Document
A FLIGHT AND WIND TUNNEL
INVESTIGATION OF THE EFFECT
OF ANGLE-OF-ATTACK RATE
ON MAXIMUM LIFT COEFFICIENT
by Fox Conner, Cmig Willey, and WilZium Twomey
Prepared under Contract No. NAS 4-471 by LOCKHEED-CALIFORNIA COMPANY Burbank, Calif.
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NATIONAL AERONAUTICSAND SPACE ADMINISTRATION l WASHINGTON, D. C. l OCTOBER1965 TECHLIBRARY KAFB,NM
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0079788.
NASA CR-321 A FLIGHT AND WIND TUNNEL INVESTIGATION OF THE EFFECT OF ANGLE-OF-ATTACK RATE ON MAXIMUM LIFT COEFFICIENT By Fox Conner, Craig Willey , and William Twomey Distribution of this report is provided in the interest of Responsibility for the contents information exchange.
resides in the author or organization that prepared it.
Prepared under Contract No. NAS 4-471 by LOCKHEED-CALIFORNIA COMPANY Burbank, Calif.
for NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sole by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - Price $3.00 ..-....- -.- . - ..------ .~. - TABLE OF CONTENTS Page ., . . . . . . . . . . . . v LIST OF FIGURES ...........
SUMMARY ...............
INTRODUCTION ............
..............
SYMBOLS ...............
WINDTUNNELTESTS ..........
..............
Description of Models ....
Description of Test Apparatus ..............
..............
..............
Measurement Errors .....
FLIGHTTESTS ............
Description of Test Airplane Instrumentation .......
Test Procedure ....... ..............
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Measurement Errors .....
..............
RESULTS AND DISCUSSION .......
General ...........
Parameter Variations .... ..............
. . . . . . . . . . . . . .
FWKEXENCES ............. . . . . . . . . . . . . . .
iii LIST OF FIGURES Figure Title Page FJing W-2 Installed in Wind Tunnel Wing W-5 Installed in Wind Tunnel Block Diagram of Servo System 16 4 T-lA Airplane 5 Example of Wind Tunnel Data, M = ~47, ,RN = 2.79 x 106, Wing W-2 Example of Wind Tunnel Data, M = -264, RN = 1.75 x 106, Wing W-2 Effect of Oscillations 8 Example of the Effect of Angle-of-Attack Rate on the Lift Curve Effect of Angle-of-Attack Rate on the Maximum Lift Coefficient of Wind Tunnel Wing W-l Effect of Angle-of-Attack Rate on the &ximum Lift Coefficient of Wind Tunnel Wing W-2 11 Effect of Angle-of-Attack Rate on the Maximum Lift Coefficient of Wind Tunnel Wing W-3 12 Effec,t of Angle-of-Attack Rate on the Maximum Lift Coefficient of Wind Tunnel Wing W-4 Effect of Angle-of-Attack Rate on the I&ximum Lift Coefficient of Wind Tunnel Wing W-5 14 Effect of Angle-of-Attack Rate on the I&ximum Lift Coefficient of Wind Tunnel Wing w-6 Reynolds Number Effect on &ximum Lift Coefficient for Six Wind Tunnel Model Wings 16 Effect of Wing See-tion Thickness on Maximum Lift 40 Coefficient Effect of Camber on Maximum Lift Coefficient 18 Effect of Sweep on Maximum Lift Coefficient Effect of Aspect Ratio on Maximum Lift Coefficient Example of Flight Test &ta 21 Example of Processed Flight Test &ta Effect of Angle-of-Attack Rate on the &ximum Lift Coefficient 47 of T-IA Airplane Effect of Reynolds Number and Angle-of-Attack Rate on Maximum 50 Lift Coefficient of T-IA Airplane Compared with Wind Tunnel Wing W-2 V A FLIGHT AND WIND TUNNEL INVESTIGATION OF THE RFFECT OF ANGLE-OF-ATTACK RATE ON MAXIMUM LIFT COEZ'FICI3NT By Fox Conner, Craig Willey and William Twomey Lockheed-California Company SUMMARY The effect of angle-of-attack rate on maximum lift at stall was investi- gated for a related series of six half-wing models in a blowdown wind tunnel as Mach numbers from 0.25 well as for a single-engine, jet-propelled airplane.
to 0.75, Reynolds numbers from 1.4 to 21 x 106, thickness ratios of 9, 13 and sweep angles of 0 and 35 degrees, aspect ratios of 3 and 6 and cambers 16%, corresponding to ideal lift coefficients of 0 and 0.2 were tested. All wings were composed of 651-xxx (a = .5) airfoil sections.
The increase in the maximum lift with angle-of-attack rate was small and, in general, linear. There were no clear indications of a limit for the maximum camber and sweep had the lift obtainable. Of .the parameters ,tested, thickness, greatest effect. The effect of angle-of-attack rate on maximum lift was in- creased as camber of thickness decreased, or sweep increased.
The flight test results correlated with the .trends derived from the wind tunnel tests.
