento represent an actual may be shown to have the same eigenvalues pn (which flutter condition ( W = af, v = vf, P , = Q), then w1 will in general may be complex), and hence may be written represent the associated flutter mode shape, and the solution for a1 becomes Considered jointly, some signifi- where B = D -w' m.

Thus, This solution thus confirms the validity of equation cant relations between W n and zm may be found.

(7) presented in the bodyofthepaper. The form of the multiply equation (A2a) by zm, equation (A2b) by wn, equations is the same, but it is of interest to note integrate both over the wing surface, thensubtract the resulting expressions and make use of the fact that the more rational analysis presented here indi- cates that the generalized forces a r e associated with that J zmBwndS = J wnBzmdS and J z D w dS = the work done by the applied forces inmoving through m L n themodal displacements of the transposed system.

J wnDL'zmdS; there results the relation (Pm - P J J Z,DLWndS (A31 REFERENCE From this equation we arrive at the basic orthogonality properties of wn and zm as given by the following 1. Smith, Francis B.: Analog Equipment For Pro- equation cessing Randomly Fluctuating Data. Aero. Egnr.

Review, Vol. 14, No. 5, pp. 112-119, May 1955.

J z D w d S = O m # n (A44 m L n VECTOR PLOTTING AS A N INDICATION OF THE APPROACH T O FLUTTER E. G. Broadhent - Royal Aircrrlft EstrCblishiieizt, Frlrnborough, EuglrCizd Abstract. Because of its success in ground resonance tests the idea has arisen of adapting the technique for A binary flexure-torsion analysis has been made flight flutter testing. It is hoped that from the flight test under continuous excitation the resonances might to check theoretically a method for predicting flutter be obtained in the same way as from a ground test.

which depends on plotting vectorially the amplitudes of response relative to the exciting force and extracting with at the same time estimates of the overall damping the relevant damping rate. The results of this calcu- at each resonance frequency. Thus agraphof damping lation are given in the form of graphs bothof the rate against airspeed can be obtainedfrom a continuous vector plots themselves and of the estimated damping excitation method of flight flutter testing. In this way rate against forward speed. The estimated damping it is hoped to obtain the best of two worlds; continuous rates are compared with calculated values. The excitation allows more accurate analysis in the pres- ence of buffeting than is possible from a decaying method has the advantage that in a flight flutter test damping can be estimated from continuous excitation oscillation, and at the same time damping can be records: the method is an extension of the Kennedy plotted against airspeed; and damping gives a more and Pancu technique used in ground resonance testing. reliable warning of the approach to flutter than does amplitude response. Near the flutter speed, however, the analysis has to deal with adifferent type of equili- brium than in a ground resonance test, because the INTRODUCTION aerodynamic forces a r e powerful and do not represent a conservative system. In order to see whether this leads to any difficulty in application, a simple flexure- The measurement of normal modes in a ground torsion binary example has been worked out in Che resonance test needs an elaborate technique both to present paper and analysed by the Kennedy-Pancu ensure .that the modes are reasonably orthogonal, method at various forward speeds up to the flutter The presence and to ensure that no mode is missed.

speed. The dampings are obtained and plotted against of structural damping presents one of the main dif- airspeed and the results are found to agree well with ficulties. Kennedy and Pancu have suggested a method calculated dampings. Some low speed wind-tunnel tests of analysing the recordings taken by plotting vector- carried out by Bristol Aircraft Limited show that the ially the displacements relative to the exciting force.

method can give results with a high degree of repeat- are obtained for each resonance and Near circles ability, even in the presence of buffeting.

practical experience seems to show that this type of plot considerably reduces the likelihood of missing a resonance and also improves the accuracy of deter- mining the resonant frequency. This in itself leads to THEORY O F THE METHOD modes being measured which are a better approxi- mation to the true normal modes than is usually possible from amplitude plots alone. In addition the The basis of the theory i s outiined here for structural damping can be estimated directly for each convenience.

resonance.

One Degree of Freedom Hence The equation of motion for one degree of freedom can be written in the form:- and for a generalized exciting force Fez& , where a is an inertia coefficient e is an elastic coefficient A s w is varied the locus of points (qr, qi) is a smooth curve obtained by eliminating 2; from these two equa- q is a generalized co-ordinate

tions: -

g is the phase angle of the restoring force (the damping coefficient).

(9) The steady solution will be motion of the form e , SO we substitute q = ; e ' & .

o r Equation (1) now becomes:- This is the equation of a circlewithits diameter lying on the negative imaginary axis and passing through the origin (see Figure 1 ) .

We let w0 be the natural frequency of the one degree The Position of Resonance of freedom, i.e., w,' = 5 and we obtain:- 0 .

Resonance occurs when 2 = 1 andfrom Equation (7) q r = 0 , i.e., the vector OC on Figure 1 represents the amplitude at resonance. We can obtain a relation between the rate of change of frequency along the curve at resonance and the damping g, so that if the curve itself i s obtained from measurements on a structure of unknown damping, the damping can be estimated.

D in Figure 1 when the fre- Consider the point

quency is o0 + b~ . At D

For the purpose of vector plotting is written the form:- (4) ;r = 4 , t 2 4 ,

For any exciting frequency, w , the quantities qr

and qi can now be calculated and plotted on an Argand diagram to give the response vector at that frequency relative to the exciting force; Le., F is taken to lie along the real axis.

Substituting Equation (4) in Equation (3) and equating real and imaginary parts leads to:- Figure 1. Vector Diagram for One Degree of

Freedom - Hysteresis Damping

-2 Comparing this with equation (1) 1 - wo -- (12) g d i = e i g q from Eduations (7) and (8).

Hence and substituting q = eiWt bw bw B g = - 12 +--I c o t - LJO w0 2 bw Hence

It can be seen from Equation (13) that if 0 , is

small, equal angles will be subtended by equal fre- L i d e = quency increments on either side of the resonance. (20) In the particular case when B = -we have:- C C

But d = 2 - where - is the fraction of critical

CC CC

damping: -

Hence

and when 0 = - -

Hence It should be noted that if the damping is of the form given by Equation (17) the locus of points (qr, w; - w; qi) is no longer a circle; the steady solution will be

2g = -

motion of the form e rut , and substitutingq =% e the

wO , (15) equation becomes:- 2 2 wA t wbl 2 = - and 2 I - am2 t d r w t e ) ? = F (23) ' " 0

Proceeding as before we obtain: -

Whence 'I, =- F I - (24) (I - Z 2 l 2 t %222 am,' and ( W A - z - 2% It is common practice in this country to express the Here 2 = so that the two systems represented by dz- damping a s a percentage of the critical damping. A s long a s the damping is small, g can be directly related Equations (1) and (23) will have the same properties to the percentage of critical damping which is derived at resonance if g =g. The vector q defined by Equa- from the concept of velocity damping: i.e., the ap- tions (24) and (25) now describes a quartic curve propriate differential equation is:-

starting at the point ( $ , 0) when w = O and finish-

ing at the origin when W-UD ; any other branches are for unreal frequencies. In practice for small values of g the curve is indistinguishable from a circle ex- lating the response of a simple binary example at cept at lowfrequencies; this is shown in Figure 2 where various speeds up to the flutter speed.

the circle of Equations (7) and (8) is compared with the quartic of Equations (24) and (25).

BINARY EXAMPLE Basic Data: Geometry For simplicity a 2-dimensional rigid wing, re- strained by springs in vertical translation and pitch was considered. The two degrees of freedom are: Vertical translation: z = cql (representingwing flexure) Pitch: a = q2 (representing wing torsion) Figure 2. Vector Diagram for One Degree of in general z = cq1 + xq2 Freedom - Comparison Between Hysteresis and Velocity Damping The axis of pitch is at the half chord.

The axis of centre of gravity is at the half chord.

Two Degrees of Freedom Since the modes are uncoupled at zero flight speed they are normal modes and the frequency ratiois Kennedy and Pancu suggest that with N degrees wz:wa:: 0.4676:l.

of freedom there will be N near circles. For any particular resonance, the best circle is put through Structural damping at a value of g = 0.02 is the points and the resonance is given by the minimum assumed to be present in each degree of freedom. It bw

- , where s represents distance along the curve. If

is assumed that displacements to be recorded in flight W S tests are linear displacements at the half chord, equal increments of w are taken the greatest change quarter chord and leading edge and the angle of pitch.

of phase gives the resonance. The damping (g) can Thus the first and last of these 'pickups' give meas- then be extracted as for one degree of freedom.

urements proportional to the generalized co-ordinates q1 and q2 respectively. Finally it is assumed that Because this method appears to be the best way the excitation is linear vertical excitation applied at of estimating damping in ground resonance tests, it the quarter chord.

has been suggested that it might well be extended to the estimation of damping in aflight flutter test, where continuous excitation is being employed. The method may be difficult when the dampings are high at medium Wing Flutter flight speeds, but should improve again for low damping near the flutter speed. The difference between the The aerodynamic derivatives are 'assumed to be constant both with the frequency parameter and for- flight condition near the flutter speed and the ground ward speed, i.e., any Mach number effect is neglected.

condition, where the damping is low in each case, is that in flight there will be large asymmetric couplings The equations for free oscillation can be written arising from the aerodynamic forces. It was decided to see how important these were in practice by calcu- in the form:- -14.04v2 + 1 . 9 f W U l + (1 + 0.0211Y0 O . f i 3 J U l t 2.2w2 E O - . 4 9 U I -0.S80fiV2 + 0 . 2 4 ~ ~ ~ - .565u2 + . 2 8 (1 + o.0211yo where Vc = flutter speed wC

t ti

v 5 - v, V El 1 Y o = - p V : S C 2 c is the wing chord s is the wing span The equations were solved for yo with v = 1 (cor- responding to the critical flutter speed), and gave yo = 2.92 and V = 0.666.

From a knowledge of yo it is possible to relate any known E11 (the spring restraint against vertical translation) to an actual flutter speed (Vc), knowing the dimensions. Here, however, we are only interested in the relative speeds, i.e., v, the fraction of Vc.

Response Calculations

J - 2 . 0

With the excitation at the quarter chord and Figure 3. Vector Diagram for Binary Example: after the substitution for yo = 2.92, Equation (26) v = 0.75, displacement 1

becomes: -

2.2w2 + 0.63WVl f-14.04U2 t 2.921 + (1.86Uv + 0.059411 (-.900Bu2 - 0 . 5 6 5 ~ ~ + 0.946@ - .49UUl 9 2

I t ( 0 . 2 4 ~ ~ + 0.01693611

which gives a direct measure of the first co-ordinate where F is an arbitrary force level. For simplicity F is taken to be unity in the calculation which follows. in the calculation. At zero speed the co-ordinates are Values of v = 0, 0.25, 0.5, 0.75, 0.9 and 1.0 were normal co-ordinates so that the vector diagram re- chosen, and in each case q1 and q2 were calculated sults in a single pure circle with a resonance fre- a set of increments i n w . Assuming perfect quency given b y o = 0.456. As speed is increased the for accuracy of recording the measurements taken in flight size of the circle reduces (the same scale has been from the four 'pickups' (half chord, quarter chord, kept throughout each of Figures 4 to 7, althoughof leading edge, pitching angle) would be ql, ql-1/4q course different scales were used to estimate fre- 2' quency rates of decay in practice) and a small sec- 91-1/2q2, 92.

ondary circle starts to appear near the origin. This second circle occurs at the frequency of the pitching These quantities were plotted vectorially and the is now beginning to couple slightly with frequencies and rates of decay were estimated from mode which the near circles; a typical example is shown in Figure the bending mode due to the presence of the aero- 3 for pickup 1 at 3/4 of the flutter speed. dynamic forces. The new circle continues to increase in size until at a speed of nine tenths of the flutter speed it is the greater of the two. The last diagram Comments on Figures in this series is drawn for the flutter speed itself at The change in character of each vector diagram which one of the circles must have increased indefi- as the forward speed is increased is indicated in Fig- nitely in size. This is in fact the new circle cor- ures 4 to 7. Considerfirst Figure 4 for displacement responding to the higher frequency.

1, i.e,the displacement of the first pickup (see above) V . O . 2 5 v. 0-5 v.o.75 V. 0.9 V.I.0 Vector Diagram for Binary Example: Displacement 1, Varying Speed vv.0 ‘v 0.25 v * o * s lF0.0.75 -80-9 v . 1.0 1 ’ ; - 2 - 2 -2 - 2 ‘5.r 4 r ?

- 5 -5 -5 Figure 5.

Vector Diagram for Binary Example: Displacement 2, Varying Speed J-20 vco.0 V I 0 25 v . o . 5 l J - 0 . 7 5 v-0.9 V = I 0

1S”i

-2

5 OT ~ er - ~ . . er -~~~ Pt -~f. $1 l k 9 T

-5 -5 -5 -5 -5 Figure 6. Vector Diagram for Binary Example: Displacement 3, Varying Speed -, -20 V.0-25 'IT-0

Lo Figure 7. Vector Diagram for Binary Example: Displacement 4, Varying Speed

L . 1 Figure 5 gives the diagrams for displacement 2, the quarter chord, which shows two circles evenat 4.0 I I I al- zero speed; neither of these circles are perfect though the e r r o r is not detectable on the scale shown.

Both circles reduce with increasing airspeed for a time

OISPLACE?i€NT 1 ; I - I

and the smaller (corresponding to the higher fre- OISPLACECID(T 2- -I quency) changes its position relative to the origin.

i' - 9 DI5PLACEMEM 3---' 1 Ultimately, as before, the higher frequency circle increases in size to an indefinite extent at the flutter speed. Similar sequences are shown for the other pickups in Figures 6 and 7, although in the last figure the higher frequency circle remains the larger throughout.

Estimation of Damping in Flight and Conclusion 0 6 A s outlined in paragraph 2 we estimate the

damping + from the circles. Near each resonance

C suitable equal increments in frequency a r e chosen, and these a r e marked on the curves of Figure 3. The 0.

actual resonance is picked out from the figures by using a pair of dividers to get the maximum phase In this example there was never any difficulty change, in putting a circle through the points (a typical circle is shown in Figure 3) and the damping was estimated from convenient increments of frequency as can be seen from the construction on Figure 3.

0 . a The damping as obtained from each pickup was then plotted against forward speed, and the results are shown in Figure 8. Since our example is completely specified mathematically, the dampings can also be calculated exactly. In Figures 9 and 10 the calculated roots are plotted and compared with the estimates r - v from each of the four 'pickups'. FigureQA, shows the change in frequency of the lower frequency with for- Figure 8. Damping Estimates from the Vector ward speed and Figure 9B, shows the change in damp- Diagrams Against Forward Speed ing: Figures 10A and B give the corresponding re- sults for the higher frequency root, which is the one that leads to flutter at v = 1.0. The agreement in wo I I 1 I 0.75 1.0 -?r 0 25 EXACT CALCULATION- -

DISPLACEMENT I -

DISPLACEMENT 2 - -- DISPLACEMENT 3- -- - -- 4- -- - - -- -- .

DISPLACEMENT 0 6 O I M P l f f i Figure 9 . Comparison Between Estimates of Damping Figure 10. Comparison Between Estimates of Damping and Frequency, and Exact Calculation, and Frequency, and Exact Calculation, Bending Mode Torsion Mode general between the different estimaes and the calcu- be however, that with many degrees of freedom pres- lated values is very good. The only serious e r r o r in ent, as on real aircraft, the choice of pickup position the lower frequency root i s obtained from the rota- is more important than in the binary example. In tional lpickupl; this seems to give the wrong trend of general the flight analysis would be carried out for frequency with speed when the damping exceeds 10% of two o r three pickups as a normal safety precaution.

critical - a condition which would in afiy case be

unimportant in practice. For the higher frequency root the accuracy is good throughout, and best for RESULTS FROM A LOW SPEED WIND-TUNNEL this same rotational pickup, as might be expected on MODEL qualitative grounds. Any of the pickups, however, would give a good prediction of flutter speed (see Figure 10B) provided the speed increments chosen The method outlined above has been applied by were not too large. Bristol Aircraft Limited to a wind-tunnel model de- signed to investigate flutter of a T-tail configuration.

From flight measurements in practice one could Figure 11 shows a typical vector diagram at a for- ward speed that is about 83% of the extrapolated scarcely hope to get such a consistent set of results flutter speed. The diagram is for the mode which as has Wen obtained from the estimates in this simple binary example. On the other hand the example starts at zero speed as tailplane fundamental sym- does suggest that the method is sound in principle so metric torsion, and which provides the main pointer that if there are practical arguments which favour to the critical flutter condition as did wing pitch in recording from continuous excitation rather than the theoretical example of section 3. The experimental decaying oscillations the Kennedy and Pancu type of results are consistent and define a very good circle.

is likely to provide good results. It may well Figure 12 shows the variation in frequency anddamp- analysis ing with airspeed of the fundamental bending mode of the tailplane and Figure 13 gives the corresponding results for the fundamental torsion mode*. Thegraph of Figure 13 can be extrapolated to the flutter speed.

It is not the purpose of this paper to deal with the experimental. technique involved but one or two points should be made. It is necessary to have a phase meter available that gives accurate readings in the presence of buffeting. The instrument used by Bristols measures in-phase and quadrature compo- nents, and is arranged to descriminate against noise (as in a wattmeter type of phasemeter). It can give 5% even with a signal to noise an accuracy of about ratio a s low a s unity. The rate of sweep of the ex- citer (in terms of frequency) is determined by trial and error, and a satisfactory rate will depend on the damping in each case. The frequency control of the exciter must be accurate, i.e., high short term stabil- ity is required, and in practice at low dampings the frequency increments may need to be a s small a s 0.4% in order to get a reliable measure of the damping.

*These terms are used for descriptive purposes only: in practice, of course, the modes change shape under the aerodynamic forces.

Figure 11. Example of P,hase Against Amplitude Plot with Damping Analysis Figure 12. Tailplane Fundamental Symmetric Bending Resonant Frequencies and Damping Against Airspeed Figure 13. Tailplane Fundamental Symmetric Torsion Resonant Frequencies and Damping Against Airspeed List of Symbols (cont) ACKNOWLEDGEMENT The author wishes to express his thanks to v is a frequency parameter 2 Bristol Aircraft Limited for making available the VC c is the wing chord results of their wind-tunnel tests, and to M i s s E. V.

Hartley for carrying out the binary calculations.

s is the wing span P is the air density is the spring restraint against vertical trans- E11 LIST OF SYMBOLS lation El * a is an inertia coefficient

Y o = 7

P V C S C d is a damping coefficient e is an elastic coefficient z is vertical displacement is the phase angle of the restoring force (a Q is the angle of pitch g damping coefficient) is a generalized co -ordinate q F is a generalized exciting force REFERENCE is the natural frequencyof one degree of freedom mo .

w is the exciting frequency Ref. No. Author Title, etc.

1 Kennedy, C.C. Use of vectors in vi- Pancu, C.D.P. bration measurement WO and analysis.

Vc is the flutter speed Journal of the Aero- nautical S c i e n c e s.

V is the forward speed Vol. 14, No. 11.

V v = - November,' 1947.

V C A FLIGHT INVESTIGATION OF OSCILLATING A I R FORCES: EQUIPMENT A N D TECHNIQUE W . H . Reed 111 - N A C A , Langley Luboratory, Langley Field, Virgirziu Abstract our knowledge of oscillating air forces in this speed range.

A description is given of the equipment and techniques to be used in a project aimedat measuring To help meet this need, the Flight Research oscillating air forces and dynamic aeroelastic re- Division at NACA-Langley has undertaken a project sponse of a swept wing airplane at high subsonic aimed at measuring oscillating air forces in flight, speeds. Electro-hydraulic inertia type shakers in- It is hoped that these measurements, obtained under stalled in the wing tips will excite various elastic full scale flight conditions and free from wind tunnel airplane modes while the related oscillating chordwise as a check on the interference effects, may serve pressures at two spanwise wing stations and the wing accuracy of unsteady aerodynamic theory. In essence, mode shapes are recorded on magnetic tape.

the test method will consist of exciting various elastic modes of the airplane in flight by means of sinu- The data reduction technique, following the soidal shakers installed in each wing tip. Oscillating principle of a 'hNattmeter" harmonic analyzer em- air forces will then be investigated two ways: First ployed by Bratt, Wight, and Tilly, utilizes magnetic the aeroelastic response of the airplane to knownforce tape and high speed electronic multipliers to record inputs will be studied to obtain information on the directly the real and imaginary components of oscil- integrated effects of oscillating air forces; and, sec- latory data signals relative to a simple harmonic ond, the oscillating chordwise pressure distribution reference signal. Through an extension of this tech- at two spanwise stations will be measured to gain a nique an automatic flight-flutter -test data analyzer is detailed insight into the nature of oscillatory flows at suggested in which vector plots of mechanical admit- high subsonic speeds. Experimental measurements of tance or impedance would be plotted during the flight both the forced response and pressure distributions test. will then be compared with theoretical predictions.

While obtaining experimental data on oscillating INTRODUCTION air forces is the primary goal of the project, a sec- Most theoretical methods for computing oscil- ondary, and perhaps equally important, aim is to gain air forces are based on linear potential flow experience which would be applicable to flight flutter lating testing techniques. This experience would include the theory, and as such may be expected to deteriorate development of excitation equipment and instrumenta- in accuracy as shock wave and flow separationeffects come into play at high subsonic and transonic Mach tion, data reduction techniques and flight test methods numbers. The experimental data available for evalu- involving the measurement of forced response.

ating the accuracy of theory in this Mach number range is extremely limited, and the accuracy of the This paper discuses some of the equipment and data is frequently uncertain because of wind tunnel testing techniques planned for the project and points interference effects. In view of the need for accurate out, where possible, their application to flight flutter testing. .

predictions of flutter, it is important that we extend FORCED RESPONSE ments of the influence points. And the accuracyof the mathematical representation of the airplane struc- ture can be readily assessed by comparing ground measurements of forced response and mode shapes Theoretical Forced Response Method with calculated results in which the air forces have been omitted.

We will first consider the forced response phase of the project -but before discussing the experimental Matrix equations for aeroelastic forced response techniques, it is of interest to take a brief look at the theoretical analysis with which the experiment will be have been formulated by C, E. Watkins and J. L. Sewall compared. The mathematical representation of the of the Dynamic Loads Division, NACA-Langley, for use with an existing program of the kernel function airplane wing panel is shown in the first figure.

method on the IBM 704 computer. Preliminary results An influence coefficient type dynamic analysis obtained by the method for the forced response of a is used wherein the inertia, the aerodynamic, and the wind tunnel model show good agreement with experi- excitation forces acting on the wing are assumed to mental data. In the present tests, measurements will be made of the response at the 8 influencepoints be concentrated at the eight discrete points shown.

shown in the figure together with the shaker input Associated with these points are a set of measured flexural influence coefficients and lumped masses force. The next figure (Figure 2) shows these and other vibrations pick-up locations on the test air- representing the wing structure. The aerodynamics of the problem are obtained from the kernel function plane.

method of Watkins, Runyan and Woolston (ref. 1). As used here, the method, which is a three dimensional Airplane and Instrument lifting surface theory, provides the aerodynamic load distribution in terms of the wing displacements at the test airplane is an F-86D. The sweepback The influence points. The air loads concentrated at each angle of the 1/4 chord of the wings is 3 5 ' , the aspect of the influence points, are then obtained by inte- ratio is 5, and the thickness ratio is about 10 percent.

grating the load distribution over the appropriate The normal slotted leading edge for this airplane areas that are shown by the dashedlinesin the figure.

has been replaced by a fixed leading edge inorder The response problem approached in this manner has to eliminate certain flow irregularities and struc- several advantages. It can be conveniently pro- tural vibrations presented with the slotted configur- grammed on large scale digital computers. The mode ation.

shapes are defined directly by the vector displace-

LUMPED PARAMETER REPRESENJATI ON

OF FLEXIBLE WING SECTION A A

z

{z} = w * [c] [mJ {z} + [c] {FSHAKER} + [c] {FAERO.)

Figure 1. Lumped Parameter Representation of Flexible Wing

f VELOCITY PICKUPS t ACCELEROMETERS

(OCI LLOGRAPH)

CUAKFR-

(MAGNETIC TAPE)

v, 18-51 \ L a % Figure 2. Location of Vibration Pickups on Test Airplane effect of outside temperature on the damping o f the The vibration pick-up locations a r e indicatedby the arrows in the figure and the direction of the units. The accelerometer outputs are telemetered to a ground recording station and recorded on magnetic arrows depicts the sensing axis of the transducer.

tape. Vibration data from other locations on the The primary measurements, indicated on the figure airplane, shown in the figure by arrows without by the circles, are from accelerometers located at circles, are obtained from MB type 124 self-gener- the 8 influence points on the wing and also in one of ating velocity pick-ups and are recorded in the air- the shaker masses. These accelerometers are NACA plane on a recording oscillograph. A complete listing variable inductance telemetering transducers equipped with temperature regulated ovens to minimize the of the flight instrumentation is given in Table I.

TABLE I - AIRPLANE INSTRUMENTATION LIST

(a) Response Data (Telemetered and recorded on magnetic tape) No. of Channels Measurement Description or Location Acceleration 8 influence points on left wing Acceleration Shaker mass on left shaker Eo cos w t, Eo sin ( A t Shaker input signal and input signal with 90" phase shift 1 Timer 1 Voice (b) Oscillating Pressure Data (Recorded in airplane on magnetic tape) No. of Channels Measurement Description or Location 9 Pressure 9 chordwise locations at 0.60Z or 0.852 spanwise station Acceleration Front spar at 0.60 2 or 0 . 8 5 2 spanwise station 1 Acceleration Rear spar at 0.602 or 0.852 spanwise sta- tion TABLE I (cont) (c) Miscellaneous Data (Recorded in airplane on oscillograph) No. of Channels Measurement Description or Location 2 Velocity (vertical) Right and left wing on front spar at 0.701 spanwise station (to check symmetry of airplane response) 2 Velocity (vertical) Fuselage nose, fuselage tail 3 Velocity (vertical) Fuselage and wing center section (to deter- mine rigid body pitch, roll, and translation) 2 Velocity (vertical) Stabilizer tips 1 Velocity (horizontal) Vertical tail tip 3 Angular displacement Position transducers located on left wing at 3 aileron hinge points Shaker input signal 1 . From shaker input signal generator 2 Shaker feedback Right and left shaker displacement potenti- ometers 2 Airspeed, altitude Airspeed head on nose boom Maneuver Acceleration 3-component low -frequency accelerometer mounted near airplane cg 2 Log of wing tip acceler- Vibration amplitude from accelerometer on ation left wing tip; vibration frequency from input signal generator. Data recorded whenever shaker operates.

Shakers back. A mass, which is free to translate i n a direction perpendicular to the plane of the wing, Shakers are installed in each wing panel in the is driven hydraulically by means of an electro- vicinity of the tip. In the next slide (Figure 3) is hydraulic servo valve. The valve i s actuated by an shown a schematic diagram of one of the shakers. electrical e r r o r signal proportional to the difference between the position of the mass called for by the input signal generator and its actual position which The principle of operation is that of a s i m p l e electro-hydraulic servo system having position feed- is sensed by a slide wire potentiometer. The force WING SHAKER BLOCK DIAGRAM I I

d d SHAKER POSITION FEEDBACK

Eo SlNUt E o C O S U t SIGNALS UTILIZED FOR DATA REDUCTION Figure 3. Wing Shaker Block Diagram The shaker frequency may be varied either by output and frequency of the shaker can be controlled manual tuning to any desired frequency in the range independently through adjustment of the voltage level from 4.5 to 40 cps o r by scanning the frequency range Eo and frequency w of the electrical input signal by means of a programmed automatic frequency which is obtained from a mechanically driven sine- sweep device. With the shaker in automatic sweep cosine potentiometer. Note that in addition to pro- operation, the variation of frequency with time is such viding the input signal Eo cos w t, the signal gener- ator also provides a signal that is 90" out of phase that the percent change of frequency per cycle is with the input, i.e., Eo sin t. Both of these signals constant ( h I w 2 = constant). Thus the sweep rate h increases a s the square of the frequency. It can be are recorded on magnetic tape for use in data re- shown, on the basis of the response of a lightly duction which will be discussed later.

damped single degree of freedom dynamic system, The weight of the moving part of the shaker that use of the above frequency sweep relation makes can be varied on the ground from a minimumof the errors due to sweep independent of where in the surveyed range of frequencies resonance occurs (ref.

60 lbs. to a maximum of 100 lbs. The maximum displacement amplitude of the moving mass is i0.8 2). The time required to cover the frequency range in one direction is adjustable from 15 to 100 seconds.

inches. With shaker mass known, the input force to the wing can then be drived from acceleration meas- urements on the moving mass together with similar The amplitude of both shakers is controlled measurements on the wing structure ahead of and simultaneously by means of one knob which controls behind the shaker location. The maximum force output the voltage level of the input signal.

of each shaker is limited by the hydraulic system to Selector switches a r e provided for choosing a value of about 1,000 lbs. which, for the heavy shaker condition, occurs at frequencies of 11 cps and higher. between symmetrical and antisymmetrical excitation.

To make the excitation a s nearly symmetrical or By flight flutter testing standards, a forcing antisymmetrical as possible an effort has been made function of this magnitude is probably several times t o match the dynamic characteristics of the two shaker servo systems.

greater than would be necessary for adequate response of an airplane of the size used here. In the present The input signal can be either a sine wave for application, however, force inputs of this magnitude are believed necessary in order to provide measur- forced response measurements or a square wave, able oscillating pressures in the pressure measuring having a period of 10 seconds for transient response phase of the project. measurements. Note that the square wave signal calls for a succession of abrupt position changes of the In the next figure (Figure 4) is shown a listing mass. Therefore, the force input to the wing is of the primary shaker controls and indicators to the dependent on the dynamic response characteristics of pilot the shaker to a step input signal.

PRIMARY SHAKER CONTROLS

I . FREQUENCY 4 . INPUT SELECTOR

(a) SINE WAVE ANUAL TUNING (b) SQUARE WAVE

5. QUICK CUT OFF

(FOR DECAY RECORDS) 3. PHASE SELEGTOR (a) SYMMETRICAL (b) ANTlSY MMETR ICAL

INSTRUMENT PANEL DISPLAY

I. FREQUENCY

2. WING TIP ACCELERATION

3. SHAKER AMPLITUDE

Figure 4. Primary Shaker Controls The last control is the quick cut-off switch, a flat stretched diaphragm which is installed vertically with which the shaker can be stopped within halfa in the wing in order to minimize acceleration effects.

By referencing an oscillating pressure to its steady cycle. This will be used when measuring the decay of various modes excited by the forced response state value through a suitable acoustical filter, only technique. the oscillating part is detected by the gage. The pressure difference between the upper and lower To aid the pilot in tuning to resonance and surfaces at a given chordwise location is thenobtained keeping the amplitude of wing response at the desired by electrically combining the outputs of the upper and level, meters are provided which give an indication lower gages.

of the shaker frequency, the amplitude of acceleration at the wing tip, and the amplitude of shaker displace- Pressure measurements at the two spanwise ment relative to the wing. stations will be made at the 9 chordwise locations shown in the figure. In order to improve accuracy This concludes the discussion of the forced when integrating the pressure distributions, the gages response phase of the project. We will next consider have been placed at points given by Gauss’s formula the second phase which is aimed at measuring oscil- for numerical integration (ref. 4). The locations of lating chordwise pressure distributions by shaking the four cells within the 0 to 25 percent chord band the wing at various resonant frequencies. re- satisfy the four ordinate Gauss formula and the maining five cells between 25 and 75 percentband are positioned to satisfy the 5 ordinate formula.

PRESSURE MEASUREMENTS The theoretical pressure distribution given in the figure indicates approximately the magintude and phase angle of oscillating pressure that might be ex- The primary measurements in this phase are pected in flight at the 85 percent semispan station.

the pressure differences between the upper and lower These results were obtained from the kernel function surface of the wing at the 60 and 85 percent semispan procedure using the ground measured first bending stations together with acceleration measurement on the mode shape to define the downwash boundary condi- front and rear spar at these stations. Again the data tions. The pressures shown are for a Mach number will be recorded on magnetic tape. The pressure of 0.9, an altitude of 5,000feetanda wing tip vibration pick-ups to be used are NACA miniature inductance displacement amplitude of +2 inches. Note that the type gages designed to accurately measure high fre- average pressure amplitude is about +0.3 psi, but to quency fluctuating pressures (see ref. 3). These provide for the measurement of much larger pressure gages, schematically illustrated in Figure 5, utilize fluctuations occasioned by the oscillation of a shock

WING SECTION SHOWING PRESSURE PICKUP LOCATION AND

THEORETICAL OSCILLATING PRESSURE DISTRIBUTION I20

I I I I 1 1 1 1 1 1 1

INDUCTIVE TYPE PRESSURE PICKUP Figure 5. Wing Section Showing Pressure Pickup Location and Theoretical Oscillating Pressure Distribution wave over an orifice, the gages selected have a range W i n g Fatigue Consideratiomi of i 2 . 0 psi.

Mention should be made here of the steps that have been taken to assure that the relatively large amplitude shaking, planned in the pressure measure- MEASURED GROUND MODES ment phase of the project, will not induce structural fatigue failures in the wing. A check against the As an indication of the vibration amplitude at the occurrence of such failures was made by shakinga duplicate wing which had the same structural modifi- pressure measuring stations, the measured ground cations and shaker installation as incorporated in the mode shapes and node line patterns for the test air- flight wing. In these tests each of the modes shown in plane are shown in the next slide (Figure 6). These the figure was excited at the amplitude desired in modes were excited with electro dynamic shakers attached to the rear spar near the tip of eachwing flight and for a duration ten times as great a s the estimated testing time in flight. No evidence of fatigue panel. The flight shaker was simulated for these was discovered. During the flight tests the amplitude measurements by attaching 130 lb. weights at the and frequency of vibration at the wing tip willbe location of each of the flight shakers. Note from the continuously logged and also monitored by the pilot to plot of node lines that the first antisymmeterical assure that the safe limits established by the fatigue bending (f = 9 . 7 5 cps) mode crosses the inboard tests are not exceeded in flight.

pressure station at about the 1/4 chord point and the second symmetric bending (f = 2 1 . 7 cps) node crosses the outboard pressure station at approximately the DATA REDUCTION TECHNIQUES same chordwise position. The angle between the node lines and pressure orifice bands is about 4 5 ' in both cases, indicating that the wing motion at these stations involves considerable torsion. The torsion mode at Wattmeter Principle of Data Reduction f = 3 2 . 5 , however, may not be adequately excited in In reducing the flight forced response and os- the flight tests because the center of the shaker force is very close to the torsional node line. cillating pressure data it is essential that accurate MEASURED WING MODE SHAPES AND NODE LINES 1st ANTI SY MMETRIC Is t SYMMETRIC 2 n d SYMMETRIC

f = 21.7cps I TORSION

I f =32.5cps

-

1 . 0 Z

-

Z~~~ 0 .

X

-ID -

I

- FRONT SPAR

0 Y 1.0

- ---- REAR SPAR

YTI P Node Lines Figure 6. Measured Wing Mode Shapes and measurements are made not only of the amplitude of In a similar manner, B1 may be computed by multi- oscillation but also of the phase angle. With most data plying the data signal by the reference signal shifted reduction techniques the primary difficulty lies in 90" in phase, i.e., Eo sin w t. The computer com- This is es- measuring the phase angle accurately. ponents used for multiplying the signals are high pecially true when unwanted harmonics are present speed quarter square multipliers. These are com- in the data. This difficulty i s avoided, however, by mercially available electronic devices which have the use of a technique employed by Bratt, Wright, negligible phase shift at frequencies below 100 cps and Tilly (ref. 5) in which separate measurements (ref. 6 ) .

a r e made of the vector components of vibration data.

The method is known as the "wattmeter" principle A s mentioned earlier, the reference signal and of harmonic analysis because just as a wattmeter its quadrature component a r e obtained from the input measures power by indicating the average value of signal generator which drives the shaker. This as- the product of the potential difference and current, sures that the frequency of the reference signal is the the analyzer measures the component of a data signal same as the fundamental frequency of the forced in phase with a simple harmonic reference signal by response. Since the reference signal is used as the indicating the average value of the produce of the two common frame of reference to which all data vectors

signals . a r e referred, its phase angle relative to the shaker

force is entirely arbitrary. The real and imaginary In the present application of the principle, use components of a data vector are, then, respectively, is made of an electronic analog computer coupled the vector's components in phase and 90" outof phase with magnetic tape play-back equipment. In Figure 7 with the reference signal Eo cos o t.

we see that the principle involved is precisely that of a Fourier analysis. Thus, a periodic data signal An Automatic FligRt Flutter Test Data Analyzer A 0 m

F(t) = - + 2 (Ancos n o t + Bnscn nwtl

2 n = l Since this Symposium is concerned primarily is multiplied by a simple harmonic reference signal with flight flutter testing it is of interest to consider having the fundamental frequency of the data signal the possibility of utilizing the wattmeter principle as a basis for an automatic flight vibration data reduc- E(t) = Eo COS o t tion and analysis system. Three advantages which make this technique of data reduction particularly attractive for handling flight flutter test data are: The resulting product, when averaged, is proportional first, the data can be reduced as the test is being run; to the Fourier coefficient A i , the factor of proportion- second, undesirable harmonics are automatically ality being E0/2 which is known o r can be measured.

filtered from the data; and, third, the reduced data, This is readily seen from the equation for A 1 being in the form of vector components, can be con- veniently compared with theoretical results.

The system shown in Figure 8 would display a vector plot of the frequency response or admittance

= - (Average value of product F(t) E(t) )

(the ratio of the displacement amplitude of a point on EO the structure to the amplitude of the sinusoidal force WATTMETER PRINCIPLE OF HARMONIC ANALYSIS

I T

AVERAGE VALUE OF E(I) F(I) Figure 7. Wattmeter Principle of Harmonic Analysis AUTOMATIC DATA REDUCTION AND STABILITY INDEX PLOTTER

/[FORCE: RESI? : ZI(t)> F(t) ZZ(t) .... Zn(t) } \ / e

REF. SIGNALS: 0; FM RADIO TELEMETER

i

X - Y PLOTTER Figure 8. Automatic Data Reduction and Stability Index Plotter that causes the displacement) for a selected pick-up with the shaker input force signal and the two refer- location on the airplane as the frequency of excitation ence signals. The acceleration response is double is varied over the range of interest. The use of integrated to give Z(t) which, in turn, is multiplied vector response plots in the analysis of airplane by the reference signals and averaged to give outputs ground vibration response data has been discussed by proportional to the real and imaginary components of Kennedy and Pancu in reference 6 and much similar Z. In a like manner, F(t) is multipled by the refer- work of this type has been developed for stability ence signals and averaged to give an output propor- analyses relating to feedback amplifiers (reference tional to the real and imaginary components of F.

7) and servo mechanisms (reference 8). Having the vector components of Z and F, an analog computer performs the arithmetic operations re- No attempt will be made here to discuss the quired to obtain the vector components of the fre- merits of vector plotting other than to say that re- quency response (Z/F)red and (Z/F)imag,. Note sults of theoretical forced response analyses, such that since the vector components of Z and Fare as the influence coefficient method discussed earlier slowly varying quantities whose rates of change with in the paper, can also be conveniently presented in time for a given system depend upon the frequency the form of vector response plots for ready compar- sweep rate, high speed multipliers are not required ison with experiment. in this stage of the analog computer.

Next, the real and imaginary components of Z/F To illustrate the system, assume that the test are connected to an X-Y plotter in a manner such vehicle is instrumented to telemeter the following X- data: acceleration r e s p p s e ai various points of. in- that (Z/F)red drives the recorded pen along the axis of the plotter and (Z/F)imag. drives the pen

terest on the structure Zl(t), Za(t) . . . . . . . . . zn(t)

along the Y-axis. Thus, as the shaker frequency is the excitation force F(t), a simple harmonic reference varied, the plotter maps the locus of the vector Z/F.

signal Eo cos w t that has the fundamental frequency The amplitude of the vector at a given frequency is of the exciter, and the component 90" out of phase determined by the length of a line drawn between the with the reference signal Eo sin w t. These data are curve and .the origin of the real and imaginary axes, recorded on magnetic tape at the ground telemeter and the phase angle is the angle between this line and receiving station while at the same time the acceler- the positive real axis. The frequency of forced ation response signal selected to be analyzed during response is indicated by feeding the reference signal the frequency sweep is fed to the analyzer, together to a frequency measuring device which pulses the Stability with Application to Flutter Testing.

recorded pen at equal frequency increments. I. A. S. Reprint No. 822 (Presented at the IAS 26th Annual Meeting, January 27-30, 1958) Thus the frequency response for one of the pick-up locations is plotted during the test. At a 3 . Patterson, John L . : A Miniature Electrical Pres- later time, perhaps while the pilot maneuvers for the sure Gage Utilizing a Stretched Flat Diaphragm.

next test run, the data on magnetic tape can be played NACA TN 2659, April 1952 back into the analyzer and other channels selected 4. Scarborough, J. B.: Numerical Mathematical for plotting.

Analysis. Edwards, Ann Arbor, 1947 5 . Bratt, J . B., K. C. Wight, and V. J. Tilly: The CONCLUDING REMARKS Application of a "Wattmeter" Harmonic Analyser to the Measurement of Aerodynamic Damping for Pitching Oscillations. R & M No. 2063 To sum up, we have discussed some of the (5827), A. R. C. Technical Report (Ministry of equipment, instrumentation and data reduction tech- Aircraft Production), May 27, 1942 niques to be used in a project aimed at measuring oscillating air forces in flight. Also, we have con- 6. Giser, S . : An All-Electronic High-speed Multiplier.

sidered some possible applications of these techniques to the problem of flight flutter testing. The equipment Massachusetts Institute of Technology Instru- mentation Laboratory Report R-67. November and instrumentation is now being installed in the air- plane and flight test data on the forced response phase of the project should be available in the near future.

7. Kennedy, Charles C., and C. D. P. Pancu: " U s e of Vectors in Vibration Measurement and Analy- REFERENCES sis." Journal of the Aeronautical Sciences, Vol. 14, No. 11, November 1947, pp. 603-625 8. Nyquist, H.: "Regeneration Theory." The Bell 1 . Watkins, Charles E., Harry L. Runyan, and Donald System Technical Journal, Vol. 11, pp. 126- S. Woolston: On the Kernel Function of the Integral Equation Relating the Lift and Down- 147, July 1932 wash Distributions of Oscillating Finite Wings in Subsonic Flow. NACA Report 1234, 1955 9 . Chestnut, Harold and Robert W. Mayer: Servo- mechanicms and Regulating System Design.

Effects of a Time-Varying Vol. I. John Wiley & Sons, Inc, New York, 2 . Reed, Wilmer H., 111: Test Environment on the Evaluation of Dynamic T H E APPLICATION OF MEASUREMENT TECHNIQUES T O T R A C K FLUTTER T E S T I N G Abstract aircraft damage, ejectable components, and for the development and calibration of inertial guidance sys- This paper discusses the application of meas- tems and components. On the high-speed track, urement techniques to captive flight flutter tests at large test items can be brought up to supersonic the Supersonic Naval Ordnance R e s e a r c h Track velocities and sustained at these velocities long enough to make the observations and measurements (SNORT), U. S. Naval Ordnance Test Station, China Lake, California, required and stopped intact. One of the paramount virtues of the supersonic track lies in the relative The high-speed track, by its ability to prove the ease with which instrumentation, both photographic validity of design and to accurately determine the and electronic, can be precisely applied to the point actual margin of safety, offers a unique method of of action to insure optimum coverage.

flutter testing for the aircraft design engineer.

of flutter has, in recent years, The prob1e.m been given primary consideration in the design of INTRODUCTION high-speed aircraft and missiles. The application of the supersonic track to flutter testing has been the In the few years that high-speed tracks have result of efforts to find more adequate means of been in existence, their usefulness has been demon- evaluating and testing new designs in their progress strated as a vital laboratory instrument in expanding to the flight test stage.

knowledge in many scientific fields. Capable of pro- viding high linear accelerations of relatively long duration with dependable recovery of the test item for SLED DESIGN examination and retesting, the supersonic track offers nearly all the advantages of laboratory testing, com- In supersonic track flutter tests, the test item bined with the advantages of free flight.

i s mounted on a track vehicle properly designed to realize the required degree of simulation, and a The versatility and control of the test environ- s e r i e s of runs are made, each at discrete incre- ment offered by the high-speed track provide an opti- ments of velocity until either flutter of the test item mum medium for experimental studies in the best of occurs o r an adequate margin of safety has been analytical procedures. Tracks have been successfully demonstrated. A general-purpose sled is used where used for the captive flight testing of rockets, guided the flutter characteristics of these surfaces are not missiles, model o r full-scale airplanes, or their com- unduly influenced by the aerodynamic effects of the free flight ponents, under conditions approximating vehicle itself.

into the supersonic range, including measurement of thrust, acceleration, velocity, lift, drag, vibration, shockwave effects, flutter, and aerodynamic heating.

They have been used also for aeroballistic tests of high-velocity launching of rockets o r projectiles, as tests of a horizontal stabilizer. It may be necessary well as tests of fire-control systems, fuze function, to incorporate an entire fuselage into the sled design to preserve the aerodynamic and structural effects on the stability of the tail structure, as shown in Figures 3 and 4. It is, of course, necessary that the complete control systems associated with the tail structures be incorporated into the design of the sled structur e.

