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HEADQUARTERS AIR MATERIEL COMMAND

WRIGHT FIELD, DAYTON, OHIO

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RM No. LgllO

RESEARCH MEMORANDUM

EFFECT OF MACH NUMBER ON THE MAXIMUM LIFT AND

BUFFETING BOUNDARY DETERMINED IN FLIGHT ON A

NORTH AMERICAN P-51D AIRPLANE

By

John P. Mayer

n

hii Documents Division, AMC, Wi1|M Field

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Field Ketweflce Lib-ary Section fients Division - Intelngence (I -2)

light held, Dayton, Ohio.

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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

WASHINGTON June 12, 1947

CONFIDENTIAL

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SACA IM No. L6I1D COHITDEKTIAL

HA.TIONAL ADVISORf COMMITTEE FOR AEPCHAUTICS

HE8EABCH MEMORANDUM

KFFBCT OF MACH NUMBKP. ON THE MAXIMUM LIFT AND

BUFFFTHK BOUNDARY DETERMINED IN FLIGHT ON A

NORTH AMKUCAN P-51D AIRPLANE

By John P. Mayer

SUMMARY

Flight teats were conducted on a North American P-'plD airplane to establish th-3 maximum lift coefficient and the buffeting boundary line as a function of Mach nntibev. Abrupt ate 11s vere made at Mach numbers from 0.21 to 0.63 and gradual stalls vere made at Mach numbers from 0.1»1 to O.65. Tho baffotiiy; boundary wns determined In abrupt pull-ups through a Mach number range from 0.?'1 to O.60.

The results Indicate that the maximum lift coefficient and the buffeting boundary Dine as established In abrupt pull-up3 were very much affected by Mach number and that Reynolds number had no apparent effect on maximum lift coofficiont In abrupt pull-ups vlthln the limits of the test data.

Up to a Mach number of 0.6% the buffeting boundary vas defined by the actual limit maximum lift coefficient attainable vlth the P-51D airp2ane In abrupt pull-ups. Above a Mach number of 0.6U the buffeting boundary dropped sharply and vas belov the actual maximum lift coefficient of the airplane.

A comparison betveen the buffeting boundary found in the flight tests and a calculated ving buffeting boundary shove good agreement up to a Mach number of 0.1*2 vlth a leaser degree of agreement at higher Mach numbers.

The gradual stalls of the airplane indicated that the maximum lift coefficient was affected by Mach number in a manner similar to that for the abrupt stalls.

COOTDEnTIAL

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COHFUEHTIAL HACASM No. L6I10

INTRODUCTION

Although there is considerable wind-tunnel material available on the variation of the maximum lift coefficient with euch factors as Reynolds number and airfoil shape, there is loss known about the effects of either Mach number or rate of chance of angle of attack on maximum lift coefficient, both of which are becominr; increasingly important. Also, the occurrence of buffeting at high Mach numbers and lift coefficients lover than the maximum lift coefficient has imposed an effective limit in lift on the airplane beyond which pilots havo seldom ventured. Relatively few data exist on this latter phase of the problem and little is lenown concerning the prediction of thin limit.

In the course of a high-speed dive tost profsram on a P-51D air- plane at Langley Memorial Aeronautical Laboratory of the National Advisory Committee for Aeronautics at Langley Field, Virginia, some data on the variation of maximum lift coefficient and buffeting lift coefficient with Mach number were obtained. This report presents the rccults of these teats. The true maximum lift coefficients wore meaeurei in abrupt and gradual stalls up to a Mach number of O.63, whereas the buffeting boundary was established up to a Mach number of O.80.

The present rosultn extend the available flight data on abrupt stalle of airplanos with lov drag winga (results of Ames Laboratory testa of t'ne Boll F-63A-6 airplane) from a Mach number of 0.1A to O.63. Although t'io tecto of the 1--51Ü alrplano did not extend the Mach number range of other investigations with regard to the buffeting boundary (references 1 and £), the instrumentation of the airplane was siich that the buffeting boundary could be quite accurately determined. In addition, since tail loads were measured on the P-51D alrplano, wing lift coefficients as well as airplane lift coefficients were evaluated.