INTRODUCTION The stalling characteristics of a wing are determined by a number of wing profile and planform, and Mach factors including free stream turbulence, and Reynolds numbers. One of the least understood factors is the effect of an angle-of-attack rate which is present during dynamic flight conditions such as pullups and which cannot be ignored in the design of an aircraft. A program to explore the effect of angle-of-attack rate was undertaken during the 1940's and early 1950's by the National Advisory Committee for Aeronautics (now the National Aeronautics and Space Administration). Reference 1 discusses wind tunnel tests of a l/20 scale partial reproduction of a conventional single- engine aircraft with an elliptical wing of modified NASA 230-series section.
The results of flight investigations with propeller-driven, single-engine, fighter-type aircrafts are presented in References 2 and 3.
Aircraft design continues to grow more and more sophisticated with the years and the need has arisen for research which would extend the earlier ex- periments. Specifically, there was a need to define the effect of an angle-of- attack rate on maximum lift coefficient for a greater range of &ch and Reynolds numbers and for a variety of wing sections and planforms. Only tests and empirical analysis could provide the answer as boundary layer and potential flow theory was found to be lacking. Even qualitative guides are difficult to establish from the theory, and quantitatively ,the problem is hopeless unless greatly improved mathematical tools are made available. The basic difficulty lies with boundary layer theory. It is conceptually feasible by relaxation methods, as discussed in Reference 4, to obtain theoretical solutions for com- binations of sub- and supersonic flows although a large amount of computing is required. Boundary layer theory for non-steady flows is extremely difficult and poorly developed even for laminar boundary layers. Add to this the diffi- culties of calculating .the point of instability and the point of transition for a laminar boundary layer changing to a turbulent boundary layer and the problem is compounded. Knowledge of whether the boundary layer is laminar or turbulent is necessary for calculating the separation point for the pressure distribution imposed by the potential flow solution. Still another complication arises. If a separation "bubble" exists, then consideration must be made for a free boun- dary in the potential flow solution. Finally, it may not be possible even to separate the boundary layer from .the potential flow solution if small shocks exist close to the section contour.
In answer to the need for additional research, the Lockheed-California Company conducted wind tunnel tests on six half-wing models and flight tests on a jet-propelled, single-engine aircraft under contra& NT&+-471 with the National Aeronautics and Space Administration.
The six models were derived from NASA 651-xxx (a = .5) sections and varied in thickness, camber, aspect ratio and sweepback. One of the models closely represented the wing of the test aircraft.
SYMBOLS a longitudinal acceleration X a normal acceleration Z A aspect ratio mean aerodynamic chord coefficient of lift cL maximum lift coefficient %llaX M Mach number R radius RN Reynolds number .t time t/F thickness ratio true airspeed true boom angle-of-attack boom angle-of-attack corrected for upwash indicated angle-of-attack angle-of-attack at the wing three-quarter chord point angle-of-attack rate A sweep angle pitch attitude WIND TUNNEL TESTS Description of Models The test articles were six half-span wings which were tested on a floor All models had mounted support system in a 4 ft by 4 ft blowdown wind tunnel.
a taper ratio of one and zero geometric -twist. Other section and planform characteristics of the models are given below: Sweepback Pi&form Chord Aspect angle, deg Wing section area, ft2 length, ft Model ratio 6 0 651-209(a = .5) W-l l/3 l/3 651-213(a = .5) w-2 6 0 l/3 l/3 6 0 651-216(a = .5) l/3 l/3 w-3 651-213(a = .5) w-4 0 3 2/3 2/3 6 651-213(a = .5) w-5 35 l/3 l/3 w-6 6 0 65,-013 l/3 l/3 Photographs of models W-2 and W-5 installed in the tunnel ready for testing are presented in Figures 1 and 2.
Description of Test Apparatus The special model support system consisted of a hydraulically-operated The disc was positioned rotating disc suspended on a force measuring balance.
three inches off the .tunnel floor with the model mounted vertically on the disc. The system permitted a model angle-of-attack range from -5 to +70 degrees. The acceleration to and the deceleration from the programmed angle- of-attack rate was rapid and resulted in the angular velocity being constant A simulated fuselage faired the model from approximately +lO to +40 degrees.
disc wi-th the tunnel floor and smoothly directed the tunnel floor boundary layer away from the model.
A constant angle-of-attack rate was obtained through the use of a servo system operating the hydraulic drive system. The drive system consisted of a hydraulic cylinder powered by a 3000 psi pressure source which rotated the disc through a cam device. A hydraulic damper was included in the system to aid in decelerating the model at the end of each run. Control of the servo system was achieved by electronically regulating a hydraulic control valve with an analog computer.
This system provided controlled angular velocities up to I200 deg/sec. A block diagram of the system is given in Figure 3. In order to prevent exces- a switch was provided which limited the sive quantities of extraneous data, data acquisition to the part of the run where the angular velocities were constant.
Instrumentation The wind tunnel test conditions were obtained from a static pressure measurement in the test section plus air temperature and total pressure meas- urement in the "stilling chamberU upstream of the test section. This instru- mentation is standard for all tests in the 4 ft by 4 ft blowdown tunnel.
The force measuring unit consisted of two load cells to measure lift.