Figure 1 . General Purpose Flutter Test Vehicle with Vertical Stabilizer Figure 4. Navy Flutter Test Sled Utilizing Entire Fuselage of Plane CONTROL OF SLED VELOCITY The design of the sled vehicle and the propul- sion system to be used is mainly a problem in attain- ing the required velocities.

It is convenient to con- sider the progress of the sled down the track as being in four distinct phases: the acceleration phase, the low-acceleration phase (or in other types of track tests, the sustain phase), the coast phase, and the braking phase.

Figure 2. General Purpose Flutter Test Vehicle Adapted for Horizontal Stabilizer Tests The acceleration phase is achieved by several rocket motors firing together or in sequence, or by the use of one or more detachable booster sleds ac- celerating the main vehicle. When the thrust of the rocket motors is equal to the aerodynamic dragof the sled, a condition of zero acceleration is achieved, and the sled is sustained at a constant velocity. In cer- tain flutter tests, it is required that the test item be accelerated to a velocity well below the expected critical velocity, and then accelerated more slowly to the critical velocity. For such tests, additional thrust is staged as required to bring about the low acceleration desired.

In the coast phase, the test sled i s decelerated by the action of aerodynamic drag and track sliding friction. The braking phase adds the water-braking forces.

Accurate evaluation of all the acceleration and deceleration forces is necessary in designing the test It is desirable, vehicle to meet the test requirements.

Figure 3. Track Flutter Test Vehicle Incorporating of course, to accelerate the sled as rapidly as possible Entire Fuselage in Sled Design to the required velocity so as to conserve range dis- allow the final velocity to be controlled within very tance and to permit adequate time for observation close limits. It can be seen, therefore, that by the and measurement of the behavior of the test item careful selection of available rocket motors and by the use of such techniques as coast periods, sled before the braking phase must be started.

velocity can be regulated in controlled increments The structural strength of the vehicle places for flutter tests.

limits on the acceleration that can be a p p l i e d .

Strengthening the carriage to withstand more acceler- I ~ S T R U ~ E N T A T I O ~ FOR FLUTTER TESTS its weight. The loads imposed on the ation increases sled structure for any specified maximum velocity a r e in almost direct proportion to the total weight of Photographic and electronic instrumentation is the test vehicle. It is mandatory, therefore, that used to observe and measure the motions of the test weight be conserved not only to reduce these loads item throughout the entire high-velocity portions of a but also to reduce the amount of thrust required to easurements on these records are made achieve the desired velocity. It is perfectly possible to determine the velocity at which flutter occurred, that the addition of more thrust can result in a lower the frequency of the flutter, and the shape of the maximum velocity due to the weight of the additional flutter mode.

rocket motors.

Electronic Instrumentaton Figure 5 shows a typical velocity-distance pro- The flutter frequency and the flutter mode file of a flutter test in which a single staging of the shape can be determined by the use of transducers propulsion rockets was used. Figure 6 shows a typical attached to a sufficient number of points on the test three-stage velocity-distalice profile of a flutter test item to measure the deflections of the surface, The requiring a low-acceleration phase near the critical use of the accelerometer type of transducer, although velocity of the Lest item.

offering the advantage of direct measurement, com- plicates the instrumentation system and the assess- In this test, an additional coast phase w a s pro- grammed between the first and second stages to ment of the data.

Figure 5. Typical Single -Stage Flutter Test Velocity-Distance Profile I I I I I I I I I I I I I I I I I I I

0 1 2 3 ' 11 12 13 14

RANGE DISTANCE (1000s of FEET)

Figure 6. Flutter Test Velocity-Distance Profile Achieved by Three Stages of Propulsion Since the output of the accelerometer is pro- portional to the absolute acceleration, the acceleration of the sled is added to the output as "noise" and must be subtracted to determine the primary data. Accel- erometers sense, in addition, the random vertical, longitudinal, and transverse motions of the sled during its run. These motions must be measured by addi- tional transducers and instrumentation in order to obtain the relative deflections of the test item itself.

Accelerometers a r e expensive and must be mounted internally, and are lost if the test item i s destroyed during the test. Strain gages, on the other hand, are inexpensive, can be mounted either intern- ally or externally, and, by proper calibration, will indicate the direct structural deformation of the sta- bilizer assembly. Conventional static load-deflection tests a r e made to convert strain gage readings to structural deflections in the calibration process.

Figure '7. Section of Telemetry Receiving-Recording FM/FM telemetry systems are normally used Station at SNORT to transmit the transducer outputs to the, ground- based recorders. In the FM/FM system, the outputs of the transducers modulate sub-carrier oscillators a composite sig- and received at the ground station (Figure 7), where whose outputs are multiplexed into it is demodulated and the multiplexed signal recorded nal. This signal is then used to modulate a carrier on magnetic tape. The magnetic tape or "master" frequency. The carrier is transmitted from the sled is played back through bandpass filters, which separ- ate the frequency-modulated sub-carrier frequencies, to the various discriminators. One discriminator is used for each sub-carrier used in the sled-borne sys- tem. The output of each discriminator, which is a replica of the respective sled-borne transducer out- put, is then recorded, along with other discriminator outputs, on a recording oscillograph for evaluation and assessment.

Figure 8 illustrates a typical sled-borne FM/ FM telemetry system for flutter tests. Figure 9 is a typical FM/FM telemetric record obtained on a track flutter test. This record shows the initiation of flutter with build-up to destruction of the test item. The timing trace permits correlation with other recorded data while the track coil record indicates range distance.

Instead of a telemetry system, sled-borne re- 8. Typical Sled-Borne Telemetering System Figure corders, either the magnetic tape or recording os- for Flutter Tests cillograph type, can also be used to record trans- ducer outputs. However the rather rugged environ- ment of the sled o r the need for many channels of information may preclude their use. There is also a problem of time-correlation of data if sled recorders a timing oscillator are used. Means must be provided to correlate the range master timing system. If sled-recorded information, either by sled-borne os- is used it must be very stable, or its output must be cillator or by a sled-borne timing receiver, to the telemetered for comparison with the master system.

Figure 9. Typical FM/FM Telemetric Record of a Flutter Test Photographic Instrumentation In flutter testing high-speed photography is invaluable in determining the nature of the lifting surface motions. Photographic coverage can be either by sled-borne cameras to view the test surface in its own frame of reference, o r by ground-based equipment, either fixed in place so as to cover the significant portions of the test run o r installed on tracking mounts.

Sled-Borne Cameras Due to the rather extreme physical environment of the test sled, special photographic recorders are used. Some instruments normally used for ground installations, such as the Fastax, have been modified to withstand this environment. The newer prism-type as the Wollensak Fastair and the cameras, such Fairchild HS100, have been used very successfully for on-board recording, and offer sampling rates up to 5,000 per second. Various lenses are available for use with these cameras, the choice dependingupon the configuration of the sled and the test item. These cameras offer certain weight and power advantages over the Fastax camera, although the Fastax is still Figure 10, M-45 Tracking Camera Mount used for used for on-board recording. In addition to these Tracking Studies of Sleds cameras, two pin-registered cameras for sled use a 35mm half-frame have been developed; one has format, the other a 16mm full-frame, offering frame length lenses, for tracking studies of high-speed test rates at 200 and 300, respectively. These cameras vehicles. These units a r e mobile, self-powered, and will operate at better than 50 g's in any axis.

provide tracking rates up to 60" per second. These mounts are normally used on %-foot highdirt mounds Ground-Based Cameras located 3,000 feet off-track at various distances down range. Placing the mounts above the desert terrain tends to minimize image degradation due to heat waves while their 3,000-foot off-track position not Ground-based photographic instruments a r e lo- only protects the operator but gives him some advan- cated either off the track or on track overheads.

tage in tracking fast-moving sleds.

Their down-range location and field of view a r e pre- set on the basis of the best available prediction of the position of the test vehicle during flutter of the test item. Several cameras can be set up at different lo- INSTRUMENTATION CONTROL cations to provide over-lapping coverage if requhed.

The Eastman High Speed camera, offering 16mm Photographic ground instrumentation is usually black and white o r color recording a t frame rates up controlled on a time-basis by an automatic sequencer.

to 3,000 per second, and the 16mm and 35mm Fastax, Figure 11 is a view of the SNORT programmer which for black and white recording at up to 5,OOC frames supplies control signals a t the proper time and duration per second, are used for high-speed recording from to start and stop instrumentation equipment. It also ground locations. Various lenses, up to 48" in focal provides the pulse at "zero" time which actuates the length, are available for these cameras. The 16mm firing contactors in the blockhouse. At each instru- and the 35mm Mitchell cameras a r e used for medium ment location down range, a control box receives the speed recording (up to 120 frames per second) with signal and in turn controls power to the camera.

lenses to 96" in focal length available.

The control of ground-based cameras operating at high-frame rates becomes critical since such Tracking Mount cameras may provide only fractions of a second re- cording time. Since it is necessary that such cameras be properly sequenced with the event, carbon rods o r The "M-45" tracking-camera mount (Figure 10) micro switches, which are broken o r actuated by the is a basic tracking unit capable of supporting both passage of the sled, are used to effect camera control Mitchell and high-speed cameras with long focal the photograph. Figure 13 is a rear view of a general purpose flutter test sled showing the knife blades used for control of rocket staging and f o r instrumentation equipment. This view also illustrates the water- brake probe extending below the sled.

Figure 11. SNORT Programmer for Control of Instrumentation During Test Firings on a sled-position basis instead of the time-basis control afforded by the programmer.

Control of sled-borne photographic and elec- tronic equipment is accomplished by either the range programmer (with pull-away plugs) or by the use of a sled-borne pistol switch actuated when knife blades on the sled cut charged screens mounted on the track beam. Squibs in the switch a r e fired in this manner to either open o r close contacts for the control of the on-board equipment. Knife blades are also used to effect rocket staging.

Figure 13. Rear View of General Purpose Flutter 12 shows a typical instrumentation con- Test Sled Showing Knife Blades and Water Figure Brake Probe trol panel mounted in the sled. The battery pack for photographic cameras is located on the left, and the pistol switch assembly is shown on the lower right of The frame rate of the high-speed cameras used in flutter tests must be sufficiently high to permit detailed examination of the test item motion on an extended time basis. At least 20 frames of recording is required per cycle of flutter motion, and s o the minimum frame rate must be at least 20 times the expected flutter frequency. The film capacity of the particular camera and the required recording time set limits on the maximum frame rate that can be used.

Sled-borne cameras are usually started before the sled rockets a r e fired to eliminate their starting under high linear accelerations. In determining the maximum frame rate of these cameras, adequate con- sideration must be given to the times involved in the acceleration, and high-velocity phases of the test as well as the required coverage during the coast phase.

Timing Systems Time correlation of photographic and other recorded data is obtained by the use of master range Figure 12. Typical Sled-Borne Instrumentation Con- timing systems. Timing pulses at various rates are trol Equipment transmitted by radio links to the instruments down range requiring time-correlation. Timing signals Instantaneous velocity determinations can be are provided to sled-borne instrumentation by either made by the use of two magnets mounted aknown a sled-borne fixed-frequency oscillator, or by a sled- distance apart on the test sled or by the use of track- borne receiver for reception of the range time sig- mounted current-conducting glass rods connected to nals. When required, the fixed-frequency oscillator the track coil system. Measurement of the time signals can be telemetered and recorded for compar- interval between the magnet pulses or pulses gener- ison with the range master system. The rocket- ated by the breaking of the rods, yields velocity firing pulse is used as a reference or staring point in determinations a t specific points down range. Figure time, which is usually considered as "zero time". 14 is a section of a sample record of the track coil At SNORT, two radio links are used: (1) a nine- system using two sled-mounted I'U" magnets and the channel pulse coded modulated carrier of 505mc, and glass-rod break system.

a single channel pulse amplitude modulated carrier (2) of 360mc. The single channel equipment is used to More precise velocity data can be obtained at carry the lOOBCT signals. The 9-channel PCM SNORT by means of a precision velocity measure- equipment transmits the 100BCT, and 8 other signals ment system, more commonly known as VMS". The as required between d.c. and 10KC. instrumentation of this system consists of two data sources: sled-position vs. time is measured with the magnetic track coil system, and sled-acceleration Acceleration-Velocity Data Systems vs. time is measured by a sled-borne accelerometer Sled position as a function of time is the primary a PDM telemeter system. The tape recorded data and data requirement of every flutter test conductedon the is converted to digital form and entered into the IBM supersonic tracks since it yields, by calculation, 701 computer by automatic assessment equipment.

information on velocity and acceleration. The posi- The two different sets of data a r e combined by a tion-time measuring system at SNORT is a track coil near-optimum digital-f iltering technique to provide a or magnetic-pickup system. set of hybrid wide-bandwidth data.

It consists of a permanent magnet, either of the This system is capable of measuring the vel- "U" or "E" configuration, mounted on the test vehicle, ocity of a test vehicle over a range of 200 feet per pickup coils mounted every 100 feet for the entire second to 2,000 feet per second, to an accuracyof 21,500-foot length of track, and transmission lines 0.1 feet per second o r better, and with a bandwidth connecting the coils to the terminal equipment in the of 50 cycles. Figure 15 is asection of a typical track Test Control Building. When the magnet passes over coil record using a sled-mounted "E" magnet. The the coils, pulses are generated which are recorded V M S precision pulse, shown on the record, accurately by the terminal equipment. The time between succes- indicates the cross-over o r "zero" point of the magnet sive pulses determines the average velocity and pulse.

average acceleration of the test vehicle between coils.

1000- PPS

REFERE~CE

LINES

Figure 14. Section of Sample Record of Time-Position Data Using Sled-Mounted "U" Magnets and Glass-Rod Break Circuits

BINARY DECIMAL

CODED TIMING,

'100-PPS BINARY CODED TI~ING \

THS

~000-PPS

REFERENCE

L l ~ E ~

Figure 15. Section of Sample Record of Time-Position Data Using Sled-Mounted "E" Magnet CONCLUSIONS trolled velocities, the high-speed track offers a unique method of flutter testing. By its ability to prove the validity of design and to accurately deter- With the development of measurement techniques mine the actual margin of safety, the high-speed track has become a much needed test facility for the and testing procedures, coupled with the ability to reproduce realistic free-flight environments at con- aircraft design engineer.

E X C I T A T I O N BY ROCKETS C. E. Tummudge - Cunuduir Limited, Montred, Cmudu the aircraft and the damping of the structure is deter- Abstract mined.

Standard methods of excitation a r e not always The most usual form of continuous excitation practical when a single mode of known frequency requires investigation. This form of investigation is is by using inertia weights and it is preferable to use often required on a modified aircraft. The simplest multipoint phased excitation. This of course if a major installation which would necessitate grounding method of excitation is by "Stick Jerks", but this may the aircraft for a considerable time. Any form of not be successful owing to: power controls; high inertia excitation would however have a low frequency frequency modes; or inability to force a t the required limitation of approximately 3 c/s caused by the im- points on the structure.

practicable large size of weight required to excite A new method of excitation has been developed these low frequency modes.

and proved in flight, which consists of firing small rocket charges attached to the aircraft structure. For impulse excitation stick jerk tests have been Damping values at gradually increasing airspeeds are made and some very good results have been obtained.

obtained, as in "Stick Jerk" tests, and flutter speeds This system is very attractive as it is simple, but the force applied at each impulse is not constant, predicted.

overtone modes a r e difficult to excite, and on an air- craft with fully powered controls it is difficult to INTRODUCTION excite modes above about 10 c/s.

When a full flight flutter program is planned on a new aircraft to investigate several modes, fairly A requirement therefore existed for a methodof elaborate excitation and recording equipment is re- excitation which was simple to install and would excite quired and can be justified. However whenunexpected a mode of either high or low frequency by applying flutter occurs during the flying stage of a prototype, a repeatable force to the aircraft stucture. To meet this requirement, rocket units have been developed.

or modifications are made to a standard aircraft which may result in reduced flutter speed, tests are required with a minimum of installation and ground- ing time of the aircraft, and yet give the required THE IDEAL IMPULSE prediction of flutter.

The methods by which aircraft can be excited When considering the ideal impulse required to can be divided broadly into two techniques: First excite a structure in a given mode three things should continuous excitation, in which a sinusoidal force, be considered: capable of frequency variation is applied to the air- (1) The point of application of the impulse to craft and flutter prediction is determined from the amplitude response of the structure; and second the obtain the maximum response in the mode impulse technique, in which an impulse is applied to of interest, The maximum safe load that can be applied to (2) The maximum safe load that the selected any part of the structure is fairly readily determined point of application on the structure can from static considerations, but it is desirable to work withstand without damage; and, with standard units and a thrust of 200 lb. is consid- ered to be a reasonable standard.

(3) The shape and duration of the impulse in relation to the period of the mode of inter- The shape of the impulse capable of maximum est, to obtain the maximum amplitude re- ponse. energy transfer to the structure will be of a rectan- gular form with the force equal to the maximum safe load and the time equal to the ideal duration. To To find the effect of the point of application, consider determine the ideal duration, consider the response of an undamped single degree of freedom system the response of a cantilever beam in its first three subjected to a rectangular impulse, the response normal modes, to a unit impulse applied at various pointsalong its length as shown in Figure 1. It will be curves obtained will be a s shown in Figure 2. It will seen that the maximum response occurs in all modes be seen that the maximum response will occur when when the impulse is applied at the free end, that in the duration of the impulse equals half the period of the second and third mode a node occurs at approx- the mode of interest. An impulse of less time than imately 0.80 length, and that when the impulse is ap- this will result in less amplitude and of greater time plied at this 0.80 length position there is little o r no than this, while resulting in the same initial ampli- response in these two modes. Also it will be seen tude, the response immediately after the initial peak that at no matter what position along its length the will be distorted and the subsequent amplitude will be beam is exicted, the maximum response is always reduced. The effect of damping will be to reduce the will be approximately in the fundamental mode. Therefore we may say peak amplitude, this reduction that: 5% for the damping factors applicable to aircraft near a flutter condition.

(1) A mode will not be excited if an impulse is applied at its node, and, To return to the problem of exciting overtone modes. It was shown that on a cantilever beam, (2) If the second of third modes are of interest, positioning of the impulse would not make the over- positioning alone of a single unit will not tone modes predominate. Therefore, an impulse make them predominate. applied for half the period of the first overtone would also excite the fundamental mode which would pre- dominate. If however a second impulse is applied in the opposite direction to the first, and after a specified time interval the overtone mode can be made A to predominate, the time interval between such im- R pulses to obtain maximum response can be shown to be half the period of the required mode. This double impulse technique is also advantageous when at a point on the structure at which trying to excite the load is limited, and also when the amplitudes excited by a single impulse are too small for analysis.

ROCKET CONSTRUCTION AND PERFORMANCE To obtain a suitable impulse to meet the ideal requirements stated, rockets have been developed.

The first rockets used at the Royal Aircraft Establishment to produce an impulse on an aircraft structure was in 1953. The case of each rocket shown in Figure 3 consisted of a steel tube, threaded internally at each end, the ends of the tubes being closed by end caps. One end cap was a solid disc while the other was a disc machined with aventuri at its centre. This case was filled with a number of hollow sticks of cordite in the centre of which was located an electrically fired gunpowder igniter. The electrical leads for firing the igniter were brought out through the venturi, and an internal grill was Figure 1. Response of Cantilever Beam in First Three Normal Modes to a Unit Impulse Applies located between the cordite and the end cap to prevent at the Points Indicated large pieces of cordite blocking the venturi. The Figure 2. Response of Simple Undamped System to a Rectangular Impulse I G N I T E R G R I L L I G N I T E R L E A D S S E C T I O N TWROUhW R O C K E T Figure 3. Construction of Rocket Using Cordite Sticks overall dimensions of this unit were approximately with its axis horizontal. A hole was drilled in one 4-1/2" long and 1-3/4" diameter. end of the rod to accommodate the rocket, andan accelerometer was mounted on the opposite end. The impulse of the unit a s measured on this balistic pen- of this first unit was measured by The impulse dulum w a s approximately 200 Ib. for 50 milliseconds, a balistic pendulum. This pendulum consisted using as shown in Figure 4. The build up of force was fast of a length of 4" diameter steel rod weighing approx- and a small initial peak occurred, there was a slight 40 lb. suspended on wires such that it hung imately I D E A L IM PULSE SHOWU OOTTCO 2 O O l b T H R U S T

---

Figure 4. Impulse from Cordite Rocket New rocket units were therefore developed at fall-off of force over the burning period, at the end the R.A.E. specifically to meet the requirements of of which the reduction of force was reasonably rapid.

The current required to fire these units was approx- aircraft excitation. These units, shown in Figure 5, consisted of a tube with a platenised propellent de- imately 5 amps.

posited on the walls of the tube, the overall dimensions were 7/8" diameter by 4" long. Three rockets were Although this rocket was not specifically de- designed to give thrusts of 200 lb. for 50,25 and 12-1/2 signed for flight flutter excitation the response was milliseconds in order to excite modes of 10,20 and very close to that required ideally to excitea 10 C . P . S .

mode, but it contained two basic faults. First the 40 C . P . S . respectively. The actual thrusts produced by these units as measured on a balistic pendulum cordite used in this rocket w a s temperature sensitive were very similar in shape to that obtained from the and would lose 40% of its thrust at -50°C or 40,000 feet. This loss in thrust can only be overcome by first unit.

using a platenised propellant. Secondly, the overall A new problem did however reveal itself which size of the unit i s large compared with the space affects sequential firing of these units. It w a s found available inside the ex'cremities of the main surfaces that the variation in the time from closing the electric of a large number of modern aircraft. This space switch which fired the igniter, to the commencement limitation was overcome in part by turning the jet of of thrust w a s large compared with the overall burning gasses through 90" such that the thrust was produced time. This could be as high as 6 milliseconds o r at right angles to the longitudinal axis of the unit.

approximately i50% of burning time in the case of the This permitted mounting of the rocket parallel to the 12-1/2 millisecond units. Therefore if two units in outer skin surface of the aircraft. The change were fired either together or half a period apart to direction of the thrust was producedby weldinga right excite a mode, it was possible, if the firing time angled tube over the venturi. This may not be the delay tolerance on each unit was a maximum and in most efficient way of producing the desired effect, the opposite direction, for the impulses to completely but tests showed that only about 5% of the thrust w a s cancel each other. This problem requires further lost. However, this still left a tube of nearly 2 " di- investigation.

ameter to be mounted between the outer skin surfaces.

V E N T U R I

PLAT E N IS E 0 G R I L L

PftOPELLE N +

i

I G N I T E R L E A O S H E A . O C A P l C N l T E R Figure 5. Construction of Rocket Using Platenised Propellent I G N I T E R I G N I T E R N I T E R R I N G S N I T E R R I N G S HEA I G N ITE Figure 6. Construction of Rocket Using Propellent & Igniter Rings A third type of rocket construction is shown in ly on the type of aircraft. Generally, external Figure 6. This again is a 10 lb. sec. impulse unit mounting is the simpler and this should be possible producing 100 lb. thrust for 100 milliseconds, it is on low speed aircraft. Internal mounting will be about half the length of the original unit used at the more difficult, but by choosing the best position and shape of rocket this should be possible without ex- R.A.E. This rocket was designed by the Canadian ternal fairings. The rockets should be attached to, Armament Research and Development Establishment, or held against a firm thrust plate, this may be done and consists of rings of propellent interspaced with a central igniter similar to that in the case of straight thrust rockets, by welding the rings of igniter with head disc to the thrust plate and assembling the used in the other two units. In this unit the igniter rockets on the plate.

leads are brought out through holes in the head cap of the unit, and a thin aluminum disc covers the ven- turi. Tests with this unit have given very little The safety precautions required in handling scatter in the time delay which may be the result of these rockets are few. If the ends of the ignition leads are connected, by twisting the bare ends, no the aluminum discs, but further testing is required to potential can occur across the leads and the igniter confirm this.

is safe, in addition the head caps should be removed during transit.

USE O F ROCKETS ON AIRCRAFT In Figure 9 a circuit diagram is shown for firing 8 rockets in four pairs with a time interval between each pair. This is the most that would be When using these rocket units in practice it is required to excite a mode and for a lower number of fairly obvious that safety precautions must play an be simplified. The wire runs important part. The cases of these units a r e of units the circuit can course given a good safety factor but the weak part of between the rocket units and intervalometer should the construction is the threads. In the case of the be kept as short as possible to avoid possible voltage platenised rockets, the threads have been known to pickup along the wires. If long runs are unavoidable fail, but the deposits left by this propellent are very or the wires pass electrical equipment liable to pro- duce pick-up, some provision should be made in the corrosive and the cases should only be used once.

switch to keep the igniter leads shorted until just By comparison, the cases used with the cordite sticks prior to firing.

were used many times without a single failure.

Additional safety precautions against possible When connecting the rockets to this circuit it is failure of the cases should in general not be necessary recommended that the aircraft wires are shorted just when these units are mounted on an aircraft, but un- prior to connecting the rockets. The firing circuit avoidable positioning of the units close to a fuel tank should contain two removable safety links, a supply or in equally dangerous positions might call for a switch which breaks both leads and a firing button.

safety tube around the rocket case. The mounting of As the actual recording time required is short it these units internally o r externally will depend main- is considered worthwhile to include the operations of - ,It. . 3 Figure 7 . Rockets Being Fired to Excite an 8 C.P.S. Symmetric 7 shows two pairs of rockets being switching the recorded in the intervalometer, this excitation. Figure also avoids the possibility of forgetting to start the fired to excite a 8 C.P.S: symmetric mode on a recorder. Most recorders start almost instantane- Meteor aircraft at the R.A.E. The rockets used in ously and a s the first motion of the aircraft structure these tests were the cordite stick type.

is usually a little distorted the recqrder can be start- A of interest, this type of excitation ed at about the same time a s applying the volts to the first rocket. The switching off of the recorder can can be structures having very low natural be obtained by passing the signal from the interval- f requen re 8 shows 18 rockets, eachpro- ometer through a delay switch which will allow a ducing a thrust of 1,000 lb., being fired at the top of sufficient length of record to enable the decaying a 425 feet chimney stack. The rockets were attached waveform to be analyzed. to the architectural lip and fired simultaneously.

The response of the stack w a s measured at the top APPLICATION OF ROCKETS using accelerometers, the amplitude was approximate- ly 2", the period w a s approximately 2 seconds, and the This form of excitation has been used ss- actual damping structural 'damping factor critical damplng was 0.01.

fully on a number of aircraft, with wing fin CONCLUSIONS A s with any system, rockets have certainlimit- ations, but they are very suitable when a single mode of known frequency required investigation. The ideal duration of the impulse is half the period of the mode of interest and sequential firing may be employed to isolate a mode, or to obtain a larger amplitude response of the structure. The installation required for rocket excitation is simple and there is virtually no frequency limitation to the use of rockets in the range of flutter frequency experiencedon conventional aircraft.

Figure 8. Eighteen 1,000 Ib. Rockets Being Fired from Top of a 425 ft. Chimney Stack

n n

INTERVALOMETER FlRlN 6 SUPPLY 0UTTON VOLTS 0 , I S A F ETY SUPPLY I L f NKS S W f T C U I I I I O N

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DELAY R O C K E T U N I T S Figure 9. Firing Circuit for Four Pairs of Rockets FLIGHT FLUTTER T E S T I N G U S I N G PULSE TECHNIQUES R, H . Stringhum, Jr., E. J . Lenk - D o u g h Aircruft Co., EL Segzmdo, Culiforniu GATHERING AND DATA INTERPRETATION Abstract A case of flutter developed at a speed lower than In conducting pulse tests the structural response had been flown previously. This incident precipitated has been measured primarily with accelerometers and the routine procedure of pulsing control surfaces a s occasionally with strain gages. Outputs have been well a s the firing of explosive charges during speed recorded by oscillographs installed in the test air- build-ups. In the interest of rapid evaluation of re- plane. With accelerometers, low pass filters usually sults, simple methods of data reduction were used. A have been used for suppressing the high frequency case history is presented where i n the pulse technique disturbances excited by buffeting, turbulence, and predictedflutter by extrapolating decay rates obtained noise.

at subcritical speeds; i n addition, a case is presented where no valid extrapolation could be made.

This filtering has been necessary in view of the method by which data has been reduced. Data reduction has consisted simply of measuring the decay envelope directly from the oscillograph rec- ord, computing the percent of critical damping, and INTRODUCTION plotting this damping as a function of speed. In this way, the damping is plotted for each frequency ap- pearing on the record in a form sufficiently undis- The need for systematically evaluating the torted to establish the decay envelope. Ideally the structural stability of aircraft by flight testing has damping speed plot thus obtained will form a smooth arisen out of the need for confirming the results of curve enabling an extrapolation to the flutter speed.

the flutter analysis as well asfor searchingout modes unforeseen by the analysis. It t s the purpose of this paper to describe how the pulse technique has been GENERATION O F PULSES used to fulfill this need during the flight testing of airplanes designed by the El Segundo Division of the Douglas Aircraft Company. In view of the means of data reduction the primary requirement of pulsing is that the airplane are structure be excited in the proper mode o r modes Methods used for the generation of pulses at an amplitude substantially above the noise level.

described and the results of their application shown.

In an attempt to fulfill this requirement, pulses have The pulse technique has been used at Douglas because been generated primarily by two methods: (1) man- of its simplicity as compared to other methods such as the frequency response technique. Also, a mini- ual control pulses, and (2) the firing of explosive charges.

mum of auxiliary equipment is required, and data can be obtained without prolonged speed stabilization which is an advantage when exploring the speed envelope For piloted aircraft, the advantages of manual beyond the airplanes level flight capabilities. control surface pulses are obvious in that no special equipment is required and the number of pulses per flight is practically unrestricted. However the shape I and magnitude of the force-time curve a r e important.

Thus limitations are imposed upon the manual pulse t by the response characteristics of the control system, I together with the rapidity by which the pilot can move the control. Based upon experience, it has been found that pilot technique is an important part of ob- taining a satisfactory pulse. Usually, sharply applied control inputs of iow amplitude have resulted in better excitation than those of large amplitude. Large amplitude inputs have invariably resulted in pulses of prolonged duration which fail to disturb the struc- tural modes.

Figure 1. Impulse Generator Installation For single engine type airplanes with fairly rigid control systems, manual control surface pulses have been effective in exciting antisymmetric modes with frequencies as high as 20 cps. Symmetric nization between two pulses is required, e.g., when a greater problem. Attempts exciting symmetrical modes.

modes have presented to excite symmetrical wing modes with elevator con- trol pulses have been ineffective; however, there has Figure 2 shows an oscillograph record illus- been some success in exciting the first bending sym- trating the satisfactory excitation of the first sym- metrical stabilizer mode with the elevator. metrical wing mode during low-speed flight with an external store configuration. It can be seen that the The second pulse method which has been ex- wing tips are in phase following the firing,with a tensively employed is that of firing explosive charges. well-defined decay envelope. At high-speed, although With this method, control over the force-time curve the "hash" level was considerably higher than for the is possible, allowing a broader frequency spectrum low speed case, it was still possible to sketch a rea- to be examined a s compared to the manual pulse sonable decay envelope for computing the damping.

method. Also, the pulse shapes formed by explosive Antisymmetric modes were excited by aileron and charges are likely to be more consistent. Of course, rudder pulses.

a means for containing and firing the charge is re- quired and, for this purpose, a breech-nozz' le assem- bly has been developed by the Douglas Armament DEVELOPING PULSE SHAPES Group. This device has been called an "impulse Some work has been done at Douglas, E l generator", with a length of 3-3/4 inches and a cross Segundo in shaping the pulse of the explosive charges section of 1-1/2 x 1-1/2 inches. The breech of the in order to emphasize the response of a given struc- impulse generator has been designed to accept a tural vibration mode. The impulse generator, when standard Mark 1 bomb ejector cartridge. These used with a standard ejector cartridge, generates a units have been installed on wing tips, stabilizer force curve similar to that shown at the top of Figure tips, and fin tips.

3. The pulse rises sharply, reaching a peak value of A wing tip installation is shown by Figure 1 about 1000 pounds in 7 milliseconds. With this pulse, one would expect the higher frequencies to be excited consisting of four units. Here the nozzles can be at the expense of the lower. The lower curve of Fig- seen firing upwards. Thermostatically controlled ure 3 shows an approximate half-sine pulse as gen- heating blankets are wrapped around each unit to erated by a specially developed reload. This half- insure that the ignition delay time and burning rate sine reaches a peak value of about 500 to 700 pounds in remain unchanged with ambient temperature. Uni- approximately 17.5 milliseconds; longer rise times, formity of ignition delay and burning rates are always desirable, but a r e especially important when synchro- it was found, could not be developed by reloading the

- - I , - - - -

RIGHT WING TIP NORMAL- ApN---

RIGHT STORE NORMAL

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LEFT STORE NORMAL-

-__y_- - ._I____-_rr_l_yc -

- t v -

LEFT WING TIP NORMAL

Figure 2. Symmetrical Wing Mode Excited by Dual Impulse Generators (Low Speed) dicted by analysis. No systematic pulsing ip conjunc-

PULSE GENERATED BY

tion with the speed build-up program had been done

EJECTOR CARTRIDGE prior to the flutter incident. This incident led to a

flight program with an unstable configuration using manual rudder pulses and pulses by impulse genera- tors while cautiously approaching the flutter speed.

N N It was believed necessary to obtain a damping plot of the known unstable configuration in order to demon- strate the value of the pulse technique in predicting the approach to instability, thereby establishing a method whereby a”fix” could be demonstrated. There-

4 I-=.oo~sEc. TIME

fore, a speed build-up program was conducted where- in the decay rates, measured from the fin response, were plotted vs speed, a s shown by Figure 4.

SINGLE-ENGINE AIRPLANE FIN TIP RESPONSE Figure 3. Pulse Generated by Ejector Cartridge ejector cartridge without an unacceptable reduction in peak force and a deterioration of reliability.

e An analog computer study was made to deter- mine the response of a cantilever wing to the pulse shapes shown by Figure 3. Mass and elastic proper- ties of the wing were included together with normal 0.7 0.8 0.9 1 . 0 computer damping. Aerodynamic forces were not VELOCITY simulated. The computer study showed that best re- sults, as measured in terms of maximum displace- Figure 4. Single-Engine Airplane Fin Tip Response ment response of the first bending mode per peak force input, could be expected when the rise time of a half- sine pulse equaled about 1/3 the period of the first bending frequency. For pulse shapes generated by a This damping plot indicates a definite trend to standard cartridge load, a rise time of 1/4 the period neutral stability. Since tests were carried out at an gave the maximum amplitude response per peak force altitude higher than where flutter had originally oc- input.

curred, the speed where the actual flutter occurred is not plotted. Figure 4 also shows a plot of the The analog results indicated that standard ejec- damping data obtained after making the fix. All tor cartridge loads were satisfactory for frequencies flights were made with a rudder damper installed of about 40 cps. However, our critical flutter modes and adjusted with one degree of free-play. This have been from 5 to 30 cps and, therefore, special damper arrangement was used to limit the rudder reloads have been used. These special loads have amplitude, thereby preventing destructive oscillations For lower fre- operated effectively down to 12 cps.

in case the flutter speed was exceeded.

quencies, reliance has been placed upon control sur- face pulses.

Case 2: The next example concerns aflight test program APPLYING THE PULSE METHODS wherein flights were conducted in the speed region The success, a s well as lack of success, in where fin stability was predicted to be marginal.

using the pulse methods described can best be shown Manual rudder pulses failed to excite the instability by citing three cases wherein- the pulse method was or definitely indicate approaching instability. The used. technique was for speeds to be advanced with control surface pulses, followed by an impulse generator firing at a slightly lower speed. Flutter was excited Case 1 : at a speed 5 h o t s lower than by an impulse generator A small attack airplane experienced a fin- where a rudder pulse had been made. Figure 5 shows rudder flutter at a speed lower than the airplane had the oscillograph record of the oscillating surface with been flown previously. This flutter had not been pre- the amplitude limited by the free-play rudder damper.

FIN-RUDDER

EXCITED BY IMPULSE GIENERATOR

C . G . LATERAL , - -

WING TIP N O R M A L -

-,. "....

IL CONE LATERAL

Figure 5. Fin-Rudder Flutter Excited by Impulse Generator This case does not speak well for the pulse TWIN-ENGIN€ AIRPLANE technique in that a flutter case was actually allowed HORIZONTAL STABILIZER RESPONSE to develop; however, it does illustrate the importance of proper excitation. W e believe that the investigation of this case was complicated by static friction, as are most investigations of flutter involving control surfaces.

DAMPING %C/CC Case 3: 8, @ A twin-engine airplane had been given control 1 0 1 1 3 , surface pulses during the initial speed build-ups but, t I as attention had been directed to modes which were 0.7 0.0 0.9 I .o thought to be critical but in fact were not, a mode VELOCITY involving horizontal stabilize'r yawing was not detected as becoming unstable. The flutter frequency was rel- atively low and did not involve sufficient response in Twin-Engine Airplane Horizontal Stabilizer the cockpit area for the pilot to be aware of its exis- Response tence. After the flutter incident, speed build-ups were again made with proper attention given to the stabilizer yawing mode. The damping measured from the tests is presented by Figure.6 and shows the approach to tests instability. After stiffening the structure, pulse Systematic pulsing is necessary to minimize were again made. These results are also shown in the possibility of flying into a dangerous Figure 6. Although the damping appears to be good, speed range.

the data is scattered and a definite trend is not indi- cated; consequently, the flutter speed for the fixcould Where flutter is known to exist, proper not be predicted by extrapolating the damping plot. pulsing has yielded damping data which be extrapolated to the flutter speed.

could CONCLUSIONS A conscientious effort must be made to instrument and watch for unpredictedflutter modes; we must not be distracted by watch- Based on experience gained from flutter flight ing only those which have been predicted to testing in general and from using the pulse techniques be critical.

in particular, the following conclusions have been reached: Although it does not always establish the flutter speed, the pulse technique is useful (1) It is possible to fly beyond the critical speed in showing the margin of damping within without exciting flutter. the speed range of the airplane.

STABILIZER FLUTTER INVESTIGATED BY FLIGHT-TEST E. F. Buird, N . S. Sinder, R. B. Witttmun - Grzmmun Aircruft Engineering Corp., Bethpuge, New Y o r k coverage of important parameters for all configura- Abstract tions over the complete speed and maneuver en- Flight flutter tests were conductedon an experi- velope. The recorded data from such tests must be mental airplane which resulted in the successful pre- adequate to enable prediction of incipient flutter at diction of a limited amplitude stabilizer flutter at subcritical speeds, and to indicate the source and supersonic speeds. The flutter obtained was unusual nature of any existent flutter. These requirements in that fore and aft bending of the stabilizer carry- a r e especially important in the testing of current through structure contributed to the flutter condition.

aircraft that a r e designed to probe into high Mach During flight tests the impending flutter condition was number, temperature, and dynamic pressure regimes observed from force per unit amplitude, damping where many unknown parameters must be defined.

coefficient, and frequency measurements. A descrip- tion is given of the physical and operational charac- The testing procedures that were used in in- teristics of the test equipment and telemetering vestigating the flutter problems encountered in the facilities. A flutter analysis using measured modes transonic speed transition of our F9F-6 and F9F-8 and incompressible two-dimensional strip air forces airplanes were direct and simple. The excitation yielded a conservative flutter speed. Sled tests of a medium consisted of transient inputs of rudder pedal similar stabilizer configuration had lead to the con- kicks and control stick lateral and longitudinal jabs clusion that flutter would not be encountered. Certain to force primary surface oscillations. An airborne overall conclusions a r e reached regarding this par- oscillograph was used to record the data. The re- ticular flight flutter testing program and the need for sults obtained from these tests were also direct and a concerted research effort in this field. simple and merely served to show the absence or presence of flutter without indicating the build-up to INTRODUCTION or margin from the critical speeds. These tests also showed that considerable refinement of the flutter Development of higher performance aircraft with flight test program would be necessary to permit a margins has increased the need for rapid, yet safe, evaluation of future aircraft through- reduced flutter out speed envelopes that were expected to be almost early and accurate determination of an aircraft's twice the ranges previously investigated. Considera- flutter characteristics and establishment of its safe tion of these refinements along with the experience flight envelope. The resulting emphasis on flutter investigation during the initial stages of the flight gained in the production and flight testing of previous test schedule has produced considerable advances in aircraft played an important part in the design of the flutter testing equipment and techniques. Grumman F11F-1 Navy supersonic fighter that has been demonstrated to be flutter free to its maximum Two apparently contradictory requirements are EAS of 848 knots, a dynamic pressure of 2456 PSF.

paramount in the flutter flight testing of present day These refinements and the present methods, aircraft. The tests must be conducted with full techniques, and philosophies applied to the flutter assurance of maximum safety, yet must be satis- flight testing of the Grumman F11F-IF high per- factorily completed in the minimum time. Further, are discussed in the following text.

the test program must provide a comprehensive formance airplane These procedures are familiar to all flutter special- ists, however, mere is little evidence to establish their accuracy, validity, and scope. The primary objective of this paper will be to examine an applica- tion of these techniques in the investigation of stabil- izer flutter.

The techniques and equipment used for the F11F-1F flutter tests were essentially the same as those developed on the F11F-1 airplane. The data link used in the conduct of the flight tests is shown in Figure 1. Accelerometers were appropriately mount- ed on the wing, stabilizer, fin, and fuselage to sense the excitation from an unbalanced mass shaker mount- ed in the afterbody. The accelerometer outputs were relayed to an FM/FM telemeter package, amplified, and transmitted to the ground station, a mobile van.

The signal received at the van was appropriately dis- criminated and sent to several simultaneously dis- playing mediums for immediate and rapid analysis by flight test and flutter engineers. These flight data were compared to calculations and model test results.

Figure 1. Airplane-Telemeter Data Link Through the use of appropriate charts and overlays, as frequency, amplitude, and decay rates were plotted fin, fuselage and wing modes. The shaker consists of functions of airspeed and Mach number and the results relayed to the pilot along with recommendations for a rotating unbalanced mass which is driven by a hy- continuance of the flight. draulic motor. An unbalance of 2.5 in. lbs. was used for the flight tests. This weight was the minimum The compact shaker assembly shown in Figure that could satisfactorily excite the required modes and 2 is approximately eight inches high, seven inches the maximum excitement that the pilot wanted to wide, and fifteen inches long. This unit was designed tolerate. Motor speed and consequently excitation frequency is governed by a cam positioned flowvalve.

to f i t into the tail skid compartment of the F11F-1F The cam and valve are integrally designed to provide and consequently was ideally suited to excite all of the critical stabilizer modes as well a s many of the optimum frequency sweep characteristics for the Figure 2. Eccentric M a s s Shaker particular phase under consideration. For the subject A data recording system revolving around tele- metry has been successfully developed for the high tests the frequency programming started at 10 cps, linearly progressed to 28 cps in 30 seconds, more risk flutter flight testing of the F11F-1 and F11F-1F rapidly advanced to a maximum of 35 cps within 5 aircraft. A small twelve channel, self calibrating seconds, and returned to the initial frequency inabout telemeter package translates the D.C. voltage outputs of eleven data transducers and one communications 7 seconds where the cam motor was automatically channel into a frequency modulated signal which is stopped preparatory to another start signal from the amplified and transmitted on an FM carrier. For the pilot. The pilot was also able to stop or reverse the cam motor at any point of the cycle and thus maintain flight testing of the FllF-lF at Edwards A i r Force constant frequency shaker operation. This was usually Base, the signal was received in the Grumman de- done at a resonate mode of particular interest. A set signed and build telemetering van. An interior view of hydraulically actuated brakes within the shaker of the van is shown in Figure 3. This van was de- signed with special attention to the incorporation of could also be used by the pilot to stop the mass rota- features that would optimize the data recording and tion within 3/4 of a cycle at 60 cps and even faster at w a s placed upon the lower frequencies. Brake actuation also closed two analysis. Particular emphasis solenoid valves which trapped the hydraulic fluid with- rigid requirements of flutter flight testing. The in the shaker motor thus increasing braking effective- present system includes: ness. This was followed by cutoff of hydraulic pres- a) Two receivers sure to the shaker system. Thepilotwas thus able to: Sweep the unbalanced mass through a pre- b) Complete signal monitoring equipment to a) scribed frequency cycle. insure the validity of the data Select and maintain a specified shaker fre- c) Two tape recorders b) quency.

d) An automatic sequencer Rapidly start and stop the shaker at anyre- c) Analog computer for direct and immediate quired frequency.

e) data processing such as addition, subtrac- These several shaker operations, surprisingly tion, multiplication, integration, filtering, a minimum of pilot attention and and other applications.

enough, required effort to accomplish. Throughout the design and de- velopment of the shaker components considerable coordination between design engineers and flight test pilots evolved a rather simple operations system.

Pilot requirements ultimately resulted in: Pressing a thumb button on the side of the a) control stick to start the shaker and program it through one frequency sweep.

Pressing another button on top of the control b) stick to stop the shaker immediately.

Actuating a switch near the throttle quadrant c) to maintain constant frequency or reverse cam rotation.

The pilot was informed of shaker frequency by a dial gage located on the instrument console adjacent to the airspeed, Mach number, and altitude gages.

A unique component of the shaker system, and one that sometimes worked too effectively, was the shaker controller. This unit was an automatic safety device that stopped the shaker through actuation of the shaker brakes when and if the wing, stabilizer, or fin oscillations exceeded pre-determined accelerations.

When so stopped, the shaker could be restartedby the pilot's depressing the start button. However, the shak- er would operate only if the surface oscillations were Figure 3 . Interior of Telemeter Van below the controller cut-off limits.