APPARATUS

Description of Airplane

Tho airplane used in the tests was a North American P-51D, reinforced structurally to withstand the high loads expected in a high-speed dive program in progress at Langley Laboratory. Figure 1 shovB a side view of the airplane used in the flight teats.

CONFIDENTIAL

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MCA m No. IÄI10 COKFIDEJJTIAIi

The general specifications of the airplane aa flovn are as follows:

Airplane North American P-51D Army Air J'orc3S No. Wt-13^57

Engine Packard built Rolls Royce V-1650-7 12 cylinder

Propeller Hamilton Standard 4-bltde hydrometlc

Diameter, feet 11.17 Blade number K65^%-2k

Weight at take off, pounds 8850 Center-of-gravity position (at take off),

percent M.A.C 25.1

Wing: Span, feet 37.03 Area, square feet plfO.l Dihedral (at 2"5 percent chord), degrees 5 Sweepback (leading ertge), degrees , 3.6 M.A.C., Inches 79.6 Airfoil . NAA-NACA lov drag

Horizontal tail: Area, square feet 28.0 Incidence, degrees 1

Xnst rumentatlon

Airspeed, pressure altitude, and airplane normal acceleration were measured as functions of time with standard NACA recording Instruments. The tall normal acceleration vas measured with a Statham accelerometer In connection with a Miller 15-element recording oscillograph. Loads on the vine and tall were found fey using strain-gage measurements recorded on the Miller oscillograph.

The airspeed head was mounted on a boom extending 1.? local chord lengths ahead of the leading edge of the wing and located near the right wing tip of the airplane. The airspeed-altitude recorder vas located In the right wing so as to minimize lag effects. This airspeed system was calibrated for position error, due to lift coefficient and Mach number effects, up to a Mach number of O.78.

The strain-gage Installation on the airplane was calibrated periodically by applying known loads to the wing and tall of the airplane.

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FLIGHT-TEST PBOCUJOEE

NACA BM No. L6I10

All flight teats were made with the airplane in the clean condition and with power on.

Abrupt stalls wore macle et pressure altitudes of 10,000, 20,000, and 30,000 feet at Mach numbera from 0.21 to O.63. In these stalls the airplane was pulled up aa abruptly as possible, the degree of abruptness depending upon the inertia, control power, and stability of the airplane aa flovn. A series of gradual stalls was also made Jn turns at 30,000-foot-'pressuT,e altitude fit Mach numbers from 0.1*1 to O.65.

In the pull-ups within the Mech nurher ronge from 0.64 to O.60, maximum lift coefficients were not reached because of buffeting. In this renp,e the airplane vas pulled through the buffeting boundary until the vib>-at!on of the airplane became objectionable to the pilot at which point recovery from the pull-up was made and buffeting stopped. The pull-ups through the buffeting boundary were made somevhat more slowly than the low- speed pull-ups.

METHOD

In order to illustrate the definitions and methods employed In evaluating results, throe typical load-factor time-history diagrams obtained in abrupt pnll-upa are shown in figure 2. Point A in each of the diagrams represents the point where buffeting started; B, the point of peak mean loed factor} and C, the point where buffstins stopped. In figures 2(e) and 2(b) the first two points coincide, while in figure r(c) the peak load factor occurs after buffetlnc starts and between points A and C.

From the data of the type shown in fijTure 2 the airplane and wing lift coefficients were evaluated for e number of runs at the points where buffeting started and stopped as well as at maximum lift. In computing lift coefficients the lift was assumed to be equal to the normal force, and fuselage and propeller normal loads were neglected. The equations used in determining lift coefficients were:

C0N5TDEBTIAL

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MCA DM No. L6I10 COHFIDEHTIAL

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qS

nW qS

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C^ airplane lift coefficient

Cj^ ving lift coefficient

n

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S

normal load factor (aeesurod perpendicular to airplane thrust Jine)

dynamic preasuro, pounds per square foot

wing area, square feet

W airplane veight, pounds

Ly horizontal tall load, pounds, as determined from the strain K850E und occeleroLieter records