A complete calibration of the unit was performed prior to the tunnel installa- tion and check loadings were performed periodically during the tests. The angle-of-attack was measured with a calibrated, infinite-resolution dual pot- entiometer attached to the rotating disc. Electrical signals from the force measuring unit and the angle-of-attack potentiometer were transmitted to the data gathering system where the signals were digitized and subsequently re- corded on magnetic tape. The lift and angle-of-attack data were sampled at 1160 points per second for the dynamic stalls.
Test Procedure Static lift data were obtained by rotating each model at 2 deg/sec for various conditions of Mach and Reynolds numbers. Dynamic runs were completed by rotating the models at eight different rates from 200 to I200 deg/sec at the same Mach and Reynolds number conditions.
All dynamic tests were run twice as a check on repeatability. During the runs, inertia tares were obtain- ed occasionally by rotating the model at the desired rate with .the tunnel air- flow shut off and recording the loads resulting from mass imbalance.
Tests were completed at I&ch numbers from 0.25 to 0.75 and at Reynolds numbers from 1.4. to 5.6 x 10~.
Measurement Errors Based on an analysis of the data, past experience and repeatability, it is estimated that typical values of the errors are; Mach number 1% Reynolds number 1.5s Lift coefficient 2% Non-dimensional angle- of-attack rate 1% where the errors are root-mean-square values.
FLIGHT TESTS Description of Test Airplane The test aircraft was the Navy Model T-lA; a two-place, single-engine, jet-propelled, navigation trainer. It was powered by a 533-A-24 gas turbine engine. For the test program the tip tanks were removed and replaced with wing tip fairings, the wing leading-edge slats were locked in ,the fully-retracted position and the stall inducer strips were removed. All holes were filled in order to obtain a "cleantl wing comparable to the wind tunnel models. Figure 4 presents a photograph of a T-IA airplane.
Basic airplane data follow: Test gross weight 11 700 to 12 200 lb Test center of gravity, wheels up 25% mc Wing span 37.5 f-t Fuselage length 36.5 ft The geometric parameters describing the wing are: 232.8 ft2 Area Aspect ratio 6.05 Taper ratio 0.381 Mean aerodynamic chord 6.72 ft Sweepback of the 50% chord line 0 deg Dihedral 3.83 deg -1.5 deg Geometric twist Airfoil section NASA 65,-213 (a = .5) Instrumentation Flight data were gathered from an automatic observer panel and a four-inch The automatic observer consisted of the rear cockpit recording oscillograph.
panel with the test instruments installed and a 35mm automatic camera. The panel included a counter ,to establish the identity of each oscillograph record and a light to establish the length of the record. Correlation between the automatic observer panel and the oscillograph was established by a pilot's signal which appeared on bo-th recording devices and by marks on the oscillogram which indicated the frames being taken by the movie camera.
The automatic observer panel recorded the airspeed and altitude from the production pressure sensors: a "dog-leg" total pressure tube and static pres- sure ports which were located on the lower portion of the nose of the aircraft.
No other instruments were plumbed into .the airspeed system and the pressure lines were as short as possible in order to keep airspeed lag small.
The auto- matic observer panel also included a "fuel remaining" gage and an engine speed indicator. All instrumen-ts were calibrated before -the test program.
The oscillograph recorded time histories of the longitudinal and vertical accelerations at the aircraft center-of-gravity, pitching velocity, and boom angle-of-attack. To measure the angle-of-a,ttack, a loo-inch boom with a flow vane near the tip was installed on the nose of the aircraft.
Free air temperature was determined from the regular, twice-a-day meteor- ological balloon soundings from San Nicolas Island and Point Mugu.
Test Procedure At each of the three test altitudes; 10 000, 25 000 and 35 000 feet, and at Mach number increments of 0.1, windup turns and pushover-pullups were con- ducted to and through the stall. The windup turns were done slowly to es-tab- lish the maximum lift coefficient for a near zero angle-of-attack rate, while the pushover-pullups were done to obtain various pitch rates. Pushovers to zero g's were performed in order to assure a uniform starting condition and no separation prior to the test.
Measurement Errors The errors (root-mean-square values) were determined for a typical ,test point for the non-dimensional variables of interest as tabulated below.
Mach number 1% Reynolds number 2.5% Lift coefficient 2.5% Non-dimensional angle-of-attack rate 2% DATA PROCESSING AND ANALYSIS Figure 5 presents representative basic data for wing W-2. The data show typical curves of the lift coefficient versus the angle-of-attack for static and dynamic stalls and time histories of the angle-of-attack.
Examination of -the wind tunnel data indicated large oscillations in the force data a-t low tunnel speeds. Figure 6 shows an extreme example of this phenomenon at two angle-of-attack rates.
The largest peak-to-peak amplitude of the oscillation prior to the stall averaged over all the dynamic runs at each Mach and Reynolds number is given in Figure 7.
As shown, the amplitude was low above I&ch 0.4 but increased rapidly at low mch numbers.
Consideration was given to discarding the few runs where the oscillations were large. Since a pair of runs was performed at each angle-of-attack rate, it was possible to compare the degree of repeatability.
These data are also pre- sented in Figure 7 in terms of the frac-tional spread in the maximum lift coef- ficients be-tween data points. Note that the difference between a pair of points is only 0.03 on the average and -that there is no increase at the low Mach num- bers.