THE G R U M W RIP If AIRQLANE A single channel long persistance oscil- loscope for x-y data presentations A 50 channel oscillograph Two banks of Sanborn recorders of eight channels each for immediate anddirect time history display of vital parameters A special two speed feature, ten to one in ratio was built into the Sanborn recorders to permit accu- rate recording of higher frequency flutter data. Paper speed could be controlled either by ground personnel or remotely by the pilot through the telemeter link.

Another feature added to these recorders consistedof two tables, seven feet in length, especially constructed to permit viewing and analysis of a large quantity of data. Special take-up reels allowed stopping of the paper while the pens continued to transcribe the tele- meter signal at the proper paper speed.

The validity of the techniques developed for flutter flight testing with the shaker and telemetering was determined by a flight investigation of the F11F- 1F stabilizer flutter problem. The second aero- dynamic prototype F11F-1F airplane is shown in Figure 4. This airplane is a modification of its pre- decessor, the F11F-1 Tiger, and has the same wings, fin, and fuselage center section. The stabilizer plan- form, which is also shown in Figure 4, is also un- changed but the airfoil section was decreased from a varying 6-4% section to a constant 3% thickness and the weight increased by 45%. The major changes were necessitated by the installation of a more powerful 5-79 engine in place of the J-65. The larger diameter of the 5-79 required increasing the afterbody cross- section and in turn the breadth of the stabilizer yoke.

Figure 4. The Grumman FllF-1F Airplane Stabilizer These revisions to the stabilizer and its yoke have from the F11F-1F Airplane changed the surface's vibration characteristics by lowering the first symmetric mode, primarily verti- cal bending, from 20.0 to 12.7 cps and the second symmetric mode, primarily yaw, from 2 5 . 4 to 17.8 cps to produce a limited amplitude stabilizer oscil- 1ST FUSELAGE lation that has been encountered in flight throughout V. B. MODE a wide Mach number and altitude range. The node lines for this revised stabilizer-yoke combination a r e shown in Figure 5. No structural damage has result- ed from the oscillations and the mild onset of the vi- SYM STAB 2ND bration permitted an investigation of this flutter MODE (17.8 CPS) through flight test with relative safety.

Prior to the first flutter incident transient in- puts of aft stick jabs had been made from 200 to 510 knots as a cursory check of the overall stability characteristics. These test failed to indicate any in- 1ST S Y M STAB cipient flutter and in some instances actually showed MODE (12.7 CPS) increased damping. The results of these tests led us to delay the planned flutter flight test program until after a flight evaluation of the airplane had been com- pleted and to extend the initial restrictions of 450 knots to speeds in excess of 500 knots. During the ex- tension of these restrictions the flutter condition that had been predicted by theoretical calculations but had Figure 5 . Stabilizer Vibration Node Lines Shortly after the completion of the flight evalu- not been totally substantiated by model o r sled tests ation program the delayed formal flight flutter pro..

was first encountered at a speed of approximately gram was conducted with extremely encouraging re- 530 knots, 80 knots in excess of the initial restrictions sults. Within five flights, throughuse of the unbalanced and within about 10 percent of the predicted critical mass shaker and the telemetering, we were able to de- speed. Appropriate restrictions of 475 knots below fine the problem area, extrapolate the test results to 35,000 feet were imposed.

the critical speeds, and define the flutter modes.

The speed capabilities of the F11F-1F air- This flight test investigation was conductedover plane permitted these restrictions to be exceeded an area of .45 to 1.52 Mach number and 200 to 500 easily. A s a result stabilizer flutter on the F l l F - l F knots at the altitudes of 35,000, 27,500, and 20,000 has been encountered a total of nine times, twice by feet. The test points that were attained are shown in Grumman pilots, and the remainder by evaluation Figure 6. The initial flights started at the highest pilots. In all cases the onset of the vibrations were noted on telemetering records and the pilots were told altitude and scheduled shaker sweeps from approx- imately 200 knots to the maximum safe speed based to decrease speed. They all did so immediately.

upon flutter considerations. The results of these sweeps served to define the critical resonate fre- The oscillations have occurred in a narrow air- quencies and their variation with air speed and to speed band, 500 to 580 knots E M from 5000 to 38,000 feet and from Mach .95 to 1.80 as shown in Figure 6. indicate the regions of decreasing stability. A more In only three instances were they of sufficient mag- accurate definition of the decay rates was accomplished nitude to be felt by the pilots. These particular os- by having the pilot attain a given speed and Mach num- ber and operate the shaker at the prescribedfrequen- cillations imposed a maximum acceleration of about cy by referring to the cockpitindicator. The indicator i15 g normally and i 5 g fore andaft on the stabilizer.

0 100 zoo 300 400 500 600 700 EQUIVALENT AIRSPEED KNOTS Figure 6. Flight Flutter Points accuracy of about i1 cps, however, was inadequate for Identification of the critical modes from flight the tests and the actual resonate frequency was at- data was made through use of accelerometers mounted tained by having a ground observer guide the pilot in in the fuselage as well a s the stabilizer tips. The re- selecting the true resonance. This was accomplished sults of a theoretical flutter analysis for the F11F-1F rather simply by comparing the frequency and ampli- stabilizer as shown in Figure 7 indicated a possible tude of a particular telemetered data channel with a coupling between the stabilizer first symmetric mode, preset oscillator frequency on a dual channel scope. primarily vertical bending, and either the stabilizer After a bit of practice with the airplane on the ground second symmetric mode, fore and aft bending, o r the the actual resonance could be attained in flight within fuselage first vertical bending mode with either of the five to ten seconds. Once the resonate frequency was latter modes increasing their frequency with increas- attained the pilot stopped the shaker then restarted it ing airspeed. The telemetered data, however, as in- at the same frequency to define the decay rates three dicated in Figure 8, showed that the fuselage mode times. The damping characteristics of three modes frequency remained relatively invariant with airspeed were investigated by the technique. Aft stick jabs whereas the stabilizer first symmetric mode frequency were made on the last flight to show the trends that increased with airspeed from 12.7 cpsonthe ground to 17 cps at 500 knots to couplewiththe second symmet- could be determined by this transient input method.

ric mode which itself varied but little with airspeed.

In these five flights a total of 31 shaker sweeps, These results along with the marked increase in am- 37 resonate stops, and 11 stick jabs weremade to de- plitude of these modes at speeds in excess of 400 fine rather completely the mechanism of the flutter knots focused our attention on the stabilizer modes as problem. Through the use of telemetering and im- the fundamental problem.

mediate data evaluation the airplane was tested to 95% of the critical speed at the three altitudes in- In this method of testing with forced harmonic vestigated where in each case the tests were discon- excitation the amount of damping in the modes can be tinued when the monitored data indicated marginal examined in two ways. First, the loss of damping may damping. be evidenced by the sharpening of the resonant peak I I I I I

I I I

I SECOND SYM STABILIZER MODE

I 1 I I FIRST FUSE ALTITUDE 20,000 FT.

0 100 20 0 300 40 0 500 60 0 700

EQUIVALENT AIRSPEED - KNOTS

Figure 7. Results of Theoretical Flutter Analysis accompanied by amplitude increases. A sharp peak tions of problem areas are certainly evident from is defined a s one which has a pronounced amplitude peak occurring over a narrow frequency range. The amount of damping may thus be expressedby the ratio of the incremental frequency that defines equal am- plitude boundaries of the resonate mode. Qualitative- ly this is a good indication of damping but because of were used to flutter program well below the the sensitivity of the ratio to frequency ina of the airplane.

it becomes impractical for use in the flight data. The second method permits a direct indication of the damping in the termination of the amplitude of surface vibration at a to determine a more precise indication of the critical particular resonance. The data accumulated from speeds. The ratio of shaker force inputto unit veloc- ity of the stabilizer oscillation was plotted as a function shaker sweeps is summarized in Figure 8. These data of airspeed and Mach number. The results of this show a rapid reduction in the magnitude of the recip- analysis are pr rocal o f the Stabilizer tip vibrational amplitude, 1/A, nce the numer- for both stabilizer modes as the flutter speed is ical values of modes closely approached. This reduction of 1/A for both modes is coincided the individual test points are omitted and in good agreement with the theory which predicts that the resulting faired curves are separated by applying the damping of both modes will decrease at higher an appropriate weighing factor.

These results agree relatively well with the 1/A data and a mathematical speed.

extrapolation yields a critical speed of 560 knots.

Extrapolation of these frequency and l/Adata to predict incipient flutter and the critical speed may The measured values of damping coefficient not be done with absolute certainty. Definite indica- which were obtained once the modal frequencies had EQUIVALENT AIRSPEED KNOTS ts of Flutter Flight Tests FREQUENCY-RESPONSE MEASUREMENTS 0 100 200 300 40 0 500 600 700

EQUIVALENT AIRSPEED - KNOTS

Figure 9. Results of Flutter Flight Tests Frequency Response Measurements reflect thegradualdeteriorationof damp- been defined over a 300 knot span of airspeeds while the damping ing with airspeed as shown in Figure 10. The reduc- coefficients from decay measurements onlydecreased tion near the flutter speed, however, does not seem to by one-half. This variance of data may in part be ex- be compatible with the 1/A and the F/A curves where plained by the changes in mode shape with increases the stability had decreased to one-fourth its value in airspeed which effect the output o f stabilizer tip EQUIVALENT AIRSPEED KNOTS Figure 10. Results of Flutter Flight Tests Decay Measurements contains integral cylinders which are hydraulically accelerometers and by the possibility that the reson- actuated by an electro-hydraulic valve. The oscil- ate peaks m d frequencies were not always attained lation of the mass can be controlled both in frequency during the decay maneuvers.

and amplitude and programmed to any desired fre- quency sweep. In addition, a theoretical development A comparison of damping coefficient data ob- program has been undertaken using an analogue com- tained from aft stick jabs with the shaker excited decays showed that transient inputs were unable to puter that is set up to describe a discrete mass repre- sentation of an aircraft wing. Some objectives of this excite adequately the critical modes, yielded a great program are: deal of random scatter, and allowed no proper pre- diction of the critical speed. Even a roughextra- polation of the damping coefficients excited by the 1) To determine stability criterion which can transient induced oscillations would show a flutter be applied to subcritical response data and speed 5 a higher than that predicted from shaker de- extrapolated to predict critical speeds.

cays. In fact, a series of aft stick jabs was made prior to the initiation of this flutter program at 20,000 2) To examine physical behavior of a surface ft. and at 15 knot increments from 300 to 520 knots. in the vicinity of critical speeds in order to understand more fully the reasons for the These tests showed absolutely no evidence of impend- sudden decrease in damping for small ing flutter.

speedincreases.

The results of this F11F-1F flutter program 3) To evaluate the effects of configuration

> corroborated the theoretical calculations and iden-

changes.

tified as well as partially explained the mechanism of mode coupling. Since the restrictions imposed by Our experience from the F11F-1F and other the stabilizer oscillations do not hinder the F11F-1F flight test program, no major effort has been under- flutter programs has indicated that: taken to eliminate the problem. However, a simple change to the stabilizes yoke which increased the fore 1) A controlled well defined excitation force and aft stiffness and raised the second symmetric mode is necessary to permit a thorough evaluation 24.5 cps was flight tested. The results of all pertinent modes.

frequency to from this second series of flutter tests indicated that Incipient flutter may be predicted at sub- the critical speed of this configuration was substan- 2) critical speeds from the results of flight tially increased.

tests.

Certain limitations in the testing techniques and By the use of shaker excitationthree related data analysis were quite evident at the conclusion of 3) this flutter program. First, the means of determining indications of incipient flutter are readily available for rapid analysis. The first, the stability criteria are far from adequate and may be reduction of frequency ratio, and the second, classed as being part of the current state of the art; the decrease of 1/A and F/A, proved to be second, the methods of establishing adequate margins more effective than the third, the deteriora- from incipient flutter and predicting critical speeds tion of damping coefficient.

a r e rather difficult to define; third, the mechanics of exciting a structure at a desired resonate frequency needs improvement; and fourth, a single tail shaker 4) Telemetering flight data for analysis by does not excite all of the wing modes requiredfor ground personnel greatly reduces the time required to complete the tests, increases complete definition of the flutter spectrum.

the safety of the program, and permits a wide latitude of data processing techniques.

To overcome some of these limitations, we, at Grumman Aircraft, have developed a resonance de- The limitations and problems in the testing tector to obtain, automatically, excitation cut-offs at techniques and equipment realized at the conclusionof resonances that are determined during shaker fre- quency sweeps. This device will shut o f f the shaker the program are currently being investigated. Appro- for a predetermined interval at a prescribedresonate priate modifications to future flight flutter tests will be made based upon our findings, the experience of mode then will allow the shaker to continue the sweep others, and the information acquired at this sym- until a new resonance is excited. To excite wing modes posium.

more adequately a reciprocating mass shaker, three inches in depth has beendeveloped. The shaker weight G R O U N D VIBRATION T E S T I N G OF COMPLEX STRUCTURES C. V . Stable 6 W . R. Forlifer - T h e Martin Co., Bdtimore, Md.

Abstract of the predicted flutter behavior by establishing the accuracy of the calculated vibration modes and reso- Planning of flight flutter testing and interpreta- nant frequencies of the aircraft and are used for the tion of results require reliable information about interpretation of the flight flutter test results.

the ground vibration behavior of the aircraft. Con- ventional GVS techniques are unsatisfactory in that In the past, two methods have been used to internal damping and closeness of frequencies lead determine the vibration behavior of complex struc- to sensitivity of the measured frequencies and modes tures but neither is satisfactory. The first method at several points to the specific excitation points used. measures the response to excitation on the structure. Since the response of the Structure In fact, there is no unique definition of resonance using this method is a combination of all the struc- of a multi-degree-of -freedom structure having in- tural modes, it, is unsatisfactory in that the mode ternal damping. Following suggestions by DeVries, shapes and resonant frequencies depend on the ex- a method of measuring separately the in-phase and citation points selected. The other method uses a multiple Shaker system to separate the structural quadrature components of the vibration response, designed by APL, has been developed and applied. modes with excitation techniques. Because a large Both analysis and test results show immediately a number of exciting points a r e required and the in- much improved definition of mode shapes and fre- dividual exciting forces must be adjusted for each quencies. mode, this method is undesirable since it i s extreme- ly time consuming. When the structure being tested The approach has been further developed. It has resonant frequencies close together, the diffi- are magnified and a mode may be obscured and allows to measure damping in the different natural culties modes, and to determine the exact shape of the nor- lost. The need for a simple technique which permits mal modes, i.e., to eliminate the coupling effect due the accurate determination of the resonant frequen- to structural damping. It is expected to be used in cies, mode shapes, and modal damping coefficients flight flutter testing also. without utilizing complicated methods of excitation has been evident.

INTRODUCTION Our approach i s to measure quantities which decrease the effects of modal interaction and to The present paper presents a method for accur- analytically separate the modes of vibration from the ately determining the vibration characteristics of com- measured data. Hence, the vibration characteristics plex structures from test data obtained during a can be accurately determined with simple methods of excitation.

Ground Vibration Survey using only simple excitation techniques. The accurate measurement of the vibra- tion characteristics of an aircraft during a Ground The components of response in-phase and90" Vibration Survey is necessary for the planning of out-of-phase with the exciting force are used to de- flight flutter tests. These data provide the first check termine the resonant frequencies and damping coeffi- cients. Our analytical method separates the structural the by the dashed-dot line and can be measured with modes of vibration from the component of response Component Analyzer. The dashed lines represent the 90" out-of-phase with the exciting force when the quadrature response in each of the modes and the peak structural damping is small. Figure 1 illustrates the values when taken at a number of locations define the components of response and their relation to the mode shapes of the system. The negative quadra- ture response in the second mode is caused by a mode exciting force. The total response is defined a s the between the point of excitation and the point we are structural displacement per unit force. The total response can be resolved into a vector component considering. If we comparethe totalresponse with the in-phase with the force, the in-phase response, and quadrature response, it can be seen that the quadra- ture response determines more accurately the reso- the vector component 90" out-of-phase with the force, nant frequencies and mode shapes of the system. In the quadrature response. The representation of the fact, only one resonant frequency is apparent froin vibration response in this manner was suggested by the total response. Finally, we can analytically DeVries. (1) Kennedy and Pancu, (2)in a later paper utilized vector response to determine modal proper- separate the quadrature response at each resonant ties from polar plots. Theoretical calculations of frequency into the response of the resonant mode and Veubeke (3) indicated that the quadrature response the response of the non-resonant mode. Therefore, we can accurately determine the mode shapes.

determined more accurately the modes of vibrationof a uniform beam excited at a single point. A device In the body of this paper we will: which enables us to measure separately the in-phase and quadrature response, a Component Analyzer, was developed by Kearns of John Hopkins Applied Review the significance of the in-phase and 1) (4) The results of their inves- quadrature responses.

Physics Laboratory.

tigations are used as the basis of our method and its application to actual structures. 2) Present our method for analytically sepa- rating the modes of vibration from the quad- rature response.

The problem that concerns us and our method of solution are illustrated in Figure 2. This graph 3) Describe the Component Analyzer which we presents the frequency response at a particular point usedand the results of some of our labora- of a two degree of freedom system with resonant fre- tory tests.

quencies close together. This example has been selected to illustrate the problem which occurs often 4) Discuss the application of the Component in complex structures. The solid line represents the Analyzer to flight flutter testing.

total response which is the quantity generally meas- ured. The quadrature response of the system is shown

D E ~ ~ N I T I O ~ OF IN-PHASE 6 q~ADRATURE RES

IN-PHASE RESPONSE FORCE

QUADRATURE

RESPONSE

TOTAL RESPONSE

x

IFI

Figure 1. Definition of In-Phase and Quadrature Response

TOTAL REPONS

RESPONSE

INCHES/1000 LB QUADRATURE RۤPONSE I N MODE I

I

-I IN MO

t - - ~ U A D R A T U ~ ~ RESPON

Figure 2. Theoretical Response of Two-Degree-of-Freedom System with Resonant Frequencies Close Together SIGNIFICANCE OF THE IN-PHASE If there is more than one degree of freedom, the AND QUADRATURE RESPONSE response of the structure will be the sum of the re- sponses in each of the modes. This implies that each First we will review the significance of in-phase mode will retain the response characteristics of a and quadrature response for a single degree of freedom single degree of freedom. However, we canno longer system. Then we will consider more degrees of define resonance of the system by a 90' phase relation- ship between the total response and the exciting force freedom. When the structural damping is small, we can represent the forced response of a single or by the maximum total response. The peaks of the degree of freedom system by equation (1) of Figure 3 quadrature response will determine the resonant fre- where R is the total response at any frequency, quency and response of each mode more accurately R* is the total response at resonance, g is the struc- than the total response since the quadrature response tural damping coefficient, o is the exciting frequen- of each mode peaks more sharply and the quadrature cy, and uN is the resonant frequency. The real and response contributions of non-resonant modes are imaginary terms are the in-phase and quadrature smaller. Although the non-resonant modes effect the response, respectively. The frequency variations of in-phase response more than the quadrature response, the total, in-phase, and quadrature responses are also we can still use equation (2) to determine the damping shown in Figure 3. Note that the shape of each curve if we select a point such that the response is pre- is completely determined by the resonant frequency dominantly t h a t of the mode of interest. Damping can and damping coefficient. We can use the frequencies be determined by this method under conditions where at which the in-phase response peaks and up, the decay of the total response fails to give valid re- to determine the structural damping coefficient from sults. Although the mode shape which we obtain from equation (2). For this single degree of freedom sys- the quadrature response will be more accurate than tem, resonance is defined mum total response that of the total response, it will be necessaryto and a 90" phase relations tween the total re- separate the quadrature response into the response sponse and exciting force. This is indicated by equal mode when the structure has resonant fre- peak values of the total and quadrature responses quencies close together.

with zero in-phase response.

T GR€E OF F R E E ~ O ~

D

Figure 3. Theoretical Response of a Single Degree of Freedom System with Structural Damping ANALYTICAL SEPARATION OF MODES sponses. Figure 4 shows the equations which we ob- tain for this two degree of freedom system. RQ1 is Our method of analytically separating the modes the measured quadrature response at the resonant of vibration from the quadrature response, is pre- frequency of the first mode, FQ2 is the measured sented below. We will refer again to Figure 2 t o ex- as applied to plain our method of analytical separation the two degrees of freedom system. The modal re- E Q U A T I O N S FOR M O D A L RESPONSES FOR sponses are indicated by the dashed lines and define TWO-DEGREE-OF-FREEDOM S Y S T E M the mode shapes of the structure. First, we will ob-

RQ, =

W'WN,

4 2 =

w"wNZ Figure 4. Equations for Modal Responses for solved for the peak amplitude of eachof the modal re- Two-Degree-of -Freedom System Our analytical method is easily applied since the quadrature response at the resonant frequency of the inverted matrix, , is the same for all locations.

second mode. R1* and R2* are the maximum modal Hence, the modal responses at all locations can be responses in each of the modes which determine the These are found from found by a simple matrix multiplication once the mode shapes of the system.

[AI-' matrix has been determined. It will be noted the solution of the equations. Effectively, the equa- tions eliminate the response of the non-resonant modes that only the test data normally required is used for caused by the structural damping. the application of our analytical method; that is, the resonant frequencies, the mode shapes at each res- The extension of our method of separation to onant frequency and the modal damping coefficients.

more degrees of freedom can easily be seen. For n degrees of freedom, there will be n simultaneous equations which can be solvent for the n modal re- sponses. The ease of application of our analytical COMPONENT ANALYZER method can be seen by expressing the equations i n matrix form. We now proceed with the third point of the dis- cussion, the description of the Component Analyzer and the results of some of our laboratory tests. To apply our method to the tests which we performed, we where { R ~ } is the column matrix of the meas- used a Component Analyzer which measures separate- ured quadrature response at each ly the in-phase and quadrature response. Figure 5 is re sonant frequency.

block diagram of our Component Analyzer. It con- sists of an undamped strain gage accelerometer [ A ] is a square matrix determined by powered by the exciting force signal. Our Component the modal damping coefficients and Analyzer differs from that of Kearns in that the actual the resonant frequencies.

is used where Kearns used the exciting force signal current of an electro-magnetic shaker. This modifi- { R = } is a column matrix of modal re- cation was necessary since the inertia and spring sponses.

force of the shaker armature can cause large phase shifts between the armature current and the force Transposing, we write the equation in the de- applied to the structure particularly at resonance.

sired form: The accelerometer was undamped to eliminate phase { R " } = [ A ] - ' { R g } shifts in the transducer. When the in-phase response

~ O ~ P O N E N T ANALYZER

-

AMP LI F I ER

ACC~LERAT~ON = A, SIN ( W t +-@

I N -PHASE

UNDAMPED RESPONSE

c /

A C ~ E L E ~ O M E T E R

/ / I , I

4 AMPLIFIER r , , d ~ d

PHASE

I S H I F ~ E R I

QUADRATURE

RESPONSE

Figure 5. Component Analyzer a7 the peak responses, variation in amplitudes, and causes is measured, the force signal, F, SIN t isampli- fied and applied to the accelerometer. The acceler- oscillations in the response. These curves are based on the theoretical results of Hok (6) which were ob- ometer multiplies the force signal and the acceleration, A SIN (wt + $) with the steady componentof the out- tained for electrical circuits and agree qualitatively with those observed during tests.

put, 1/2 A, F , COS $ being proportional to the in- parts of the signal phase response. The oscillatory are filtered out and the steady signal recorded. In the EXPERIMENTAL RESULTS FROM TESTS same manner, we obtain the quadrature response by shifting the phase of the force signal 90" before applying it to the accelerometer. Since the electrical signal from the Component Analyzer is not oscillatory, Although we have used this technique for Ground it can be applied to recording equipment such as an Vibration Tests of the YPGM, we will confine our dis- cussion to results obtained from laboratory tests. We x-y plotter o r an array of vertical deflectinggalvano- will describe the results we obtained from tests on a meters providing immediate records of frequency two degree of freedom system with resonant frequen- response and mode shape. The use of the accelero- cies close together. The system on which our tests meter in this manner provides a measurement of the were conducted is shown in Figure 7, a rigid beam response only at the frequency of excitation. (5) The block diagram indicates the simplicity of the Com- mounted on rubber vibration isolators at the approx- imate radius of gyration. The resonant frequencies of ponent Analyzer.

the beam on the isolators, rigid translation and pitch about the center, were close together. We applied One parameter which can cause considerable excitation at a single point slightly o f f the center of error in the Component Analyzer measurements is the beam. The total, in-phase, and quadrature re- the rate of change of excitation frequency, the sweep sponse at each end and the center of the beam were rate. The effect of sweep on the in-phase and quadra- first mode at 16.9 cps is the trans- ture response is much greater than the effect on total measured. The rate on lation mode. The mode shape determined from the response. Figure 6 shows the effect of sweep total response is indicated by the solid line. The mode the quadrature and in-phase velocity responses of a shape obtained from the quadrature response i s shown typical single degree of freedom system. The dashed by the dashed-dot line and the mode shape obtained lines represent the steady state response and the solid from the analytical separation of the modes by the lines represent the swept responses with increasing dashed line. The translation mode shapes obtained frequency. Sweep causes a shift in the frequencies of Figure 6. Effect of Sweep Rate on In-Phase and Quadrature Velocity Responses

TEST RESULTS FOR ~ ~ O - D ~ ~ R E E - ~ - F R E E D O M

S Y S T E M WITH RESONANT FREQUENCIES

CLOSE TOGETHER

RUBBER MOUNT MOUNT

TRANSLATION MODE

RESPONSE ONs16.9 CPS

g = 0.097

INCHES/IOOO LB

x-x TOTAL RESPONSE

0---0

QUADRATURE RESPONSE

--- -v ANALYTICALLY SEPARATED

QUADRATURE RESPONSE

RESPONSE

PITCH MODE ---

WN=18.6 CPS

g=0.053

Figure 7. Test Results for Two-Degree-of-Freedom System with Resonant Frequencies Close Together with the various techniques are practically the same. ent from the total response. Figure 2 which was dis- The slight pitch in the mode shapes was caused by a cussed before shows the theoretical response at this point. The measured and theoretical responses are in lack of symmetry in the beam and mounts, that is, the very close agreement. In addition, the values of the beam was not uniform and the mounts were not equal- re- ly stiff. However, the mode shapes obtained for the damping coefficients obtained from the in-phase pitch mode at 1 8 . 6 cps are substantially different. sponse agree within 5 percent with those measured Since the excitation was applied near the mode of the from the decay of the total response.

pitch mode, the response in the translation mode w a s sufficiently large to distort the pitch mode. It is barely recognizable from the total response but be- APPLICATION TO FLIGHT FLUTTER TESTING gins to take form when determined from the quadra- ture response. The mode shape which we obtain from our method of analytical separation agrees almost The fourth and last point of thepaper, the appli- exactly with the predicted mode shape (a straight line cation of the Component Analyzer to flight flutter test- through the center of the beam). ing, will now be presented. ,The Component Analyzer has one intrinsic property which makes it particular- If we compare the quadrature and total responses ly suited to flight flutter testing with sinusoidal exci- in the pitch mode at the end of the beam farthest away tation. The Component Analyzer measures only the component of response at the excitation frequency from the shaker, we see that the total response does either in-phase or 90" out-of-plhse with the exciting not indicate the node line but the quadrature response does. Figure 8 shows the measured quadrature and force. Therefore, the response caused by atmospheric total responses at this point. We have already demon- turbulence, which has been a problem in the past, strated the improvement in mode shape. Now let us will have a substantially decreased effect on the re- consider the resonant frequencies indicated by the sponse measured with the Component Analyzer. A measurements. The frequency of the translation mode procedure which might be suggested is to use the Com- indicated by the quadrature response differs only ponent Analyzer with the usual sweep technique of slightly from the actual frequency of 1 6 . 9 cps. The excitation. This procedure, however, has an unde- rate would be total response, however, indicates a resonant fre- sirable feature since a very slow sweep quency of 17.15 cps, a shift of 1/4 cps. The resonant required to obtain accurate measurements, a s we have frequency of the pitch mode indicated by the quadra- pointed out earlier. A technique which would elim- ture response is 18.65 cps a shift of only . 0 5 of a cps. inate the undesirable feature would be to slave the The resonant frequency of the pitch mode is not appar- exciter frequency to the resonant frequency of the I I ITCH I I I I I

F R E Q U E N C Y -CPS

Figure 8. Measured Response at Far End of Beam The variation of mode which we want to investigate. REFERENCES the quadrature response with aircraft velocity will be observed; an increase in this response amplitude with

1 . G. De Vries - Beitrag zur Bestimmung der

increasing flight speed will indicate approach to flutter.

Schwingungseigenschaften von Flugzeugen im Standversuch untqr Besonderer Beruecksichtigung In the procedure just discussed, each mode has eines neuen Verfahrens zur Phasenmessung,” to be investigated separately. A possible extension of Z W B, Forschungs Bericht, No. 1882, 1942, p.115 this technique is to investigate several modes simul- taneously. One exciter and one Component Analyzer

2 . Kennedy and Pancu - U s e of Vectors in Vibration

for each mode has to be provided. Since each Com- Measurement and Analysis Journal of the Aero- ponent Analyzer responds only to its specific excita- nautical Sciences - Vol. 14 No. 11, pp. 603-625.

tion, several modes may be investigated simultaneous-

3. B. M. J. DeVeubeke - AVariational Approachto

ly.

Pure Mode Excitation Based on Characteristic - AGARD Report 39 - April 1956.

Phase Lag Theory CONCLUSION

4 . J. P. Kearns - Development and Use of a Device

The results of our tests indicate an immediate for the Measurement of Structural Vibration Re- marked improvement in the determination of the

sponse Components - Proceedings of the Instrument

vibration characteristics without the use of com- Society of America - Vol. 11, 1956.

plicated methods of excitation. Analytical separation of the quadrature responses of the several structural 5 . J. J. Earshen -ANew Method for Measuring Phase modes yields a further improvement when the struc- and Amplitude Response of Physical Systems Using ture has resonant frequencies close together. Bridge Connected Transducers - Proceedings of National Electronic Conference - Vol. 13.

A procedure for extending the present technique to flight flutter testing has also been suggested. This 6. G. Hok - Response of Linear Resonant Systems to procedure would decrease the effects of atmospheric Excitation of a Frequency Varying Linearly with turbulence; it might also be possible to eliminate the Time - Journal of Applied Physics, Vol. 19 No. 3 errors caused by a finite sweep rate. pp. 242-250.

FLIGHT FLUTTER T E S T I N G OF T H E P6M G. Kuchudowian, R. L. Goldman, D. M . Rohu - T h e Martin Co., Baltimore, Md.

Abstract On the P6M the shake behavior, i.e., the re- sponse to random excitation at subcritical speeds of lowly damped airplane modes, is as important a s the actual flutter speed, The approach is to first study the problem by means of analyses and wind-tunnel tests. With these predictions are compared flight test data obtained by spectral analysis of tape re- cordings of the airplane vibration responses to ran- dom aerodynamic turbulence.

A similar spectrum analysis approach has been used in high speed wind-tunnel tests. Furthermore, a resonance excitation technique has been developed for low speed wind-tunnel testing, and surprisingly well defined V-g curves have been obtained. The effect of various parameters on both shake and flutter of T-tails with and without dihedral have been studied.

Figure 1. Martin P6M "SEAMASTER" Preliminary flight tests yielded good correla- tion; they also yielded interesting information con- cerning a low frequency transonic snaking mode and degrees of freedom). Also, the swept back wings, concerning excitation by shed vortices. as might be expected, introduce flexibility and there- fore additional degrees of freedom to the dynamics behavior problem.

The approach to the problem of predicting the INTRODUCTION dynamic behavior of the P 6 M has been to use the standard flutter tools, Analysis, Model Test, and The P6M is a large four jet seaplane whose Flight Test. Since it would be dangerous not to know development provides a new weapons concept for the an aircraft's basic dynamic behavior prior to flight naval aviator. For the flutter engineer, however, test, we first studied the problem by analysis and in it introduces an aero-elastic problem that is fairly wind tunnel tests. The results predicted that the aircraft would be flutter free within the designed typical for most modern large scale aircraft. Looking flight envelope. During the current flight flutter at a picture of the P6M, Figure 1, we see, for in- stance, that the T-tail stabilizer sits on the tip of a test program we are, therefore, only concerned with tall, flexible, swept back fin which in turn is attached checking these predictions and determining whether to a long, slender, flexible hull (a system with many the aircraft behaves in any unusual manner.

In carrying out this approach we have developed V-SPEED - - B both a specific and a random excitation technique for obtaining experimental data. A specific resonance

,J /*q- MODE E

excitation technique was developed for use in low- speed wind tunnel tests, and a random excitation tech- nique was developed for flight flutter testing after earlier investigations in a high-speed wind tunnel.

This random excitation method, as will be shown later, is a technique involving spectral analysis of aircraft response to aerodynamic turbulence and has proven so far to be a reliable approach to our sub- critical investigations of the P6M.

MODE I

\&

Past experience on large flexible aircraft has shown that of equal importance as the prediction of Figure 2. Incompressible P6M T-Tail Analysis the flutter speed itself is the determination of the aircraft's sub-critical behavior. A large aircraft therefore not indicated on the plot. Mode 111, how- usually has vibration modes that are lowly damped ever, is one of the previously mentioned lowly at sub-critical speeds; this lowly damped sub-criti- damped modes. Mode III, as shown in Figure 2, cal response, although it is not immediately dangerous, stays close to the zero damping axis throughout the can limit both the life of the aircraft and its accepti- usable flight range. The illustration also shows bility.

that Mode I I I is characterized by a stabilizer yawing motion. Mode I (Figure 2) bears further considera- On the P6M it became apparent, through early tion, although this mode (hull lateral bending mode) is analysis and model tests and from early flight tests highly damped in this incompressible analysis it on a previous model, that the response of lowly suffers from the common transonic "snaking" inst- damped modes to random excitation at sub-critical bility and becomes lowly damped in the compressible speeds would be as important as the actual flutter analysis. (Reference 1).

speed. Changes were incorporated in the present P6M configuration to control the sub-critical behavior In order to provide quantitative correlation with and one purpose of the current flight flutter tests is the analysis, the usual series of flutter model tests, to check whether these changes are as effective as both low and high-speed, were undertaken. (Reference predicted.

1) The low-speed tests included tests of complete and empennage models while the high-speed testswere SUB-CRITICAL BEHAVIOR concerned only with empennage models.

Before proceeding, let me establish what we tests, a specific For the low-speed wind tunnel mean in the analytical sense by the phrase "lowly resonance excitation technique was developed for damped, sub-critical behavior . I t In typical V-g obtaining in-flight or more accurately tunnel flight plots, the lowly damped mode is characterized by damping information. (Reference 3) This technique a curve which runs relatively close to the zero incorporates the system of strings, springs, and damping axis. Such modes are susceptible to at- pulleys shown in Figure 3. By pulling on the control mospheric turbulence and if they are predominantly handle and varying the motor speed the model could tail modes they are continuously excited by turbulent its resonant modes at any one be excited in any of flow from the wing-engine area. When the excitation selected tunnel speed. The control handle was sharply band is broad enough and strong enough, all such modes are continuously excited and aircraft response can become large.

ANALYSIS ON THE P6M Turning now to the flutter analysis of the P6M, 2, we see a typical V-g plot based on an in Figure I incompressible analysis of the ship's T-tail. (Ref- TO erence 1) This analysis includes five degrees of P freedom, three of which are shown here, and takes into account the effects of sweep and the well-known detrimental effect of stabilizer dihedral for T-tails, Mode 1 1 , (Reference 2) the flutter mode, rises sud- denly from a highly damped condition to the flutter speed. This mode, a s shown here in the illustration is characterized by a stabilizer rolling or rocking Figure 3. Specific Resonance Excitation System motion. Modes Iv and V are all highly damped and M O D E 1 M O D E I I M O M --ZERO AIRSPEED released when the selected mode was at resonance.

I I I FUEQ

This removed the excitation force and permitted the motion to damp out. These damped motions were recorded and the logarithmic decriments of decay were then calculated for each mode. 10 RESPONSE By using this simple method, the damping in

AMPLITUM $

all the modes was measured at one tunnel speed and well defined experimental V-g curves of the type I shown in Figure 4 were quickly obtained. Figure 4 also indicates the analytical plot for comparison.

I Again we see the flutter mode 1 1 which is highly

FREQUENCY (CPS) -

damped but rises sharply to the critical speed. The Figure 5. Spectrum Analysis o f Flutter Model analysis to test comparison indicates some conserva- Response in High Speed Wind Tunnel tism in the analysis. Mode 1 1 1 as predicted in the analysis is lowly damped and in the peak area it w a s During the high-speed wind tunnel tests the exis- susceptible to tunnel turbulence.

tance of the lowly damped %naking" mode I was also experimentally verified. This low-frequency hull During the high-speed wind tunnel tests, mode lateral bending mode did not appear in the low-speed 1 1 was also found to be the flutter mode. In this case, tests but showed up a s expected inthe transonic range it was not possible to obtain sub-critical however, of the high-speed tests.

damping information through use of any of the usual specific excitation techniques. Instead strain gage RANDOM EXCITATION FLIGHT FLUTTER responses to tunnel turbulence were recorded on tape TESTING ON THE P6M for a few runs and analyzed. In Figure 5 we see a composite of the spectral analysis for these runs From the proceeding analysis and model tests, at several Mach numbers less than the flutter Mach the basic behavior of the aircraft was rather well number. The amplitude and width of the peaks known. Now we are only interested in checking these give some indication of the variation of damping in predictions, expecially, the "sub-critical behavior," the flutter mode a s the f1utte.r speed is approached.

by flight flutter testing. To do this a random exci- This type of analysis has a distinct advantage in that tation method was developed involving spectral anal- it makes use of a type of random excitation (tunnel it is to this to?ic that I ysis of aircraft response, and turbulence) that is always present in tunnel testing.

shall devote the remaining part of the paper.

This method is being further developed and it is planned to obtain quantitative evaluation of the tech- Normally, flight flutter testing employs methods nique in a forthcoming development program.

which require specific excitationtechniques using such devices a s control s u r f a c e s, explosive charges, shakers and so forth. (Reference 4) The limitations of these specific excitation methods center around SPEED rapid data evaluation and high costs for equipment, ever, is that flights have to be made specifically for the purpose of flight flutter testing.

The random excitation method a s applied to the P6M appears to us to overcome many of thesedif- ficulties. Random excitation as a vibration source is not a new concept but in fact has been suggested as an approach to this problem for some time. (Ref- erence 5) Today, with the use of efficient tape re- STRUCTURAL cording systems and corresponding spectrum ana-

DAMPING - 9

lyzers, this technique becomes fairly attractive. In fact, from our most recent results it appears to be a relatively inexpensive technique that gives results that are a s reliable a s those obtained using other more expensive and complicated methods. Of parti- cular importance is the fact that data canbe collected from every flight test run without resorting to special flights.

The technique takes advantage of atmospheric turbulence a s a source of random excitation. The "hash*' usually associated with normal flight response Figure 4. Experimental V-g Plot records comes primarily from this turbulence. In In practice this procedure is not so simple.

the past it was advantageous to get rid of this re- sponse by performing tests in turbulent free air. In The actual turbulence spectrum on the aircraft is modified by buffeting and flow separation, the tur- the random excitation method this "hash" is recorded bulence level can vary greatly in a normal flight and analyzed.

and in addition local resonances can confuse the meas- THEORETICAL RESPONSE O F AN AIRCRAFT urements.

TO ATMOSPHERIC TURBULENCE P6M FLIGHT TESTS Theoretically the procedure involves correla- tion of power spectrums of turbulence and power Because of these difficulties the random exci- spectrums of response at a given air speed and alti- tation method used on the P6M lacks the exactness tude. This process is illustrated in Figure 6. The required by the theoretical approach and instead con- input power spectrum of atmospheric turbulence, centrates on the spectral analysis of the response in-

$ ( w ) , a s derived by several authors (Reference 6

By analyzing the data from many formation alone.

and 7) using a statistical approach, is a function of a runs it is possible to minimize the effects of varia-

turbulence level L, airspeed U and frequency o . The

tions in turbulence and obtain a clear picture of the output power spectrums of aircraft response, $(a) , aircraft's behavior.

are easily obtained from analysis of accelerometer tape recordings. By taking the ratio of the output An early approach to this random excitation curve to the input curve, the square of the mechanical method of flight testing was used on a previous model admittance o r transfer function, fi21w) , is obtained.

P6M and involved a simplified harmonic analysis The admittance term is an indication of the energy of oscillograph records of aircraft flight response.

passing from the input to the output response and A particular investigation into transonic vrsnakingv9 on therefore is proportional to damping. The lower the this ship yielded significant results a s shown in At the response damping the larger the admittance.

Here the average response in a given fre- Figure 7.

peaks, the admittance terms are therefore a measure quency range 2.5 cps, is plotted against Mach number of the modal in-flight damping. By plotting the modal for different altitudes, and clearly shows a transonic admittance terms for several aircraft speeds it is "snakingv' boundary. On the basis of such information theoretically possible to obtain an indication of the it became possible to eliminate the vlsnaking"problem approach of flutter o r a measure of the sub-critical on the present model of the P6M.

behavior.

An improved random excitation technique has been developec! for the present P6M flight test pro- INPUT SPECTRUM

h

gram for the evaluation of all sub-critical behavior.

The limited results obtained so far have yielded good correlation with Analysis and Model Tests.

The technique involves spectral analysis of air- craft acceleration responses and is illustrated in ATMOSPHERIC TURBULENCE Figure 8. Accelerometer responses are telemetered to the ground where they are visually monitored and

L

w - recorded on tape. The frequencies are first increased I up to 16 times to provide longer sampling times and

1 20,000'ALT f

AMPLITUDE .

uJ+ I

l2,OOO'ALT / - 7

OUTPUT SPECTRUM

L

~I i. 30,OOO'ALl

MACH NO. -

'' ~ TRANSONIC

I 0- Figure 6. Theoretical Aircraft Response to Figure 7 . Transonic Snaking Response Atmospheric Turbulence ACCELEROMETER 5 RECORDER TRANSMITTER

-0 FILTER

U LOG

TIME : 2S:OO - 26 :OO MIN

CONVERTER x-Y

2 R D CYCLE FLT. 5-1 '/29

D ANALYZER

RECORDER

R. WING TIP - VERTICAL

PLAY BACK

I

.12

IO

.08

SPECTRAL ANAlY SIS SYSTEM . o ,

O N THE P6M t , ?06

$ .04

* O 2 * 0 w

Figure 8. Spectral Analysis System on the P6M easier handling by the available playback systems. The This gives us a large statistical source fromwhich to output is then placed on a continuous loop and detected obtain an average response.

on an Ampex record playback unit.

this store of information, a turbulence To unify factor, based on the rigid body response, is determined This signal i s then fed into a Technical Products for each run and the plots normalized to a unit rigid Wave Analyzer. This analyzer determines the ampli- body response level. By statistically integrating these tude and frequency of the complex wave input within normalized results, we obtain cross plots of responses the desired frequency range. These data are then i n each mode for various altitudes, speeds, and con- processed through a band pass filter and a log con- figurations. These plots yield the information neces- verter, and plotted on an X-Y recorder. Thus the sary to establish the dynamic behavior and the effec- tape loop is automatically scanned and a plot of the tiveness of changes designed to improve the in-flight mean RMS acceleration amplitude versus frequency damping.

is obtained as shown. In Figure 8 we see a completed analysis for one-minute of flight time at aconstant speed and altitude. The peaks coincide with the air- CONCLUSION craft vibration modes.

To date the amount of data analyzed has not been large enough to either prove o r disprove the As stated before only the response data are adequacy of this technique for flight flutter testing.

evaluated; no correlation of these plots with a specific We are presently analyzing several flights inorder turbulence input has been tried because of our in- to determine the repeatibility and clarity of the ability to represent the actual turbulence. T h i s does spectral plots. The method, although it still has some not lead to any difficulty, however, since information developmental problems, appears to offer the flutter I s obtained every minute while the aircraft i s flying.

engineer several attractive advantages, foremost of 2. Goldman, R. L. Flutter of T-tails with Dihedral- which is the fact that every minute of flight time Martin Engineering Report No. 8205, 1957.

yields dynamics information without the necessity for the conduct of special test flights for flutter.

3. Goldman, R. L. XPGM-1 T-tail Flutter Model Low

Speed Tests with Revised Fin Stiffness - Martin

The combination of analysis and model tests Engineering Report 9086 (Confidential), 1957.

has proven to be a good approach to sub-critical investigations on the P6M. In particular, a specific 4. Schwartz, M. D. Investigation of Flight Flutter resonance excitation method has been developed for Testing Techniques, -MIT, Aeroelastic and Struc- low-speed wind tunnel tests that yields damping in- tures Research Laboratory Report, 1951.

formation in all the modes at one tunnel speed. When this information is coupled with the random excitation

5. Bisplinghoff, R. L., Ashley, H., Halfman, R. L. -

technique of flight flutter testing, a means of correla- Aeroelasticity - Addison - Wesley Publishing Co., tion is provided that is more simple and apparently 1955.

a s accurate as any of the many more expensive and complicated techniques in use at the present time. 6. Liepmann, H. W. - On the Application of Statisti-

cal Concepts to the Buffeting Problem - Journal

of the Aeronautical Sciences, 1952.

References

7. Press, H. and Houbolt, J. C. - Some Applications

of Generalized Harmonic Analysis to Gust Loads 1. Tomassoni, J. and O'Hearne, C. Vibration and

-

Flutter Studies Models YP6M-1 and P6M-2 on Airplanes -Journal of the Aeronautical Sciences, Martin Engineering Repoi t No. 9204 Volume I-II7 1954.