Since the tests of the P-51D as veil as other Investigations (references 3 and h and results of Ames Laboratory tests of the Bell P-63A-6 airplane) indicate that the maximum Uft coefficient depends on the yltchirif; angular velocity, the maximum lift coef- ficients obtained in the abrupt pull-ups vare plotted versus the angle of pitch per chord length traveled. This parameter is

C da V dt

where

C mean aerodynamic chord, feet

V airspeed, feet per second

da dt time rate of change of angle of attack, radians par second

CONFIDENTIAL

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COMKlDJUI'riAI. MCA HM No. LÖ10

The rats of change of angle of attack da/dt was In turn determined from the measured rate, of client of load factor with tine and the equation

da dt

W,fe dn/dt dCjydä q

where

dC^/da slope of lift curve, per radian

dn/dt time Kite of clicngo of load faotor

The elope of the lift curve dEjJda a*, the various values of Mach number ves obtained from unpublished data from wind-tunnel tests made at Atn&e of the TP-?1 a irr lane. The slo^o of the load-factor time diapram was taken at the tirio corresponiin;j to 6 chord lengths before the maximum accelrretion ves rocchsd. This corresponds approxi- mately to +he tin».: the lift coefficient lags the ancle of attack when the angle is changing rapidly.

ACCURACY

CLA

or cIy» < 3 peicnt, M, *0.01, and The estimated accuracy in the determination of the pertinent

results is as follows:

|||, +15 percent.

Those probable errors arise principally from errors in the measurement of dynamic pressure, pressure altitude, load factor, and, in the casa cf lift coefficients, in the; assumption that the lift vas eoual to the norwil force. In the dptarmir.ation of

V dt* however, the listod error is attributed to (1) the necessity of using wird-turjT;l data from tpste of a mo*.el of the XP-51 for lift-curves elope, (l.1) the; 0oacwhnt arbitrary selection of the point at which the slopes vere read, and (3) graphical errors in the differentiation process.

CONFIDENTIAL

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IMCABM Ho. L6nO CONFIDENTIAL

RESULTS AMD DISCUSSION

Rio Effects of Mach and Eoynolds number on the

Maximum Lift Coefficient

Ilia results of a number of abrupt pull-ups to the maximum lift coefficient for those cases where points A and B coincide (fig. 2) and the results of gradual stalls are presented in figure 3. She results shown indiceto that the airplnne maximum lift coefficient obtained in the abrupt stalls decreases rapidly as the Mach »umber inrreaseo from 0.21 to O.kS whore a minimum point ia reached. The maximum lift coefficient then increases until a secondary peak is reached at a Mach number of O.56 after which it agf.in te^im to docreaso rapidly to the limit of the present tests. "Die secondary peak in the maximum lift coefficient is characteristic of low drng airfoile end ia cauued by the broadening of the i>ppcr surface lou-jrenaurc region vhich offsets the reduction in the negativ« pressure peak an the Mach number Increaeen. As the Mach number increases further the decrease in the negative preenuro peak mere than accounts for the broadening upper surface pressure and the maximum lift coefficient again begins to decrease. It can also be seen from figure 3 that altitude, and therefore Reynolds number, has no apparent effect on the maximum lift coefficient obtained in abrupt stalls within the limits of the data obtained. Biis result lies rlao been shown in reference 5 for the T-kJU airplane and in the reßultc of MOB Laboratory tests of the P-63A airplane. In the c;;rve of figure 3 it is also seen that the general trend for the gradual stalls is similar to that for the abrupt stalln with tho minimum and peak martmum lift coefficients occurring at similar Mach numbers.

A comparison of tho roeultn obtained in the abrupt stalls with similar raeults obtained with a I-63A airplane (fig. k) qualitatively indicates the sane sort of variation for the two cases. The differences noted between the two cases may be ascribed to the fatt that, althout^h both win.^3 ere of the low drag type, the sections era dissimilar; those on the P-63 being obtained from the NACA 66 sorter of airfoile while those of the P-51D are a North Anorican-KACA compromise section. It is to be noted, also, that tho abrupt pull-ups for tlie 1-63 were not carried sufficiently far to indicate any minimum point in the CT curve.