Another reason for not discarding the low Mach data was the belief that the large oscillations were due primarily to inertial reaction forces in the model and supporting structure which was undergoing small amplitude structural vibra- tions. The predominant frequency was slightly over 100 cps and this frequency Structures remained about constant for all the high amplitude oscillations.
vibrating at these frequencies are nearly always dominated by inertia forces which increase as the square of the frequency.
The progressive increase in the maximum lift with the angle-of-attack rate Note is given in Figure 8 which is a replot of the faired curves of Figure 5.
that angle-of-attack rate changes the slope and position of .the lift curve but does extend the lift curve to only slightly at low values of the lift, considerably higher values.
The next step in processing the wind .tunnel data was to plot the maximum lift coefficient from the lift versus angle-of-attack curves against the non- dimensional angle-of-attack rates. Figures 9 through 14 are plots of the wind tunnel data presented in this manner. In fairing the curves, the static stall point was favored, but in a few cases, crossplots of the figures suggested a revised fairing which did not favor the static stall point.
Figure 15 presents crossplots of Figures 9 through 14. The data in Figure 15 were replotted in Figures 16 through 19 to.aid the discussion to follow* The basic flight data were time histories of which Figure 20 is an exam- ple. The variation in airspeed and altitude is typical. The tests were con- ducted to achieve the desired values of airspeed and altitude at the moment maximum lift was achieved.
The non-dimensional parameters of interest were calculated from the basic flight data and replotted against the angle-of-attack as in the example of Figure 22. Since aerodynamic ,theory indicates that the wing lift acts at the one-quarter chord point and is determined by the downwash at the three-quarter chord point, the flight test data were plotted against the angle of attack at the three-quarter chord point. To obtain this value of the angle-of-attack, the indicated angle-of-attack was corrected for boom upwash by the relationship discussed in Reference 5: where R is the radius.
A distributed load proportional to the boom weight was applied and the deflection angle at the flow vane measured to obtain a correction for boom bending1 a = a f + 0.14 ( az - 1) b where az is the normal acceleration in g's and "b is the true boom angle-of- attack in degrees. The position error was found to be negligible. Vane asymmetry could have resulted in a large error, but no correction was applied since this error is typically a constant at all values of the angle-of-attack (Reference 5) and hence does not affect the angle-of-attack rate. Finally, the vslue of the angle-of-attack at the three-quarter chord point was calculated from the relationship: X de %3/4 c’ = ab + 7 dt where x is the distance from the wing three-quarter chord point to the flow vane location on the boom (242 inches).
The angle-of-attack rates were determined from the angle-of-attack time history prior to and at stall. Each of the flight data points was obtained from the time derivative of a quadratic function fitted to seven points equally distributed and neighboring the data point being reduced.
The seven points spanned roughly a one-second time interval. Figure 21 is a typical flight stall and shows that, generally, the angle-of-attack rate was nearly constant preceding stall.
Various definitions of the angle-of-attack rate have been used in other investigations which try to account for the angle-of-attack history prior to stall by some sort of an average. In Reference 1 the rate was -taken from the slope of a line joining the angle-of-attack curve at points corresponding to zero and maximum lift. Another method of accounting for the angle-of-attack history is to fit a polynominal to the data points and take the second, third, etc. derivatives at some point preceding stall. In this report, however, the first derivative just prior to stall appeared to be sufficient for the flight data. The wind tunnel data presented no difficulties in defining an angle-of- attack rate for stall since the angle-of-attack rate was constant well before the stall (Figures 6 and 7 show typical examples).
In calculating the lift coefficient from the flight data, use was made of the longitudinal acceleration data. Also the component of the engine thrust directed up along the lift vector was subtracted before the lift coefficient was calculated. The thrust was taken from a non-dimensional engine curve at the engine speed read from the flight records. The engine curves were derived during early flight programs with the T-IA airplane.
A brief analysis was made of the incremental lift due to the tail and the fuselage. Both were found to be negligible partly because of a favorable location of the center of gravity near the 25% chord point.
The data describing the stall points were taken from curves such as those given in Figure 21 and are---presented in Figure 22. The Nach and Reynolds isted in the figure are averages with variances less than 0.01 and numbers tz respectively.
0.5 x 10 , The flight data in Figure 22 were crossplotted in Figure 23 at constant values of the angle-of-attack rate. The plot also includes wind -tunnel data for the W-2 wing. This model was similar to the wing of the -test airplane ex- cept the taper ratio was 1.00 instead of 0.38 and .the geometric twist was 0 in- The data in Figure 23 was grouped according to Reynolds stead of -1.5 degrees.
number. Curves of con tant Reynolds numbers are presented at values of 1.4, fz 2.8, 8.6 and 12.0 x 10 . The variance in Reynolds number is 18, 10, 8 and 14$, at Reynolds numbers of 18.5 and 21.1 x 106, were not respectively. Two points, grouped with any other points.