(Confidential) 19 57.

T R A N S I E N T FLIGHT FLUTTER T E S T OF A WING W I T H T I P T A N K S R. J . Werdes - McDonnell Aircraft Corporation, St. Lozlis, Missozlri Abstract Wing flutter was encountered during flight test- ing of the F2H-2 airplane with full wing tip tanks.

A s a result, more refined theoretical analysis as well as flight flutter tests were initated to establish cor- rective measures and to experimentally verify the stability of the improved system. The results from the flight flutter tests, utilizing the transient response technique, are presented. The method of excitation consisted of abrupt deflections of the ailerons result- ing from %tick bangs" and data were measured by wing tip accelerometers.

Figure 1. McDonnell Model F2H-2 with 200 Gallon Wing Tip Tanks A comparison of the results with theoretical pre- is presented and indicates that reasonably dictions good correlation was obtained. The influence on wing For flight testing the aeroelastic properties flutter of tip tank fuel transfer cycle, which was in- two accelerometers were installed in each corporated to control the center of gravity range of of the wing, the tank during defueling, is indicated by the measured wing tip, one located forward and one aft a s shown results and compared with the theory. The final in Figure 2. The outputs from these accelerometers configuration utilized a transfer cycle which w a s were recorded on an oscillograph. By comparison proven stable as a result of flight flutter testing. It of the magnitude and phase of the various records, wing motion could be identified as symmetrical or is concluded that transient response measurements asymmetrical, and some idea of the magnitude of resulting from stick bangs provide a reasonably re- at the wing tip could be deter- liable and safe technique of flight flutter testing for bending and torsion wings wrth external tanks or heavy stores. mined.

The means of excitation - of inducing oscilla-

tions of the wing - was provided by the pilot. An

INTRODUCTION asymmetrical pulse was induced by a sharp lateral blow on the control column by the pilot's fist. A The Model F2H-2 Airplane is a single place, symmetrical pulse was induced in the same manner carrier-based, two-engine jet fighter. Its gross weight by the pilot striking the control column forward or is approximately 20,000 pounds and it was designed aft. The. pilot excited the system by these "stick to fly in the high subsonic region. All controls are bangs" at each small increment in speed for a con- manual except for the power-boosted ailerons. It stant fuel loading condition, or at each small incre- differs from its predecessor, the F2H-1, in that it mental change in fuel loading for a constant speed carries 200-gallon fuel tanks on each wing tip. condition.

Figure 3. 200 Gallon Wing Tip Tank Geometry Showing Compartments nearly neutrally stable for several tip tank fuel con- ditions during initial flight flutter testing.

Figure 2. Three View F2H-2 The empty tank was the first configuration to be tested. Adequate stability was demonstrated and Since the rate of transition from a stable to an is seen in Figure 4 to be in fair agreement with the unstable condition with increase in speed was quite results of theoretical analysis which are also shown.

low, as predicted by the initial theoretical analysis, All theoretical results are based on the use of in- this was considered to be a reasonably safe technique.

compressible flow three -dimensional strip theory and were conducted for the test altitude of 10,000 feet.

The oscillograph records obtained in this fashion The aerodynamic properties of the tip tank were rep- were analyzed to establish the rate of decay, fre- resented by an equivalent rectangle which produced quency, and mode of the wing oscillatory motion, the same steady aerodynamic force and moment co- as a means of defining the wing aeroelastic stability. efficients relative to the wing elastic axis as deter- Most of the flight testing was performed at approxi- mined by wind tunnel tests. Fuel was considered as 10,000 feet altitude in order to test to the a solid mass.

mately highest q possible for this Mach number limited air- plane.

DISCUSSION Prior to the flight of the production model of the F2H-2, its prototype, the XF2H-1, modified to carry 200-gallon wing tip tanks having slightly smaller diameter and slighly greater length, had been thor- oughly flight tested and had demonstrated adequate aeroelastic stability for all tank fuel contents from full to empty. Because of this, no problem areas were anticipated for the F2H-2 configuration, the two airplanes being considered fairly similar dynamically.

as well as for the Each tip tank for the F2H-2, XF2H-1, was divided into three compartments as shown in Figure 3, and by means of internal plumbing was defueled in a forward-aft-center (F-A-C) se- quence by means of pressurized air. This defueling Figure 4. Flight Test Correlation Empty Tip Tanks sequence was selected since it kept the tank center Fwd Tank Fitting Preloaded of gravity travel at a minimum, generally in a for- ward location with respect to the wing elastic axis The next fuel configuration tested was the full which vias considered stabilizing, and did not impose tank. Near neutral stability was encountered at 450 maneuvering load restrictions on the airplane.

knots equivalent airspeed in the asymmetric mode.

Because the symmetric wing mode exhibited It can be seen in Figure 5 that the test points show extremely good aeroelastic stability properties for less stability than the theory at the higher speed end.

all tip tank fuel conditions, the following discussion is This i s probably due to the system being so nearly confined to the asymmetric wing mode which became neutrally stable that any external disturbance would quency. The minimum point is associated with a ratio of wing torsion frequency to wing asymmetrical bending frequency equal to one. A comparison of the operating conditions of the XF2H-1 and F2H-2 Air- planes in Figure 6 shows clearly why near-neutral stability was encountered at 450 knots equivalent airspeed for the F2H-2 while the XF2H-1 was ade- quately stable. One means of improving the F2H-2 stability is also indicated here. If the wing torsional frequency could be reduced in some way, it would approach the more stable XF2H-1 operating condi- tion. This, as will be seen, is exactly what was done.

Tests were conducted to compare the tank-to- wing attachment stiffnesses of the F2H-2 and XF2H-1 Airplanes and the forward attachment of the F2H-2 Figure 5. Flight Test Correlation Full Wing Tip was found to be much stiffer than that of the XF2H-1.

Tanks Fwd Tank Fitting Preloaded By rigghg the forward tank-to-wing attachment, rep- resented schematically in Figure ?, so as to permit some motion between the upper ball-socket arrange- necessarily be amplified under this condition. The ment which had previously been pre-loaded to an is the result of an extensive pro- theory shown here equivalent of 3 g's normal force on the tank, the stiff- gram of ground testing and a prodigious amount of ness contribution of the attachment was effectively theoretical analysis which was initiated subsequent reduced.

to this incident and which continued during and after the flight testing program had been concluded.

In examining the flight test results for the F2H-2 and the XF2H-1 Airplanes with full and empty tip tanks, it was noted that the frequency of the critical asymmetrical mode was ten to fifteen percent higher for the F2H-2 Airplane than for the XF2H-1 Air- plane. A similar difference was noted during the ground vibration tests, but the full significance of this difference was not indicated by the relatively limited theoretical analysis for the XF2H-1 Air- plane.

When more extensive analyses were conducted Figure 7. Schematic Diagram of Forward Wing-to- for the F2H-2 Airplane and the effect of a wide vari- Tank Attachment Fitting ation in wing torsional frequency was studied, the primary difficulty was uncovered. A s shown in Figure The system, so modified, was flight tested and 6, a region of relatively low flutter speed is en- with adequate looseness in the forward fitting as countered for certain values of wing torsional fre- established by trial, proved to be a satisfactory configuration. A comparison of experimental and is theoretical flutter stability for this configuration shown in Figure 8. It was found that the frequency of the critical mode which had been theoretically shown to be proportional to the wing torsional fre- quency, had decreased by 12 to 15 percent a s a re- sult of loosening the forward fitting. This effect can by a comparison of Figures 5 and 8.

be seen Having improved the full tank stability suffici- ently, testing was continued at gradually increasing speeds, with the tank fuel decreasing from full to empty at each speed. At 450 knots equivalent air- speed, a condition of low damping was foundfor a fuel is content of from 150 to 120 gallons. This region shown by theory in Figure 9. Figure 10 shows a Figure 6. Stability Diagram for Full Tip Tank Config- "slice" taken through Figure 9 where the variation uration of XFIH-1 and Original F2H-2 Airplanes of damping with minutes of fuel transfer measured Figure 8. Flight Test Correlation Full Wing Tip Tanks Fwd Tank Fitting Loose Figure 1 0 . Correlation of Flight Test Data Logarith-

-

mic Decrement Versus Minutes of Fuel Transfer Cycle F-A-C Ve= 464 Knots EAS for a flight velocity of 465 knots is compared with theoretical results. Good correlation i s seen to greater than unity (1.44). It follows, then, that some- exist. (It might be mentioned here that it took about where along the fuel transfer cycle, the operating 27 or 28 minutes to transfer the 200 gallons of fuel frequency ratio must approach and pass through a from each tank.)

value of unity, traversing the characteristic dip in the stability boundary. Whether o r not this results in an unsatisfactory condition depends on the value of the minimum velocity of the dip.

It was found from theoretical analysis that the minimum velocities of the dip in the stability bound- ary were lower in the early stages of the fuel transfer

cycle - when the tip tanks contained a large quantity

of fuel - than in the latter stages of the fuel cycle.

This indicated the desirability of making the trans-

ition through the critical frequency - which was un-

avoidable - late ih the cycle when the tip tanks were

nearly empty. The essential short-comings of the original fuel cycle (forward-aft-center) was that it did not accomplish this. The transition through the characteristic dip in the stability boundary occurred quite early in the cycle when the minimum velocity of the critical region was well within the operating Figure 9. Variation of Flutter Speed Along Original speed range of the airplane.

Fuel Transfer Cycle - Cycle F-A-C

By altering the internal plumbing of the tip tank the sequence in which the three fuel compart- The region of relatively low speed instability ments of the tank were emptied could be changed.

was found, from a theoretical analysis, to be caused Without modifying the compartmentation of the tank by the wing torsion to asymmetric bending frequency there were just two alternate fuel transfer cycles ratio being close to unity. Though the stability boundaries for various fuel loadings do not follow the same variation with change in the wing torsional did not yield a value of the wing torsion to as shown for the full tank condition, Figure frequency asymmetric bending frequency ratio similar 6, the boundaries do have the common characteristic to that of the original cycle in the region of of a rapid transition in the oritical velocity of the 120 to 150 gallons, and system as the torsion to asymmetric bending fre- quency ratio of the wing approaches and passes through maintained a stabilizing tank center of a value near unity. In the full tip tank configuration gravity location well forward of the wing the torsion to asymmetric bending frequency ratio is elastic axis.

somewhat less than unity (.85), while in the empty tank configuration the frequency ratio is somewhat As seen in Figure 11, the tank moment of in- ertia for both the intermediate cycle (A-C-F) and the final cycle (C-A-F) in the range of fuel content from 120 to 150 gallons is substantially greater than that for the original cycle (F-A-C) and consequently each produces a lower ratio of wing torsional fre- quency to wing asymmetric bending frequency, that is, in the direction of increased stability.

Figure 13. Correlation of Flight Test Data Logarith- mic Decrement Versus Minutes of Fuel Transfer

Cycle - Cycle A-C-F V = 470 Knots

e The theoretical variation of flutter speed with fuel usage is shown in Figure 14 for the final fuel cycle. It exhibited the greatest stability of the three cycles becoming neutrally stable at about 600 knots Figure 11. Wing Tip Tank Inertia Properties for equivalent airspeed, which was far in excess of the Three Fuel Transfer Cycles maximum velocity for this airplane. Here again in 15 flight test stability data in the form of log- Figure arithmic decrement versus minutes of fuel transfer Both fuel cycles were flight tested. The theo- obtained for the final fuel cycle at a velocity of 470 i s retical variation of flutter speed with fuel usage knots equivalent airspeed is compared with theoretical shown in Figure 12 for the intermediate fuel cycle. results. It is to be noted that good agreement has Adequate stability is seen to exist to about 500 knots been obtained here between the theoretical and test equivalent airspeed. In Figure 13 flight test stability data for both the value of damping and frequency of data in the form of logarithmic decrement vereus the lowest damped mode. This fuel transfer cycle minutes of fuel transfer obtained for the intermediate was incorporated as the final fuel sequence configura- fuel cycle at a velocity of 470 knots equivalent air- tion because of its greater stability plus the fact that speed i s compared with theoretical results. Good it did not impose flight load restrictions on the air- agreement is seen to exist.

Figure 12. Variation o f Flutter Speed Along Inter- Figure 14. Variation of Flutter Speed Along Final

mediate Fuel Transfer Cycle - Cycle A-C-F Fuel Transfer Cycle - Cycle C-A-F

plane since the centers of gravity for conditions for large fuel contents were always relatively close to the wing elastic axis.

It has been shown how flight flutter testing by the transient response technique provided a reliable measure of the flutter stability of the wing tank con- figuration when employed in conjunction withtheoreti- It is concluded that transient response cal analysis.

from "stick bangs" can provide a reasonably reliable and safe technique of flight flutter testing for wings with external tanks or heavy stores.

Figure 15. Correlation of Flight Test Data Logarith-

mic Decrement Versus Minutes of Fuel Transfer -

Cycle C-A-F Ve = 470 Knots FLIGHT FLUTTER T E S T I N G OF MULTI-JET AIRCRAFT

J . Bartley - Boeing Airplane Co., Seattle, Washington

Abstract Structural characteristics and internal wing fuel distribution of the jet transports a r e generally similar Extensive flight flutter tests have been con- to the B-52, although the structural frequencies are somewhat higher.

ducted by BAC on B-52 and KC-135 prototype air- planes. The paper will discuss the need for and importance of these flight flutter programs to Boeing Initial appraisal of the B-52 flutter problems airplane design. Basic concepts of flight flutter testing indicated that a comprehensive theoretical analysis of multi-jet aircraft and analysis of the test data will would require approximately 20 degrees of freedom, be presented. Exciter equipment and instrumentation a prohibitive number for the computing machinery will be discussed. available at that time. The alternative which was employed in these tests decided upon was to build dynamically scaled flutter models for wind tunnel flutter testing. Results of INTRODUCTION a the wind tunnel flutter investigations indicated During the past 6 years the Boeing Airplane marked sensitivity of flutter speeds to moderate Company has accumulated an extensive experience changes in wing and nacelle strut stiffness and weight with the flight flutter testing of multi-jet aircraft, distribution. Also, flutter occurred in approximately including the B-52, 707-80 commercial prototype and 5 different modes all of which involved strong coupling the KC-135 tanker. This has been occasioned by the of the wing and fuselage.

complex flutter characteristics associated with the FLIGHT TEST EQUIPMENT AND PROCEDURE general design of these airplanes involving a high aspect ratio wing carrying flexibly-mounted nacelle pods and a long slender fuselage. The resulting as- Although the wind tunnel flutter investigations sembly presents a large number of possible flutter indicated adequate flutter speed margins for the nom- modes of the basic structure. Figure 1 shows the inal B-52 configuration, it was decided to embark on number of anti-symmetrical modes and frequencies a flight flutter program which would provide maximum of interest from a flutter standpoint for one distri- safeguards against the occurrence of unanticipated bution of fuel on the B-52. These data were obtained flutter on this airplane. This decision was based on from a ground vibration test of a B-52 flutter model, the feeling that the overall complexity of the B-52 and the frequencies shown are model values which are structure made it necessary t o provide an additional 4.5 times actual airplane frequencies. measure of safety over and above that provided by the wind tu.mel test results. A systematic monitoring Furthermore, added complicktion comes from of the flutter behavior of the airplane as test speeds a r e increased in increments up to the design speed the fact that fuel is carried internally throughout the limit was established as the basic flight flutter test wing and fuselage, and in the case of the B-52, the external tanks are mounted on the outboard wing, plan. Telemetering of response data to a ground sta- presenting a wide variation in fuel configurations tion permitting a crew of flutter personnel to analyze to be cleared for flutter. Figure 2 illustrates the the behavior of the airplane carefully during flight distribution of fuel tanks in the B-52 wing and fuse- flutter tests was considered an essential part of the plan to provide maximum overall flight safety.

lage.

BODY FREQ MODE CPM AA 1st BODY SIDE BDG.

BB 1st WING BENDING CC R H. NAC. STRUT BDG.

L H. OUTBD. NAC. PITCH DD L H NAC. STRUT BDG.

R H OUTBD. NAC. PITCH EE WING BDG 8 TORS.[SOME CHDWISE) 654 BODY ROLL RR BODY TORSION 715 FF BODY TORSION 7 2 0 OO2nd WING BDG.

GG 2nd BODY SIDE BDG.

HH VERT. TAIL BDG., HORIZ. TAIL 1218 RESPONSE JJ LH.OUTBD NAG. ROLL 8 YAW R H INBD. NAC. ROLL 8 YAW WING RESPONSE, VERT. TAIL BDG.

HORIZ. TAIL RESPONSE K K EXT TANK PITCH. WING BDG. 8 TORS, H O R I Z . ~ VERT. TAIL RESPONSE M PP HORIZ. TAIL YAW 8 BDG. 17J7 LL VERT TAIL BDG., HORIZ. TAIL 2730 RESPONSE -N MM VERT. TAIL ROT. 8 BDG , HORIZ. 2880 H TAIL RESPONSE L VERT. TAIL ROTATION FOO 3740 -R NN HIGHER EMPENNAGE MODE Figure 1. Antisymmetrical Modes and Frequencies - High Gross Weight Excitation of the airplane structural modes is

A

provided by two methods: through control impulse and by an oscillating airfoil shaker located at one wing tip. In the simpler of the two methods, the in- put pulse from abrupt displacement of the control surfaces is used to excite response in those modes of vibration most easily excited by each control sur- face, generally the lower frequency modes. Tests are conducted at successive speeds, in increments of 5 to 20 knots, up to limit test speed based on pre- dicted placard or design speed limit as shown in Figure 3. Trend in the rate of decay of the response (damping) with increasing airspeed is used as an in- dication of approach to flutter in each mode which can be excited by the dontrol pulse.

A telemetered record of response to an elevator impulse is shown inFigure 4. Note that the pulse excites two super- Figure 2. B-52 Fuel Distribution imposed modes at nearly the same frequency (this is most noticeable on the trace of wing chordwise re- sponse). The mode of lower frequency damps out The general philosophy of flight flutter testing rapidly leaving the higher frequency mode to decay at Being is to employ it as a check o r confirmation by itself. Figure 5 shows the samping curve vs air- of margins of safety predicted by wind tunnel testing speed obtained for one mode using control impulse o r analysis, and not as an investigative technique.

testing techniques.

That is, flight test plans call for configurations to be flown only at speeds which have been cleared pre- Generally, a great deal of judgment on the part viously with adequate margins by wind tunnel tests of the ground crew is involved in analysis of the decay or by analysis.

1 04

OVERALL PING (9) VERSUS

SPEED§ - FLIGHT ~LUTT€R

AIRSPEED - CONTROL IMPULSE

YB -52

TESTING 8-52 AIRPLANE MACH NO.

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w 0 01 , I D ,so , . o .IO ,eo . I O .IO . P O 100 110 I 2 0 $10 1 . 0 110 I60 170 110 $90 600 IRUf AlRSPffD ~ KNOTS AUfOll VIBRATOR AND NACA 5TANDARD ATMOIPHfRI TRUE AIR SPIfD. KNOTS

* CONIROI IMPULSI

@ CONTROL IMPULSI ONLY Figure 5. Overall Damping (g) Versus Airspeed - Figure 3. Test Speeds - Flight Flutter YB-52 Control Impulse Testing B-52 Airplane data. Repeatability is only fair, although it tends the disadvantage of being limited in the number of to improve a s damping decreases. modes which can be excited, generally 2 or 3, and mode separation is not altogether satisfactory.

Responses from 29 locations on the airplane, and force input from the wing tip vibrator, are re- An alternate method of flight testing employs corded on a Miller Model J oscillograph installed an electric motor-driven airfoil installed at the right i n the airplane. Figure 6 shows the location of pick- wing tip of the test airplane. The unit which was ups on fixed structure and the airfoil force vector.

designed and constructed in the Structural Test Unit The double headed vectors indicate the measurement at Boeing, has a programmed frequency sweep which of angular motion about the axis of the vector. In covers the range of critical frequencies of the air- addition, there a r e 7 control surface and tab deflec- plane. The sweep from the lower to the upper limit tion indicators. The 5 starred locations in Figure 6, of frequency is accomplished in about 7 minutes. The plus the vibrator force, are telemetered to the ground slow rate of sweep is required in order to allow each station using a Bendix FM TXV-13 transmitter and structural resonance sufficient time to build up and TGRS receiving station. Flight test time required decay as the vibrator continues through its sweep.

for each test condition, using this technique, averages A section of Brush record showing typical response about 3 minutes including analysis. However, it has to the vibrator sweep is given in Figure 7.

Figure 4. Telemetered Record of Typical Airplane Response to Wing Tip Vibrator Excitation Initial efforts at providing controlled mechani-

LOCATl ON OF PICKUPS AND

cal vibratory excitation on a B-52 airplane in flight were aimed toward the use of a rotating unbalance

MEASUREMENT

DIRECTION OF

vibrator. Such a unit, hydraulically driven, was designed, fabricated and installed in the tail of the YB-52 airplane. Required to provide a reasonably uniform rotating force Vector over the frequency range, with good speed control and powerful braking in the event of control failure, the tail vibrator emerg- ed a very complex system which taxed the limit of auxiliary power available on the airplane. Although it provided adequate excitation of wing and body mMes, the tail vibrator, because of its overall complexity, failed to perfom as reliably as is necessary for flight test work. It was replaced bythe more reliable airfoil vibrator unit upon completion of the early phases of B-52 flight flutter testing.

FORCE Theairfoil vibrator is comprised on an unswept

* * - TELEMtTERED TO GROUND

tapered airfoil driven by a 1/2 horsepower DC elec- tric motor. The airfoil has an area of 2 square feet, with a 2-foot span, 16-inch root chord, 8-inch tip Figure 6. Location of Pickups and Direction chord, and a thickness ratio of 6 percent. The axis of Measurement of rotation is along the quarter chord, and the airfoil is mass bdlanced uniformly along the span to main- tain the center of gravity slightly forward of the ro- Flight test time required for each test condition, tational axis. This provides a safequard against which employs both control impulse and vibrator flutter involving the airfoil in the event of a free sweep, averages about 15 minutes including analysis.

Figure 7. Telemetered Record of Airplane Response to Elevator Impulse airfoil resulting from failure of the driving system.

The oscillatory angle of the airfoil canbe varied from 0 to a maximum of rt4 degrees. The oscillatory fre- quency can be varied between 85 and 600 cycles per minute. Both the angle of attack and frequency of oscillation can be controlled by the pilot during flight. In addition, the programmed automatic sweep of @e frequency range is provided by electronic con- trol of the amplidyne power supply for the electric drive motor. Frequency control during the program- med sweep is within 1/2 percent of the prescribed frequency.

An emergency stop is provided which will halt oscillatory motion of the shaker in less than 1 cycle.

Figure 8. Wing Tip Vibrator - YB-52 This may be used to collect damping data from decay of the shaker-induced structural oscillation.

The weight of the entire unit at the wing tip is approximately 150 pounds. The vibrator weight is When the vibrator is used, force to produceunit counterbalanced by an equivalent weight at the oppo- response is plotted against airspeed since this ratio site wing tip to maintain symmetry of weight distri- tends toward zero as damping of a mode decreases.

bution of the outboard wing of the test airplane. of vibration are excited through use of More modes the airfoil vibrator than with the pulse technique Figure 8 shows the airfoil installed at the wing (roughly 8 or 9 compared with 2 or 3) and frequency tip of the B-52 airplane.

separation is highly superior. Figure 9 shows plots of force/displacement amplitude versus speed for 6 The entire drive unit (motor, gear box, support, of the modes which were excited by the vibrator etc.) is housed in the wing tip fairing. during testing of one B-52 configuration.

RESPONSE DATA USING WING TIP

VIBRATOR 5 4 2 AIRPLANE

R.H. W.S. 1377 VIRTICAL R.H. W.S. 1377 ANGULAR 12OCPM U S ) s.0 s.0 4.0 3.0 g 2.0 2.0

3 1 . 0

1.0 YI a 420 460 500 5 4 0 420 460 5 0 0 340 420 460 5 0 0 540 1RUE AIR S N E O - KNOlS a.n. STABILIZER 362 VERTICAL R H. SlABlLlZER R.H. W.S. 1377 V€RlICAL 315 CPM I AS1 190 CPM (51 5 0 10.0 4.0 8.0 3.0 6.0 2.0 4.0 I .o 2.0 '420 460 500 540 420 460 SO0 140 420 460 5 0 0 540

TRUE AIR SPfEO - KNOTS

(I) Spm.tricml (Ais) Anti-symetricd Figure 9. Response Data Using Wing Tip Vibrator B-52 Airplane During level flight test conditions, both methods what smaller number of configurations were tested of excitation are employed at each test speed, and the on the B-52 with 1000 gallon external tanks andon plots of damping and response to vibrator input are B-52 airplanes and jet transports without external made concurrently. Flight flutter tests in level flight tanks.

are conducted up to level flight maximum speed (400 knots EAS, M = .89 at 19,500 f t for the B-52). Be- The external tanks carried on B-52 production yond this speed, up to 400 knots EAS, M = .93, the airplanes contain baffles which prevent significant tests require diving the airplane and the interval of shift of fore-and-aft center of gravity during transient time available at test conditions is necessarily brief. response conditions. Holes in the baffles allow fuel Therefore, control impulse testing only is employed to flow through slowly thereby permitting a substan- at these speeds. By the time the level flight high tial shift in fore-and-aft center of gravity for sustained speed is reached, the modes of concern have been climb or dive attitudes. The flight speeds associated identified from the combined shaker and impulse with sustained climb are limited by power considera- testing, so it is relatively. safe at that point to con- tions and do not present a critical flutter problem.

tinue on up in speed employing control impulse only. However, sustained dive attitudes at high speeds are possible, and configurations with external tank fuel Because the amplitude of airplane response to distributed forward in the tank a r e studied inthe wind pulse and airfoil excitation i s quite small (one-half tunnel and checked in the flight test program. The to three-fourths of an inch double amplitude at the external tanks of the test airplane are divided into 3 compartments, and each compartment is loaded with wing tip) it is essential that the tests be flown in (in smooth air. Although flutter tests have been dis- the proper amount of ballast mixture to represent continued because of turbulence, it has been a rare a level flight condition of the flutter test airplane) occurrence and not a major problem. High speed the weight and cg of external tank fuel in the uncom- partmented tank on an airplane i n a 25" dive attitude.

buffet becomes significant only at the maximum test Figure 11 illustrates this simulation. The ballast is Mach number, M = .93, where strong buffet is made up of a mixture of water and glycerin (anti- encountered.

freeze).

Results of wind tunnel flutter tests have indi- cated that variation of outboard internal and/or ex- ternal wing fuel is more effective i n altering flutter

3000 GALLON COMPARTMENTED

characteristics than variation of inboard wing and

TEST TANK

body fuel. Accordingly, the configurations tested in the flight flutter program involve a more detailed breakdown of fuel in these tanks than in the main wing and body fuel tanks. An illustration of the 1ANK 514.

S A . SIA number of flight flutter test configurations involving 14.

combinations of outboard wing internal and external T I T

tank loadings is shown in Figure 10.

Twenty-eight configurations were tested on B- Asome- 52's carrying 3000 gallon external tanks.

FLIGHT FLUTTER TEST CONFIGUR-

ATIONS 6-52 WITH 3000-GAL.

EXTERNAL TANKS

Figure 11. 3000 Gallon Compartmented Test Tank €Xt.."rnl i d RESULTS in I . r . 1 llipht oltilud.

Before discussing flight test results and com- paring with wind tunnel data, some description of the nature o f our wind tunnel testing should be presented.

The wind tunnel program has been conducted using dynamically scaled models of the complete B-52, 707 and KC-135 basic structure. A flutter model of the B-52 airplane is shown in Figure 12.

Figure 10. Flight Flutter Test Configurations B-52 Structural stiffnesses of the wing, fuselage, nacelle strut and empennage structure are repre- with 3000-Gal. External Tanks ation of damping in this mode was experienced at maximum true airspeed during testing of configura- tions carrying empty external tanks with a capacity of 3000 gallons. Wind tunnel tests had indicated adequate flutter margins for these configurations.

A detailed reanalysis was made of structural representation of the airplane on the part of the elastic model. A carefully controlled stiffness test of the airplane nacelle strut and local wing attach- ment structure revealed that the flutter model was considerably out of scale in this parameter. Cor- rection of this deficiency resulted in good correlation between model and airplane data where airplane con- figurations had been flown near enough to flutter to permit a reliable extrapolated prediction of the critical speed, Figure 13.

Figure 12. Flutter Model of the B-52 Airplane COMPARISON OF WIND TUNNPL AND FLlGHT FLU TER RESULTS sented by single dural spars which are covered by slotted balsa sections forming the geometric external contour of the model. The flutter model tests have been conducted in low-speed wind tunnels, with maxi- mum test speeds being in the neighborhood of 200 is flown in the wind tunnel miles per hour. The model on the rod-trunnion arrangement shown in Figure 12, gradually increasing tunnel velocity until flutter occurs 1 I I Measurements of damping ma in the most critical mode.

of the various modes present in the model below the I critical flutter speeds are not obtained. Wind tunnel

turbulence provides generous excitation of the model, o&-u 0 15 100

so that flutter occurs once the critical speed is O U l b O A R D WING FUtL - yo FULL reached.

12,000 FI A L l l l U D f - H I N D TUNNEL M O D f L DATA

W I N D TUNNfL MODEL D A l A f M P l V 3000 GALLON f X I E R N A 1 1ANKS - -

Yb-SZ AIRPLANE FllGHl I f 5 1 DATA - Because the procedure used up to the present tests at Boeingdiffers in conducting wind tunnel flutter Figure 13. Comparison of Wing Tunnel and Flight from that employed in flight flutter tests, it is not Flutter Results possible to obtain a direct comparison of wind tunnel model and airplane flutter characteristics in the The figure shown is for configurations flown stable area below the critical flight speed. A s stated with various amounts of fuel in the outboard wing previously, the policy at Boeing has been to avoid flying into a region of known or suspected flutter. and with empty 3000 gallon external tanks. Similar A s a consequence, our experience has been pri- correlation exists for B-52 configurations carrying marily one of negative agreement; that is, the wind empty 1000 gallon external tanks.

tunnel results predict freedom from flutter up to a specified limit, and the flight flutter tests provide It is noteworthy, in considering the application of these flight test techniques to the B-52, 707 and confirmation.

KC-135 flight flutter programs, that wind tunnel tests Actually, during the early B-52 flight flutter had shown that potential flutter modes are of the testing, correlation with previous wind tunnel test %on-explosive” type. That is, evidence of a flutter results could be classified as no better than fair. condition (reduced damping trend) appears on the Although no flutter incidents occurred, the mode of model at speeds appreciably below the critical speed.

Furthermore, because of the low frequencies associ- the airplane which exhibited lowest damping during the ated with the basic structure of these airplanes and flight test program had not fluttered nor indicate low rate of divergence of damping during the wind tunnel testing of comparable the large masses involved, the configurations. The mode involved was a symmetrical the flutter oscillations against time is low.

higher order mode of the wing coupled with body vertical bending. There was an appreciable chordwise In summary, flight flutter tests have been con- component of wing motion. The frequency was ap- ducted on B-52, 707 and KC-135, airplanes totalling proximately 160 cpm. Finally, indication of deterior- approximately 250 hours of flight time. The airfoil vibrator has been used successfully on about 25 flights of the KC-135 airplane and 85 flights of B-52air- planes. Almost 450 sweeps have been conducted during the flutter testing of these airplanes using the airfoil vibrator.

The flight flutter techniques employed provide adequate safeguard against catastrophic flutter of the FLlGHT FLUTTER TESTlNG OF SUPERSONlC INTERCEPTORS M. Dublin, R. Peller - Conuair, Sun Diego, California Abstract results in a considerable expense of time, money and material to obtain a fix; it delays getting the vehicle This paper presents a summary of experiences into operational use; and it can sometimes result in in connection with flight flutter testing of supersonic permanent restrictions on the airborne vehicle which interceptors. It contains a description of the planning limits its operational capability.

and operational aspects involved, comments on the From an analytical point of view the deter- difficulties encountered, and shows correlation be- mination of the flutter stability boundaries is difficult tween measurement and theory. The paper con- because of lack of precise knowledge of all the para- cludes with recommendations for future research and (1) development to advance .the science of flight flutter meters used in the equations of motion; Reference outlines these difficulties in more detail and also testing.

considers difficulties encountered in flutter model INTRODUCTION testing. Flight flutter tests a r e therefore made to insure freedom of the vehicle from flutter over its During the last ten years, as noted inReference operating envelope and environment, and to assist (l), more than fifty different casesof flutter have been the flutter analyst in improving his ability to make air- analytical predictions.

encountered on United States piloted military craft. In addition a certain number of cases of flutter have also been encountered on United States commer- cial and private aircraft. Further, a number of cases PLANNING ASPECTS of flutter have been encountered on United States military missiles. Although detail statistics a r e not The steps which must be taken in planning a available, it is known that a number of cases of flutter flight flutter test program are as follows: have occu’rred on foreign aircraft and missiles. Thus, a. Establish desired data and measui-ements.

over the last ten year period, it is estimated that at least several hundred cases of flutter have been b. Selection of test equipment and installation.

encountered in airborne vehicles of the world.

c. Establish test procedure and execute test.

These cases of flutter have had various con- sequences. In some cases mild structural damage occurred and the aircraft w a s landed safely. In some d. Data analysis and interpretation.

cases very severe structural damage occurred and the Although there a r e a variety of approaches for aircraft had to be abandoned. With regard to the flutter each of the above steps, this paper will only consider cases encountered in theunited States over the afore- the approaches used by Convair in flight flutter testing mentioned time period, insofar as the authors know, no loss of life w a s encountered; whether the same of supersonic interceptors. Figure 1 shows a photo- applies to flutter cases encountered on foreign air- graph of one of the configurations tested. Practical craft is not known to the authors. Other aspects of difficulties encountered during the flight flutter test encountering flutter which are important are that it program will also be discussed.

1 1 1 fuel tank configurations. Three fuel tank configur- ations were selected, namely external tanks with full fuel, external knks with half fuel and forward center of gravity, and external tanks with half fuel and aft center of gravity.

Special compartmented tanks were used for these tests.

TEST EQUIPMENT AND INSTALLATION The equipment used for the tests consists of: a. Excitation system b. Pickups.

c. Recording system d. Data analysis system Description of this equipment is discussed hereunder.

EXCITATION SYSTEM Figure 1. USAF F-102A Supersonic Interceptor Based on an examination of the theoretical vibration modes, it was established that the shakers Desired Data and Measurements should be located near the wing tips in order to obtain satisfactory airplane response for all desired The method chosen for establishing flutter exciting frequencies. The wing depth available at the stability was to obtain plots of the damping co- selected location was 4 . 5 inches for the shaker and its at selected locations on the airplane versus efficients mounting. Since no commercially available shaker airspeed for selected resonant frequencies (i.e., both existed which met this space requirement and at the symmetric and antisymmetric), for selected altitudes same time provided desired force output for satis- and for selected airplane mass configurations. Re- factory airplane response, it was necessary to design quired measurements using this method were the air- and develop a shaker system specifically tailored for plane responses (at the selected locations due to an this airplane. Convair developed such a shaker sys- excitation of the airplane), the airspeed, and the tem which is essentially a closed loop servo system altitude.

combining hydraulics and electronics to command and control the movement of two reciprocating masses.

Two excitation methods were employed, namely A functional block diagram of the system is shown in sinusoidal excitation by two inertia shakers, and Figure 2; detail description of the system is contained pilot control excitation. To establish that the shakers in Reference 2. The essential elements of this system were functioning properly, it was also necessary to consists of the following: measure the frequency and the displacement of each shaker mass and the phase of one shaker mass a. Pilot's stick switch. This is a spring loaded displacement with respect to the other shaker mass on-off switch which when actuated causes the displacement. Pilot control forces o r displacements shaker to perform the functions selected on were not measured since movable control surface the pilots control panel.

responses were adequate to establish initiation of pilot control excitation.

b. Pilot's control panel. Three two position toggle switches are located on the pilots A problem area arose in selecting the airplane control panel which permit him to select mass configurations. For the airplane configuration either a manual o r an automatic mode of without external wing fuel tanks, the fuel weight is operation. If the manual mode of operation approximately 25% of the airplane takeoff gross is selected this causes the shakers to sweep weight. Since fuel is expended at a fairly rapid through a specified frequency range at a rate, it was not practical to specify a mass configur- programmed rate of sweep, and at a p r o - ation for which measurements should be taken at grammed shaker force; in this case the specific speeds and altitudes; it was necessary to take pilot must also select the phasing of the measurements at points on the flight envelope at the shakers (i.e., symmetric or antisymmetric), mass configuration which existed. This, of course, and he must also select the sweep cycle leads to one of the difficulties in correlating mea- (i.e., ascending frequency o r descending surements with theory since in practice analytical frequency). If the automatic mode of oper- investigations are usually made for a limited number ation is selected this permits obtaining However, for the airplane of weight configurations.

decay responses; in this mode of operation configuration with external wing fuel tanks, it w a s six frequencies (either symmetric or anti- possible to take measurements for various external

t t t

Hydraulic Power Power Supply Figure 2. Functional Block Diagram of Shaker System e. Two hydraulically actuated shakers. These symmetric) can be preselectsd and the shak- supply the force input to the airplane. Figure ers will excite the airplane for a specified 4 shows a photograph of an assembled time at a given frequency; stop the shakers shaker. Figure 5 shows a photograph of the for a specified time and automatically step shaker partially disassembled; the cylinder

to the next frequency -- this process is

in the photograph is the shaker mass.

repeated as long as the pilot stick switch is engaged. A programmer is used to accom- f. Electrical power supply. This consisted of plish these functions in the automatic mode of operation. Figure 3 shows a photograph the airplane 400 cycle A. C. and 28 volt of the programmer. D. C. power supplies.

c. Function generator. This is used to gener- g. Hydraulic power supply. A separate 3,000 psi hydraulic power supply was installed in ate the desired sine wave shape.

the airplane for the shaker system.

d. Two servos. These are used to control the force output of the shakers.

Figure 3. Shaker Programmer Figure 4. Assembled View of Shaker b. Sweep rate. In sweeping from 5 cps to 50 cps the sweep rate could be made variable from 55 seconds to 90 seconds.

c. Stopping time of shaker. To obtain decay curves the shaker could be stopped in one- half of a cycle.

d. Synchronization of shakers. Excellent syn- chronization of the shakers was achieved.

Phase desired between one shaker force out- put and the other was within the accuracy cf reading the traces.

e. In the automatic mode of operation, the excitation time could be varied from 2 seconds to 7 seconds; the time for decay, after stop- ping excitation, could also be varied from 2 seconds to 7 seconds independent of the ex- Figure 5. Exploded View of Shaker citation time.

Other pertinent design characteristics of the f . The shaker mass weight was 8.5 lbs. and its shaker system are: travel was i1.0".

a. Force vs frequency. A linear variation of Trouble encountered with the shaker system How- force versus frequency was desired.

were: ever, due to valve characteristics the force- frequency curve actually obtained was as a. Hydraulic leaks.

shown in Figure 6. It is noted that identical force outputs for both starboard and port b. Deterioration and failure of tubes in the shakers were not obtained.

electronic control system.

c. Shorts in programmer stepping switches.

3 50 d. Potentiometers in programmer were sen- sitive to temperablre.

e. Human errors in operating and maintaining the shaker system.

The shakers were installed in the wing on rigid

-

structure as shown in Figure 7. Shaker force was ui established from measurements of the shaker mass

t ; 200

displacement and frequency.

ii v r.4 Pilot control excitation simply consisted of the is0 (Le., longitudinally pilot "banging" the control stick and laterally) with his hand or the rudder pedal with his foot. This method would only excite the lowest symmetric and the lowest antisymmetric vi- bration modes.

PICKUPS Fixed surface responses were obtained by seven MB-124 linear velocitypickups locatedas shown in Figure 7. Movable surface responses were obtained 10 20 30 40 50 by three MB-124 linear velocity pickups which were FREQUENCY (cps) modified (i.e., by counterbalancing the movable arma- ture) to sense angular velocity; these were located Figure 6. Shaker Force vs. Frequency as shown in Figure 7.

Legend: Linear velocity pickups .

Angular velocity pickups

//

Figure 7. Sketch of F-102A Showing Location of Instrumentation plane airspeed, altitude, and outside air temperature The displacements of the shaker masses were were recorded on a photopanel by means of a movie obtained by a variable reluctance pickup excited by a 3,000 cps voltage source. camera.

Difficulties encountered with these pickups were: Correlation between the photopanel and the telemetered signal was maintained by a data correlator a. Linear velocity pickups bottomed at in- which recorded a counter number on the photopanel cremental airplane c.g. normal load fac- as a series of lights and a s an electrical pulse on the w a s changed every tors of approximately k0.4 g's. telemetered signal. This number two seconds throughout the flight.

b. Sensitivity of angular velocity pickups was not as high as desired for easy reading of The telemetered signals were received at a traces. ground station where they were: a. Recorded as an electrical signal on magnetic The airplane speed was obtained by a Kollsman airspeed indicator, Type 739 DX-6-059. With this tape.

instrument, as with any other available instrument, it was difficult to predict exact speeds in the transonic b. Recorded on an oscillograph (to check instru- speed regime due to position e r r o r s existing in the mentation in the field).

system.

c. Put through appropriate discriminators and recorded on Sanborn recorders.

The altitude was obtained by a Kollsman alti- meter, Type 1846 X, -4-01. In the transonic speed regime it was difficult to predict exact altitudes due Communication between the ground station and to position errors existing in the system. Addition- the aircraft w a s maintained by radio at all time.

ally, during dives at high rates of descent it was dif- Difficulties encountered with the recording sys- ficult to predict exact altitudes due to lags in the altitude measuring system. tem were: RECORD'ING SYSTEM a. Loss of telemetering signal due to airplane position or distance from the ground station.

Outputs of the velocity pickups and the shaker b. Loss of telemetering signal due to electrical pickups were fed into an FM/FM telemetering trans- failure in the airplane.

mitter for transmittal to a ground station. The air- c. Necessity of changing tape during the flight slow paper speed of approximately 0.5 inches per when only one tape recorder w a s available. second.

d. Failure of recording pens on Sanborn equip- The data correlation trace was recorded on ment.

the oscillograph records along with the airplane responses. This allowed complete correlation with e. Radio failure (either airplane o r ground the speed information obtained from the photopanel.

. radio).

Photopanel records were developed by standard procedures and read by means of projection equipment.

DATA ANALYSIS SYSTEM The data station proved to be a very reliable as were en- The data which w a s stored in the form of an piece of equipment. Such difficulties electrical signal on magnetic tape was processed in a countered could be attributed to human errors.

The signals were put through appropriate data station.

A discriminators and oscillograph traces obtained. TEST PROCEDURE AND EXECUTION O F TEST standard procedure which recorded all pickups with An initial plan was made outlining the desired 60 cycle low-pass filters was run off first. If these records proved unreadable because of excessive res- speed-altitude points which were required. This plan ponse due to atmospheric turbulence, a band-pass was flexible in that speed increments could be in- filter from 25 to 50 cps was used to eliminate the creased or decreased depending on the results obtained low frequency responses. If the higher frequencies from each flight. Figure 8 shows a typical speed- altitude test plan. Tests were initiated at subsonic made decays in the fundamental modes unreadable, speeds at the highest altitude chosen. Tests at a 5 to 25 cps band pass filter was used.

lower altitudes were always made in such a manner The oscillograph records were, in general, that the equivalent speed obtained at high altitude recorded at a paper speed of 4 inches per second. w a s not exceeded. Frequencies at which decays For special conditions, (i.e., obtaining an overall were obtained were established from sweep records a sweep) the records were recorded at a taken in flight at selected intervals.

view of Legend: 0 Symmetric & anti-symmetric sweeps Symmetric & anti-symmetric decays Pilot control pulses (elevator & aileron or rudder) x V e = Equivalent airspeed, knots V c = Indicated airspeed corrected for instrument and position error, knots Figure 8. Typical Speed-Altitude Test Plan b. Meteorological problems. Examples are ex- Prior to flight a ground checkout procedure was cessive winds preventing take-off, excessive established which accomplished the following tasks: turbulence and gusty air which would mask a. Insured proper functioning of shaker system. the response due to shaker o r pilot excitation, and excessive outside air temperature which prevented achieving some of the desired b. Insured proper calibration of instrumenta- speeds.

tion.

c. Insured proper operation of telemetering C. Operational problems. Examples are un- availability of chase airplane or chase air- equipment.

plane mechanical problems, limited fuel sup- ply, necessity of going off-base for low alti- d. Set programmer parameters in accordance tude testing, conflicts with higher priority with desired measurements, testing, short time for taking measurements During flight, ground monitoring was used to: during dives at high descent velocities, and location of data reduction equipment away from test base.

a. Check proper functioning of shakers, instru- mentation and telemetering.

The above difficulties either contributed to lengthen- b. Check proper positioning of pilot‘s shaker ing the duration of the flight flutter test program or controls. decreased the reliability and accuracy of the mea- surements.

Notify pilot if data is unsatisfactory (i.e., due C.

to turbulence or gusts). qequest repeat DATA ANALYSIS AND INTERPRETATION measurements or flying an alternative flight plan.

The two conventional methods were used to ob- tain the experimental damping coefficients, namely d. Inform pilot of satisfactory completion of from the response of velocity versus frequency plot, frequency sweep (Le., to reduce test time).

and from the response of velocity versus time (i.e., decay) plots.

e. Estimate damping coefficient’s from decay records, and infQrm pilot either to continue A typical section of a sweep record is shown testing at higher speeds o r to discontinue in Figure 9. Figure 10 shows a sampledecay testing until records can be analyzed in record.

detail.

A typical plot of the experimental damping Following the analysis of data for each flight, versus Mach number curve is shown in Figure 11 at it is necessary to re-examine the test planand deter- a 35,000 foot altitude for the second coupled anti- mine what modifications, if any, need to be made.

symmetric vibration mode. Points on this curve which Typical changes in the plan are: are dotted were simply demonstrated and no mea- a. Decrease speed increments due to a large surements with excitation were taken. A negative decrease in the damping coefficient, o r damping coefficient denotes a stable system. Similar alternatively, increase speed increments due plots were obtained for all other significant vibration to a steady increase in damping coefficients. modes at various altitudes to demonstrate that the airplane is free from flutter over its design envelope.

to failure of photopanel b. Repeat test points due camera, which results in no speed and altitude The experimental results shown in Figure 11 data. were also compared with theoretical results. The following explanatory comments are made in con- c. Repeat test points to check scatter in data. nection with these theoretical calculations. Theor- etical anti-symmetric mode flutter calculations at a The main difficulties encountered in executing 35,000 foot altitude were made using the lowest five test program were: the flight anti-symmetric coupled vibration modes and for a gross weight corresponding to a 60% full fuel con- a. Development problems with the airplane. dition; two dimensional oscillatory aerodynamic co- Some examples are electrical power failure, efficients were used in the analysis. Reference 3 malfunction of cabin pressurization system, contains details of these calculations. The minimum compressor stalls, failure of afterburner to damping occurred in the second anti-symmetric a natural frequency of light, malfunction of fuel quantity indicator, coupled vibration mode with malfunction of fire warning indicator, and a 13.4 cps. Figure 11 shows this theoretical damping supersonic noise problem. These resulted plotted versus Mach number -- in the transonic speed in either aborted flights or temporary re- region the curve is shown dotted since no calculations

strictions on the airplane. were made -- at zero airspeed the structuraldamping

Time -

NOTES: 1 . Record is for right wing pickup 2. Anti-symmetric resonant frequencies, 36 cps and 43 cps 3. M = 1.15, h = 15,000 ft.

Right wing pickup

NOTES:

1, Symmetric resonant frequency = 43 cps

2 . M = 1.3, h = 35,000 ft.

Figure 10. Sample Decay Record h = 35,000 Ft.

\ -.14 \ \

g = Damping coefficient - Theoretical

g M = True Mach number

- Experimental

r h = Altitude Figure 11. Comparison of Theoretical and Experimental Damping Coefficients Second Anti-Symmetric Coupled Vibration Mode coefficient was obtained from response curves ob- d. Because excitational forces could not be tained during a groupd vibration test. It i s noted made exactly equal, unsymmetric responses that the general shape of the experimental and were obtained.

theoretical plots are similar; however the actual magnitude of the damping coefficients differ by a the temperature sensitive po- e. Because of noticeable amount, tentiometers in the shaker programmer unit, difficulty was encountered in setting the desired frequencies for decays. Thus, less The following problems arose in connection with than the maximum possible response was analysis of the data and its interpretation: obtained.

Considerable scatter was found in the damping a.

f. Indication of "false resonances" were ob- coefficients obtained. This lead to difficulty tained because of necessity of using sweep in extrapolating the speed-damping curve times less than theoretically desirable.

to the next intended speed. Possible reasons for these apparent discrepancies were: g. Masking of the lowest coupledvibration modes responses by a gust response gave an erron- 1 . Use of two different methods for ob- eous indication of damping.

taining damping factors.

RECOMMENDATIONS FOR FUTURE RESEARCH AND DEVELOPMENT 2. Transfer of energy of vibration between various portions of the airplane.

Flight flutter testing is an ever changing type of testing in which no technique may be considered 3. Difference in mass configurations of the ~ A s with most any type of testing, hindsight perfect.

airplane during test.

is a wonderful thing and many changes in technique and different avenues of approach present themselves Measured damping factors varied between b.

as testing progresses.

different pickups in the same vibrational mQde .

Experiences with the testing discussed in this paper lead to the following recommendations for future C. Altitude trends were difficult to establish.

research and development in the field of flight flutter bility characteristics in lieu of damping testing for manned aircraft flying at moderate super- coefficient versus speed. This approach sonic speeds: is analagous to the method outlined inRefer- ence 4. Purpose of this is to determine a. Make the excitation system completely auto- flutter stability from a single output (i.e., matic. This system should have a pro- work) instead of multiple outputs (Le., damp- grammer where the desired excitation and ing coefficients at a number of locations on duration can be pre-set on the ground for a the vehicle).

given flight plan. It should have an auto- matic force and phase synchronizer when Extrapolating current experience to very high two o r more shakers are used to accurately supersonic or hypersonic manned and unmanned ve- contrdl the force inputs. Further, it should hicles, a number of new factors enter into the have an automatic vibration mode seeker problem of flight flutter testing. The most important which would determine the peak responses of these are high temperatures, flights at very high in flight.

angles of attack, very high rates of climb o r de- scent, and very high longitudinal, lateral and vertical b. Make the data recording and data reduction accelerations. For some configurations in this systems completely automatic. An auto- category it will not be possible to stabilize the matic plot of the data is desired in the form vehicle for specified parameters long enough to obtain which i s used to interpret the stability measurements concerning flutter stability. In this characteristics of the vehicle.

case, it appears that we will have to revert to a "go-no-go" type of testing.

c. Consider the possibility of using plots of work versus speed for interpreting the sta- REFERENCES 1 . NACA RM 56 I 12, "A Survey and Evaluation of 3 . Convair Report ZU-8-032, "Theoretical Flutter Invesitgation of the F-102A Airplane", (CONFI- Flutter Research and Engineering," (CONFIDEN- TIAL) DENTIAL) 4. N. 0. Myklestad, Vibration Analysis", McGraw- 2 . Convair Report 56 -51, "In-Flight Vibration System, Hill Book Co.

Engineering and Operations Manual" 1 20 FLlGHT FLUTTER TESTlNG THE B-58 AIRPLANE

P. T. Mahaffey - Conuair, Ft. Worth, Texas

Abstract To be frank about it, when we started planning this program back in 1952, we weren't sure what The flight flutter tests 011 the B-58 airplane will portion of the flight envelope of the airplane would be described, and the philosophy of flight flutter be critical for flutter. By the time we were ready testing at Convair, Forth Worth, discussed. A de- to flight test the airplane, we were pretty sure that the critical region was transonic speed at low altitude.

scription of the instrumentation used in the airplane and in the telemetering receiving station on the However, there were still enough unknowns to cause ground will be given. The methods used for excit- us to proceed rather cautiously.

ing the airplane and the flight test procedure will be covered. Also described will be the type of data INSTRUMENTATION AND TELEMETERING TECHNIQUES obtained and its reduction. An evaluation of the procedure and instrumentation will be given with a With this as a background, I would like now to discussion of desirable improvements for future proceed with a description of the instrumentation which testing we used on the B-58. W e approached thisproblem with the thought of pushing the state of the art to a INTRODUCTION certain extent, but at the same time staying with items which we felt pretty surf: would work. We wanted To lay the ground work for what we have done to get both frequency response data and damping in the program, I would first like to describe the records. Basically our thought w a s to determine the problem with which we were faced and our philosophy principal response frequencies in flight and to take of approach to it. To begin with, we had to consider damping records corresponding to these as a function a low load factor airplane designed to fly into the high of speed. We also wished to telemeter this informa- speed flight regime which had hitherto been breached tion. By telemetering we could accomplish several only by research airplanes and a few. fighters. To things.

make matters worse from the flutter prediction stand- point, we had four pylon mounted nacelles on a delta First, we wished to be able to proceed with wing planform. This was the first time anyone had more than one speed increment per flight. This produced a configuration like this. So we hadvery automatically ruled out recording the data in the air- little background information on which to draw.

plane and reducing it later on the ground.

The basic approach to the flutter problemonthe Second, this procedure would relieve the flight B-58 on which we decided was as follows. We would crew of the responsibility of monitoring the records put fie basic emphasis on flutter models. Analysis in flight in addition to their other duties.

would be used to predict the character of flutter to be expected and the flutter trends arising from the Third, we would be able to display a number of variation of parameters. Finally, flight flutter channels of information on the ground. Also we could testing would be employed to demonstrate that the airplane was flutter-free. employ certain kinds of bulky, special equipment on the ground such as band pass filters and automatic sweep elevons and at about their midspan to excite a high plotters. frequency vibration mode which flutter model tests had indicated might produce elevon flutter.

Fourth, the flutter information could be monitor- ed by flutter specialists. We used the same frequencycontrolunitfor both types of excitation. This w a s operated by the flight To cover the desired frequency range from 1 to test engineer from his post in the third crew station 40 cycles per second, we had to provide two types of in the airplane. The heart of the unit was a variable excitation. For the range of 1 to? cps, we introduced test frequency electrical oscillator. The flight a sinusoidal electrical signal into the airplane auto- engineer was able to set desired frequencies manually, pilot servos. This produced a sinusoidal oscillation o r to activate an automatic frequency sweep mechan- of the control surfaces about the trim flight position. ism. Selector switches enabled him to use either the The amplitude was proportional to the input voltage high o r the low frequency range, and to direct the and could then be adjusted in flight by turning a knob. excitation to the appropriate autopilot servos o r We had used this system on the B-36 and YB-60 vibrators.

airplanes and knew it would work. However, the characteristics of the autopilot and power control W e used two types of pickups to detect response.

system limited its useful frequency range. For linear motion we employed strain-gauge type Statham accelerometers. These had ranges varying For the range from 5 to 40 cps, we decided to from *2g to *15g, depending on the location. They use vibrators of the type developed by our San Diego were fluid damped and had built-in electric heaters Division. These are inertia shakers, hydraulically to maintain a constant 165°F operating temperature.

powered, and electrically controlled. The ones we used had overall dimensions of 4.5 x 4.5 x 8.5 inches For detecting angular motion of the rudder and and weighed 25 lbs. The force output increased lin- elevons, we used Eclipse-Pioneer AY503-8 autosyns.

early w i d frequency from 40 lbs. at 7.5 cps to 150 lbs. With our instrumentation, these were capable of mea- at 40 cps. W e installed one vibrator in the tip of the suring surface deflections down to 1/20 of a degree.

vertical tail, and one in the trailing edge of each wing. Figure 1 shows the location of these pickups. The The wing vibrators were placed just ahead of the output from the 9 encircled pickups w a s telemetered

+

VERTICAL ACCELERATION

A L A T E R A L ACCELERATION

+ POSITION PICKUP

Vl6RATOR LOGATION \

0 TEtEMETEREO PICKUP

Figure 1. Pickups and Vibrator Locations For B-58 Flight Flutter Tests along with the excitation signal. The signals from all of the pickups were simultaneously recorded on tape in the airplane.

On the ground the telemetered signals were dis- played on two Sanborn direct writing oscillographs as shown in Figure 2. Before going into the recorder, however, each signal w a s passed through a variable b a d pass filter. The filters were used as required to remove any unwanted hash from the traces.

Figure 3. Frequency Sweep Recorder corder. This i s shown in Figure 3. The penwas driven across the paper in proportion to the excitation frequency by a circuit similar to that of a frequency Figure 2. Sanborn Recorders and Filters meter. The paper w a s moved up and down in pro- portion to the amplitude of the signal from the pickup being monitored. Figure 4 shows a typical sweep We recorded frequency sweeps directly with a special unit made by adapting a two axis Brown re- record from this equipment.

Figure 4. Fin Frequency Sweep Taken in Flight FLIGHT TEST PROCEDURES First, the instrumentation and techniques that we used proved to be practical and worked pretty Next I would like to describe out test procedure much the way we expected. This is not to say that in flight. I wanted to say "typical" test procedure, they always worked perfectly, but they proved to be but conditions varied so much from flight to flight servicable.

that there wasn't a set pattern. Basically, however, we went through the following procedure. The flight Secondly, we a r e pretty well convinced that was test engineer informed the ground station when he frequency sweeping yields more information than any ready to start. H e then activated the automatic other one thing that we can do. Damping records excitation sweep on the tail, the response to which essentially confirm what we expect from the sweep was recorded on the ground. Next, automatic sweeps data. In a since damping records give one dimen- were taken for symmetric and antisymmetric ex- sional information while sweeps give two dimen- citation of the wing. While the wing sweeps were being sional data.

taken, the tail sweep record w a s reviewed to determine For another thing, we have found that the ampli- the major response frequencies. These were then transmitted by radio to the flight test engineer with tude of excitation is important. We don't know how a request for damping records. He thenproceeded to specify the minimum acceptable level, but we know to set the requested frequencies manually and to give from our experience that low excitation amplitudes tend to give erratic damping values. These values short bursts of excitation to the tail for damping also tend to indicate lower damping than actually records. During this period the wing sweeps were reviewed for major response frequencies. These exists. On the B-58 fin which has an exposed span frequency values were then passed on to the flight of about fifteen feet excitation double amplitudes of test engineer as soon as he finished with the tail about one inch gave much better results than am- damping records. The procedure of excitation and plitudes of one quarter of an inch. On the wing, w a s then repeated for amplitudes of one inch also gave better results than recording of damping records amplitudes of one quarter of an inch. I am not able the wing.

to define all the pertinent parameters, but I am sure In the ground station we had a group of about that the ratio of the excitation amplitude to the ran- six flutter engineers. These men monitored the dom steady state amplitude is important. We try to information. as it was received. They determined obtain excitation amplitudes of at least three to four damping and response frequency on apreliminary basis times the normal random amplitude, I suspect that the boundry layer thickness may also have a bearing within a few seconds and added these new points to the plots of data previously taken. All during this on this problem. At any rate, the amount of ex- time, the new data points were being monitored and citation amplitude required to give good flutter data considered by a senior member of the flutter crew. is a subject on which research i s needed.

If everything appeared in order at the conclusion of the planned testing at the speed point, the senior O.K. for the airplane flutter engineer would give his IMPROVEMENTS IN FUTURE FLUTTER crew to increase speed to the next scheduledpoint.

TESTING Normally this increment was one tenth of a Mach number.

I might pass along the following comments on The procedure described above takes about ten what we consider to be needed improvements in the minutes to accomplish three sweeps and six damping field of flutter testing. One very important practical runs. In practice, however, we found that we never problem is the amount of time required to obtain quite followedthisprocedure for one reasonor another.

data. This definitely needs to be shortened. But One thing which effected the plan was the time avail- directly opposed to this requirement is the need to able. We were limited in telemetering range to obtain more complete and better data. I think the about ninety miles radius, and it doesn't take long to best solution of this dilemma lies in automatic data fly by at high speed. Also, we often found it necessary reduction equipment. Our sweep plotter is a step to make repeat runs to get good data. As a result in this direction.

of this, other items in the flight test plans, and the inevitable descrepancies which always show up from a definite im- Another thing which would be time to time in experimental airplanes and instru- provement in our system would be to recordinfor- mentation, we usually were in the position of trying mation on how much response is being obtained for a to finish one point and start another.

given input. Our current B-58 instrumentation does not give this. However, I think that this could be achieved if the necessary development work were done TEST RESULTS I believe it is entirely on the instrumentation.

feasible to obtain an automatic sweep plot in terms I have some comments and observations that I of response amplitude per pound of excitation or per might pass on as a result of our experience on the degree of control surface rotation.

B-58.

CONCLUSION A very basic need has become clearly apparent during this program. I think this is a need which To us at this time, it appears that the best applied to all of us who are engaged in flight flutter approach to the problem lies through frequency re- testing. This is to be able to predict in advance sponse data. It is technically feasible to obtain in- what our test results should be. To do a real engin- formation of this type which would be directly com- eering job on flutter, we need to make our pre- parable to the airplane data by both calculation and dictions in terms that we can measure directly on an model test. This would be costly, but I believe it airplane in flight. Then we could spot check enough would save money in the long run if we could do a points to prove that our engineering predictions were good job in this respect. Certainly it would enable correct and greatly reduce the costly task of proving us to do a better, safer, and shorter job of flight an airplane is free from flutter.

that flutter testing.

DOUGLAS EXPERlENCE IN FLlGHT FLUTTER T E S T l N G

J . Philbrick - Douglas, Santa Monica, California

Abstract The Douglas Aircraft Company has required extensive flight flutter tests on all aircraft models and versions which have been produced since 1954.

Douglas Aircraft Company experience in flight The objectives of these demonstrations have been flutter testing is reviewed briefly, with comments on state-of-the-art excitation and instrumentation 1) verification of analytical predictions, and 2) de- techniques used up to the present time. The limita- monstration that unpredicted instabilities do not exist.

tions of previous techniques are discussed with em- The responsibility for these demonstrations is shared jointly by the Design Engineering and Testing Divi- phasis on the problem of: sions. A policy, based on the airplane type, perfor- (a) Establishing a flutter margin of safety for mance capabilities, and the aero-elastic character- predicted marginal flutter modes. istics predicted by theoretical analyses and flutter model tests, has been established for the flight conditions, airplane configurations, instrumentation, (b) Resolving instances of flutter not predicted by theoretical calculations in advance. and the data reduction techniques to be used for these flight demonstrations.

(c) Delaying the airplane demonstration by time consumed in acquisition and reduction of Experience has shown that neither the theore- flutter data. tical predictions nor the flight test techniques used to date have been infallible. The intent of this paper Current Douglas philosophy in flight flutter test- is to show the shortcomings of earlier techniques as revealed by flutter experience obtained from tests ing is presented and a description given of: of current aircraft.

(a) Steady-state vane excitation system develop- ment. EVOLUTION O F TECHNIQUES The initial flutter programs were conducted by (by An automatic data handling system.

monitoring the decay of structural motion excited by (c) The potential application of automatic com- manual control surface pulse inputs. Instrumentation puting methods for increasing flutter data consisted of strain gage type accelerometers installed yield. at the aircraft extremities or at locations having large response amplitudes in the predicted flutter modes.

INTRODUCTION Control surface positions were measured using elec- trical potentiometers to define the character of the The development of high performance aircraft input pulses and to detect coupling of control sur- of various configurations with increased flexibilities faces in the flutter mode. Data were usually obtained and concentrated weight items at structural extrem- on airborne oscillographic recorders; however, direct ities has made the consideration of flutter not only a writing pen type recorders have occasionally been design criterion but also an important flight demon- used to allow immediate monitoring of the data as stration item. obtained.

Sharp control surface inputs were made at The next figure (Fig. 2) shows the damping incremental airspeed and Mach number as the flight trends as indicated from the above aileron input envelope w a s extended. The tests were run at a investigation. Data scatter and failure to excite the symmetric flutter mode lower than about 85% of the relatively low altitude to minimize Mach buffet required demonstration speed did not allow extrapola- effects during airspeed advances, and, conversely, at a higher altitude to minimize rough air effects tion to the zero damping speed or instill much con- during Mach number extensions. It was also found fidence in investigating this flutter case further. It advantageous to schedule flutter flight tests in the is obvious that a more efficient excitation method early morning and/or over the ocean to minimize would be desirable in this case.

atmospheric turbulence.

Although this approach to flutter testing re- quired a minimum of test equipment and installation, the quality of the data obtained did not always pro- vide consistent stability indications. Data scatter resulted primarily from 1) the manual pulsing de- pended on pilot ability for repeatability of pulse duration and magnitude, 2) the pulse energy w a s not directed to the desired mode, that is, symmetric wing modes were poorly excited by elevator pulses and not at all by conventional aileron inputs, and 3) the tranducer outputs were often masked by buffet and other extraneous vibration.

Various harmonic analysis methods were used to extract information from the recorded data. The Fourier analysis and transfer functions proved useful for separating frequency components which could be used to follow flutter trends.

Figure 2.

The results of several flutter programs illus- trate many of the above difficulties. A s an example, Figure 1 shows an oscillograph record obtained during Figure 3 shows the structural response of a sin- an aileron input while investigating a symmetric wing gle jet airplane following a rudder pulse. The exci- tation in this instance was adequate for exciting the bending-torsion flutter case on a twin jet airplane.

The initial asymmetric response degenerates to the aft fuselage torsion-vertical stabilizer bending mode; however, the airplane had been previously flown be- desired symmetric mode after approximately four yond the flutter speed where rough air was sufficient cycles; however, in view of the background noise, to precipitate an instability which had not been ex- it was extremely difficult to obtain accurate structural cited during the initial pulsing program. Fortunately, damping from the decay in the required symmetric mnrlp the flutter, although severe, was non-destructive and Figure 3.

Figure 1.

Sinusoidal excitation from manual elevator in- the pilot had an opportunity to perfect his rudder puts has proved successful for exciting structural pulsing technique by using sharper and harder inputs.

response at frequencies below five (5) cps. The inppt Subsequent investigation using the perfected rudder for single frequency and frequency sweeps was con- pulsing provided consistent stability data which allowed trolled by having the pilot synchronize his input rate a definite extrapolation to the flutter speed. This trefid a is shown in Figure 4. to the response of tuned reeds. In one instance, photograph of a rather voluptuous lady encased in a plastic projector had the exact mass required to tune Manual control surface pulse excitation has been adequate for certain flutter flight testing; however, a reed for a particular frequency, Airplane and pilot in many instances, its use was restricted by pilot response to this device was excellent. For some un- ability, response of the control system, and poor known reason, the reed was lost on the last flight of pulse energy transfer to various parts of airplane this flutter program.

(Le., elevator to wing). Except for control systems Instrumentation for flutter flight testing has al- with extremely slow response rates and the cited difficulties, structural modes with frequencies below ways posed a problem. The frequency response and output of most commercially available transducers re- 10 cps can be excited by manual pulsing techniques.

quire some compromise to cover the required flutter The shortcomings, as noted above, of manual acceleration and frequency ranges. The strain gage pulsing have led to the investigation of auto-pilot type accelerometer has been an usefuldevice from the inputs, ejection of bombs and stores, and devices standpoint of size, calibration, and maintenance. Strain gages for load and stress measurement in oscillating to pulse flight controls. The low frequency re- components provide cleaner data than the accelerom- sponse of auto-pilots (below 5 cps) and the inadequate energy transfer from control surface inputs have, in eter; but the installation, calibration, and maintenance general, negated this method of excitation. Bomb and of gages is much more difficult. Control surface store ejections have been satisfactory in some in- positions from electrical potentiometers are fairly reliable, but frequency response and lack of sensitivity stances; but, usually, the sharp input, limited bomb carrying capacity, and cost of ejected items have at low amplitudes limit their usage. Greater reso- Devices for lution and frequency response a r e possible from strain made this excitation method prohibitive.

gage bending beams operated by a cam onthe rotating control system pulsing have extended the input capa- bilities but are still subject to the limitationsas cited member. The output and linearity of these items can for manual pilot inputs. The need for a consistent be adjusted by their physical geometry.

pulse input that could be applied at a discrete Extraneous vibration at frequencies above the structural point has led to development of an impulse flutter range tends to mask the accelerometer outputs.

generator unit. These units are essentially small Several types of electrical filters have been developed.

rocket motors having a specific impulse and burning A unit package in a case similar to the standard time dependent on the amount and type of propellant 350 fl galvanometer shunt has proved most useful used. The size of these devices has allowed installa- tion in fairly limited spaces and has provided ex- and provides a 6db/octave attenuation o r can be cellent pulse inputs. The details and usage of the seriesed to give multiples of this attenuation. The units have been designed for roll-off frequencies of 20, impulse generator excitation method were presented in a preceding paper * at this symposium. 30, 40, and 60 cps.

Airborne recorders have beenutilizedfor flutter data recording. The standard 18, 36, and 50 channel CEC oscillogarphs have been used mainly for their frequency response, adaptability to the transducer outputs, and the analogpresentationof the record. The photographic developing the oscillograph record has been a delaying factor in some flight flutter programs.

The currently available direct writing oscillographs and magazines have largely eliminated this problem.

In an effort to increase the airspeed range per flight and to provide simultaneous flight coverage, FM/FM telemetry has been used during recent flutter (8) standard sub-carrier frequencies testing. Eight from 5.4 to 30 KC combined and transmitted on 230.0 megacycle carrier has been used. The composite signal is received at a ground station where it is tape recorded, discriminated, and displayed a s an analog record. One o r two flight test engineers can reduce the flutter data from these records and keep a running plot as the flutter test progresses. Portable FM/FM Figure 4.

response of auto-pilots and the indefinite cut-off of telemetry stations and relay stations have been used inertia devices have made these excitation to extend the receivable test area. rotating methods undesirable.

Occasionally, the manner in which the flutter test is conducted does not reveal the existence of a The Douglas Aircraft Company is presently Figure 5 illustrates a flutter evaluating the use of auxiliary airfoils for steady critical flutter case.

state flutter excitation. The first system was deve- incident of this type. The initial data obtained during loped by Electrosystems, Inc., Burbank, California,

10,000 and 35,000 foot altitude airspeed - Machnumber

extensions indicated adequate stability in the hori- and consists of two vanes to be mounted a t the zontal stabilizer yaw - aft fuselage roll case. Subse- airplane wing, horizontal stabilizer, and/or vertical are driven in pitch by quent data obtained at intermediate altitudes showed an stabilizer tips. The vanes hydraulic servo valves and actuators which are con- adverse Mach-airspeed combination withan instability trolled by an electronic programmer.

within the required flight envelope. Based on this result, flutter flight programming. has specified that The inter- tests be accomplished at three altitudes.

The vane system is designed to provide sym- mediate altitude is chosen at an estimated maximum metric and antisymmetric excitation in the frequency "q" - Mach number combination.

range from 1/2 to 15 cps a t a maximum input force of 250 pounds (vector). Individual mode tuning, auto- matic and manual frequency sweeps, and instantaneous cut-off for decay monitoring are possible. The equip- ment will operate with 3 square feet vanes to an air- 300 knots and with 2 square 'foot vanes to speed of The system is schematically shown above 400 knots.

6.

in Figure The vanes are hinged and mass balanced forward of the 25% chord to maintain a stable aerodynamic trail position when inoperative o r following an emer- gency shut-off. The emergency shut-off will be a by-pass valve in the actuator.

accomplished by Viscous damping can be introduced for vane stability by varying the restriction in the by-pass valve and line.

Airplane protection is afforded by a force feedback system which maintains the mean vane position at the zero force angle of attack. Automatic shut-off is provided for in the event that the input force or airplane structural response exceed a Figure 5.

The various flutter programs have shownthat the excitation methods, data availability and reliability, and the necessity for a complete airspeed-Mach number build-up for eachairplane configuration and/or flutter f i x have been the primary sources of airplane demonstration program delays. The cost of flight test time and the hazards involved on current airplanes provide sufficient justification for a determined effort to eliminate the items cited above.

FUTURE PLANNING For a number of years steady state excitation has been advocated for flight flutter testing. Auto- pilot cycling of control systems and rotating weight Figure 6.

devices have been used; however, the low frequency pre-selected value. In the event that the automatic look, playback and editing facilities are included in the computer station for scanning and editing flight test shut-off items do not operate, a fracture joint in the data. The required flight data, transducer calibration vane torque tube is designed to failandshed the vanes are fed automatically at an input load below the airplane structural limit. data, and the analysis program into the digital computer allowing analysis of flight test data in greatly reduced time.

The vane system provides a means for exciting airplane vibration modes in-flight and willallow mode surveys for comparison with the calculated and ground In addition to the above, further savings in the vibration modes. The system also allows excitation time required for flight flutter testing may be possible of the modes deemed flutter critical for monitoring with multiple mode excitationusing mixed input signals frequency shifts and damping trends during Mach- with the flutter excitation equipment previously men- airspeed advances.

is compared tioned. The composite response signal to the frequency components of the input signal through It is expected that the vane excitation system an analog-integrator, which rejects the frequency will conserve flight flutter test time, as compared to components different from the selected period of the" previous methods, by providing a more positive ex- integral. The chief advantages of this technique are: citation of the flutter modes, increasing the data 1) various modes can be simultaneously tracked confidence factor, and allowing an evaluation of con- throughout the airplane speed range, 2) modal response figuration changes o r flutter fixes from data obtained can be extracted in the presence of noise. The most from a single flight.

serious disadvantage of this approach is the long integration time necessary to establish the response In conjunction with a general effort to improve of a lightly damped mode in the presence of noise overall flight test procedures, the Douglas Aircraft or another mode at nearly the same frequency; i.e., Company in conjunction with the Consolidated Electro- a number of integration processes are necessary to dynamics Corporation is currently developing an auto- reject the close sideband frequencies. Evaluation matic data handling system (ADHS) to expedite the of this technique and efforts to overcome the cited acquisition, handling, and reduction of flight test data.

are being continued.

disadvantage Although the ADHS was not designed specifically for flutter flight testing, the fiutter data requirements were Separation of the structural response of modes integrated in the design specification.

of small frequency difference may be improved by selecting locations for pickups such that each pickup The ADHS consists of an airborne system, a will discriminate against one or more modes and ground station at the test site, and a computer station.

enhance others. By feeding the selected pickup out- The airborne system will sample the analog voltage puts into an analog-type computer, the read-out willbe outputs of the various test data transducers, convert several independent signals, each corresponding to a these outputs to binary digital form, record the single degree of freedom representing an orthogonal digitized information on magnetic tape, telemeter mode of the airplane. A simplified example of this the digitized information to the ground station over approach would be a sum and difference of the outputs a PCM (pulse code modulated) link, and provide in of pickups located at opposite wing tips of an airplane.

larger airplanes, a "quick-look" facility for a flight Summation of the pickup outputs would magnify sym- test engineer's control information. The sampling metric mode response and minimize anti-symmetric rate and accuracy allow frequency resolution up to response. The selection of pickup locations and the 100 cps and to 1 part in 1000 for 100 data channels.

analog circuitry and constants necessary would be Super and sub-commutation of the input channels al- accomplished either during ground vibration tests or lows either higher frequency resolution or an in- while surveying the in-flight vibration modes. The creased number of input channels, respectively. By combination of pickups and analog to accomplish this modular design, the physical size of the airborne function has been termed a "modal pickup."

unit can be tailored to the aircraft size by restriction of number of data channels. The maximum uncom- A combination of the "modal pickup" and multi- mutated high frequency capacity (100 channels) can be utilized in the larger transport and bomber airplanes frequency excitation techniques may be used to follow and approximately thirty (30) channels in an airplane the amplitude and phasing of several airplane modes.

This could be accomplished by driving a common ex- of the A4D size.

citation system from severaloscillators, each of which The ground station is mobile to permit coverage is tuned to a different modal frequency, andby cross- of many test sites and contains the telemeter receiver, correlation integration of the modal pickup outputs a tape recorder, and a "quick-look" analog presenta- with the proper input signal the sine-cosine component tion to allow safety monitoring of the flight test data. and frequency of each mode will be obtained.

The compatibility of the ADHS with a digital computer has been one of the design premises. Although the above equipment and concepts have not been fully flight demonstrated, their preliminary The computer station is somewhat similar to the evaluations appear promising.

ground station; however, it will not be mobile. Quick- CONCLUSIONS safe execution of a flight demonstration program.

Similarly, adequate i n s t r u m e n t a t i o n, excitation methods, data analyses, and coverage of design flight Although the validity of analytical predictions envelopes must be provided to insure valid flight test and flutter model tests have not been discussed, it is apparent that the character of the flutter coupling results.

(catastrophic o r otherwise) must be known for the THE APPLICATION OF PULSE EXCITATlON TO GROUND A N D FLIGHT V l B R A T l O N TESTS W . R. Laidlaw, V , L. Beals - North Americcln Avicltion

Corporatioiz, Colr~n2biis, Ohio

Abstract ing characteristics from either a transient o r steady- state structural response have been devised. Never- A discussion of the relative merits of sinusoidal theless, the measurement of the aircraft mo,dal versus non-harmonic excitation for flight flutter test- damping characteristics, even on the ground, repre- ing is presented. It is concluded that the use of sents a not in-considerable experimental effort both in transient excitation is rapidly becoming a necessity. time and in the accuracy of the experimental techni- ques required. Thus, it is not surprising that con- The application of small-scale rocket motors to the excitation of the aircraft is suggested. The design siderable difficulty should be experienced in any and development of rocket motors specifically for attempt to determine the modal damping in flight.

flight flutter testing is described. Methods of measur- ing and analyzing the transient response of the aircraft The technique most frequently employed in are discussed, and the techniques of theoretically ground vibration testing is to excite the aircraft in a predicting the structural response a r e described.

natural vibration mode using external sinusoidal ex- citation. By rapidly removing this excitation and INTRODUCTION causing the structure to decay exponentially the structural damping can be measured. With careful In considering the multiplicity of problems experimental techniques it is possible in this way to associated with the development of adequate flight measure the structural damping during ground tests flutter testing techniques, ones attention is im- with reasonable accuracy.

mediately focused upon the initial problem of exciting It is quite reasonable when first contemplating the aircraft. Since there are basically only two flight vibration testing to attempt to extend this

methods of exciting the aircraft; namely - sinusoidal

o r non-harmonic, it would appear at first inspection sinusoidal testing technique to the determination that the choice would be simple. It becomes rapidly of the aircraft vibration and modaldamping character- apparent to the experimenter however that eachof these istics in flight. This has, in fact, been done with methods has associated with it a unique series of both varying degrees of success. By varying the forcing theoretical and experimental problems which must frequency it is possible to determine the damping of be solved in order to insure the success of the flight the system from a knowledge of the frequency re- program. sponse characteristics of the structure. However, attractive the sinusoidal excitation may be con- A large number of experimental methods have ceptually, it presents many serious problems practi- been employed in flight flutter testing in the past cally, which in many instances preclude its use.

and improved methods are constantly being developed. Not the least of its limitations is that the airborne Common to all of these, however, is the basic neces- equipment required to provide the sinusoidal ex- sity to determine the effect of varying flight conditions citation is extremely heavy and requires considerable on the damping characteristics'of several of the lower space for installation. In the case of small aircraft aircraft vibration modes. A wide variety of techni- this single factor may be sufficient to preclude the ques for experimentally determining the modal damp- use of this technique.

With the size of sinusoidal excitation equip- ducted on short notice. This technique is ideally suited to many types of testing and no further ment i s alSo associated a high degree of complexity sophistication is required. However, it is frequently which reduces reliability and increases the cost of the impossible to adequately excite the aircraft vibration program. Existing aircraft power sources a r e fre- mode desired by pulsing a control surface. For quently inadequate and it becomes necessary to in-

example - symmetric wing bending modes are ex-

stall supplementary power supplies. In many cases tremely difficult to excite by any abrupt control input.

it is necessary to install major portions of the The increasing, and now almost complete, use of excitation equipment during the construction phases powered or boosted controls further decreased the of the aircraft. Further, in order to provide the usefulness of this technique. "Stick-banging" will required force levels, the actual shaker itself may be continue to be a frequently used tool but it is not sufficiently massive to compromise the free vibration cabable of meeting all the requirements for a com- characteristics of the flight surfaces being studied.

In the practical use of sinusoidal excitation it is neces- pletely general technique which will handle all pro- sary for either the pilot or a suitable servo-mechanism blems which arise.

to vary the forcing frequency over a prescribed fre- The second method for providing transient ex- quency range. By measuring the response of the citation to the aircraft is by attaching a suitable flight surface, the modal damping can be determined.

"disturbance generator" to a lifting surface. This If the forcing frequency is vatied too rapidly, the basically can be any device which is capable of storing response is no longer simple harmonic and the test energy and releasing it rapidly, thus applying an becomes transient in nature. Therefore, there is a impulsive force to the structure. This might be finite time required to sweep the desired frequency accomplished in any number of ways; such as re- range during which steady flight conditions must be leasing a high velocity liquid or gaseous jet or by maintained. The pilot's complete attention i s re- releasing a concentrated mass from the surface. The quired during this period in maintaining the flight a device would require that optimum design of such conditions constant and in some cases in actually the unit be simple, light, small, reliable and self- performing the frequency sweep. In highperformance

contained - that is, not require extensive aircraft in-

aircraft, where quite often the flutter-critical flight stallations. A small solid propellent rocket motor condition can only be achieved momentarily, these attached to the structure satisfies these requirements requirements are impossible to meet and a transient nicely.

Further, a rocket motor is easily designed testing method is required.

to provide a variation of force-time histories to suit test requirements.

varying Thus, for many reasons (light weight, installation simplicity, minimum requirements for pilot's attention The idea of using rocket motors (ballistic im- and the ability to obtain data during transient flight pulse units) to provide an impulsive excitation to an is led to a choice of conditions) the flutter engineer aircraft structure for flight flutter testing purposes transient testing techniques. Basically, in transient i s not at all new. Although no published record of flight flutter testing, the response of the structure such experiments i s known to the authors, it i s appar- to a non-harmonic forcing function is studied to deduce ent that many experimenters inthis country and abroad the modal damping of all significant vibratory modes.

have used this technique with varying degrees of suc- One possible source of non-harmonic excitation is the cess. Two major difficulties can be expected in using onmipresent aerodynamic turbulence. This is an

ballistic impulse units for in-flight excitation; namely -

that it required no ideal forcing function in the sense the difficulty in obtaining simultaneous ignition of airborne equipment for its generation. However, it is multiple rocket motors and the difficulty of exciting necessary to determine the exciting force in order to all flutter significant vibration modes with a limited interpret the meaning of the response using this number of impulse units. Since the prime danger in technique. This alone is a problem which could easily flight flutter testing is that of not observingthe modal consume several careers in its solution. Due to the damping of the least stable flutter mode, it is present technical diff iculties encountered in attempting mandatory that whatever technique of excitation is to exploit this means of excitation no further dis- employed provide adequate knowledge of the damping cussions of this form of transient excitation will be characteristics of all flutter-significant modes. The pursued.

decisions as to what mode i s significant must be made in advance by the flutter engineer.

Two other basic types of transient excitation however a r e considered sufficiently practical to be In the following sections the development of useful at this time. One of these has beenaptly ballistic impulse units specifically designed for flight described as "stick-banging" o r "rudder kicking", is described, as well as the associated flutter testing according to the surface under investigation. It has instrumentation and supporting analytical and data seen considerable use in the past by several flight reduction techniques.

flutter experimenters. This technique does not nor- mally require special airborne equipment for gener- OPTIMIZATION OF IMPULSIVE FORCING FUNCTION ating the impulse except for a robust pilot. In this respect it provides a minimum weight, maximum On the basis of the reasoning in the previous simplicity installation and is suitable for tests con- section, it i s concluded that the use of transient flight flutter testing techniques is inevitable and that the IAXIMUM RESPONSE OF AN UNDAMPED use of airborne impulsive excitation is a practical SECOND ORDER SYSTEM TO A means of providing the required transient force. The TERMINATED STEP AND TO A application of rocket motors (ballistic impulse units) SEMI-SINUSOID to this purpose offers apractical engineeringapproach to the accomplishment of transient excitation. It Maximum Response is recognized that past use of such devices has met to Square Wave with some difficulties, however, it is felt that by designing special rocket motors for their special task and by utilizing them in an-efficient manner that Max Response to Semi- many, if not all, of the previous problems can be Sinusoid Occurring it was eliminated or ameliorated. Specifically, initially felt that by careful design of the rocket Function is Still motor's ignition system utilizing the lastest techno- logical advances available to the ordnance engineer, simultaneous ignition of multiple motors could be accomplished. Recently it has been demonstrated

\ 1

in actual tests of several prototype motors, + a t ex- \ Maximum Response to cellent repeatibility of ignition times is realizable. Semi-Sinusoid Occurring After Forcing Function For all practical purposes it can now be stated that is Removed simultaneous ignition of several motors is a readily accomplished fact. Details of the actual ignition system design are presented in a later section.

The problem of exciting all flutter significant 0 1 a 3 4 5 6 modes by an impulsive force has been given consider- able study. By optimizing the forco-time history of $e impulse unit and the location of the motors, the required force level to excite the desired mode can be minimized (and thus the size of the motor). Thus Figure 1. Maximum Response of an Undamped Second optimization increases the probability of getting apure Order System to a Terminated Step and to a modal response to transient excitation.

Semi-Sinusoid It can be shown analytically that the maximum response of an undamped second order system can be maximum amplitude response after removal of the obtained by a step function input. More specifically, transient forcing function. It is notedthat the optimum when considering an impulsive forcing function, the time duration for this impulse is somewhat less than maximum dynamic response of the system (twice static for the response during the time the forcing function deflections under the applied loading) can be achieved is applied to the structure. A brief study has shown that the mere accompliswent of a maximum response by applying a terminated step-function of period equal is not necessarily the optimum for flight flutter to the half-period of the vibration mode being sought.

testing purposes. It can be shown that a considerable If the period of the forcing function is less than the half-period of the vibration mode being excited the improvement in the purity of the desired mode C ~ Q dynamic response will be less than maximum. The be achieved by proper selection of both the impulse maximum response will be constant for periods greater shape and duration. Analyses to date have been than the vibration mode half-period. For all impulsive confined to a comparison of terminated step-function and semi-sinusoid inputs. Appendix I shows typical forces other than terminated step-functions (greater examples of the modal purity as effected by the time than half-period), the dynamic response is less than duration for both shapes of inputs. It can be con- twice the static deflection under the applied load.

cluded that the square-wave input behaves like a high The dynamic response of an undamped second pass filter and the semi-sinusoid like a bandpass order system has been studied when the impulsive filter.

force is a semi-sinusoid (i.e., the first half cycle Assuming the duration of boththe semi-sinusoid of a sinusoid). This represents approximately the force-time history that can be rather easily obtained and the terminated step-function impulses to have a from a ballistic unit. Figure 1 shows a comparison duratioq which will provide maximum response, it can be seen that all frequencies above the desired mode of the system response characteristics when excited will have maximum response (assuming the force is by either a terminated step-function or a semi-

fed into the mode optimally - not at a node line)

sinusoid of varying duration. It is observed that when excited by the square-wave. The response of the maximum dynamic response is achieved when the higher modes to the semi-sinusoid become attenuated.

period of the forcing function is approximately 1.6 times the half-period of the mode which is to be The lower frequencies of both are attenuated approxi- mately equally. Even though the square-wave will excited. The dashed curve of Figure 1 shows the produce a greater response than the semi-sinusoid, Further improvements in the response purity can the addedadvantage of high frequency attenuation offer- be achieved by careful location of the rocket motors ed by the semi-sinusoid leads one to a selection of on the aircraft structure. In general, the maximum this form of excitation. purity would result if the ballistic unit could be located simultaneously at an anti-node of the desired mode A further improvement in the purity of the and on the node lines of all other modes. This would structural response can be achieved by deviating from at the same time maximize the generalized force the "amplitude-optimum" period of the semi-sinusoid. provided to the desired mode and minimize the gener- all other modes.

By increasing the period the high frequencies are alized force in Since it would be an further attenuated, but not without amplifying the low extremely unique structure that would meet the above frequencies. Since generally the lower vibration modes conditions, carefully selected locations, which will a r e more likely to mark the desired modal response, come as close as practical to this ideal, should be it is more desirable to lower the periodof the forcing sought. Practical considerations will further dictate function to attenuate the "lows". A slight increase in that the rocket motors be located on major structural the response of the higher frequencies will accompany

elements - not on skin panels. A typical installation

this, however, the response characteristics are such a s pattern is shown in Figure 2. It should be noted to produce a much more marked effect on the "lows" that charges a r e located onboth sidesof the structure.

than on the "highs". The exact period of the semi- This is to allow the application of force in directions sinusoid which will produce the purest possible wave compatible with the modal deflections.

shape must be determined for each case as a function of the ratio of the frequencies to be suppressed to the Practically, it is impossible to manufacture desired frequency. a ballistic unit which terminates as abruptly a s a semi-sinusoid. In truth, an unavoidable trailing off It appears that further improvement in the purity of a force-time history over a reasonably long time of the response could be realized by suitable design period, as compared to the characteristic time, is of the force-time history - the final objective being observed. However, by careful design it has been to provide an impulsive shape which would give a possible to achieve a very close approximation to large response in the mode desired and a minimum the semi-sinusoid (see Figure 3). Details of this motor design are discussed in the following section.

response in all modal frequencies, either higher or lower. For the development program being described, this refinement w a s not considered warranted. Accord- DESIGN DETAILS OF NAA ROCKET MOTORS ingly, a semi-sinusoid of one-half the period of the mode to be excited was selected. This, as can be The actual details of the NAA rocket motor seen from Appendix I, gives substantially greater design and their physical installation is worthy of response purity at all frequencies than the square- further discussion. In particular, those aspects of the wave. The reduction in absolute response can be design which give repeatibility of ignition periods compensated for by approximately a 25% increase deserves special mention. Also a discussion of how in force level.

@ THRUST DIRECTION - U P

0 THRUST DIRECTION DOWN

0 3 I

0 3

-

I

Figure 2. Typical Placement of Ballistic Impulse Units on an Airfoil to Excite the Usual First Three Symmetric Modes the force levels and time duration are controlled i s COMPARISON OF MAXIMUM DEVIATION pertinent.

ENCOUNTERED IN EXFERIMENTAL

THRUST - TIME HISTORIES AND

The basic cartridge is fabricated out of 4140

I DEVIATION FROM TRUE SINUSOID

steel in two pieces; - namely, a base unit which is

bonded directly to the aircraft structure andthe motor unit which is attached by means of screw threads to the base. This two-piece design minimizes the exposure time. of both the aircraft and personnel to the live rocket motors and provide a high degree of interchangeability. Further, since the ballistic units must be replaced after each firing, it allows re- placement of the rocket motors without disturbing the airplane attachment. The base of the two-piece unit is externally bonded to the aircraft structure using a polysulphide type bonding material. A curing period of two hours at a temperature of 140°F is required.