RESULTS AND DISCUSSION General Wind ,tunnel and flight test data showing the effect of angle-of-attack rate on the maximum lift coefficient, cLmax, are presented in Figures 9 through 14 and Figure 22. In spite of considerable sca,tter, 'L,, shows a genoaally linear increase with increasing non-dimensional angle-of-attack rate, x (Y , v The generally linear trend has been found before; as, for example, in Ref- erence 1 which appears to be the most thorough investigation of the effect of + & on previously undertaken. However, in this reference a limiting cLm,X value of was reached (which decreased with increasing Mach number) after cblax which 'L,, remained constant with further increases in c & . It is sus- v petted that the appearance or non-appearance of a limit (?&ax might depend on the airfoil sec,tion being tested. No limit CLmax appears in the data reprted herein for fl?ht and tunnel tests of wings with 651-xxx (a = .5) airfoil sec- = 0.047. Reference 1 investigated a wing model with a mod- tions up to 7 & ified NASA 23O- series section and showed limiting values of cL Reference 2 reported on flight -tests of an airplane with a 66,2- (1.8) (ls.F(a = .6) root wing section and a 66,1- (1.8) (12) (a = .6) ,tip section and did not show any limiting values of "Lmsx up to -$- & = 0.0115. Hence 651- series section ap- pear to behave similarly to 66,1- and 66,2- series sec,tion. In Reference 3, however, limiting values were reported from flight tests of a wing with a 66,2x-116 (a = .6) root section and a 66,2x-216 (a = .6) tip section. It would appear that ,this reference would disprove the dependency on section characteris- tics; however, it may be the 66,2x series sections differed sufficiently from 651-, 66,~ and 66,2- series sections to result in the appearance of limiting values of 'Lmsx such as also were observed for the 23O- series section.
Another factor investigated was the slope d ("Lx) /d (-j- k)- The slopes found in both the wind tunnel and the flight .test data were in general less than those reported in References 2 and 3 for flight tests and far less than the slopes found in wind tunnel tests of a modified 230 series section, Reference 2, being only one-fourth to one-third as large. It appears the slopes are related to the existence of a limit cLmax in the sense that a limit 'Lmax appears whenever the slope d (C,>/d(q) is high. A limit ?Gmsx might be reached even for those ca$es where the values of the slopes were small if tests at exceptionally high 7 & were conducted.
A significant exception to the generally increasing 'Lmax with increase F in - &Y was found in the wind .tunnel data. This was a "hump" in the v versus curves at low values of the angle-of-attack rate which c&X occurred for certain configurations at Kach numbers near 0.6 (Figures 9, 10, cannot be dismissed as data scatter since I2 and 14). It is felt the "hump" it was repetitious and occurred for three different wing configurations.
Another exception to linearit was found in ,the flight test data at %ch 0.57 and Reynolds number 21.1 x 10 (Figure 22), the highest Reynolds number tested.
In this case, a decrease in was observed. The maximum + & was low %liLX and it may be a "hump" effect would have appeared if the airplane could have been tested at higher angle-of-attack rates.
Parameter Variations Tests were conducted to determine the sensitivity of -the effect of & on various parameter changes. To this end the aerodynamic variables %ax t 0 [rhzd Reynolds number), as well as the wing configuration variables ic ess, camber, aspect ratio, and sweep angle) were varied.
Mach Number. - In Figure 16, chx is plotted versus &ch number for values of -C- & equal to 0 and 0.01. It can be seen that in general the v c 0 'trends are similar both for a - cy of 0 and 0.01; namely, an initial V decrease in with increasing I4ach number followed by a secondary peak. The %RBX same trend also exists in the flight data as Figure 23 demonstrates. This is in agreement with the trends found in Reference 3 where it was felt that the second- ary peak was caused by a broadening of the upper surface low pressure region which offset the reduction in the negative pressure peak as mch number increased.
The reference implies that the reduction in peak pressures delayed stall separ- ation until higher values of '%max were reached.
c 0 Although %tmax for both steady-state and - a = 0.01 vary consider- v ably with Mach number, the difference between them (i.e., the increase in of 0.01) remains fairly constant with Mach number. This c& due to a
+t5
result differs from that found in Reference 1 where $- & had no effect on ch for ?&ch numbers greater than o .6.
Reynolds Nmber. - The wind tunnel models were each tested at two Reynolds numbers, 1.4 x lo6 and 2.8 x 106 (2.8 and 5.6 x lo6 for the model having a low aspect ratio). In Figure 15 it can be seen thatFan increase in Reynolds number generally caused an increase in cLmsx for both 7 & = 0 and 0.01.
In most cases this increase in 'Lmsx is roughly the same for c' & = 0.01 -F as for C & = 0; the incremental increase in 'Lmex due to v ir & thus V remaining relatively unaffected by Reynolds number.
The flight test data, al- though somewhat sparse, indicate a similar trend for the higher Reynolds num- bers (Figure 23).
Thickness Ratio. - Figure 16 shows that increasing the thicknegs ratio from 13 to 16s had a smaller effect on the increase in "Lmsx with v & com- pared to decreasing the thickness ratio from 13 to 9%. There is reason to be- lieve the type of stall changed going from 13 to 9s since Figure 15 shows a de- crease in maximum lift as Reynolds number is increased. This unusual behavior with Reynolds number was also observed to a lesser degree for wing W-5, which has a sweepback of 35 degrees as Figure 15 shows. With sweepback, the stream- wise sections become thinner and an effect roughly equivalent to a thinner wing without sweepback would be expected.
Airfoil Camber. - Airfoil camber had the largest effect on the ability c - & to increase Figure 17 shows how the effect of % cLmaX* & onCJJmx v .V is greatly reduced by increasing the camber of the wing.
Apparent camber was investigated to determine if this factor could be largely responsible for the increase in maximum lift with angle-of-attack rate.
In potential flow it is known that pitching velocity can be considered equivalent to a parabolic camber with vertex at the axis of rotation (Reference 6). From experiment it is known that increasing the camber of an airfoil in- creases its maximum lift, for example see Reference 7. Figure 17 gives an indi- cation of the amount of incremental change in 'Imax of an uncambered,wing due to -$- (y ' that could be attributable to its having an "apparent camber".
The apparent camber of wing w-6 undergoing a pitching velocity of = 0.01 was computed from potential flow theory as follows; a@arent camber = ++ S = .F, = 0.00125 me difference in cLmax. due to geometric camber can be obtained from.
the data for wings W-2 and w-6 wh ch had cambers of 0.Ol.l and 0, respectively.
- was assumed to be similar to that due The effect of apparent camber on to geometric camber and also that a linear increase occurs. Hence the incre- due to apparent camber is O.OOl25/O.Oll of.the static lift in- ment in 'Lmsx 'It is seen in Figure 17 that the apmrent crement between wings W-2 and W-6.
camber effect accounts for only a small, mrt of the increase in ?Lmsx due G & of 0.01. While the camber of wing W-2 is not parabolic it was to a v felt that the analysis sufficed for an order of magnitude answer.
Sweep Angle. - As seen from Figure 18, increasing the wing sweep angle c’ on 'L greatly increases the effect of v & msx' - Figure 19 shows a limited comparison between the aspect No significant effect due to aspect ratio is evident.
ratio $?EZ%%Es.
CONCLUSIONS The results of subsonic flight and wind tunnel tests on wings composed series sections (651-213'section standard for commrison) led to of NASA 65,- the following conclusions for the range of Mach and Reynolds numbers, thickness ratio, camber, sweep and aspect ratio tested: c' 1. The increase in cLmsx with 7 6 was usually moderate (13-30s) and linear. No evidence of a limit in maximum lift appeared for values of + Near Mach 0.6 a "hump" effect sometimes appeared such that the up to 0.047.
maximum lift first increased rapidly with angle-of-attack rate, then decreased rapidly and then returned to the typically slow increase at higher rates.
2, Although Mach number had a considerable effect on static 'Lmax, it generally had little effect on the incremental increase in maximum lift with angle-of-attack rate.
Increased Reynolds number usually Increased 'Lmsx and the sount of 3e increase generally seemed to be unaffected by either Mach number or * & .
4. Increasing wing thickness from p$to 13s greatly reduced the effect of an angle-of-attack rate on maximum lift.
An increase from 13% to 16s had a relatively small effect.
Increasing the camber from that corresponding to zn ideal lift coef- 5.
on incremental ficient of 0 -to one of 0.2 greatly reduced the effect of maximum lift.
6. Increasing .the wing sweep from 0 to 35 degrees greatly increased the effect of angle-of-attack rate on maximum lift.
A limited comparison between wings of aspect ratios of 3 and 6 showed 7.
no significant effects attributable to aspect ratio.
8. The trends observed in the wind tunnel data were also observed in For the most part, the magnitude of the maximum lift from -the the flight data.
flight tests appears to agree with that from the wind tunnel tests. However, no direct comparison is possible due mainly to a difference in the Reynolds numbers tested.
Lockheed-California Company Burbank, California JUIY 26, 1965 83 48 8R Figure 1. Wing W-2 Installed in Wind Tunnel , , . : 83 45 P3R
L-
Figure 2.
Wing W-5 Installed in Wind Tunnel STEPPING SWITCH
I
- START STEPPING ' CONTROL - START DATA SYSTEM SWITCH
I
rc STOP DATA SYSTEM ROTARY PLATFORM I I AND MODEL I GAIN VARIATION STEPPING SWITCH I I
I
--
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-c TO RECORDER DlFFERENTIATOR -cl-- I SVDC
I
FEEDBACK MPLIFIER I UP AND DOWN SIGNAL I \ C IAMPLIFI~R 1 ‘ CONTROi I VALVE i
,,,,ERt-rMrl
-
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ZERO RATE - ANALOG COMPUTER ISERVO DRIVE SYSTEMI Figure 3. Block Diagram of Servo System Figure 4. T-lA Airplane 1.2 1.0 .8 .6 .4 .2 16 20 24 8 12 Angle of attack, deg Wing W-2 Figure 5 -- Example of Wind Tunnel Data, M = .547, RN = 2.79 x 106, .02 .04 .Ol .03 .05 Elapsed time, sec.
(b) Time history of angle of attack -- Continued Figure 5 1.6 - - , ($ $$= .0096 1.2 .8 . cop (d) -$+$= 1.6 1.2 .a 1.6 1.2 .a .4 4 8 16 20 24 12 28 Angle Of attack,, deg.