The base unit includes the electrical contacts to which the electrical fire control system is attached.

A drawing of the rocket motors and attachment pads are shown in Figure ( 4 ) . A suitable aerodynamic fairing is placed around the motors to minimize drag.

Due to the small volume of the charges it was im- practical to design the steel case to withstand the "lock-shut" pressures, This is the pressure which would build up within the cartridge were the exit orifice plugged. Normal operating pressures of the internal ballistic unit range from 4000 to 10,000 psi.

A typical "lock-shut" pressure ranges between 40 and Figure 3. Comparison of Maximum Deviation 50,000 psi. Internal temperatures during detonation

Encountered in Experimental Thrust - Time

are of the order of magnitude of 3000" Kelvin.

The Histories and Deviation from True Sinusoid STEEL BASE MAGNESIUM DISC -SCREEN SPACER RING STEEL BODY SEALING DISC CARTRIDGE NOZZLE MAIN PROPELLANT - ELECTRIC PRIMER CAP M2 Figure 4. Cutaway of Ballistic Impulse Units sonable repeatibility can be expected over a range of total rocket weight varies from 0.6 to 0 . 8 lbs and produces a thrust of 50-200 pounds as required. The 4 0 ° F . With special propellents which possess the unitsare approximately 2-1/2"long and 1 " in diameter unique characteristics of having a range of Combustion except for the base. chamber pressure over which the burning rate is con- stant, it is possible to successfully increase the The ignition system consists of two parts: temperature range within which reproducible force- A M52A3 electric primer (Lead Styphnate), which time histories can be achieved. Since the aircraft a wide range of temperature this is an becomes unstable when an electric current is passed operates over through it, triggers a black powder igniter charge, absolutely necessary design condition. All rocket (type A4BP) which in turn ignites the mainpropellant. motors for use in flight testing must have reasonable A thin magnesium disc separates the igniter charge temperature insensitivity. Since the burning rate is from the main propellant. By delaying release of the independent of the combustion chamber pressure for this special propellent, it is then possible to control energy generated by the igniter until a more complete the time duration of the impulse by the quantityof burning of the charge occurs, this disc serves to improve the repeatibility of ignition time. This disc propellent provided and the force level by the nozzle also serves the function of providing a moisture design. With the M-2 propellent these two design seal for the black powder igniter. When this seal is requirements are inseparable. Thus, using the special ruptured, the igniter triggers the main propellant propellent it is within the realm of practicability for the flutter engineer to maintain a storehouse of rocket (M-2). This propellent consists of several cylindrical charges to which he can f i t a variety of nozzles; thus single-perforated grains. The total charge weight varies from approximately 1.1 grams for short dur- he can construct a force-time history at the test ation impulse units (7 to 9 milliseconds) to 2.8 grams site without recourse to further ballistic testing.

for longer duration impulses (28 milliseconds). This Such a kit of motors and nozzles is one of the final compares to approximately 3 grams of propellent aims of this development program.

in a typcial 12-gauge shotgun shell.

By the above design procedures and by paying The propellent grains are each individually careful attention to details, it has been possible to selected by hand to minimize burning irregularities. achieve virtually simultaneous ignition of several Approximately 10% of the grains a r e rejected in this motors. The time elasped between receipt of the hand selection process. In order to obtain a sharply electrical impulse to the electric primer and the start termmated long duration impulse (28 milliseconds) of the pressure build-up in the rocket motor is less each individual propellent grain is oriented in a spe- than 0.1 milliseconds. Figure 3 shows the repeatibility cial direction in the rocket motor. The main pro- of the force-time history. The deviation between the pellant is sealed from the combustion chamber by an two traces of Figure 3 is the maximum deviation aluminum disc. This is done to achieve a maximum observed over a large number of tests on prototype burning rate of the propellent prior to the release units. It has further been possible to tailor the force- of the energy. This provides a maximum repeatibility time history to very nearly approximately a semi- of the characteristic rise time and improves control is a much easier task for short dura- sinusoid. This of the force amplitude. A screen is provided between tion impulse units than it is for the larger duration the aluminum disc (which is ultimately ruptured) units.

and the exhaust nozzle. This screen prevents plugging Certain safety considerations were observed of the nozzle by propellent particles, thus achieving throughout the design of these rocket motors. In a clean force-time history by minimizing higher order

particular the two-piece design minimizes the per -

disturbances as well as reducing the possibility of sonnel hazard by allowing the actual propulsion units explosion. The volume of the combustion chamber is to be stored in a magazine until just prior to the test carefully designed to achieve the desired internal flight. For indoor firing, an inexpensive personnel pressure and hence force level. A nozzle is located shield can be provided at a distance of approximately in the end of the combustion chamber of the rocket 15 to 20'. This shield can be constructed of 1/4" to motor. Very careful hand reaming techniques a r e 1/2" plywood o r plexiglass and provide adequate necessary to get good repeatibility of both force am- safety. The only personnel hazard at a reasonable plitude and time duration from the rocket motor. A distance from the charges is that of explosion, The retaining ring and blowout seal are provided over the normal firing of the charges, except for the danger nozzle to prevent the intrusion of foreign objects.

of explosion, could be observed from as close as 5 feet. The charge produces a flame pattern of ap- The burning rate of the M-2 propellent, which proximately 2' with flame temperatures considerably is being used in the prototype rocket motors, is less than 1500" Kelvin. The charges are capable of approximately a linear function of the internal com- bustion chamber pressure. Since the internal pres- operating or being stored in an environment of up to sure is critically dependent upon the temperature of 160°F with very adequate margins of safety.

the propellent at the time of ignition, it is necessary to confine the operation of the prototype ballistic The only auxiliary equipment required to be units to a narrow range of temperatures. They are used with the rocket motors is a fire control console.

designed for a normal temperature of 70°F and rea- This unit provides the required triggering voltage to the electric primer. This is accomplished in most sents the true damping and bears no relationtothe cases by a condenser discharge across a resistor.

familiar V-g curves used in "critical" flutter an- The actual airborne fire control circuit provides for alyses). This plot provides the analytical equivalent sequential selection of multiple rocket motors. For of the flight flutter test. The possession of such an example, it will fire units in the following sequence: analytical result can well save the flutter engineer the embarassment of watching the wrong mode with (1) 2 units to excite first bending possibly disastrous results.

(2) 4 units to excite second bending (3) 4 units to excite first torsion AIRBORNE INSTRUMENTATION This sequence can be either qt the pilots dis- The entire paper has been centered so f a r on a cretion or can be done automatically. In order to discussion of the techniques of providing the excitation minimize pilot-attention during the flight flutter pro- to the aircraft structure.

Equally impartant is the gram the automatic feature is recommended. The necessity of measuring the structural response and fire control console will draw its power from the this data to obtain the modal damping of the reducing aircraft electric system, the output of which will be flutter-significant vibration modes. The transient rectified and filtered to provide the desiredelectrical nature of the response substantially increases the impulse to the electric primer.

degree of sophistication of airborne instrumentation required.

ANALYTICAL METHODS OF PREDICTING TRANSIENT RESPONSE The structural response can be observed by several types of transducers; either accelerometers o r strain gauges can be used to measure the deflee- In many instances flight flutter programs have tion, phase relationship and frequency of the structural been conducted without benefit of any concomitant theoretical analysis. In fact, many times flight response. Strain gauges are more difficult to eali- programs have been performed specifically iq lieu of brate; however, accelerometers pick-up high fre- an analytical program. For low-speed aircraft with quency structural noise and require the use of an auxiliary low-pass filter network. Either pick-up reasonably straight-forward aeroelastic configura- can be made to provide a signaltoa recording device.

tions, there is practical engineering justification for The conventional recording oscillograph is not practi- this approach. However, when flight flutter testing is being conducted on a modern, high-performance air- cal for high speed data reduction. It is virtually a craft, a thorough analytical program becomes an necessity that the structural response signal be avail- absolute necessity. At every phase of the flight pro- able in electrically retrieveable form for automatic gram, a correlation of theoretical predictions with the data reduction purposes. Thus, it is necessasyto use measured data is necessary before proceeding to probe a multichannel airborne tape unit. This is preferable untried flight regimes. A flight program improperly to telemetering all structural data to a ground stationed supported by theoretical analyses is a highly danger- tape recorder, since it minimizes the data trans- ous experiment! mission problems. If the number of channels required the number of channels available on the air- exceeds The theoretical tools required to support aflight borne tape recorder the analog form of the structural program are straight-forward extensions of the basic response can be preserved by frequency modulating critical flutter analysis. The flutter analyst has the data to be recorded using conventionaltelemetering already at his disposal the homogeneous set of equa- subcarrier oscillators. In addition to using an airborne tions which he is accustomed to solving. These are tape recorder a s the primary recorder, it is necessary of the same form whether based on a matrix o r as- to telemeter selected channels of information to the sumed mode approach. The only modification to the ground for monitoring by the flutter engineer. The basic equations is the addition of an external time- telemetered signals are received, recorded on tape in dependent forcing function which renders the equations singly-modulated form and passed through suitable non-homogeneous. The solution of the resulting set band pass filters onto a direct writing recorder for of equations although elementary mathematically, can immediate observation by the flutter engineer. By be extremely laborious even on the most modern of recording the received telemetered signals imme- computing machines. However, it has been demon- diately, a permanent record is available which has strated that the transient response of complex elastic been unaltered by any filtering techniques and thus structures can be obtained satisfactorily. The result- contains the raw data from the flight program. Im- ing transient response, consisting of the individual mediate discrimination (demodulation) and display of responses of each mode can be compared directly to the telemetered data to the flutter observer is the recorded structural response at a given location necessary to minimize the hazard of flight flutter on the aircraft. The damping associated with each testing. The signal after being demodulated andprior vibration mode canbe separatelydetermined if desired to being displayed on the direct writing recorder i s and a series of velocity-damping plots constructed run through a series of variable-width band pass for each root of the equations. (The damping deter- filters so that all frequencies which are not of mined at each airspeed for a given altitude repre- interest in the immediate test are eliminated, thus the purest possible trace i s presented to the flutter A direct comparison of the structural response engineer. data with that predicted theoretically can be made.

However, it is anticipated that sufficient disagree- During the entire flight program direct radio ment will result between this data that a comparison communication must be maintained between the pilot of more basic quantities will be required. Thus, the and the flutter observer on the ground, both to measured transient response will be passed through minimize flight time and test reruns a s well as to a series of variable width bandpass filters. By provide the best possible technical advice to the pilot suitably adjusting the width of the filters, it will be during the test program. Inaddition, the response of a possible to isolate a response at a single frequency single selected transducer is presented to the pilot and to subsequently determine its decay character- on a miniature Cathode-Ray oscilloscope. The pilot istics. Since several different modes will be decay- can observe the decay envelope and is advised prior ing simultaneously it will be necessary to perform this to flight of the anticipated envelope and of the safe operation several times using different filters band- widths. Finally, by this technique a progressive operating limits. He is obviously at liberty to dis- record of the measured damping of all flutter signi- continue flight testing at any time within his judg- ment. ficant modes can be obtained as a functionof airspeed at a given altitude. This then, when compared to the It would be very desirable to measure the predicted damping will aid the flutter engineer in extending the flight boundaries.

force-time history of the input to t k structure to verify that the rocket motors are performing as predicted. However, the design of a force trans- ducer with adequate response characteristics to DEVELOPMENT PROGRAM accurately monitor the force input would be extremely complex. It has been repeatedly demonstrated in The design and present state of development of ground tests of the motors that the pressure-time special rocket motors for use in flight flutter testing history i s quite dependable. Therefore, no provision has been described above. The force-time histories has been made for measuring the forcing function of these prototype units have been designed to be during flight. compatible with the known vibration characteristics of a full-scale prototype flight surface of an operational Thus, in summary, the instrumentation provides transonic aircraft. Conventionalgroundvibration tests have been conducted on this stabilizer removed from the following information: the aircraft. Transient tests using the rocket motor (a) Selected data display to the pilot. impulse units will be performed to demonstrate the (b) AH data recorded onairborne tape (including ability of transient testing to determine the known flight conditions). modal frequencies, shapes and damping ratios of the flight surface.

(c) Selected data is telemetered to the ground, filtered and displayed to the flutter engineer, The basic difficulty of evaluating any method of in addition to providing a permanent record of the transmitted data in case of accident. flight flutter testing is that, if successful, the air- craft did not flutter. After the program is success- fully completed, it is impossible to say whether this w a s because the aircraft would not have fluttered DATA REDUCTION anyway or whether it was truly a good technique.

The basic data, obtained in its entirety on the To honestly evaluate a method of flight flutter testing airborne tape and partial form on the ground-stationed it is advantageous to have an aircraft which has flut- tape recorder, will initially contain varying degrees tered in a prototype configuration. Such an aircraft of signal noise. Some of the noise will arise from configuration is available and prototype flight surface will be tested following successful completion of the the technical problems of data transmission and ground test of the individual components. Prior to recording and be basically on an electrical nature.

However, a substantial degree of '?structural noise" flight, the lifting surfaces will be subjected to transient will also be present in the recorded data. This will ground tests onthe aircraft and the structural response recorded on the airborne tape and telemetered data come from random vibration and acoustic inputs to the transmitted to a remote receiving station. This will airplane. The %tructural noise?' will be minimized be used both to verify the steady state ground vibration as much a s possible by seeking still air in which to conduct the test program. Nevertheless, it is to be test results and to checkout the entire airborne expected that there will be some residual noise which instrumentation system.

will have to be removed by filtering techniques. This will be accomplished after the data has beentaken. Theoretical subcritical response analyses will be performed for the flight conditions investigated to The basic data including '*structural noise" will be defermine in advance the anticipated modal damping recorded. The filtering will be performed upon play- characteristics. A point to point correlation will be back and will pass a sufficient bandwidth so that the basic structural response being studied will be pre- made between theoretical and experimental data served. during the flight program. Any discrepancies between the theory and experiment will be resolved prior to an application of existing techniques. The data re- proceeding with the flight program. The test will be duction techniques are complex but are not im- practical. Any flight flutter test method must have a carried to within 10% of the known flutter boundary.

careful analytical program to experimen- tal program o r it is doomed start. The CONCLUSIONS analytical techniques required by this method are reasonably straightforward to develop and do not On the basis of the ideas put forth in this report, present any unsurmountable obstacles.

it is concluded that transient flight flutter testing has a necessity. Steady state flight flutter testing become although adequate in some instances, cannot meet all requirements due to the complexity, size, weight and the necessity of maintaining steady state flight con- ACKNOWLEDGEMENTS ditions for extended periods of time. It is concluded that small-scale rocket motors are a practical means The authors wish to acknowledge the efforts of the staff of the Dynamic Science Section of the of proving a transient excitation to an aircraft. The problem of providing multiple ignition has been solved. Columbus Division of North American Aviation in the The difficulty in exciting higher modes, can be solved development of the concepts presented herein, es- by careful rocket motor design and sensible lacation pecially the efforts of Messrs. S . R . Hurley and J.A.

of the impulse units. Hill. The basic ordnance engineering of the special rocket motors has been performed by Ordnance The instrumentation techniques required are Engineering Associates, Inc., of Chicago, Illinois extremely complex but not novel. No basic develop- of Messrs. A. Kafadar, under the technical direction ment of instrumentation techniques is required, mainly R. Olson and J. Nordhaus of O.E.A.

1 ' - period of forcing function

APPENDM I - COMPARISON OF MODAL RESPONSE

- TERMINATED STEP-FUNCTION VS

rad

ma - ith natural frequency (-)

SEMI-SINUSOID EXCITATION sec

f, - ith natural frequency (cps)

Reference: North American Report, NA56H-562 "Dy- namic Response of Airplane Structures"

7, - period of ith natural mode

- F. E. Nagel - 11/20/56

Rm, - maximum response

- ratio of modal response i to response

In the above reference the basic equations for ri of desired mode the dynamic response of an undamped second order ma 1' system to a terminated step function and a semi- The parameter - can be rewritten as: (1) sinusoid were developed and studied. Figure I 7 presents the maximum response in terms of the per- w,I' hrfal' iod of the impulsive excitation. It is seen that the - = - = 2 f , T 7 r n terminated-step -function provides maximum response for a period of impulsive force equal to the half- W I T 21' - = - period of the free vibration mode being excited. The = 71 following simple examples have been carried out For study purposes, consider a three degree-of- to demonstrate the relative purity of the transient freedom system with coupled frequencies: response which could be expected from excitation by W I = 10 cps r1 = 0.10 sec.

either forcing function: wp = 50 CPS re = 0.02 see.

r e = 0.01 sec.

The following quantities will be defined w, = 100 cps Case I: Impulsive excitation of the fundamental mode: (by either a terminated step-function o r semi- sinusoid with the period, T selected for maxi- mum response) Square-Wave Semi-Sinusoid r 2 TIT r Mode 2Tl-r Rmax Rmax

- - - - -

1 1 . 0 2.0 1 . 0 1 . 6 1 . 7 6 1 . 0 2 5 . 0 2.0 1 . 0 8 . 0 1 . 0 .57 3 1 0 . 0 2.0 1 . 0 1 6 . 0 1 . 0 * 57 Case I I : Impulsive excitation of a higher mode: (by either a terminated step-function o r semi- sinusoid with the period, T selected for maxi- mum response) Square-Wave Semi- Sinusoid Mode 2 T l r r 2 T t r Rmax

- - -

1 .1 .3 .15 .16 .30 .17 2 .5 1 . 4 5 .725 .8 1.35 .77 3 1 . 0 2 . 0 1 . 0 1 . 6 1.76 1 . 0 higher modes > 1 . 0 2.0 1 . 0 >1.6 It can be concluded from a comparison of the By reducing the period, T , of the semi-sinusoid above two cases (forcing period 1 ' set for maximum it can be seen that a substantial additional attenuation response) that the semi-sinusoid behaves like a of the lower modal responses willresult. This will be bandpass filter; it attenuates all modes, both higher accompanied by a slight amplification of the higher and lower than the mode desired. The square wave frequencies. Since the basic problem is in exciting behaves like a high pass filter, attenuating only higher modes while rejecting the strong responses frequencies less than that of the desired mode.

of lower modes, the increase in response of the higher Although slightly improved low-frequency attenuation modes is tolerable. The following example will is offered by the square wave, the lack of high fre- demonstrate the possible gains in purity of response quency attenuation is serious. Thus the semi-sinusoid by shortening the period to one-half of the period is to be preferred.

of the mode being sought.

Case 1 1 1 : Semi-Sinusoid excitation of higher mode I T = TI 21 Mode r r (case II) Rmax

- -

1 . 1 0 . 2 .128 .17 2 .5 0 . 9 6 .615 .77 3 1 . 0 1 . 5 6 1 . 0 0 1 . 0 0 It can be seen that a marked improvement in It is obvious that by using semi-sinusoidal rejection of the lower frequency was obtained by this impulsive excitation and further by not using the technique. It is possible to optimize the periodof 'vaaraplitude-optimum*' period, that a reduced absolute excitation to obtain maximum rejection of the lower response has been the price paid for increased wave modes. The optimum period will be a function of the purity. This is easily compensated for by increasing ratio of the frequency to be suppressed to the frequency the basic force level - in this example, by only 25%.

desired.

TRANSONIC FLIGHT FLUTTER TESTS OF A CONTROL SURFACE UTILIZING A N IMPEDANCE RESPONSE TECHNIQUE L. I. Mirowitz -McDonnell Aircraft Corporution,

st. Louis, Missouri

Abstract "Demon", Figure 1 - a flightflutter test program was

conducted concurrently with the speed build-up of the Transonic flight flutter tests of the XF3H-I airplane. This program consisted of the transient "Demon" Airplane have been conducted utilizing a response technique of flight flutter testing through frequency response technique in which the oscillating pilot induced control surface impulse motion. How- rudder provides the means of system excitation. These ever, during the course of this flight flutter test pro- tests were conducted as a result of a rudder flutter gram, a neutrally stable empennage flutter condition incident in the transonic speed range. The technique was encountered at a Mach number of 1.04 and an employed is presented including a brief theoretical altitude of about 30,000 feet. Records taken during development of basic concepts. Test data obtained the flight indicated that the flutter condition emanated during the flight a r e included and the methodof inter- from the fin-rudder system with a frequency of 20 pretation of these data is indicated. This method is cycles per second. A s aresult of this, a program was based on an impedance matching technique. It is initiated consisting of theoretical investigations in shown that an artificial stabilizing device, such as a conjunction with flight flutter testing in order to damper, may be incorporated in the system for test establish the cause of the instability and to guide in purposes without complicating the interpretation of the the determination of corrective measures.

test results of the normal configuration. Data a r e presented which define the margin of stability intro- This paper concerns itself with the concepts and duced to the originally unstable rudder by design results obtained from the subsequent flight flutter changes which involve higher control system stiffness test program. The theoretical concepts underlying and external damper. It is concluded that this tech- the approach which was utilized, and which involves nique of flight flutter testing is a feasible means of in particular a frequency response technique in which obtaining flutter stability information in flight.

the oscillating rudder is utilized as the aeroelastic forcing system, have been presented in R. A. Pepping's INTRODUCTION paper, "A Theoretical Investigation of the Oscillating With the initiation of the first flight of the Control Surface Frequency Response Technique of

XF3H-1 Airplane - the prototype versionof the F3H-1

Figure 1.

Flight Flutter Testing", Journal of the Aeronautical system and the control system is defined as the Sciences, August 1954, Volume 21, No. 8 . The idea moment applied to each system per unit deflection to behind this approach involves the concept of impedance sustain motion at any given frequency. As seen from matching as applied to dynamic aeroelastic systems. the block diagram, the complete system consists of For convenience, a summary of the theoretical de- two feed-back loops. Loop 1, the inner loop, accounts

velopment is repeated herein. for the fact that the servo - which could be, for ex-

ample, a hydraulic actuator - acts as a root restraint

THEORETICAL BACKGROUND for the control surface, tending to return the control surface to neutral upon deflection. Loop 2, the outer In order to determine the flutter stability of a loop, accounts for the servo as part of the autopilot system which has incorporated a servo control me- system, sensing airplane motion away from the set chanism, it is important that the dynamic behavior of path with resultant corrective action.

the servo be included in the flutter investigation in combination with the structural, inertia, and aero- In this paper we will confine ourselves of the dynamic contribution of the remaining control surface- dynamic character of the inner loop, o r Loop 1, since I In addition to acting as a primary surface system. the autopilot of the airplane is not of immediate control surface restraint mechanism, the servo serves interest. The block diagram for the inner loop, also as a control actuation system which receives its Loop 1 , is again shown in Figure 3 where Za is the signal either from the pilot, a radar beam, or from a impedance of the servo mechanism, i.e., the hydraulic sensing element in the fuselage in which case it be- actuator, obtained from calculations or from measured comes part of the autopilot system of the airplane.

Ma is the moment frequency response data, and where A method showing the interaction of the servo-control surface-airplane system is the block diagram repre- FLUTTER S Y S T E M sentation used frequently in the theory of servo me- A D M I T T A N C E chanism analysis which schematically traces through (RECIPROCAL OF

the events which take place when a signal is received I I M P E D A N C E )

by the servo resulting in motion of the airplane from its predetermined or pilot-set path.

Block Diagram Representation of the Aeroelastic System B O

The system analyzed consists of the control -

I

surface-airplane flutter system, the servo system, BLOCK D I A G R A M OF INNER LOOP - LOOP I and the return loop from the airplane fuselage sensing element (gyro) back to the servo. In block diagram form, this feed-back system may be represented as Figure 3.

shown in Figure 2. The impedance of the aeroelastic

-

a

-

-

AIRPLANE -

> UY

MP L O O P I Bo

-

Figure 2 .

1 44 mathematically by a number of degrees of freedom \ h(BEND'NG)

----

ON) I OF F IMP ACTUATION S Y S T E M (HYDRAULIC SERVO) opposite to the control system impedance.

IDEALIZATION OF CONTROL SYSTEM EQUATION OF MOTION:

OUTPUT- - z g (&-) - 1

---- -

1.0 Figure 5.

INPUT _- 4i

Z a ( + . - ) + 1 I+(?)-+

-

CHARACTERISTIC EQUATION: 1.1 NEUTRAL S T A B I L I T Y CRITERION: 2.1

1 1.2

BASIC STABILITY CRITERIA Figure 4.

Idealization of Aeroelastic Impedance

ANALYTICAL EXPRESSION FOR IMPEDANCE - M B / p

From the theoretical standpoint the aeroelastic impedance of the control surface can be idealized Figure 6.

s c h e m a.t i c a 11y by the three-degrees-of-freedom: primary surface bending, primary surface torsion, and control surface rotation as shown in Figure 5.

system with free-floating or unrestrainect control sur- This idealization is the minimum required to cover face and the denominator is the flutter stability de-

all the concepts of the approach utilized herein -

terminant for infinite restraint in rotation or, in other additional degrees o f freedom may be added as neces- sary without invalidating any of these concepts. The words, rotation is not a degree of freedom, The stability determinant for the denominator would be upper diagram is the idealization of the flutter system.

the primary surface flutter stability determinant.

The lower diagram is the idealization of the control system. The equations of motion of the flutter sys- Stability Criterion tem a8 actuated by iving hinge moment Ms is shown in Figure 6, Solving from 2 . 1 for Figure 7 again shows the characteristic equa- the impedance Msl 2.2 is obtained. As tion of the.inner loop as equation 3 . 1 . Substituting equation 2 . 2 into equation 3 . 1 , the characteristic seen, the rudder hinge moment impedance is the is rewritten as equation 3 . 2 in terms of the ratio of two stabi minants: the numerator of the aeroelastic inants of the aeroelastic flutter sys- is the stability de C H A R A C T E R I S T I C E Q U A T I O N : infiiity to plus infinity. For stability, none of the

roots of the transformed characteristic equation -

3.1 the numerator of 3 . 4 - may have a positive real part.

F R O M 2 . 2 : By the use of a modified Nyquist approach, this is established by observing the behavior of the re- 3 . 2 sponse vector I M ~ I P + Z p ) as the frequency is F R O M 2.1: varied from minus infinity to plus infinity. If there ao+ zB N ~ = D = S TAB I1 I T Y D E TE R M IN A N T W I T H C O N TR 0 1

are any roots with positive real part - which denotes

SURFACE R E S T R A I N E D B Y Zd 3.3

instability - thevector I M B I P + Z p ) will perform as

many clockwise rotations about the origin when F R O M 3.3 A N D 3.2(b): plotted on a complex plane as there are roots with 3.4 positive real parts. It is possible, however, also to D E F I N E THE S T A B l L l T Y OF THE 3.4 STATES T H A T BOTH(ZB+ ? ) A N D have roots in the denominator of the vector equation FLUTTER S Y S T E M W I T H THE C O N T R O L SURFACE R E S T R A I N E D B Y 3.4 with positive real parts. Roots inthe denominator IS RELATED TO THE M E A S U R A B L E Z g , i H U S THE S T A B I L I T Y

Npp , are denoted as poles and are the solutions of

D R I V I N G H I N G E M O M E N T .

the flutter system with infinite restraint in the control STABILITY EQUATIONS system. In that case, the vector equation 3.4 will perform as many counterclockwise rotations about the origin as there are poles with positive real parts.

Figure 7 .

Since both conditions can exist simultaneously, then

for the system to be stable - o r no unstable roots in

tem. The numerator of 3.2 is the stability determin-

the numerator of 3.4 - the direction of rotation of

ant with the control surface restrained by the control the vector (MpIP + Z p ) about the origin must be

system impedance, Zp . This determinant is denoted

counterclockwise and the number of rotations must as D. Substituting 3 . 3 into 3.2, the characteristic be equal to the number of unstable poles.

equation 3 . 1 is transformed into 3.4 which states that D define the stability of the both and (zp + M ~ I B ) If there are no unstable poles, o r in other words, there are no unstable roots in the denominator, and flutter' system with a control surface restrained by therefore, the primary surface is flutter-free with an

zp . Thus the stability is related to the measurable

infinitely restrained control surface, then for the driving hinge moment. The characteristic equation system to be stable, the vector (MBIP + Z p l must 3.4 will determine the system stability. In general, not envelop o r rotate about the origin. In this latter the numerator of the right hand side of 3.4, D, is a case, simple energy concepts will also lead to the differential equation of rth order and the denominator same conclusions regarding the definition of stability, xPp is a differential equation of nth order. The for example, Pepping's paper referred to previously discusses the energy approach.

problem then, is to determine if there exist any roots of the numerator which are characterized by a posi- Figure 8 presents the ground rules for applying tive exponential decay function (divergence) which the modified Nyquist stability criterion to the imped- would indicate instability or by a zero decay function ance stability plots. It should be noted that in actual which would indicate neutral stability. If the equa- practice the frequency variation can be limited to a tions are written in differential equation form, then reasonable range enveloping the suspected flutter the roots of the stability equation o r of the stability 9 indicates a particular application frequency. Figure determinant, D, may be solved for directly. This is of the impedance plots and shows a speed which would roughly the case of theoretical flutter analysis. How- be unstable and a neutrally stable speed and relates ever, equation 3.4 states that stability may also be this to the well known flutter stability.plot of velocity determined as a measure of the driving hinge mo- versus control surface rotational frequency.

ment impedance, M , $ P , for this is a measurable quantity.

Quite often instead of utilizing the complex an alternate In the theory of servo mechanisms, a relation- plane plots of the impedance vector ship is drawn between the determination of system method is applied which makes use of the so-called stability from the solution of the differential equa- phase margin plot. This is shown in Figure 10.

tions (transient stability) and the results from the frequency response behavior of the dynamic system. The significance of the impedance matching ap- The frequency response technique is denoted as the proach is as follows. The aeroelastic impedance, case the differential equa- Mp /, may be calculated o r measured. It is then a Nyquist approach. In this tions of motion are written in transformed form and given known quantity for a given set of conditions the system is analyzed without solving for theroots The restraining independent of the restraint, Zp , by an examination of the behavior of the response (MBIP + Zp) as the frequency is varied from minus impedance, Zp , may be measured o r calculated. The MODIFIED NYQUIST STABILITY CRITERION: 1. For each forward velocity and a reasonable frequency range, measure or calculate M s / p vs. G ) .

2. Add to Mg/p the measured or calculated control system impedance Zg

and obtain Mg/p+z, vs. w . Plot on a complex plane for each forward

velocity.

3. Calculate the flutter speed or speeds of the system with infinite control surface restraint. This is designated as VFo .

4. For velocities less than V F ~ the system is stable if the vector Ms/,g+ zg

does not envelop the origin.

5. For velocities greater than V F ~ the system i s stable only if the

number of counterclockwise rotations about the origin of Mg/p +zg

is equal to the number of V F ~ ' S .

6. For any velocity the system i s neutrally stable if Mg/p+Z, passes through the origin.

Figure 8.

vector sum of the two determines the stability of the

+ I (p) I M A G I N A R Y

total system. Additional devices which modify the

I I

restraining impedance Zp , may be evaluated without

I I -----

N E U T R A L L Y N E U T R A L L Y / STABLE h V = C further experimental work in flight once the aero- elastic impedance, M p /b has been e s t a b 1 i s h e d

f

V uniquely.

TEST CONFIGURATION

1 (?)REAL

U N S T A B L E The flutter testing of the XF3H-1 rudder is I I I I I I based on the theory presented in the previous discus- sion. The hinge moment M g was supplied by the hydraulic actuating Aylinder through sinusoidalopera- FLUTTER STABILITY PLOTS-IMPEDANCE tion of the actuator valve. This is shown in Figure 11 which presents a schematic of the shaker system.

Figure 9.

L l I

I\ ~ ,RUDDER HL

BELLCRANK 19-61390-1 INSTRUMENTED WITH ACCELEROMETER 19-61305-905 VISCOUS DAMPER RUDDER HORN PILOT VALVE RUDDER POWER T E S T BELL ' FLIGHT CRANK 19-04186 8 ECCENTRIC GEAR BOX 8 COUN T E R

j UNSTABLE

EXCITER MOTOR z e FLEX SHAFT COVER -18 0- 0- FLUTTER STABILITY PLOTS-PHASE M A R G I N FLUTTER STABILITY PLOTS-PHASE M A R G I N RUDDER EXCITER INSTALLATION Figure 10. Figure 10. Figure 11.

Also added to the system was a viscous damper for * VERTICAL ACCELEROMETER stability reasons. Figure 12 indicates the type of

- LATERAL ACCELEROMETER

9 AUTOMATIC CUT-OFF SWITCH instrumentation employed on the airplane for these a P O S I T I O N INDICATOR 0 STRAIN GAGE tests. One of the strain gages shown in thisfigure was installed on the control rod leading directly into the rudder and gave a definition of the driving

hinge moment, Mp , and the other was installed on the

control rod just upstream from the damper to define the hinge moment of the rudder as restrained by the damper. The damper was a non-linear velocity squared damping device.

TEST PROCEDURE The general technique of testing consisted of at a constant Mach number at stabilizing the airplane I N S T R U M E N T A T I O N SET-UP about 30,000 feet altitude (this was the altitude at which all the test data was obtained) and varying thefre- Figure 12.

1111111111111111111llllllIlllllllllllllIIIIlllIIIllII

\ LCHAN.~ RUDDER PUSH ROD

CHAN. 17 VOLTAGE MONITOR

TYPICAL OSCILLOGRAPH TRACE

Figure 13.

RUDDER FLUTTER IMPEDANCE M%83-.86 quency of oscillation through the range of about 5 through 35 cps. This range was chosen asbeing sufficient to envelop the flutter frequency previously encountered.

Oscillations were introduced through hydraulic actuator displacement of the rudder through suitable valve motion. The upstream and downstr as well as the rudder angu cedure was repeated at succe of Mach number to establish the trend of stability with increasing Mach number, Rudder static deflections of approximately a degree and a half were employed. The frequency variation was accomplished by an automatically oper- ating rotary switch located in the cockpit and aDproxi- mately 3 seconds were devoted to each frequency point. Sufficient fatigue strength was provided in the power cylinder back-up structure and in the connecting links so that these components were good for 50,000 cycles of rudder limit hinge moment. Strategically located acceleration sensing devices were tied into the circuitry of the drive motor which were set to turn off the drive motor whenever excess accelera- tions were encountered. Dynamic. measurements throughout the airplane were taken during these tests and the data were recorded on the airplane oscillo- graph.

TEST RESULTS A typical oscillograph trace is shown in Figure 13. The instrumentation was somewhat primitive by present day standards; however, the test was con- ducted in 1952 and much of the more sophisticated types of recording transducers and data reduction FORCING FREQUENCYk P S machines were not available at that time. Several problems which were encountered with this instru- mentation were: Figure 14.

Rudder angles of about a quarter of adegree or less were difficult to measure and some drift in the measurements occurred. Con- The data shown in Figure 13 were manually tinuous calibration of the position indicators reduced and typical plots for various Mach numbers was required in order to hold down the of the test results are shown in Figures 14 and 16 errors from this source through 18. The plots cover the Mach number range of . 8 5 to 1 . 1 6 and are representative of the impedance Accelerometers in the tail assembly were data taken through M = 1 . 2 6 for the system with and not temperature compensated and no ac- without damper. Data for each Mach number plot curate definition of the characteristics of the tail oscillations could be obtained. Tem- were obtained during several flights as indicated.

Positive phase margins indicate stability. Negative perature measurements were recorded for phase margins indicate instability. To determine the several locations in the tail assembly and this data was used to correct the measured stability of the actual restrained rudder, this data test results must be combined with the control system impedance, Stability is determined by the phase margin lZ,l .

(3) Power cylinder valve'displacement and power

existing when IMp/PI is equal to lZ,l . The hinge

cylinder output displacement could not be obtained correctly. moment data obtained at M = 1.04 were utilized in a As noted, this data does not indicate a zero RUDDER FLUTTER IMPEDANCE MP1.04 phase margin point at M = 1.04 which was the Mach number of the flutter experienced during the initial stages of the flight flutter testing of the airplane.

However, the frequency of flutter is correlated.

Tests of the hydraulic actuator impedance in- dicated that in this frequency range the system was as a pure spring but that some negative not acting phase margin was contributed by the actual impedance of the hydraulic power cylinder. A measure o f this loss in phase margin is indicated as the shaded area around M = 1.04. An increase in control system stiffness to 1740 in. lbs per degree which was basically obtained by a more powerful power cylinder is shown by the dashed curve. This increase in stiffness in- creases the stability of the rudder around M = 1.04; however, it also indicates that the second unstable COMPUTED RUDDER FLUTTER IMPEDANCE BASED ON TEST RESULTS AT M.1.04 F O R C I N G FREQUENCY-CPS Figure 15.

theoretical study in order to determine which of the possible critical degrees of freedom of the aeroelastic system are influential in the flutter system. It was found that utilization of the two degrees of freedom, rudder rotation, and rudder torsion, was sufficient to describe reasonably well the variation of the hinge moment and phase margin with frequency at this Mach number. This is shown in Figure 15.

The measured test results have been plotted for two restraint conditions of the rudder; one, the

restraint of the original control system - 880 in. lb/

m

l o 15 ! m 25 30

that of the final control system -

degree, and the other, F O R C I N G F R E Q U E N C F C P S 1740 in.lb/degree. This is shown in Figure 19, for the idealization of the impedance of the control sys- tem as a pure spring without hydraulic damper.

Figure 16.

1 50 RUDDER FLUTTER IMPEDANCE M4.11-1-12 RUDDER FLUTTER IMPEDANCE Elki.15-1.16

I I . I I - - I

I I . . I

I T - I - - I 1 I

F O R C I N G FREQUENCY-C P 5 F O R C I N G FREQUENCY-C.P.S.

Figure 17. Figure 18.

Mach number range around M = 1.1 i s not stabilized control system (final configuration) is indicated in nmdwclly by t h i s stiffness change even though some Figure 20. An additional gain in phase margin is improvement in-phase margin is indicated. Fromthis shown with adequate stability existing throughout the data, it was concluded that stiffness alone will not applicable Mach number range. Similar plots were eliminate the flutter instability on the rudder. The constructed for various combinations of damper and stability of the system with the damper andthe stiffer power cylinder impedance characteristics.

El - O R I G I N A L C 0 N T R O . L S Y S T E M

A STIFFER C O N T R O L SYSTEM zB= K , = 880 IN. LB./DEG.

4 = K p 1 7 4 0 IN. LB./DEG.

e--- STIFFER C O N T R O L S Y S T E M u l n 2 2 U

f

g 1

Ly Y -8 -9 LO 1.1 1.2 1.3 I I I v) Y Y LL $ !

?

z, M A T E D EFFECT 40 F H Y D R A U L I C W v) a I n

- 40

M A C H NO.

XFBH-1 FIN-RUDDER XF3H-1 FIN-RUDDER FLUTTER STABILITY NO DAMPER FLUTTER STABILITY WITH DAMPER Figure 19.

Figure 20.

CONCLUSIONS REFERENCES 1. Pepping, R. A., A Theoretical Investigation of the On the basis of this discussion, the following is concluded: Oscillating Control Surface Frequency Response Technique of Flight Flutter Testing, Journal of the (1) The impedance matching technique of de- Aeronautical Sciences, Vol. 21, No. 8, August 1954.

termining stability i s a feasible means of conducting flight flutter testing. 2. Chestnut, Harold and Mayer, Robert W., Servo- mechanisms and Regulating System Design, Vol. 1, John Wiley and Sons, Inc., New York, 1951.

(2) The interpretationof the testdatais straight- forward . and revolves mainly around the determination of the aeroelastic impedance 3. Mirowitz, L. I., Flutter Stability of a Wing with vector of an oscillating control surface. Servo Root Restraint and Automatic Servo Control, McDonnell Aircraft Corporation Internal Engineer- (3) The aeroelastic impedance can be deter- ing Note, 1 July 1953.

mined in flight utilizing a control surface stabilized artificially and 4. Mirowitz, L. I., F3H-1 Airplane, Flutter Analysis which has been Summary Report, McDonnel Aircraft Corporation information from this data may be obtained for a variety of artificial stabilization sys- Engineering Report No. 3333, 23 December 1953.

tems. These stabilization systems may take the form of external dampers or stabilizing feed-back signals.

SYMBOLS M b = oscillatory rudder hinge moment. 0 = circular frequency.

p = rudder deflection. P = air density.

Mb/P = flutter impedance of the rudder aeroebstic bo = reference semichord.

system.

8 = phase margin - 180" less the phase angle.

Za = rudder control system impedance.

Subscripts: RI + = oscillatory flow aerodynamic I I g k derivative.

0 = output.

See Equation cao3k = inertia derivative. I = input.

2.1 wJ3 = natural frequency of a degree of E = error or input less output.

freedom in equations of motion.

I

FLIGHT TESTING AIR-TO-AIR MISSILES FOR FLUTTER C. R. Kutschinski, - Hughes Aircraft Co., Czdver City, California Abstract rence of flutter if total prevention of flutter results in a large increase in size and weight. Another The philosophy of the design of air-to-air important consideration is the tactical use of the missiles and hence of flight testing them for flutter missile and its speed-altitude profile. A salvo-type differs from that of manned aircraft. Hughes Aircraft missile, for instance, need not have a s high an Company puts primary emphasis on analytical and individual reliability a s that of a singly launched laboratory evaluation of missile susceptibility to missile.

aeroelastic and aero-servo-elastic instabilities and uses flight testing for confirmation of the absence It is clear then, that in designing air-to-air of such instabilities. Flight testing for flutter is missiles, flutter has to be kept in view right from the accomplished by using specially instrumented pro- initial stages of design and has to be given its rightful air o r ground launched with a grammed missiles, place within the ove’rall weapons system.

booster to reach the extreme flight conditions of tactical use, or by using guided missiles with tele- We at Hughes put primary effort on analytical metered performance data. The instrumentation and and laboratory evaluation of missile susceptibility to testing techniques a r e discussed along with the aeroelastic and aero-servo-elastic instabilities and success of recent flight tests. use flight testing for confirmation of the absence of such instabilities. A s is common practice, previous INTRODUCTION AND DESIGN PHILOSOPHY experience on successful designs and parametric studies of the type given in Reference 1 can be used The philosophy of the design G ; air-to-air to advantage in the preliminary design stage of a missiles and hence of flight testing them for flutter missile. By the time the missile development reaches differs from that of manned aircraft. The primary the flight test stage, considerable confidence can be consideration in piloted military o r civil aircraft gained in the structural integrity of the missile through is safety of crew and passengers. Elimination of classical studies or through analog studies and wind- the occupant from a missile, however, does not elimi- tunnel testing of designs with unusual features. How- nate the need for a flutter-free vehicle but a different ever, effects of aerodynamic heating and stabilities at philosophy prevails. The emphasis is shifted from large angles of attack and large control-surface de- personnel safety to weapon reliability. Weight and flections can, at present, be evaluated only through size are extremely important parameters in the design flight tests under actual flight conditions and time of an air-to-air missile, even more so than in other histories.

types of missiles; therefore, reliability must be com- promised and an overdesigned structure cannot be tolerated. Flutter margins have to be decided upon in the light of reliability of other components of the INSTRUMENTATION AND FLIGHT TESTING system. For example, if the system failure is one FORFLUTTER in ten, the missile need not be designed for a failure due to flutter of one in a thousand. Thus, it may Flight testing for flutter of air-to-air missiles even be found advisable to permit occasional occur- may be divided into three phases, namely, A number of experimental missiles are equipped (1) Captive flight with special instrumentation for monitoring perform- (2) Specially instrumented programmed flight ance and flutter data, and their guidance units are (3) Monitored guided flight replaced by program control timers. The instrumen- tation can thereby be optimized to measure the re- Captive Flight sponse of predetermined missile maneuvers at pre- scribed launch altitudes and speeds. The missile- booster combination is carried aloft by a suitable Transonic speeds are usually one of the critical aircraft and released by it when the attitude, speed, speed regimes for the incidence of flutter. Captive flights can be used to detect any flutter tendencies at and altitude of the aircraft are such that after transonic speeds even though such flights are only booster rocket-engine burnout the combination would free flights due to support be at the desired flight angle and the maximum partially representative of critical design launch speed, or slightly in exccss of characteristics. This can be done simply a s visual it. Timers and acceleration switches carried in the inspection of the missile after a captive flight or more its ignition by a preselected drop time thoroughly with the use of strain gauges, recorders, booster delay or telemetry. Using conventional methods of airplane and ignite the missile rocket-engine after booster flutter flight testing, one can also add shakers or burnout. The missile then carries out programmed impulse devices and measure the decay rates. This maneuvers.

phase of flight testing for flutter can be carried out at relatively low cost and yields spot checks of the Three types of flutter instrumentation have analytic work early enough to add confidence inthe been used successfully in flight tests using the structural design. booster technique. They are as follows: The first consists of apair of aft-looking 16 mm.

Instrumented Programmed Flight modified GSAP* Fairchild cameras mounted in a Normally, the missile structure and its control special recoverable nose section. These cameras have all four control surfaces in their view (see system are available long in advance of the aircraft Figure 1) and photograph them in flight. This optical which is to carry the missile a s a part of the weapon instrumentation was used in early flight tests of system. Flutter flight testing can then be carried missiles ground launched with a booster to observe out either in the speed and altitude capabilities of an control-surface flutter, if any, and separation of existing aircraft which may not meet the critical de- booster from the missile.

sign conditions of tactical use, or it has to be delayed until the availability of tactical aircraft. In order to bridge this gap, we, in cooperation with the Lockheed Aircraft Corporation, have developed a booster tech- *Gun Sight Aiming Point nique for our missiles which has proved very success- ful.