(f) $* =
.0017 Figure 5 -- Concluded (a.) gg = .0238 3; (a) Repeatability .4 .6 l 5 .8 -7 Mach number (b) Double Amplitude of Oscillations Figure 7 -- Effect of Oscillations ._- , 1.4 1.2
-~ -~ --. _
-A
,-. ._
1.0
\
\
_. _.- -
I _-- _.
---.
-dt V _----- .0017 --- -0040 ---- .0072 ----- .oog6 -_... -- .2 _. ._.
12 16 20 2L 28 0 4. 8 Angle of attack, deg m G W-2, M = .547, RN = 2.79 x 18 Figure 8 -- Example of 'the Effect of Angle-of-Attack Rate on the Lift Curve .8 _.
1.2 I ‘ . I-- -. -I - _.- M * 537 ” RN 1.38 x 106 .8 1.2 .8 .008 .012 .016 .020 5 dcu , rad Tdt Figure 9 -- Effect of Angle-of-attack Fhte on the Maximum Lift Coefficient of Wind Tunnel Wing W-l 1 .2 1.0 .8 1.2 1.0 M .642 .z RN 2.76 x lo6 .8 .4 1.2 5 10 .
8 .8 j 1.2 1.0 .8 .004 .008 .012 .016 .020 c' da -- , rad V dt Figure 9 -- Concluded .8 1.2 1.0 .e 1.2 I I I 1.0 M a535 I RN 1.3% x IO6 .% 1.4 1.2 1.0 .% 1.4 1.2 1.0 .% 0 .004 . 00% -012 .016 .020 .024 ; dcr FE- , rad -- Effect of Angle-of-attack Rate on the Maximum Figure 10 Lift Coefficient of Wind Tunnel Wing W-2 i n .8 1.2 1.0 .a 0 .004 .008 .012 .016 .020 .024 : da VaT 9 rad Figure 10 -- Concluded.
.8 1.2 1.0 .a .8 .8 .8 .008 _ .012 .016 .004 .02c c aa -- , rad V dt Figure 11 -- Effect of Angle-of-attack Rate on the Maximum Lift Coefficient of Wind Tunnel Wing W-3 .8 .a .004 .008 .Ol .016 .020 6 da -- rad V dt ' Figure 11 -- Concluded.
1.2 1.0 .% 1.2 1.0 l e 1.2 1.0 -8 1.4 1.2 1.0 .6 1.4 1.2 1.0 ,a 1.4 1.2 1.0 -8 .04 .02 -05 -03 c da rad --) V dt Figure 12 -- Effect of Angle-of-attack Rate on the Maximum Lift Coefficient of Wind Tunnel Wing W-4 1.4 1.2 1.0 .a 1.2 1.0 -a 1.2 1.0 .8 .02 .Oj .04 .05 i dct rad --9 V dt Figure 12 -- Concluded.
1.2 l.G .% 1.2 1.0 .a 1.2 .a 1.2 -8 0 .004 .008 .012 .016 .020 .C24 ; da -pg , rad Figure 13 -- Effect of Angle-of-attack Rate on the Maximum Lift Coefficient of Wind Tunnel Wing W -5 1.2 1.0 .8 1.2 1.0 .a c da -- rad TT d-t. .’ Figure 13 -- Concluded.
.8 .6 1.0 .8 .6 1.0 I --u .a M .427 RN 1.39 x 18 I .6 1.2 I I I I I, 1.0
I
-., I I .8 0 j .6 1.2 .a M .264 RN la73 x lo6 t .6 0 .004 .008- .012 .016 .020 .024 c dcu -- , rad V dt Figure 14 -- Effect of Axle-of-attack Rate on the Maximum Lift Coefficient of Wind Tunnel Wing w-6 1.0 .8 .6 1.0 .a .6 1.0 .a .6 .004 0 .008 .012 .016 ,020 .024 ; da , rad -- v at Figure 14 -- Concluded.
z-5), A = 6, A= o" (a) Wis W-l 65,~209 (a
\
\
\
C
.2 .3 .4 -5 .6 *7 .8 I%ch number (b) Wing w-2 65,~213 (a =.5 ,A=6, n=o" Figure J.5 -- Reynolds Number Effect on Maximum Lift Coefficient for Six Wind Tunnel Model Wings.
1.2 1.1 .
1.0 .
-9 om = 1.4 x lob q Fm = 2.8 x 106 Am = 5.6 x 106 .8 (c) Wiw w-3 65,-216 (a =.5), A = 6, A = 0’ 1.2 1.1 1.0 -9 .8 .2 .4 .3 -5 .6 .8 .7 Mach number (d) Wing w-4 65,213 (a =-51, A = 3, A= O" Fizure 15 -- Continued
----. ---.----
1.2 0 RN = 1.4 x lo6 q ~1!1=2.8~10~ . -- 1.1 1.0 ce> wix w-5 65,~213 (a = 5), A = 6, h=35o .8 -7 .6 .2 -3 .4 -5 .6 .7 .8 I&ch number (f) Wirg w-6 65,-013, A =6, A= O O Fipre 15 -- Concluded t/F = g $ ------ t/F= 13 $ 7 da --- t/F = 16 $ rff E= -01 A.- (a) RN = 2.8 x lo6
I \
_-
\
\
c da
\
\
\
B. \ I --
/ _- .8 .4 .t Mach r&ber (b) RN = 1.4 x 10~ Fip.re 16 -- Effect of Thickness on &ximum Lift Coefficient 1.2 c dcr -- = .Ol.