Figure 1.

MAGNETIC PICKUP

Figure 2.

absence of flutter in the tactical speed-altitude profile The second type of instrumentation is a motional pickup developed at Hughes. This cowists of a small of a missile.

horseshoe permanent magnet installed in the foot of the control-surface and a coil wound on a horseshoe Monitored Guided Flight core mounted opposite this magnet and in the foot of For missiles designed with very low flutter the stabilizer or wing (see Figure 2). Relative motion margins, a continuous monitoring of experimental, caused by vibrations generates an AC signal whose magnitude depends on the frequency and amplitude of prototype, and production missiles is necessary in vibration, and control-surface deflection. This signal order to maintain a check on manufacturing toler- is suitably filtered to flatten its frequency response ances and fabrication techniques. This can be ac- and is fed into the coder of a telemeter unit having complished by regular telemetering of control-surface 2000 sample per second pulse duration modulation. position and the three body angular rates. Addition The frequency, the amplitude, and the rate of sub- of pitch and yaw accelerometers is useful in deter- mining proper aerodynamic performance, thereby sidence or divergence of any buzz o r vibration can be obtained by this type of instrumentation. assuring the absence of instabilities which might impair the guided flight of a missile and reduce the The third type of instrumentation is a self- overall weapon realiability considerably.

generating type vibration pickup mounted in the aft end of the missile. The output of this pickup is fed In closing, we are happy to say, in all humility, into the same type of telemeter unit as mentioned that all the Falcon series air-to-air guided missiles designed so far have not experienced a single case above. Destructive flutter can also be detected by simply looping a wire into the control-surface in of flutter, and hope that we shall continue to design series with the pickup. Loss of a control-surface is them that way.

then indicated by a step change in telemeter level.

Further verification of flutter of a destructive nature can be made by regular 30 sample per second telemetering of control-surface position and missile REFERENCES response in body angular velocities and accelerations.

1. Chawla, J. P., Aeroelastic instability at HighMach The above three types of instrumentation have Number, journal of the Aeronautical Sciences, Vol.

been used successfully by us at Hughes to confirm the 25, No. 4, April 1958, pp. 246-258.

HISTORY OF FLIGHT FLUTTER TESTING L. A. Tolue - Lockheed Aircraft Corporation, Marietta, Georgia adequate to preclude flutter up to that time. One of Abstract the early accidents, which can probably be attributed A variety of aeroelastic problems have been to wing flutter, occurred in the USA during the 1924 Pulitzer Trophy Races in Dayton, Ohio. An Army encountered in aircraft from the beginning of "high entry, a Curtiss R-6 racer, was starting the race speed" flight during World W a r I up to the present from a very steep dive when suddenly it seemed to time. One of the most critical has been the oscilla- tory problem, flutter. A s a result of the many flutter vibrate and then disintegrated. The cause of the accident was never determined, but it was assumed incidents encountered in the early aircraft and the inability to obtain a satisfactory prediction of the at that time that the high engine speed has been too much for the wooden propeller and, after losing a phenomenon by theoretical methods, there emerged a tip, the prop had set up a terrific vibration which semi-systematical method of testing for flutter during The difficulties and hazards encountered in tore the engine and airplane apart.

flight.

conducting these early flight flutter tests are de- Figure 1 shows how the maximum speed of scribed. With the development of improved exciting aircraft has increased with the years. With the and measuring equipment and a better theoretical exception of the time span of the two world wars, understanding of the flutter problem, flight flutter airplane speed has increased approximately 22 mph/ testing came of age during the late 1940's and since year from 1910 to 1955. As indicated on the graph, then its use by the United States and other countries control surface flutter was first attained at about 125 has been constantly increasing.

mph and then wing flutter started to occur when air- planes had reached about twice this speed.

EARLY FLUTTER HISTORY Most of the early flutter incidents in the USA Flutter didn't become a problem to the early occurred during the air races or attempts to set airplanes until World War I, about twelve years after world speed records. In 1931, while in quest of the world's landplane speed record, a Gee-Bee racer the first flight by the Wright brothers. Up until this time the speeds had been too low to cause trouble, but encountered destructive wing-aileron flutter during a cases of control surface flutter began to appear during high speed dive start and the pilot was killed. In the early part of the war. These flutter incidents 1934, during the National Air Races, one of the racers kept encountering wing tip flutter. Each mainly involved the elevators and were caused by the time the wing span was reduced by cutting off part of lack of a stiff interconnecting torque tube. A number the wing tip until the flutter stopped. As a result, the of lives were lost in the resulting accidents before a area was finally reduced from its original value satisfactory fix could be determined. wing of 78 square feet down to 42 square feet, but the pilot A s aircraft started to attain greater speeds ended up with a flutter-free airplane.

after World War I, flutter incidents began to appear more frequently. Control surface flutter was appar- GERMAN FLUTTER FLIGHT TESTING ently the only form of flutter that occurred until 1925, most likely due to the fact that the inherent The Germans, during the early thirties, were about well aware of the growing importance of the flutter structural stiffnesses of the rigid surfaces were they had made many attempts to set up wing or tail

.IIfRPCAN€ MAXIMUM SPEED

oscillations without success, then all of a sudden at a V d certain engine rpm, flight condition, or gust intensity, at a speed at which it flutter would suddenly occur had refused to occur on previous flights.

The flight flutter tests described by Von Schlippe were conducted on the Junkers JU86 and were for the purpose of determining the effect of balance weights on the rudders. For the tests, a rotating unbalance tail of the fuselage and actuated by was located in the a flexible shaft running to an electric motor mounted in the fuselage. The recording of the oscillations was accomplished by a thin wire attached to the rudder which mechanically actuated a recorder installed in the observers seat. The test results showed, by extrapolation, that the airplane would have fluttered at approximately the same speed at which accidental oscillations had been observed on a previous flight.

During the late thirties, the Germans encoun- tered destructive flutter on several of their flight flutter tests which resulted in the deaths of the flight crews. The failure of these tests can probably be attributed to one or more of the following reasons: (1) The excitation equipment was not adequate to properly excite and control the critical modes.

" I 9 0 0 1910 1920 Q30 I 9 4 0 1950 1960 (2) The recording equipment was not satis- Y€AR factory for obtaining the required dataat the time it w a s needed.

Figure 1. Airplane Maximum Speed vs Chronological Date (3) An adequate theoretical analysis had not been problem and had already established certain criteria conducted to provide some insight into the for flutter prevention. They had considered flight possible critical flutter modes that might flutter tests for demonstrating freedom from flutter exist. O f course, at that time adequate and understood the factors involved which resulted in theory did not exist to permit this.

making such tests very hazardous. B. Von Schlippe, in an article written in 1935, states, "German criteria These accidents illustrated that flutter testing was to prove freedom from flutter by flight test at was quite hazardous. The inherent characteristics of 1.5 times the horizontal speed. Speaking from ex- each airplane, such as the damping of the structure perience, it is not sufficient to reach the required and control surfaces, and different types of critical speed, but it necessitates flying the entire range - - - flutter modes, were unknown and generally theo- if possible, in different flight conditions and gusty retically unpredictable at the time; thus, each flight weather."

flutter test was a new dangerous experiment which manufacturers at that time wanted to avoid if at all article he described a method de- In the same possible.

veloped at the Junkers Airplane Co. by which the critical velocity with respect to spontaneous oscilla- PRESENT STATUS OF FLUTTER tions of increasing amplitude can be ascertained in flight tests without undue risks, the oscillation of the By the late thirties and early forties, the surface being obtained in the tests by the application science or art of flutter had received a bad name.

of an external force. This was because few engineers and aircraft manu- facturers understood what flutter was and if an air- The Germans, in their wind tunnel flutter model plane did have it, it was difficult to get rid of it.

tests, had determined that the location of the exciter Aircraft manufacturers regarded flutter in the same was very important; that improper exciter location way that respectable people then regarded Social resulted in poor responses of the wing; prevented the Diseases. Other people might have it, but nothing determination of the onset of flutter; and resulted in like that could ever happen to my airplane. If it did, the flutter occurring unexpectedly. They had ex- it was something that wasn't to be talked about. The perienced this same phenomenon in flight tests where art of flutter has progressed considerably in the 1 60 past twenty years and today the flutter man is an This inboard position was chosen so that the excita- accepted part of the engineering department of every tion amplitudes would be small and not result in am- aircraft manufacturer. Flutter is one of the prices plitudes likely to cause structural failures during had to be paid for high speed flight.

that flight. It is noted, that at the critical frequency, that this small exciter would only put out about twelve Today, we have two types of people. One type pounds of force. The exciter was driven by a D.C.

is the aircraft manufacturer who conducts flight flut- motor through a flexible shaft. The speed control of ter tests of his airplane to establish beyond all pos- this drive system was quite unsatisfactory as during sible doubt that all types of flutter a r e absent within flight it was difficult to tune to the exact frequency the speed range of his airplane. When he can show since the motor speed would fluctuate suddenly as the is extremely happy and satisfied, and the this, he resonance peak was approached. Two accelerometers tests were successful. On the other hand, we have the were located outboard on each wing and fed into a type who is the research flutter engineer, and he four-channel photographic recording oscillograph.

isn’t happy unless he is making an airplane flutter in order to gain valuable data which can be correlated The crew consisted of only the pilot and the flut- with theory. He is extremely unhappy if, after con- ter test engineer. The test procedure was to climb a flight flutter test program, he finds he has ducting the airplane to about 15,000 feet and tune the exciter to resonance a t each incremental airspeed, at least an airplane that doesn’t flutter. For him the tests as well a s the exciter drive system would permit.

were unsuccessful. So if someone says that a flight The airspeed was then increased and the higher flutter test was “successful”, it is obviously neces- speeds were attained by diving the airplane.

sary to determine who is doing the talking to know what is meant.

At speeds above 200 mph, it was obvious from observing the oscillograph traces that the excited USA FLIGHT FLUTTER TEST EXPERIENCE wing resonant amplitudes were markedly increasing with airspeed even though the exciter would not stay Although the Germans had conducted a number on resonance. At speeds near 230 mph, the wing of flight flutter tests during the late thirties in which oscillations were so large that the pilot became very exciters had been used, it wasn’t until the early much concerned. Fortunately, the flutter engineer forties that the USA attempted this type of testing.

had to kneel on the cabin floor in order to control the The Glenn L. Martin Co. made flight flutter tests on exciter and the recording equipment, and thus was the XPBM-1 flying boat in which a rotating unbalance unable to see the large wing oscillations or the tests exciter was used. These tests were successful in would undoubtedly have been stopped before 230 mph that no indication of flutter occurred within the air- had been reached.

plane’s speed range.

The analyses of the records and the pilot’s U. S. A i r Corps at Wright Field, In 1941, the comments indicated that the wing amplitudes were of Dayton, Ohio conducted their first flutter tests in sufficient magnitude that structural failure had almost which an exciter was used. The airplane involved been attained. The increase of wing amplitude with was a Cessna AT-8 twin-engined low-wing cabin airspeed is shown in Figure 2 and quite definitely monoplane. The wings were of wood construction indicates an approach to destructive flutter.

covered with fabric and had a plywood leading edge.

During performance flight tests of this airplane, A psychological incident was noted during these persistent small amplitude torsional vibrations of the tests which was noted many more times in succeeding wing had been observed at speeds in the range of flight flutter tests in later years. This was that 200-230 mph. In addition, a similar airplane being although the pilot was concerned over the large oscil- used by the Canadian Air Force had been involved in a destructive accident while in a high speed dive and it was believed that the wings might have fluttered.

AT-8 FUGHT TEST WRIGUT FIELD, NOV 1941 The Air Corps conducted ground vibration tests 0 RIGHT WING DATA on the AT-8 and the results of twodegrees of freedom flutter analyses, based on these vibration tests, indi- cated a flutter speed at about 250 mph IAS. The air- plane was then instrumented to record the persistent wing oscillations which had been noted in flight and a series of flight tests were made without forced excita- tion.

No large wing oscillations were encountered up to 255 mph IAS although small persistent oscillations 0 40 80 I20 IO0 200 240 2 8 0 320 were recorded. For the next series of tests, a 3/8 in.

VELOCITY, V , MPU lb rotating unbalance exciter was located inboard on the left wing rear spar at approx. 42% semispan.

Figure 2, Response Amplitude Ratio vs Airspeed lations being induced in the aircraft, he was not faster aircraft to the desired speed. In case of frightened by the tests. In discussing this factor flutter o r other reasons, it could be released to fly with other pilots of aircraft involved in flight flutter own power. This particular aircraft was under its tests, most all of the pilots were of the opinion that chosen for the following reasons: if a flutter engineer was along on a test, that test couldn't be too dangerous. This is an instance of the (1) These tests occurred after World War nand old adage that 'ignorance is bliss'.

this airplane was essentially surplus. No- body particularly cared if modifications were After these AT-8 tests, the Air Corps decided made to it or if it were destroyed inthe to conduct additional flight tests on a full-scale air- course of the tests. This was an ideal plane to develop improved techniques and equipment situation; an aircraft that could be struc- for flutter testing. It was desired to flutter an air- turally modified as desired by the flutter plane in a mode involving wing bending-torsion which test engineer to make it suitable in all ways would probably destroy the aircraft. In order to do for flutter testing.

this safely, it would be necessary to fly the aircraft and control the excitation and recording equipment by (2) Approximate theoretical flutter analyses had remote control, and in addition, the data would have been conducted several years previously for to be telemetered. A high performance single wing its glider counterpart, the CG-4A. The glider was selected for these tests. The glider would results indicated that its critical flutter be towed to altitude and then dived to attain the speed, in a mode involving rudder rotation critical flutter speed. and fuselage side bending and torsion, was only slightly greater than the airpfane's The aircraft was modified by reducing the wing structural limit dive speed. The results torsional stiffness and adding ballast at the wing also indicated that a reasonable reduction trailing edge so that its flutter speed would be within in rudder dynamic balance would permit the permissible flight range. Forced excitation was flutter to occur below the limit speed.

provided by a rotating unbalance exciter located out- board in the wing. Unfortunately, this aircraft (3) The aircraft had a very large and spacious crashed during the flight flutter test program without cargo interior. It wasn't necessary to limit encountering flutter. the size or weight of the equipment that could be installed and this permitted un- During 1944-45, the Curtiss-Wright Research limited latitude in trying out various excita- Laboratory, Buffalo, N. Y . conducted an intensive tion techniques and all sorts of equipment series of flight flutter tests on a Curtiss SBZC-1 air- during the tests. In addition, it permitted plane in an attempt to produce flutter of a mass un- each member of the flight crew to have a balanced rudder. The airplane was instrumented special exit of his own in case the a i r c r d t with a rotating unbalance exciter in the tail and the had to be abandoned.

necessary recording instrumentation. Unfortunately, no approach to a flutter condition was attained due The major modification to the aircraft consisted either to the fact that the flutter speed was above the of: allowable flight range of the airplane o r that sufficient excitation was not available to adequately start the (1) Modifying the rudder by installing inside it oscillations. Theoretical analyses indicated that the a large movable balance weight which could critical flutter speed should have been within the be remotely controlled so that it could be airplane's speed range.

located any place between the rudder hinge line and the trailing edge. During flight, A i r Corps flutter test program, which was An this permitted the rudder static unbalance to conducted in 1947 at Wright Field, Dayton, Ohio was be varied by several hundred inch-pounds.

the most successful attempt in the USA, up to that In the event of flutter, a quick release device time, to obtain controlled flutter oscillations during could instantly return the movable weight to flight. Based on the information obtained from this the hinge line and stop the flutter or at test program, techniques and e q u i p m e n t were de- least reduce its severity.

veloped which have been used for a number of years (2) Installing a 16 in.-lb rotating unbalance in flight flutter testing in this country.

exciter in the aft end of the fuselage. The exciter drive system, which consisted vf an The aircraft involved in these tests was a large amplidyne controlled 1/2 h.p. D.C. motor, twenty passenger high wing cargo airplane which had had excellent speed control and would main- originally been the CG-4A glider and had been modi- tain the exciter speed at any place on the fied by installing two engines on the wings (see resonance curve. A quick stop control Figure 3). The aircraft, which was designated the PG-SA, could take off and cruise at low speeds under would stop the exciter in about 1/3 of a its own power. Since it could not attain the speeds cycle so as to permit damping decay records required for the test program, it was towed b y a to be obtained.

structural limitations. At no time were there any indications that the oscillations would become uncon- trollable.

Self-sustained oscillations started at 130 mph and the tests were stopped at 164 mph. In this 34 mph speed range, the flutter amplitudes had increased by a factor of about five as shown in Figure 4. The oscillations of the aircraft were quite severe at the higher speeds and the pilot was badly tossed around in the cockpit. The flutter engineer andthe recording equipment were located in the fuselage at a point of minimum amplitude and fortunately were not too much affected by the oscillations.

During these series of tests, a number of tech- niques were tried for exciting flutter such as kicking the rudder pedals, oscillating the rudder pedals with an elastic exciter, flying the airplane through gusts, and of course, the rotating unbalance exciter located in the tail. The most successful method and in fact the only method that could be relied upon to indicate the approach to flutter, was that which employed the rotating unbalance exciter to obtain a resonance con- dition. At resonance, the exciter was quick stopped and the peak amplitude and rate of damping were obtained and plotted against airspeed. This was done at least twice at each airspeed to insure consistent a good indication of the data, and the results gave approach to flutter.

Figure 3. PG-2A Airplane - 1947

The force output from the exciter in these tests was approximately 26 pounds at the critical (3) Installing recording equipment and about 24 frequency. The two pilots who alternated in flying accelerometer vibration pickups in the wings, the aircraft had no misgivings o r worries about fuselage, and tail; and dynamic position flying this type of test since the flutter engineer indicators in the rudder. In addition to the was always along and therefore it obviously was not photographic recording o s c i 11 o g r a p h, a dangerous. Howevgr, it should be emphasized that visual type ink recording oscillograph was very careful safety and emergency procedures had used for immediately analyzing the data been worked out and coordinated with the pilot in case during flight. High speed movies were difficulties did occur.

taken from another airplane which flew behind the PG-2A.

Beginning in the late forties, the Air Force began to require the use of flight flutter tests to The first series of tests proved adisappoint- substantiate the flutter safety of the new high speed ment as no definite indication of flutter was apparent and unconventional type of aircraft which were being up to the limit dive speed, even with the rudder developed and produced. In many instances the air- movable weight all the way to the trailing edge.

plane was excited by pilot excitation or servo excita- Preliminary flutter analyses had indicated that flutter tion of the control surfaces. These methods were would occur considerably below this speed.

P G - 2 d WRIGUT FIELD A considerable amount of balance weight had I947 been left in the rudder leading edge so that flutter G wouldn't occur at too low a speed. All of the original ELUTT€R AMPLITUDE balance weights were now removed from the rudder dMPLITUDE d T S X 4 R T and only the unbalancing movable weight remained.

OFCLUTTSR 4 Additional tests were then conducted for the new

i

configurations. These tests proved successful since

i

sustained flutter was actually attained. The oscilla-

A o u s w oF FLUTTER

tions could readily be controlled by changing the air- plane speed or by varying the rudder movable balance U 0 40 hO I20 IbD 200 i40 weight. With increasing airspeed, the flutter oscilla- VCLOCITY, v, MPU tions kept increasing in amplitude until a point was Figure 4. Flutter Amplitude Ratio vs Airspeed reached at which the tests were stopped because of satisfactory provided the frequencies of the expected speeds to which 'it was to be flown, flight tests were be readily flutter modes were not too high and could made to substantiate its safety. Since the wings were excited by the control surfaces. Gust excitation was relatively thin at the outboard stations, the rotating also used to some extent. However, in many of the unbalance exciter and drive motor was located ex- cases involving high speed aircraft the use of a ternally on the bottom of the wing near the wing tip mechanical exciter system was considered necessary trailing edge and covered with a fairing. This exciter system was very compact since the rotating weights for the tests in order to obtain adequate and satis- factory data. were built integral with the drive motor. The aircraft carried only the pilot and he manually tuned the ex- One of the first flight flutter tests to be made citer to each resonant frequency by observing the on a high speed aircraft was conducted on the Northrop metered output of a selected vibration pickup. Tests F-89, which had irreversible control surfaces without were conducted up into the transonic speed range with any balance weights. The problem of concern on this no indication of an approach to flutter.

airplane was the flutter stability of the ailerons. For these tests, a 2 in.-lb rotating unbalance exciter, There is little doubt that flight flutter testing is together with a 1/2 h.p. drive motor, was installed in hazardous and it can be exceptionally s o when the the wing tip as shown in Figure 5. This installation program is not carefully organized and carried out.

occasioned no difficulty since the wing tip thickness The following instance illustrates this. Early in the 1950's, the A i r Force at Wright Field, Dayton, Ohio was unusually great due to the fact that the wing had been designed to carry heavy tip pods. The procedure conducted some tests on a P-80 airplane to obtain flutter data on the effects of tip tank fuel c.g. travel.

for these tests was to automatically sweep the com- plete frequency range in about 1-1/2 minutes. This were In order to control the variables, lead weights was done at each incremental airspeed and the flight used in lieu of liquid fuel to vary the tip tank c.g.

stopped after a definite speed range had beencovered.

The results showed no indication of flutter up to the For these tests, the pilot would excite the maximum speeds attained and thus substantiated the wings by banging the elevator control with his hand to excite symmetric modes and the aileron control results which had been obtained from flutter model tests and theoretical flutter analyses conducted prior to excite the antisymmetric modes. The wings and to the flight tests. tip tanks were instrumented with strain gages and accelerometer whose outputs were recorded on an The first transonic delta wing aircraft produced oscillograph. The test program was planned to cover in the USA was flutter tested during 1950. This air- a predetermined speed range for each flight. At plane, the Convair F-92, had irreversible control each incremental airspeed in the range, the pilot was not mass balanced. Due to the then surfaces and would excite the wings and take oscillograph records.

unconventional design of the airplane and the high The airplane would land, the records would be analyzed Figure 5. Rotating Unbalance Exciter With 1/2 H.P. Drive Motor and the speed range to be covered in the next flight been conducted in the United States by the Navy, Air would be established. Force and Industry in order to briefly illustrate the development of this type of testing from the early days of flight to the present time. It can be said that This test program was carefully followed for several flights without incident. The pilot then practically every military airplane model flying today apparently began to think that possibly too much time in the United States has undergone some type of con- was being wasted by following the program since he trolled flight flutter tests during its develgpment.

had made a good many flights and nothing had happened. Therefore, in the next flight, instead of Although great improvements have been made in stopping at the established limit speed, he decided to flutter recording equipment, today's test techniques, obtain a few more speedincrements before terminating with a few exceptions, are essentially the same as the flight. A very large amplitude wing flutter sud- those in use 23 years ago. The progress that has denly developed which violently threw the pilot around been made in flutter testing can be attributed to a the cockpit. However, by a great effort, he was able better theoretical understanding of the flutter prob- to finally reach the jettison switch and drop the tip lems, improved test data, and better methods of an- tanks within about three seconds after the oscillations alyzing the data. It is hoped that improvements in began. The flutter stopped and the pilot was able to test techniques will eventually result in flight flutter land the aircraft. The wings were so badly ripped tests that will give all the information wanted and and torn that they could not be repaired. will be considerably less hazardous than they are today.

Complete oscillograph records were obtained of the flutter condition which was symmetrical in nature. Analysis of all the oscillograph records REFERENCES showed that very definite indications of an approach to flutter were obtained in the records which were 1. Von Schlippe, B., The Question of Spontaneous obtained before the established speed range was ex- Wing Oscillations. (Determination of Critical ceeded. The pilot could not feel a,iy change in the Velocity Through Flight-Oscillation Tests) NACA aircraft as the speed was increased, but the records TM 806, Oct. 1936 (translation).

clearly showed a large increase in the amplitude of the oscillations which were becoming very lowly 2. Burow, H. and Roos H., Flight Vibration Tests, damped.

USAF AMC translation, No. F-TS-76S-RE, Feb.

1948.

This case emphasizes the importance of follow- ing an established test program so as to minimize, 3. The Aeroplane, March 2, 1938, Account of Flutter as much as possible, the inherent hazards involved in Accident to Junkers JU90.

this type of testing.

4. England, J. L., Flight Tests of AT-8 to Deter- Since 1950, some type of controlled flight flutter mine Wing Flutter Characteristics. AMC Memo tests have been conducted on a very large number of Report, EXP-M-51/TR 317-9, May 1942.

both Navy and A i r Force aircraft. In some cases these tests merely involved shaking of the control 5. Lunney, E. J., et al., Flight Flutter Tests of a surfaces by the pilot to check for tab or control AAF TR 5132, Radio Controlled Towed Glider.

surface flutter. In other cases, the testing was much Aug. 1944.

more involved and required some type of powered excitation such as servo excitation of the control 6. Wasserman, L. S., Flight Flutter Tests of the surfaces o r an inertia type of exciter. Based on the C-54A Rudder Spring Tab Combination. AAF flutter tests which they have conducted, aircraft Memo Report ENG-51-4162-13-31, Nov. 1943.

companies have developed o r adopted certain test techniques which they consider to be the most satis- 7. Wasserman, L. S., Flight Vibration Tests of CG- factory for their particular requirements. However, 3A Glider, AAF Memo Report ENG-51/4594-1, there are some aircraft companies who don't conduct May 1943.

flight flutter testing to any extent since they don't consider the available methods to be completely 8. Bergen, W. B., Experimentai Investigations in satisfactory. In some respects this line of reasoning Aircraft Dynamics. IAS Journal, Oct. 1948.

isn't too logical and can best be expressed by a mathematician's famous retort to some colleagues 9. Frazer, R. A., Forced Oscillations of Airplanes who refused to use his theories because they didn't with Special Reference to Von Schlippe's Method understand them. He said, tfShould I refuse food of Predicting Critical Speeds for Flutter. ARC, because I don't understand the process of digestion?'' R & M 1795, Oct. 1936.

CONCLUSIONS 10. Frazer, R. A., On the Power Input Required t o This paper has attempted to cover only a f e w Maintain Forced Oscillations of an Aeroplane of the many flight flutter test programs which have Wing in Flight. ARC, R & M 1872, July 1939.

11. Peacock, H. G. S., Flight Flutter Tests on the for the Bureau of Aeronautics. Aeroelastic and Gloster Javelin, Aircraft Engineering, Vol. 27, Structures Research Laboratory, M. I. T., Sept.

March 1955. 1951.

12. Wolfe, M. 0. W., Vibration & Flutter Flight Test- 21. Pepping, R. A., A Theoretical Investigation of the Oscillating Control Surface Frequency Response Note Structures 170, July 1955. ing, RAE Tech.

Technique of Flight Flutter Testing., ATC Report NO. ARTC-6, Jan. 1953.

13. Broadbent, E. G., Flutter Prediction in Practice.

RAE Tech. Note Structures 185, Feb. 1956. Also AGARD Report 44, April 1956. 22. Grossman, E. P., Flutter. AFTRNo. F-TS-1225- lA, 1937. Russian Translation.

14. Curtiss-Wright Research Laboratories. Flight 23. Marx, A. J., A Survey of Flight Flutter Testing Flutter Tests of the Chance Vought F4U-1 Air- Techniques., Vol. 11, AGARD Flight Test Manual, plane. Report No. SB-348-S-2, Oct. 1945.

1956.

15. Cornell Aeronautical Laboratory, Model SB2C-4 Airplane. Flight Flutter Investigation of Rudder 24. Templeton, H., Flutter Research at the Royal No. SB-355s-4. 1948. Aircraft Establishment FARNBOROUGH. AGARD Mass Balance. Report Report 4, 1955.

16. Rosenbaum, R. and Scanlan, R., A Note on Flight 25. Templeton, H., A Review of the Present Position Flutter Testing. IAS Journal, June 1948.

on Flutter, AGARD Report 57, April 1956.

17. Walter, M. A. and Arrow, B., Low Speed Piloted Flight Flutter Tests of SB2C-4 Rudder. Aero- 26. Garrick, I. E., Some Concepts and Problem Areas nautical Structures Laboratory Report No. ASL- in Aircraft Flutter. IAS S. M. P. Fund Paper No.

NAM DE-213, Part 1 1 1 , N. A. M. C., Feb. 1951. FF-15., March 1957.

27. Kussner, H. G., Aeroelastic Problems of Airplane 18. Walter, M. A., High Speed Pilotless Flight Flutter Tests of SB2C-5 Rudder. Aeronautical Structures Design, NACA TM 1402, Nov. 1956. German Laboratory Report No. ASL NAM DE-213, Part translation.

V, N. A. M. C., Feb. 1951.

28. Laidlaw, R. W., and Beals, V. L., Jr. The Appli- cation of Rocket Sled Techniques to Flutter Test- 19. Schwartz, M. D., and Wrisley, D. L., FinalReport ing. IAS Preprint No. 666, 1957.

on Investigations of Flight Flutter Testing Tech- niques for the Bureau of Aeronautics. Aero- 29. Douglas Aircraft Co. Predicted Wing-Aileron elastic and Structures Research Laboratory, M.

Response to Vibratory Forces During Flight.

I. T., Dec. 1950.

Report No. SM-13379. 1948.

20. Schwartz, M. D., Supplementary Report on the Investigation of Flight Flutter Testing Techniques A REVIEW OF FLIGHT FLUTTER TESTING TECHNIQUES IN GREAT BRlTAlN M. 0. W . Wolfe - Royal Aircruft Estublishment, Farnborough, England Abstract flutter tests than not to do them pruvidcd the flight experiments a r e preceded and supported by parallel A review is made of the techniques that have theoretical and wind tunnel investigations.

been developed, o r a r e being developed in the United This in- Kingdom for flight flutter testing aircraft. Flight flutter testing has therefore become cludes a description of the instrumentation used for almost a routine stability check of high speed proto- recording the vibrational response and a compara- type aircraft and has in most cases producedvalu- tive assessment of the various methods used for able information on the flutter characteristics of the exciting the aircraft response in flight. Reference is aircraft on which it has been applied. Moreover, made to the problems' of determining the overall apart from flutter, the increasing importance of the damping from the transient responses to shock excita- fatigue problem has focussed attention on the deter- tion, and special methods of recording for subsequent mination of the sub-critical responses of aircraft in play-back and instrumental analysis a r e described. relation to gusts and other aerodynamic forces, and Some examples of measured and calculated subcritical here the application of flight flutter testing techniques responses on particular aircraft are quoted and cri- can provide important data.

tically discussed from the standpoint of experimental technique .

From the flutter clearance aspects however, to obtain the required information and to ensure, so far INTRODUCTION as possible, that no important stability trends are overlooked, the choice of experimental technique and Flight flutter testing techniques have been ac- the programme of testing adopted a r e important. It is tively developed in the United Kingdom since about my object in this paper to describe some of the 1947. Pioneering enthusiasm was at first restrained principal techniques which have been developed in the by fears as to the safety of anaircraft when subjected U. K. during the past ten years.

to experiments of this kind. It w a s felt that in the presence of a "hard" flutter mode, that is, one in THE BASIC OBJECTIVE which the overall damping is high at sub-critical speeds and falls rapidly to zero close to the critical Before going on to describe the techniques, let speed, there was an obvious danger that tests might us first take a brief look at the essentials of the lead to an inadvertent and catastrophic excursion problem. An aircraft is a complex dynamical system a flutter region. In those days, because of the having many degrees of freedom. In still air, on the into ground, positively damped natural modes of vibration inadequacies of experimental techniques and the lack of high speed computing facilities there were certainly are associated with each of these freedoms. In flight, grounds for apprehension. Since then, however, the however, powerful aerodynamic forces are brought situation has materially changed, experimental tech- into play by oscillatory motions of the aeroplane and niques have been developed enormously and there i s additional forces and couplings between the natural no lack of high speed computing machinery. It is modes are thereby introduced. Since the aerodynamic now generally recognized that even for the so called forces vary with airspeed and density, the character- hard types of flutter it is in general safer to do flight istics of what we may term the flight modes of the is rapidly cut off at a peak amplitude and the ensuing aircraft also vary. In particular, at any airspeed the modes will have certain overall damping factors transient oscillation measured. In general, the choice associated with them, and these modes and damping of method, or the combination of methods employed factors change progressively as the air speed changes. in any specific case depends on the particular cir- At a critical flutter condition the damping of one of cumstances. For example, the range of frequencies the modes becomes zero. The object of flight flutter to be covered, the nature of the modes whichare is, therefore, to obtain a measure of the thought to be suspect from pre-flight theoretical testing analysis and wind tunnel investigations, and problems dampings associated with the modes as the airspeed with the installation of the instruments, are all factors is progressively increased, so that from the damping trends at subcritical conditions the approach of a which must be taken into account. In practice some critical condition may be predicted. This canbe done compromises usually have to be made.

by applying either oscillatory o r impulsive forces to The Continuous Response Technique the aircraft and measuring the responses with suit- able instruments. An indication of the damping can A typical application of this technique is shown thus be obtained either from the peak amplitude of 1. Here a single vibrator can be seen the vibrational response to sinusoidal force excita- in Figure o r from the rates of decay of the vibration installed in the nose of a fighter aircraft. The vibra- tion, tor is driven through a gear box bya shunt wound D C response after a force impulse has beenapplied. This electric motor, which receives its supply from the is, of course, an over simplification. In practice aircraft 24V D C system. The speed of the motor is there a r e many precautions which must be taken to controlled automatically by a suitably graded poten- ensure that whichever technique is employed, the tiometer connected in series with the motor field and possibility of overlooking a significant mode or of operated by a small constant speed electric motor.

obscuring the trends by inadequate measurements and The potentiometer is s o designed that the drive motor subsequent analytical uncertainties is reduced to a can be accelerated at a predetermined rate so as to minimum.

sweep the vibrator through the desired frequency range and then stop and reset automatically. The rate of EXPERIMENTAL TECHNIQUES sweep is obviously important, because too high a rate of sweep may not allow sufficient time for the peak The techniques which have been adopted may be amplitude responses to become established.

classified broadly into the following categories: (i) The continuously forced oscillation tech- nique, and (ii) The decaying oscillation technique In the former sinusoidal force is applied to the aircraft structure, or to the controls by means of a mechanical o r some other form of vibrator. The excitation frequency is gradually increased from zero over a predetermined range and the vibration response of the aircraft is then recorded by means of multi- channel vibration measuring instruments. This pro- cess is repeated at suitable increasing increments of airspeed and Mach number and the amplitude speed responses in the significant modes a r e deduced from the measurements: an approach to a critical flutter condition is indicated by an increase in amplitude response with air speed.

In the "decaying oscillation technique" either a sudden force is applied to the aircraft, o r a sinusoidal Figure 1 . Single Vibrator Installed in Nose of Fighter force at a fixed frequency issuddenly removedand the Air craft subsequent transient responses of the aircraft struc- are measured. The overall dampings in the tures modes concerned are then deduced from the time In this particular example the vibrator w a s rates of decay of the ensuing transient oscillations; constructed to sweep through the frequency range the process being repeated at increasing increments 5-13 C.P.S. in approximately 40 seconds with the of air speed. An approach to a critical flutter condi- frequency/time relationship shown in Figure 2. Fig- tion is indicated by the damping approaching zero.

3 shows the layout of the instrumentation and the Control jerking is a crude form of this technique. ure A combination of these techniques may be employed distribution of the vibration measuring transducers.

These were of two types, inductance accelerometer excitation from a vibrator where6y the continuous 0 ACCELERATION TRANSWCERS + VELOCITY TRANSDUCERS WNTRM. GEAR AMPLIFIER Figure 3. Layout of Experimental Equipment The signals from these transducers were conducted through integrators without amplification directly tr, the mirror galvanometers of the recorder.

I do not propose to go into detail on this sys- tem at this point*. However, I should mention that 0 IO 2 0 30 4 0 x) 6 0 7 0 80 the continuous oscillation technique suffers from the TIME (SECONDS) following disadvantages. Inertia vibrators are in- efficient at low frequencies and are therefore not Figure 2. Two Typical Patterns of Variation of very suitable for large aircraft having very low Exciter Speed with Time natural frequencies. When a single vibrator is em- and velocity type transducers. The amplifiers were as in the example I have shown, there is also ployed, of the M i l l e r amplitude modulated carrier frequency a danger of it being placed in a position of minimum type with circuits for double integration to give dis- amplitude for a significant flutter mode which may not placement traces on the records. The recorders were therefore be adequately excited. To overcome this of the mirror galvanometer type. Only two velocity last difficulty we have developed a system for multi- transducers were installed; one in the wing tip and point excitation using D. C. motors driven in phase the other in the rear fuselage. In this case all the synchronism with a master motor. A diagrammatic transducers were arranged to measure in the verti- illustration of the system is shown in Figure 4. By cal plane. The acceleration transducers and their associated integrating amplifiers in this case pro- *Details of this system were presented on 35mm vided the main measurement system; the purpose film immediately following author's presentation of of the velocity transducers w a s to provide an inde- this paper.

pendent check on the accuracy of the main system.

Principle of Operation Drive shaft to gearbox -exciter

/

_ _ _ - Operating Pnnci& The angular pasition of the armature in each slave motor b locked eiectromagneticai~, r e b t i i to the angular positionofthe mastm Commutating Unit cmmutntm The master coirmtatu is then rotated over the q r o p r i a t r speed mnge(0lWng for the rat0 d Slave motor armature the reduction gearbox Mween the

- energised cyclically

s l o v ~ notor and excitedand inmce through slip rings the exciters will rotate a t identical speeds and a t fixed phase relation- ship. Other circuits permit the pilat to select the exciters to run 'i6,or oui, of phase as desired.

The slave motor shown on the meteor operates at 0-6OoO Suppl, to port slave motor cpm; the electromagnetic lock is D.C. Supply for Slave. Motor sufficient to drke a Dlb. inch slave armatures in Port Wing delivered through exciter through a 7.1 reduction gcac commututar- slip rings Figure 4 . Slave Motors for Phased Excitation ing a sharp jerk to the control, has nevertheless been means of slip rings connected to corresponding bars on the commutators of the master and slave motors used successfully in certain cases. Figure 6 shows and linked together by cables connecting correspond- some typical traces of transients excited from control ing slave ring brushes, the angular position of the armature in each slave motor is locked electro- magnetically relative to that of the master. The mas- ter is driven by a separate speed controlled motor over the appropriate speed range and the slaves are thus constrained to rotate at the same speed and phase relationship. Auxiliary circuits can easily be provided to enable the pilot to select individual vi- brators to run "in" and "out" of phase as desired.

This system has been used successfully on a large prototype bomber. It has the advantage of simplicity 3 7 0 KT5 and is generally more positive in operation than other electrical methods of driving several motors in synchronism.

A further important disadvantage of the contin- uous oscillation technique is that since the stability Figure 6. Waveforms Obtained from Stick Jerk Tests trends must be deduced from the variation in ampli- on a Jet Fighter Aircraft tude response with air speed some ambiguity can arise from the corresponding changes which occur in the flight mode. For example, it is in general, jerks from which damping values have been success- fully deduced, and Figure 7 shows a curve of damp- impossible to determine from measurements at a ing obtained from rudder jerks on a large prototype single point on the aircraft whether a variation in amplitude response is caused by a change in stability, high speed jet bomber. This is a very good illustra- or by a change in the position of pseudo-nodal region tion of the quality of the results whichcan be obtained relative to the point of measurement. This is illus- in circumstances where the technique can usefully trated in Figure 5 which shows the variation in am- be applied. However, we do not advocate the use of plitude response with airspeed as measured at two control jerking where more refined methods can be effectively be employed. The limitations of the con- positions on a fighter aircraft, one in the r e a r fuse- lage and one at the wing tip. Clearly, quite different trol jerk technique combined with the difficulty of on kends are shown at the two positions. installing equipment for continuous excitation small very high speed aircraft has led to the devel- opment of rocket excitation techniques. Small rocket charges enclosed in cylindrical steel containers hav- AMPLrmDE RE SPONSES A T TWO POSITIONS

ON A W I N - WINED JET FGHTER

ing convergent-divergent exhaust nozzles, known as FLIGHT FLUTTER TESTS ON A LARGE HIGH SPEED JET BOMBER.

(DAYPING OF II. FIN MOOC) ( Z O C P S APPROX) O A M P M l ! I 0 0 200 hdkaled A l ~ P C r d ( k n 0 l Q 400 500

Amplitude Response - Airspeed

Figure 5. Amplitude Responses at Two Positions on a Twin-Engined Jet Fighter The "Decaying Oscillation" Technique Three methods of exploiting this technique have been employed in the U.K. The crudest is control jerking, which although it suffers from the limitations R A W Q AIRSPCLD TO CLlcUuTID R U T T C R SCCID.

that the upper limit of frequency which can be excited Figure 7. Flight Flutter Tests on a Large High Speed is governed by the dynamical characteristics of the Jet Bomber control system and the virtuosity of thepilot in apply- 1 70 “bonkers” have been developed to give thrusts of employ a combination of both techniques, in the man- approximately 220 lbs for varying time intervalsdown ner I have described.

to a minimum of 12 milliseconds. Theunits a r e fired electrically, and one great advantage of the technique The second requirement is the one that gives rise to the really important difficulties of flight is that several units deployed at different positions on the aircraft can be fired either simultaneously, or flutter testing. The responses observed in a flight test are not simply composed of the responses at predetermined time intervals appropriate to the flutter frequency and nature of the mode being investigated. to the deliberately applied forces, but are in general In this way some degree of selectivity may be complicated by additional responses to extraneous achieved and unwanted modes can be suppressed. A s forces such as gusts and buffeting. The analysis of Mr. Tammadge has dealt with this technique in more records, therefore, becomes a difficult problem and detail in his paper I will confine my remarks here becomes more difficult as the critical speed isap- proached because the aerodynamic disturbances tend simply to mentioning that is has been used with some success on several high speed aircraft in the U. K. to increase with airspeed and Mach number. Before going on to discuss the ways in which we are trying The third method which has been used to obtain to overcome these difficulties I would first like to transient responses is the one previously referred to show some slides to illustrate some of the results in relation to the inertia vibrator, that is the technique we have obtained in practice.

of tuning a vibrator on to a resonance and then stop- ping it rapidly by regenerative braking or other means Figure 8 shows results obtained on tail flutter investigations on a large high speed bomber proto- and observing the subsequent transient.

type, The amplitude responses for two transducers Electrodynamic Excitation placed at the elevator tip are shown, one measuring in the vertical and the other in the fore and aft direc- W e have also developed a method of applying tion. The experimental points are plotted in each sinusoidal force to a control circuit by means of a case for several flights at nominally identical condi- moving coil electrical vibrator. Although this method tions and the degree of scatter may be seen. Figure has shown promising results it is probably only ap- 9 show relative damping estimates for the same plicable to aircraft having either pure servo-tab o r series of flights obtained by the method of tuning the spring tab controls. Its advantages a r e that both the vibrator to maximum amplitude response and then force amplitude and the frequency can be controlled stopping it suddenly and observing the ensuing trans- independently in flight, and the force may be removed ient. In this case the experimental results a r e com- instantaneously and if necessary the vibrator can be pared with those predicted from theory. The agree- used as a regenerative brake to increase the damping ment is fairly good at sub-critical conditions but here in the control system*. A vibrator was installed in again a fair degree of scatter is evident. Figures the rudder tab control system of a Lancaster aircraft 10 and 11 show similar results obtained on the same fitted with pure servo-tab controls.

General Remarks on Technique Whichever technique is chosen for a particular 0 12 ‘ Antisymmetrical Mode 4 0 cps case it is always essential to ensure that: . . (1) It is capable of exciting all the modes of 0 IO significance, and (2) The measurements are such that the sta- 0 08 bility trends are not obscured by difficulties of interpretation.

For the continuous oscillation technique com- pliance with the former is a matter of ensuring that an adequate number of properly placed vibrators of sufficient power are employed and there should also be an adequate number of measuring stations. These remarks apply in general also to the transient res- ponse technique. In fact, when vibrators are installed, in our view the most satisfactory arrangement is to I ’ 42 5 2 6 2 .72 €AS estimated finVc Figure 8. Flight Flutter Tests on a Large High Speed *The 35 mm film shown by the author also covered Jet Bomber (Continuous Excitation Tests) the details of this system.

FLIGHT FLUTTER TESTS ON A LARGE HIGH SPEED JET BCIUIBER.

FLIGHT FLUTTER TESTS (MI A LARGE HIGH SPEED JET BOMBER.

(DIMPWC OF I . ? TAIL PLANE MODE) (DAMPING OF IS' LATERAL NSZLAGL MODE) ( 6 I C P 5 APPROX ) (4 I C P S APPROX) DAMPING OIUP,NG FACTOR RLTW ff AIRSPIED TO CALCULATED FLUTTER SPEED RATBO O f IIRSPPEFD TO CALCULITLD E FLUTTER SPEED Figure 9. Flight Flutter Tests on a Large High Speed Figure 11. Flight Flutter Tests on a Large High Jet Bomber Speed Jet Bomber (Damping of 1st Tail Plane Mode) FLIGHT FLUTTER TESTS ON A LARGE STICK-JERK TESTS ON A HIGH SPEED JET BOMBER

SINGLE - ENGINED JET FIGHTER

Continuous ExcJtation Tests Antisymmetrical Mode 6 . 3 c p s . -h 2 1 C . P . S .

o.so/ 0 - 2 5

predrted values - 0 0 2

.

0 . 2 0 .

0.01 1.500 f t .

R W . 5.000ft.

350 400 450 500 550 6 0 0 650 I

A . A t

E 0.15-

t A *

Y 1.A.S (knots) 'p 3 d

.- -

Damping Airspeed 'power on* p 0.10.

Figure 12. Stick-Jerk Tests on a Single-Engined . elevator tip-vertical 0 . 0 5 .

A elevatw tip-tore L aft Jet Fighter I STICK-JERK TESTS ON A

SINGLE - ENGINED JET FIGHTER

Figure 10. Flight Flutter Tests on a Large High Speed Jet Bomber (Continuous Excitation Tests) aircraft but for different modes. Again the agree- ment between predicted and observed sub-critical response is quite good, but the experimental scatter is still fairly excessive. Figures 12 and 13 show results obtained from stick jerking tests on a high speed fighter aircraft for two flight modes, one in- volving symmetrical tailplane bending and elevator 1A.S. (knots) rotation at 21 C.P.S. and the other a mode involving Damping- Airspeed-'Power On' tailplane and elevator motion and fuselage bending at 14 C.P.S. In each case the experimental points Figure 13, Stick-Jerk Tests on a Single-Engined are again compared with the sub-critical response Jet Fighter curves. Although the experimental scatter is still . 172 Mathematical analysis of waveforms of this great the general agreement with prediction is fairly good. However, in the case of the 21 C.P.S. mode type is difficult and time consuming, even with the assistance of a digital computer. Electronic wave flutter is predicted at about 670knots I.A.S. and the analysers have been used extensively for the analysis relative damping is still quite low even at 550 knots.

of wave forms consisting of repetitive sinusoidal As it was necessary in this case to clear the aircraft components of constant amplitude, however difficul- s underlines very well the importance ties associated with the characteristics of the analyser of reducing somehow, the degree of experimental arise in the analysis of complex transients. An scatter. The trend of the curve is clearly of critical electronic analyser is essentially a single degree of significance in this case, and is obviously very diffi- freedom system having a very small degree of damp- cult to obtain from these results.

ing. If such a system is excited by an input signal it exhibits the typical transient response, which is Analysis Techniques primarily a function of the characteristics of the We are a t present investigating two methods of analyser, and a forced response to the input signal.

overcoming .the analytical difficulties of flight flutter For example, if a complex transient is recorded in a testing. One involves the application of vectorial flight flutter test on magnetic tape and played back methods of measurement and a?alysis to the contin- into a wave analyser tuned to the frequency of one of uous response technique so as to enable dampings to its components the decrement of the output transient be obtained from the amplitude responses The from the analyser will be a function of its character- method is based on one originally proposed by Kennedy istics and will bear little resemblance to the decre- and Pancu in the Journal of the Aeronautical Sciences ment of the component input transient to which it is for November 1947. The method exploits certain tuned. This is illustrated in Figure 14 which shows properties of a single degree of freedom system. If a complex transient qs recorded compared with the the in-phase and quadrature components of the res- output from an analyser tuned to one of its components ponse per unit force of such a system are plotted as into which it w a s played back. It is obvious that the rectangular co-ordinates a diagram is obtained which decrement of the output transient bears little resem- is nearly a circle. The properties of this circle can blence to that of any of the components of the original.

be used to derive damping and resonance amplitude the values. Kennedy and Pancu have shown that A novel method of overcoming this difficulty method can be extended to systems having several has been suggested by Mazet. This consists of play- degrees of freedom and can be of particular value in ing a tape record of the complex transients into a obtaining true values of resonance amplitude and tuned analyser in reverse; that is, in such a manner frequency in cases where -two modes a r e closely is presented to the analyser in such a that the signal related in frequency.

way that it grows rather than decays. It can be shown that in these circumstances the forced response The method has been used with success on of the analyser to the input signal is nearly exact and Ground Resonance Tests and has more recently been its transient response occurs at a later stage when applied to the problem of obtaining sub-critical res- the input transient has reached its maximum ampli- ponses on flutter models in wind tunnel, using the tude s o that the two may thus be disassociated. Fig- continuous response method of excitation as in flight ure 15 shows a complex transient recorded on tape flutter testing. The method shows promise of over- of flight flutter tests comprising decays at 15 C.P.S.

coming the difficulty of obtaining damping values from and 7.5 C.P.S. This record was analyzed in the man- continuous response excitation and also of determining ner described by playing it into an analyzer in re- the true excited amplitudes in the presence of extran- verse on a continuous loop of tape and the component eous responses. So far as the experimental technique transients with their respective damping coefficients is concerned it requires the accurate measurement derived in this way are shown. We have checked the of phase between the exciting force and the structure accuracy of this method with synthesized complex displacement in addition to the usual measurements transients fed into high "Q" analysers with encourag- made in a flight flutter test. Mr. Broadbent has al- ing results. For example, experiments were done on ready dealt with this in his paper.

a signal composed of a decaying oscillation and an oscillation of constant amplitude and frequency to The second method is one which was originally represent an extraneous disturbing signal. We found suggested by Professor Mazet of O.N.E.R.A. in France, that it is necessary to use an analyser witha "Q" in relation to the problem of obtaining decay functions from complex transients. The problem of obtaining the decrements of the components of a wave form containing several transients at different frequencies Wave-form _ - as recorded is an extremely difficult one. The transients associ- ated with the decaying oscillation method of flight flutter testing are usually of this type, because the Output from analyser applied impulse excites several modes simultaneously, when record 15 played back directly .

those with least damping being the more persistent.

into analyser Moreover the records are made even more compli- cated by random vibration excited by extraneous Figure 1 4 . Analysis of Transients (Wave-form as Recorded) disturbances.

I propose to confine my remarks to the ballistic missile application as this is obviously the most im- Recorded wave-lorm portant at the present time. Of the two techniques rrvrrsed which have been developed for aircraft, one can, I think, at once dismiss the continuous oscillation / technique as being unsuitable because the important / / parameters of air speed and fuel loading are changing

Exponential componmd I Free decay due

too rapidly on a missile to allow sufficient time for a 10 amlyrrr 01 record suitable frequency sweep. It therefore, seems that

I

the transient oscillation technique employing an im- is the only one worth pulsive means of excitation considering. I f space can be found on a large missile A n o l y ~ r r output and the extra weight can be tolerated the "bonker" i h c n rrvrrrrd

I

wave-lorrn 15 method appears to be a feasible one. It would of played back course be necessary to use a sufficient number of

I mlo analyse1

I "bonkers" to permit measurements to be made a t a f ii 7 5 C 1 5 significant number OB points on the flight trajectory

j-J--wwm 5& - ,028

of the missile. On this point some consideration might usefully be given to the development of a Figure 15. Analysis of Transients (Wave-form

. "bonker" which could be recharged automatically as

Reversed) a means of overcoming this difficulty. Another method of applying an impulse which appears to havepossibi- lities in, the case of missiles employing swivelling value higher than 50 if the difference between the motors is the introduction of a suitable step function decay and interfering frequency is of the order of or pulse to the inpuf of the motor swivelling controls.

10%. W e are at present using an analyser with a "Q' value of 150.

I would submit therefore that because of the importance of the stability problem in ballistic mis- Flight Flutter Testing Applied to Guided Weapons and sile design and the great difficulties involved in Ballistic Missiles making correct predictions there is a strong case for applying the experience gained in developing flight I am expressing some tentative views on the flutter techniques for aircraft to the missile problem.

subject of the application of flight flutter testing It would seem that the difficulties may not be quite so techniques to guided weapon and ballistic missile overwhelming as would appear at first sight.

stability problems mainly because it happens to be listed as one of the subjects for consideration at this CONCLUSIONS Symposium, and not because we have any direct ex- perience of the subject in the United Kingdom.

I would like to conclude by saying that flight flutter tests, valuable as they are, should never be It is perhaps erroneous to describe some of the regarded by designers of aircraft as a reason for forms of instability that occur on missiles as flutter, relaxed effort on preflight calculations and experi- nevertheless the problem of avoiding oscillatory in- mental testing. It is in fact the policy in the U. K.

stabilities is probably one of the missile designers to carry out comprehensive theoretical calculations greatest headaches. Moreover, missiles, and parti- and in most cases wind tunnel and rocket model ex- cularly large ballistic missiles, unlike aircraft, can- periments, in addition to stiffness and resonance tests not be subjected economically to progressive flight on the aircraft to determine the flutter characteris- experiments. The body modes of vibration of a tics prior to the first flight and before embarking on missile, and in some cases their associated damping flight flutter tests. Moreover, it is of considerable coefficients, a r e critical parameters in the overall value in a flight test to have some fore-knowledge of stability problem. It is in general more difficult to the probable shape of the amplitude airspeed, or determine these quantities for a missile than for an damping airspeed curves particularly when condi- or experimental means, aircraft, either by theoretical tions of low damping a r e being approached. In fact, because of the difficulty of determining o r simulating theoretical calculations and flight tests should be by experiment on the ground the effects of accelera- regarded as complimentary aspects of the problem tion, fuel motion and the general flight environment.

as a whole with "feed back" of information from both There is therefore a good case for examining the sides. In particular flight flutter tests may be ex- possibilities of adapting flight flutter testing tech- pected to provide some check on the validity of the niques to the missile problem despite the obvious aerodynamic derivatives used in the calculations and difficulties. W e have no direct experience of this as the number of important degrees of freedom in a yet in the U. K . , although the "bonkers" I mentioned previously, which have been applied to aircraft test- particular flight mode. In the present state of know- ledge we regard some form of flight flutter test as ing, were in fact originally developed and used for rigid body stability tests on missiles in roll, pitch being essential for the clearance of high speed air- and yaw. craft.

R E S E A R C H V I E W P O I N T I . E. Garrick when he finds himself in this position, it is likely that INTRODUCTION it was economics (or a skimpy program) that forced My remarks will touch briefly on following it. For one lesson w e learn is that flight flutter points: (1) objectives and economics, (2) need for testing does not mean just take up the airplane and many approaches, (3) role of margin and trend fly it by the seat of your pants, or to give an "off- studies, (4) optimizing aerodynamics and structural the-cuff" analysis or answer to a multi-million dynamics, (5) flutter indicators, and (6) future areas dollar question, but refers to the whole integrated and inferences. complex of advance calculations, experience, model work, and flight. Of course, we do not wish to give The "future of flight flutter testing" poses a flutter a monopoly on flight problems.

dilemma: Is the best future one in which no flight flutter testing is required, o r it is one in which flight Flight flutter testing is, in essence, a sophis- flutter testing (to the exclusion of supplementary O r is it neither? ticated type of flight testing. Some mathematicians methods) is required?

like to refer to Hilbert space. Flight testing in gen- eral may be said to be conducted in such a space.

The preceding speakers and papers of this By this, we simply mean there are many variables symposium have delved not only into present or and parameters (a good many more than three) and recent problem areas, but many have given their that a particular test i s a slice, cross-section, a views of some of the problem areas that lie ahead.

sample, taken in this "Hilbert" space, wherein as A most valuable record of experience and extrapo- many as possible of the numerous variables are kept lation from experience is thus at hand. Subsequent constant. Although flight testing is the ultimate test discussion of my co-panelists, all of them able and of flight research, the critical and definitive experi- throughtful, will give personal ideas, opinions, and ment in the classical sense of 'verifying a theoryor speculations with emphasis on particular viewpoints hypothesis, or of finding effects of one variable at a as already listed. Some connotations of "space- time, rare in any case, is unlikely to be accomplished craft" in the word "aircraft" will, it is hoped, be in flight.

kept in view.

OBJECTIVES AND ECONOMICS Objectives of flight flutter testing are to draw proper inferences on the safety of the aircraft from A general remark, at once trite and yet pro- flutter under all flight conditions and under marginal found, should first be emphasized. One frequently conditions not necessarily reached in flight (like refers to branches of engineering as an art a n d a #flying "below sea level"). When, in particular, the

science - flight flutter testing is such: an art (a

margins between a flight condition and a flutter con- result of experience and ingenuity), 'and a science dition are smal-l as they often are for many transonic (a result of experiment and analysis). The flutter aircraft and most aircraft of high performance, an "expert" is very often in the position of the expert integrated approach is needed and is recognized as in economics "who knows tomorrow why the things he predicted yesterday didn't happen today". Usually costly.

MANY APPROACHES AND ROLE OPTIMIZING- AERO- AND STRUCTURAL DYNAMICS OF TREND STUDIES The flutter engineer has had little temerity to Tailored programs involving multi-sided attacks suggest to the designer and introduce the thought that are thus required both f o r specific and generalflutter perhaps configurations should not be chosen on the research. Closely tied to this idea of a many-sided basis of aerodynamics alone. The swept-forward wing, for instance, foundered on the shores of aero- approach is the old stumbling block that in flutter there are exceptions even to every well-stated rule. elasticity. T-tails, all-movable wings and controls have only made the optimization problem more nec- Flight flutter testing can become, and probably will become, a standard procedure for acceptance of new essary. Modern computing capacity and instrumen- aircraft, but it can never become a standardized tation are making the optimization problem ponderable procedure. and feasible.

This is not the place to delve into the great REMARKS ON "THE" FLUTTER INDEX many areas requiring additional research work; it may suffice to merely list some of these to indicate im- provements needed all along the way. Stiffness, de- Several papers have been heard having refer- flection, and vibration analysis of simple and complex ence to a flutter index obtained either from theory or structures. Methods of excitation of natural modes, measurement. Unquestionably, a measure of degree analysis of damping. Aerodynamic coefficients for of stability is one of the most important goals of components, bodies, and aircraft f o r complete Mach flutter analysis. W e might quote the Rubaiyat on this number ranges, both oscillatory and transient. Sep- goal: "A hair perhaps divides the false and true; arated flows and transition for unsteady aerodynam-

yes, and a single aleph were the clue - could you

ics. Combining of structural dynamics and aero- but find it."

dynamics, data reduction, and efficient computational methods. Instrumentation equipment and facility Evidence has been presented that the density needs; technique and procedures. Scaling laws and itself might serve as an index, particularly for "ql' methods for models. Role of general research versus type flutter. Other indicators have dealt with differ- specific model and actual hardware research. Whole ential sweep rates, vector plots either in polar or bookfuls of research recommendations in all these Cartesian forms. It is unlikely to find a universal areas exist.

index. There are too many types of flutter, influenced An important function of flutter research is to by too many parameters. However, the searchfor and explore analytically and experimentally the ranges of refinement of these indicators should continue, It is hopeful that from a bagful of indexes withproper pre- speed and density (or dynamic ,pressure) for proposed liminary analysis and experience we may learn to and representative configurations to determine com- choose the right ones, o r what may be more signifi-

binations leading to small margins - so called trend

cant, to use them in proper combination.

studies. Thus, it is an objective of research to focus awareness in flight flutter testing on flight regions One point, for example, that has impressed me and modes of possible concern.

from years ago is that a critical mode very often '75 to are flutter critical in the tends to increase in damping to approximately Some configurations 80 percent of vf, then with further increase in speed transonic speed range near sea level, others such as rounds the maximum damping corner and rapidly some deltas may be flutter critical according to decreases. Therefore, when good evidence is found operational flight paths a t as high a Mach number as reached and at various altitudes. Flutter of controls of the rounding of this corner, we could sometimes relate the approach to the flutter speed to the maxi- has always been a tough subsonic problem; wing mum damping rather than to zero damping.

flutter a rather rare problem except when there a r e heavy stores and nacelles. The all-movable controls have merged control and wing flutter problems so that FUTURE AREAS they are of concern at transonic and at supersonic The point has been mentioned with regard to speeds.

future areas, boost-glide and re-entry vehicles, anti- missiles, etc., that if we consider the speed (or There is good reason to suspect boost-glide and Mach number) and the altitude regime, lines repre- other re-entry hypersonic vehicles will have to over- senting the flight path and those representing aero- come several aeroelastic problems, static and dy- elastic instability (or dynamic stability) may intersect namic, and much research will be required. The almost anywhere in the regime depending on mission, anti-missile missile needing to maneuver and under- configuration, mass distribution, stiffness levels, go a high value of dynamic pressure will also present * modes and frequencies, thermal effects, and SO on.

flutter problems. Of course, one can say there will Nonlinear and transient aerodynamic and structural be many flight paths far removed from a flutter path, effects must also be evaluated and these aforemen- but what will design the vehicle will not be flight tioned factors occupy and will occupy current and paths which must be safe for the pilot, but flight future reseaxc!.

envelopes which must result in structural intearitv.

?

Thus, "flutter" itself should take on a broader mean- The X-15 research airplane which will be the %& combining cybernetics, dynamic stability, and aero- subject of a separate classified conference, will pre- sent a preview of some of the elaborate range-and- elasticity. For flutter is a process of pumping energy from the external flow into t h e structure andfeedback ground-station and instrument requirements €or future control instabilities are similar processes with inter- vehicles. Boost-glide aircraft will present similar W i l l not be very nal energy sources.

problems to those of missiles. It feasible to flight test all possible ranges. Inferences

'

Along with all of this there must come also will have to be drawn more and more from transient data, trend studies from advance calculations, and better physical insight into the mechanism and phen- simulation studies. The methods of feedback control omena of instability whether through damping, o r in servo-mechanism design, of .artificial stabilization energy, o r analog simulation, or mathematical tracing and of aeroelasticity and structural feedback will of roots and modes, or whatnot. Finally, it is not merge more and more. The methods of "count- only necessary to understand, but to understand well and clearly enough so that those in research or

- the

down" for checking reliability of components engineering management who make decisions canalso methods of environmental response and "flutter" in see the problems in their proper light.

a more generalized sense will need to goon together.

FUTURE OF FLIGHT FLUTTER TESTING IN THE FIELD OF CIVIL CE RTlFlCATlON R. Rosenbaum The final panel discussion is aimed at looking stick bang or forced oscillation is used. An example of such an approach involves a current transport into a crystal ball in order to predict the future of flight flutter testing. My particular job is to cover which was flight flutter tested in 1953.

the field from the viewpoint of civilaircraft. It should For this case, analysis indicated that a critical be noted at the outset that although flight flutter flutter mode might be encountered for a specific fuel testing can be used either as a research tool or in substantiating freedom from flutter for a specific configuration at a speed below VD. After extensive airplane configuration, we in the CAA are cbncerned analysis and ground vibration testing, the applicant only with the latter phase of this problem. chose to do flight flutter testing to substantiate the airplane. He was convinced from a review of the Since the discussions to this point have covered available data that the danger of a catastrophic flutter applications to military aircraft only, I would like to condition under controlled tests was about nil and that a few moments to describe the method$ used in because of inherent conservatism in the analysis, he take the past as well as the present in the field of civil could show that 'the airplane would, in fact, be free aviation before getting into the future. from flutter over the design speed and altitude range.

A second example involves a small personal plane Flight flutter testing as described here in the which was tested during 1945-46, using boththe "stick last two days has not been, nor is it at present, bang" and with vibrator excitation. In this case, the A i r Regulations. validity of the method of analysis for the V" tail specifically required by the Civil During official CAA flight tests, our pilpts are ex- configuration was questioned.

pected to evaluate the vibration and flutter character -

The second approach to flight flutter testing i s istics of any airplane going through the certification in the category described by Templeton in his 1956 process. Such evaluation is only qualitative and in AGARD paper as the most straightforward although fact official tests start only after all structural and least sophisticated method of flutter substantiation; flutter substantiation has been completed.

that is, build an airplane, fly it and after it has fluttered, examine the remains to determine what Although flight flutter testing is not required modifications should be made to the second one. This as part of the flutter substantiation program, appli- approach, which, of course, presupposes no prior cants for years have resorted to such tests. Funda- knowledge of the flutter characteristics of the airplane mentally, there have been two approaches to the prob- is an approach which although associated with only a lem. In the first approach, flight testing is resorted small segment of the personal plane manufacturing to only after extensive calculations and ground reson- industry has been resorted to with regularity over the ance testing. Such tests have been conducted where years.

the applicant or the CAA because of anunconventional configuration suspects the validity of the analysis o r Those who embrace this approach do so because where the calculated flutter speed is below the re- they feel that flutter, if it existsatall, is a high speed quired one, and the applicant feels that the analysis problem and can not occur at low speeds. As in the is overly conservative. In such tests, the component case of people who define middle age as ten years under investigations is fully instrumented and either speeds contemplated, the newer more complex struc- older than they themselves are, the definition of high speed is at least 10 mph faster than the dive tural configurations required to achieve the higher speeds and the increased flexibility with attendant low speed of the airplane under consideration. Such people structural frequencies require a new approach to enter a flight flutter test program with no prior flutter substantiation.

knowledge of the flutter characteristics of their air- craft but with utmost confidence that the problem is a fictitious one. Applicants to whom flight flutter testing As an example of the large increases in speeds be the most expedient approach to and weights expected in the new series of jet currently may appear to undergoing certification, it may be noted that the flutter substantiation are cautioned by the CAA that maximum design dive speed of the DC-7 is 475 mph such tests may be hazardous with respect to the pilot's TAS at 28,000 ft. altitude or M = 0.7 whereas the jets life and the integrity of their prototype airplane.

such as the 707, DC-8 or 880 will have maximum An example of such a test is an uninstrumented design dive speeds of the order of 660 mph TAS at 22,000 ft. or M = 0.95. It is in the weight range that one run by an applicant within the last two years.

the differences are really outstanding; thus although Maximum dive speed for the airplane was about 150 the maximum design gross weight of the DC-7 is mph. He was advised to start his test at 60 mph with about 120,000 lb. the fuel alone in the overseas increments of no more than 10 mph from 60 to 100 versions of the 707 and DC-8 is approximately mph and no more than 5 mph from 100 to 150 mph.

He agreed, but instead of starting excitation at 60 140,000 lb. and the gross weights approach300,OOOlb.

mph as recommended, he started excitation at 80 mph.

Damping was satisfactory and his next attempts were For these aircraft, it is now recognized that it at 100 mph and 120 mph - againdamping was adequate.

would be foolish indeed to rely on analysis alone to At this point, a dive was initiated and at 140 mph a substantiate freedom from flutter over the entire mild aileron excitation was imposed by the pilot.

speed, Mach number and altitude range. Although Violent flutter developed almost immediately with details vary from one manufacturer to another, the extensive damage to the airplane. CAA personnel approach is consistent. This approach is to extensive following the airplane in a chase airplane estimated model testing in the wind tunnel, ground vibration wing tip motion of about 2 ft. Although the pilot was testing, flutter analyses and finally flight flutter able to bring the airplane back after speed had been testing. Until our analytical methods a r e improved cut, he had no aileron control and the damaged air- to the point where we can again with reasonable con- plane tended to vibrate violently at any speed above fidence rely on computation only, the experimental 95 mph and below 80 mph. He therefore maintained tools just mentioned will be an integral part of flutter 90 mph during the descent and landing. In a letter substantiation for the large transonic or supersonic written to the CAA, the next day he stated "1 am sure transport.

you can appreciate what a changed boy I am today.

Since I had been warned ahead of time, I realize I Up to this point, the discussion has touched have no one but myself to blame for scaring the hell solely on the question of substantiation of freedom out of me." from flutter for new designs under the program of type certification. Before closing my presentation, I We now come to the question of the immediate would like to cover an item which although not directly relates to the final present and the future of flight flutter testing for connected with flight flutter testing For the small, personal plane aircraft, civil aircraft. objective of having a flutter free airplane.

we undoubtedly will continue to run into individual builders or airplane modifiers who because of limited The item I am referring to is the one of con- resources or because they believe it can't happen to tinued airworthiness or maintenance of the airplane in them, will still resort to flight flutter testing with no such a manner that once found freefromflutter it will prior investigation of flutter characteristics. Although continue to remain so. Undoubtedly, the worst offender tests will henceforth not required until recently, such from the viewpoint of flutter is the loose tab. Whether be instrumented tests with means for recording as a the tab becomes free as a result ofpoor maintenance, minimum the time history of control surface rotation, as for example when a mechanic forgets to safety a main surface deflection and airspeed.

bolt or inserts a push rod in the system in such a manner that a structural failure occurs or whether In the transport field for the smaller, lower the tab becomes free as a result of a fatigue failure speed configurations similar to those currently oper- the consequences as far as flutter is concerned are ating on today's airlines, it is expected that flight essentially the same. The most recent incident oc- flutter testing will probably be resorted to only on curred within the last month on a non-sched airline those occasions when the designer feels that the cal- when violent flutter occurredat takeoff after the rudder culated flutter speed is conservative, and rather than tab failed due to ground gusts. In fact, in 1955 as a redesign will elect to test his airplane in order to result of a series of near catastrophic flutter incidents prove his contention. It is in the field of our new jet resulting from failed tab mechanisms the CAA re- transports that a real departure from past practice viewed the history of tab flutter incidents in scheduled is expected. Currently all manufacturers of jet trans- airline operations with the objective of remedial action.

ports in this country recognize that the much higher flutter free airplane can easily become a fluttering After careful review of the problem, we recom- airplane.

mended to the CAB that the Civil Air Regulations be amended to require that transport aircraft be shown In the same category of control surface balance to be free from flutter under the conditions of failure is the problem of ice, snow or sand collecting inside o r disconnect of any one connecting o r transmitting control surfaces at the trailing edge. Several such element of tab systems at all speeds up to the design incidents were encountered several years ago on one cruising speed. This recommendation was adopted airplane configuration. The leading edge of the aileron in March of 1956. All of the new transports will comply with this requirement either by means of dual was the front spar web which contained lightening holes. Although there were drain holes inthe trailing systems from the irreversible mechanism back to the edge, sand from a sand storm entered the aileron.

tabs or they will show that inthe event a tab becoming Subsequent rain which ran into the aileron resulted in free no flutter will occur up to the design cruise speed.

mud pies inside the aileron and a flutter incident.

Another maintenance problem frequently en- Another incident on the same type of aircraft countered in the personal plane field is the problem of maintaining proper control surface mass balance. resulted from snow and ice accumulating inside the surface. The CAA has issued General Maintenance There have been several cases of flutter caused by Alert Bulletins covering the problem of painting as people who like to keep their airplanes looking new well as inspection for snow, ice and sand with the and therefore paint them regularly without removing hope that such cases will not recur.

the old paint. If enough coats of paint are added, a MAGNITUDE AND OBJECTIVES OF FUTURE FLIGHT FLUTTER TESTING M. J.Tzirner INTRODUCTION Obviously there are serious limitations in pres- ent equipment and testing techniques. Insofar as A s I understand my assignment, it is expected possible we should like to obtain from the test a that I shall use the next few minutes to speculate on completely independent answer to the question of the future of flight flutter testing from the viewpoint stability margins, on the basis of experimental data Presumably I of a specialist in the aircraft industry.

alone; we want the flutter test to provide a reliable am under some obligation to comment on the magni- warning when other methods of flutter prediction have tude of future flight flutter testing, on the objectives of failed, However, some integration of the various such tests, and on the equipment andprocedures which methods is certainly desirable, and we should try to will be used. In undertaking this task I a m conscious perform our analyses and model tests in such a way of the possibility that my views may be somewhat that the results are directly comparable to the flight biased by the specific nature of the projects with flutter test data, even at speeds which are less than

which I have been associated - fortunately there will

critical. Also a negative check is insufficient; we be an opportunity for dissenters to express their need to be able to establish some quantitative cor- objections at the end of the session.

relation as the test progresses.

see a continuing increase In general we expect to MANNED AIRPLANES in the utilization of flight flutter testing techniques.

Wherever margins are questionable because of sys- I should like to begin by commenting on some tem complexity or lack of faith in the adequacy of of the problems of flutter testing of manned airplanes available methods of flutter prediction, a compre- hensive program will be required with controlled which operate within the sensible atmosphere and are excitation and quantitative measurement of response.

capable of steady, unaccelerated flight at all points case instrumentation should be utilized to ob- of the. speed-altitude envelope. It is assumed that In any all flight testing is performed with a crew aboard. tain records during initial high speed flight.

Of course the primary objective of flight flutter testing an - o f vehicle is to achieve a high level of - METHODS OF EXCITATION safety in evaluating its high speed flight capabilities.

In addition we should like very much to obtain some quantitative measure of the margin of safety or de- gree of stability throughout the flight regime. E Pulse excitation appears to be satisfactory if possible we should like to find out how much faster natural frequencies are well separated and only one we could go at a particular altitude, or how much flutter mode is critical. This technique is particu- at the same speed, or how large a change in a larly attractive for testing ultra-high performance lower vehicles because of the saving in test time. However critical structural member or control actuator could it appears to be unsatisfactory for testing vehicles be tolerated without producing a critical flutter con- dition. Finally, if unexpected trouble is encountered. with several potential modes of flutter o r withclosely spaced natural frequencies (as with elastically SUS- we want to be able to avoid a catastrophe and also to obtain sufficient data for diagnosis of the difficulty. pended engine pods, external stores, etc.), have been used extensively to evaluate changes insys- Sinusoidal excitation is much to be preferred for accurate quantitative work on complex systems. tem stability during flight flutter testing. It now Although inertia vibrators of both rotating and re- appears that a series of vector plots showing the ciprocating types have been used quite successfully, variation of both magnitude and phase of admittance are strong arguments in favor of the aero- or impedance with frequency at a series of constant there dynamic exciter utilizing an oscillating airfoil. Since airspeeds can provide a much more informative pic- ture. However limitation of the vector plot for single the inertia vibrator must supply the power to drive point excitation can arise through anunfortunate choice the structure, there is a possibility of undesirable of exciter location, if it should turn out that the interaction effects between the exciter and the vi- flutter mode exhibits small motion in the direction of brating structure. Inertia vibrators tend to be heavy and therefore subject to limitations in the selection forcing at the chosen location. This difficulty can be of a location where they can be installed without overcome in part by location of the exciter at the tip of the surface being investigated, although there is serious alteration of flutter characteristics.

still the possibility of selecting a poor chordwise location.

On the other hand, the airfoil oscillator ex- tracts energy from the airstream, it can be balanced A possible way out of this dilemma istc employ to minimize interaction effects, power requirements exciters, at the cost of doubling the time spent in two are low, the installation is comparatively light, and taking response measurements and increasing the there is much greater freedom in selecting a suitable complexity of data processing. By operating the two location for it. In testing high performance aircraft exciters separately the elements of a 2 x 2 complex one would like to use a high sweep rate to reduce admittance matrix relating displacements at the to testing time. However the features which tend driving points and the exciting forces would be deter- favor sinusoidal excitation (complexstructure, closely mined spaced frequencies) are not compatible with high sweep rates, since closely spaced frequencies tend to gen- erate beats which make record analysis very difficult.

This situation creates a serious dilemma for the flutter engineer which has not been satisfactorily resolved.

At neutral stability all of the admittances B.k DATA HANDLING become infinite; hence we might employ vector plois of the reciprocals of all four of the admittances and watch for a trend toward a common zero within- A s in the past it is expected that a few critical creasing airspeed. By inversion of the admittance channels will be telemetered to an analysis center for relations the following equations are obtained, in- immediate processing as the flight progresses, and a volving the mechanical impedances of the system, Ajk, much larger quantity of data will be recorded for processing between flights. The increased perform- ance of supersonic aircraft will intensify the need for an automatic data reduction and plotting system. How-

[ : : I = [::: : : : I [ : : I

ever some of us have been reluctant to make any large investment in automation of present data reduc- tion procedures, because of a feeling that we should try to develop a better approach to the whole problem.

Also at neutral stability these equations must be satisfied by non-zero values of z1, 22 with both z1 Over 20 years ago R. A. Frazer andW. P. Jones

and Z2 equal to zero; hence the determinant D = lAjk I

pointed out some of the difficulties of in-flight reson- must vanish. A series of vector plots of D vs o at ance testiw as a method of predicting critical flutter constant speed might be employed to detect any trend speeds, and we are still worried about the possibility toward instability. Actually it would not be necessary of encountering an explosive flutter condition which to invert the matrix IBjkl since the determinant cannot be detected by observations much below the

I A. 1 i s simply the reciprocal of I Bjkl. Similar pro-

critical speed. O f course we hope toavoid a situation ce$res may be employed to investigate flutter prob- of this kind by conducting an exhaustive series of lems involving power flight control systems.

analyses and model tests before undertaking a flight flutter test program, but the fact remains that one of the reasons for the test is to provide some protection will not permit a discussion of details, in case a mistake has been made. Evidently research Time but it may be noted in passing that we frequently need is still needed to derive a better stability index as a to determine the change in stability that would result ht flutter testing.

from losing a part of a system of multiple actuators -

preferably without actually testing the reduced system rce per unit amplitude (or absolute in flight.

point impedance) versus frequency initial flight testing of Bomarc missiles a case of ROCKET-BOOSTED HYPERSONIC VEHICLES: elevator flutter was encountered at supersonic speed MISSILES near the end of boost. The mode was clearly identi- fied from telemetered data as antisymmetrical ele- vator flutter involving interaction between antisym- Since a cautious, step-by-step approachto maxi- metrical bending and torsion of the elevator; the mum speed is obviously out of the question the objec- frequency was 45 cps. In this case the records tive of any flight flutter testing program is simply to proved invaluable by making it possible to work out obtain sufficient data for diagnosis of any unexpected a fix by mass balancing the elevators without undue flutter problems that may be encountered. In designing delay to the test program. If the records had not vehicles of this type we shall, of course, make every been available it seems likely that there would have effort to provide substantial margins against flutter; been a greater loss of time in diagnosing the dif- if that is not possible, then initial flights will surely ficulty and developing corrective measures.

be unmanned. Because of the generally rapid vari- ation of flight conditions sinusoidal excitation even with sweeping appears to be out of the question. A CONCLUSION series of programmed impulses applied through the flight control system would be of considerable help to the flutter engineer in obtaining some measure of I should like to say that flight flutter the degree of stability. Finally testing appears destined to remain an invaluable tool Telemeter channels a r e always hard to come by for the flutter engineer. There is urgent need for during the early flight testing of a missile system, research on all phases of flight flutter testing, and we FM channels that a r e required for a r e particularly anxious to see continuing advances in particularly the the applicationof automatic data processing equipment.

transmission of flutter data. Several years ago during THE FLIGHT FLUTTER TESTING STATUS FROM A MILITARY STANDPOINT

W. J , Mykytow

WADC fact that considerable effort has been devoted to studies involving wings with external stores and T- tails, and whereas these studies prevented the oc- A review of recent flutter incidents and serious currence of flutter, speed restrictions have been accidents is first given to supplement information necessary in many of these cases.

already compiled. The period covered is from the middle of 1956 to the present. The cases encountered In summary then, buzz, T-tail flutter, all mov- for US military aircraft are approximately as follows: able control surface flutter and wings-with-stores flutter are still important areas. Hence there is a (1) Two cases of trim tab flutter. definite need for continued and accelerated improve- ments i n flight flutter test equipment, procedures, (2) Approximately seven control surface buzz and in data reduction, evaluation and interpretation.

cases.

It can be expected !hat more emphasis will be placed on flight flutter proof tests in view of the growing (3) "wo cases of flutter involving stabilizer complexity of the aircraft and also in view of the bending-pitch-fore and aft bending of all movable more complex environment in which future aircraft stabilizers having underslung yokes. will operate.

(4) Two cases of stabilizer bending-pitching- At the present time the A i r Force and Navy geared elevator rotation flutter.

require that a 15% equivalent airspeed flutter margin, 32% in terms of dynamic pressure, must exist for (5) One case of antisymmetric stabilizer flutter any and all operating points within the applicable involving first and second bending-torsion-mass bal- speed-altitude range for all operating conditions, and anced elevator rotation. that this margin be evaluated by separately consid- ering a change in altitude or density 2nd then by a (6) One subsonic flutter case involving fuselage change in Mach number. The above can be demon- vertical bending -stabilizer bending-elevator rotation- strated by rational flutter analyses incorporating spring tab system. reliable compressibility and aspect ratio corrections, by dynamically similar flutter model tests, by extra- (7) One transonic incident involving fin bending, polations from flight flutter test data or by various rudder rotation, and rudder spring tab system due to In addition it acceptable combinations of the above.

loss of rudder oscillatory damping.

is generally required and expected that the margin of safety further be evaluated not only from the density- (8) One case of mild wing-with-stores flutter at Mach number dynamic pressure viewpoint but also transonic speeds. from the stability boundary viewpoint where questions of frequency ratio, center of gravity, etc., andoverall Hence the accident-incident rate for the 1957-1958 satis- damping must be fully considered to insure era is approximately the same as for the 1952-1956 factory safety. An experimentally demonstrated struc- era. However consideration should be given to the tural damping, g, of at least 3% isgenerally required.

thermal environment and why a flutter mode occurs Although not specifically required in present within the operating range, he should also turnaround specifications, the military services presently require and ask himself the question 'Why doesn't my airplane contractors to probate their aircraft by exposure to flutter" if the situation looks good. As Mr. Garrick the operational environment. The scope and degree of has already stated, an effective integration, frequent complexity of flight flutter tests varies according to cross-correlation and understanding of calculations, the expected magnitude of the marginof safety. Where model tests, ground stiffness and vibration tests, and aircraft components are simple from the flutter view- flight flutter test results are required for a hard-core point, where accurate trend data are available, and back-up.

where margins of safety are known to be large, the WADC is generally willing to accept and requires at A reliable index of stability based on subcritical least a "quickie" flight flutter test where the responses to control surface impulses by the pilot are obtained. response is certainly required. Optimum techniques for excitation must be developed, but it is considered However in general it appears desirable and advis- that these developments are within the state of the able to employ forced excitation, and to measure and present art. Further development of measuring equip- evaluate the response of each major component in ment and data analysis equipment will likely depend that high margins of safety may be spite of the fact It is on the indices used and the form of excitation.

expected. With near critical margins of safety and difficult to state the future use of stabilization o r with more complex flutter modes, such a s awing with limited amplitude destabilizing devices. Certainly, several external stores o r T-tails, a more elaborate simple forms such as flutter dampers and mass bal- flight flutter test program using some sort of forced ance will continue to be employed in doubtful cases.

excitation and increased instrumentation is generally However, the more complex stabilization method re- required together with a cautious approach to critical quires further evaluation. This approach might actu- If the odds are evaluated as un- flight conditions.

ally increase the burden of the flutter engineer since favorable, a fix is required since it is considered "on or in" and eventually the "off or out" both the extremely undesirable to attempt to define an actual condition must be investigated. In addition, it will be flutter point or boundary, or how close one can ap- necessary to insure that the device itself does not proach flutter. Furthermore, flight flutter tests introduce new instabilities.

should not be employed as the means to develop to design aircraft.

remedies or In future flight testing, today's problem areas will be of concern especially for the larger, low- The flight flutter test comes late in the cycle factor aircraft with higher speed capability. However, of mathematical, physical and model simulation and it is not optimistic to hope that actual flutter incidents the ground stiffness and vibration tests. Regardless of this type will be averted by improved prediction of the type of flutter encountered or even if it is not and prevention processes. Although supersonic and encountered in flight but only indicated, ensuing delays hypersonic flutter boundaries will be dependentto some and frequently costly retrofixes are necessary.

extent on rigidities required to circumvent low altitude flutter, additional stiffness will likely be dictated and Hence, the heart of the problem really lies in the flight flutter tests will be especially required for early stages of evolution starting with preliminary these higher speed ranges. Such testing will be more design. Many extremely useful and rapid digital and complicated and require definition of a critical speed- analog machines are available and are program coded.

altitude path, since the vehicle's history must now be use their performance requires However to efficiently considered because of heating effects. More compli- that the state of the art in unsteady aerodynamics and cated modes of flutter such as chordwise modes may thermoelasticity be advanced. This together with the occur even if the simpler modes are circumvented.

use of the flutter model should reduce markedly the The antiballistic missile will probably require special number of flutter incidents and accidents, especially attention because of high dynamic pressures through- if these tools provide the same type of (forced excita- out a wide speed range and since external surfaces tion) response data as those obtained experimentally will likely be employed for maneuverability. It is for evaluating the safety of the aircraft. The flutter

difficult to speculate further but M r . Garrick is likely

engineer must not only define boundaries and important correct in anticipating new and undefined problems flutter parameters but also develop a deep physical understanding of the instability phenomenon. It is and a fusion of various areas in flight dynamics. For only with such understanding that determination of some vehicles of the ballistic or boost-glide type, actual flight flutter testing will be impossible, but proper vibrator location, type of vibrator, pickuptype telemetered response data from strategically located and location, stability or anticipation index, etc., can pickups should be employed. Perhaps a white noise be specified. Furthermore, frequent comparisons type of vibrator would be of practical value.

should be made between important airplane parameters and subparameters and those used in flutter model tests and analyses. There have been several cases In view of structural and aerodynamic non- linearities, aerodynamic heating, accelerated flow where slip-ups have occurred because a combination conditions, and rapidly varying inertia or weight of effects was used as a basis rather than an individual conditions, several aeroelasticians have realized the part-by-part comparison. Not only should the flutter possible need to do some soul-searching with respect engineer understand the effects of density, speed and to what is meant by instability and margin of safety, the other hat and proceeding with the mandatory and serious business of flight flutter testing. In connection and the definition of acceptable number of cycles and with this area of testing we should not forget our amplitudes of instability.

cousins in the related vibrational environmental field.

Due to much higher noise and vibration levels, the Meanwhile the dynamicist and aeroelastician peed for such measurements will increase in order to

must continue to live his split personality existence: -

confirm and improve reliability and to insure satis- First, striving to achieve a safe design and elimin- ating the need for flight flutter tests. Then, putting on factory resonant fatigue life.

1 90 IMPORTANT LlNES OF DEVELOPMENT FOR FUTURE APPLlCATlON OF FLIGHT FLUTTER TESTING

M. 0. V. Wolfe

INTRODUCTION Our present policy in the UnitedKingdom,which has gained a large measure of acceptance by the air- craft firms, is to undertake comprehensive flight I would like to preface my remarks by taking vibration measurements on all prototype aircraft and the opportunity of thanking the Aircraft Industries full flight flutter tests in those cases where marginal Association and the Air Force Office of Scientific flutter stabilities have been predicted by previous Research and, in particular, M r . Haynes and M r . Baird, theoretical analyses and wind tunnel model tests.

on behalf of Mr. Broadbent and myself, for inviting us to this Symposium, and for kindly placing at our Having listened to the various papers presented disposal the "Magic Carpet" of the M.A.T.S. organ- here, two things have struck me rather forcibly, The ization to enable us to get here. first is the immense amount of effort and thought which has gone into all aspects of technique develop- I personally found this Symposium a most ment, for example, the use of small aerodynamic interesting, informative and stimulating one providing, oscillating surfaces as a means of excitation, and the employment of telemetry as a means of saving flight a s it did, an opportunity for an exchange of ideas amongst experts on an important subject which has, time are both very interesting developments which for too long, been neglected in certain quarters. The have not yet to my mind been exploited sufficiently number, variety and quality of the papers presented in the United Kingdom. The second is that one has on the various facets of the subject are in themselves the impression that you do not in the United States testimonials to the importance the subject has now appear to have had as much difficulty in analyzing the assumed. recordings in order to obtain the responses as we seem to have had in the United Kingdom. This is rather surprising, particularly a s regards the analysis FLUTTER TESTING PROBLEMS: UNITED KINGDOM of the complex transients resulting from the impulse technique. In our experience this is a very real VS UNITED STATES problem, and one which is as yet incompletely solved.

In the United Kingdom the whole question of It is, of course, of particular significance in the flight flutter testing aireraft for flutter clearance was transonic range where the stability trends may be looked upon for many years with a somewhat jaundiced expected to change rapidly, and where it is, in any case, eye, bothby aircraft manufacturers and flutter special- difficult to fly an aircraft at precise conditions of ists, mainly because it is an expensive business and speed and Mach number. In fact, regarding the latter points, the whole question of flight flutter testing in also because of doubts regarding the safetyof aircraft the transonic region is indeed avery difficult one. We when subjected to experiments of this kind. However, tend to favour a flight technique of starting the tests over the years this attitude has gradually changed, partly because of the work of a few enthusiasts at the at a high altitude and gradually working down to lower Royal Aircraft Establishment and a few enlightened altitudes, taking measurements through the transonic firms, and partly because of the number of flutter range. In this way one ensures that, in general, the incidents which occurred on prototype aircraft in the net damping force is at a maximum at the beginning of the test.

years following the war.

LOOKING TO THE FUTURE to what I have already said inmypaper. Undoubtedly, some of the techniques which have been developed for Since in the nature of things there will always aircraft work, can usefully be applied to missile be uncertainties in the theoretical prediction of flutter, oscillatory stability problems, and it seems to me the most promising one would appear to be the impulse it seems to me that flight flutter testing will become even more essential to flutter clearance in the future technique.

than it is &t present. Some of the next generations of supersonic aircraft will undoubtedlyhave long slen- der body configurations and low aspect ratio wings; it CONCLUSIONS would appear therefore that the problem of sub-critical response in relation to gusts and other formsof exci- tation may well assume great importance in view of From my viewpoint, the important lines of the difficulty of providing adequate aerodynamic development for future application of flight flutter damping on such configurations. In addition to its use testing lie in the direction of improving instrumental for the prediction of critical flutter speeds, the use of and excitation techniques for work in the transonic flight flutter testing a s a means of determining sub- region and the allied problem of improving the tech- critical responses accurately may well therefore nique of analysis of measurement. Some thought become an important feature in the future. should also be given to the employment of the tech- niques for the measurement of the general sub-critical Turning to the question of the extent to which responses of an aircraft at normal cruising speeds, flight flutter testing techniques developed for aircraft with particular reference to future supersonic aircraft can be applied to stability problems of guided weapons of slender configurations.

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