65,013 V dt I 1.1 -----65;213 -- ---657013 with l.C !'apparent camber" = .00125 (a) RN = 2.8 x 10G
Is31
1.2 '\ A-----+-- \ \ cdcu \ -- = .()I-- v dt 1.1 “\ '\ \ .
\ \ /j---d \ . .
\ /.
_--A_ \ -_,_--- .
/ 1.0 --__-- .7 -- .7 - I&ch number (b) RN = 1.4 x 10' Figure 17 -- Effect of Camber on Maximum Lift Coefficient .,,, ..,’ _ ;.
. ., : , 1.1 1.0
k
\
\
-9 (a) RN = 2.8 x 10~
\
\
\
\
\
I 2 dcY
2 -- = .Oly--
1.1 ----L--i
\T dt
‘ \
\
\
\
\
\
\
\
\
1.0
TEq
-9 \ .8 .2 .3 .4 -5 .6 .7 .8 Wch number (5) RN = 1.4 x 10’ Figure 18 -- Effec-t of Sweep on Maximum Lift Coefficient A=3 __---- A=6 / - -.
.
-.
I / .
.
\ \ _ \ \ \ .8 .8 .7 .6 .5 .4 -3 .2 Mach number R.N = 2.8 x lob Effect of Aspect Ratio on Maximum Lift Coefficient Figure 19 -- g deg deg/s 20 Elapsed time, set (a) Oscillograph Iota Figure 20 -- Example of Flight Test Data lb __~__....
10 000 Indicated alti'tude .35 -30 -25 mph 0 .4 .6 .8 1.0 .2 1.2 Elapsed time, set (b) Automatic Observer Eata Figure 20 -- Concluded.
1.4 1.2 1.0
I I II I i I
I I .8 I I I ri Lift coefficient /I .6 si .4 .2 .O .OlO ,I _-- -__ . 008 V Non-dimensional aqle-of-attack rate J .,..-\ --() --~.* f-’ 0 o-- ---+ --.:.
zir -.
11 - Reynolds number I I I I .4 I I A A A .. --- -_ 3- '-' I *3. a3-LrG-----o u i2 \l/ Mach number I I I I .2 0 4 16 8 12 Angle of attack, deg Figure 21 -- Example of Processed Flight Test Data 4-6 c 1.2 : --D V-4 M .403 RN 14.1 x106 2 1.0 1.4 1.2 1.0 0 .002 .004 .006 ,008 .Ol -0 (a) Test Altitude = 10 000 ft Figure 22 -- Effect of Angle-of-attack Rate on the mximum Lift Coefficient of T-IA Airplane 1.2 '1 . 0 a 1.2 1.0 .502 M RN 11.4 x 10 .8
.a
,010 .008 .006 ,004 .002 (b) Test Altitude = 25 000 ft Figure 22 -- Continued.
.8 .8 .8 .002 .004 .006 .OlO .008 cd0 -I V dt ' rad (c> Test Altitude = 35 000 ft Figure 22 -- Concluded.
c da -- = .OO$ (4 V dt 1.4 c da
- - = .0025
b)
V dt ind Tunnel 0 RN 1.4x10$ 1.2 1.1 1.0 -9 .2 .4 -5 .6 l 7 .8 Mach number c da -- =o (4 Vdt Figure 23 -- Effect of Reynolds Number and Angle-of-attack Rate on I%ximum Lift Coefficient of T-lA Airplane Compared with Wind Tunnel Wing W-2 REFERENCES 1. Harper, Paul W.; and Flanigan, Roy E.: The Effect of Rate of Change of Angle-of-Attack on the Maximum Lift of a Small Model. NACA TN 2061, 1950.
2.
Gadeberg, Burnett L.: The Effect of Rate of Change of Angle of Attack on ,the &ximum Lift Coefficient of a Pursuit Airplane. NACA TN 2525, 1951.
Spreiter, John R.; Galster, George M.; Blair, William K.: Effect of Mach 3.
and Reynolds Numbers on the Maximum Lift Coefficient Obtainable in Gradual and Abrupt Stalls of a Pursuit Airplane Equipped with a Low-Brag Wing.
NACA MR A5GO6, 1945.
4. Shapiro, Ascher H.: The Dynamics and Thermodynamics of Compressible Fluid Flow. The Ronald Press Co., 1.954.
McFadden, Norman N.; Holden, George R.; Ratcliff, Jack W.: Instrumentation 5.
and Calibration Techniques for Flight Calibration of Angle-of-Attack Sys- tems on Aircraft. NACA RM A52l23, 1952.
6. Garner, H. C.: Note on Aerodynamic Camber. R. & M. 2820 British A.R.C., 1953 - Summers, James L.; Treon, Stuart L.r The Effects of Amount and Type of 7.
Camber on the Variations with I&ch Number of the Aerodynamic Characteristic NACA TN 2096, 1950.
of a 10 Percent-Thick NACA 64A Series Airfoil Section.
NASA-Langley, 1965 CR-321