A Comparison between results of gradual stalls of a P-5IB (reference 6)

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•ad those of the P-51D (fig. k) show fair agroement throughout. Whatever differences exist may be attributed to the fact that the two airplanes have a slightly different configuration.

Effect of Mach Number on the Buffeting Boundary

Figure ^ Is an extension of the results given In figure 3 to Include those pull-ups where buffeting prevented the attainment of true maximum lift. (See fig. 2(c).) Ihr. pull-up traced out 1>y the curve A, B, C Illustrates the Banner of variation of lift coefficient with Mach number obtained in a typical high Mach number pull-cut.

From a Mach number of 0.P1 to 0.6k the buffeting boundary is defined by the actual limit maximum lift coefficient as obtained in abrupt pull-ups of the airplane. Above a Mach number of 0.64, however, the buffeting lift coefficients are below the maximum lift coefficients. It is seen from figure r> that the lift coefficient at vhtch buffeting either starts or stops decreases rapidly with Mach number and that at e Mpch number of about. 0.83 buffeting would occur even at zero lift. The implication of the results of figure "5, insofar as they specifically apply to the P-51D airplane, is given in figure 6 where the lift capabilities of the P-5W are shown for several altiiudes. The portions of the curves below M => 0.6k were established from the solid part of the curve in figure 5 end the portions above M = 0.6k were established from the dotted part of the curve. It is seen that at 40,000 feet the airplane would be capable of only the mildest maneuvers and that evnn ot 1 g buffeting would occur at M = 0.79.

It may also be suen from figure ? that the lift coefficients where buffeting starts and stops apparently define a single curve In the region from M = 0.64 to M » 0.80. In the Cr^ region

(solid curve) the lift coefficient where buffeting stops lies below the point where it initially started. An indication of this result may be obtained from figure 2(b). However, in this range, the lift coefficient where buffeting stopped depended upon the rate cf change of angle of attack, and, in general, seemed to be lower than the gradual stall line.

Several papers have presented charts by which the low-speed negative pressure coefficients may be expanded to account for effects of compressibility. In general, such charts when used to expand each pressure point along the airfoil can be made to yield a

COKITDERTIAI.

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JMGAHM Ife. X£O0 COMFIEENIML

variation of a critical lift coefficient vlth Mach number; the ward critical," then, being associated vlth the attainment of the Telocity of sound over some portion of the airfoil. In general, flight observations as vail as wind-tunnel experience hare not Indicated serious effects when the local velocity of sound is first reached, therefore, curves of critical lift versus M would he expected to lie well below the curve shown in figure 5 and could only serve as a rough guide to the buffeting limit. The charts of reference 5 make possible a prediction of the buffeting limit rather than a critical lift coefficient.

Hie charts of reference 5 have been applied to expand the theoretical pressure distributions over the moan aerodynamic chord section of the P-51D In order to obtain the variation of the limit lift or buffeting lift coefficient with Mach number. Fißure 7 illustrates the agreement between the results calculated in this Banner and the experimental results of figure 5« It can be Been that although the computed limit lift curve follows the trend of the measured results It is not as close as would be desired for quantitative purposes.

Effect of Angular Velocity on Maximum Lift Coefficient

Figure 8 shows the results of tho effect of rate of chance of angle of attack on the maximum lift coefficient for the P-51D airplane, In abrupt stalls, at four mean Mach numbers. The values of the maximum lift coefficient for zero angular velocity were taken from the mean line for the gradual stalls. The linos of constant Cj-

shown In the figure for the four mean Mach numbers were taken from the mean line through the test points, given In figure 3, for the abrupt stalls.

Figure 6 Indicates that throughout the Mach number and range £ & V dt

covered in the P-5ID teats the variation of maximum lift coefficient

with the angle of pitch per chord loncth traveled ~ |• in relatively

constant. This is In agreement with results of Moo Laboratory tests of P-63A-6 airplane in which it was shown that the maximum lift coef- ficient increases almost linoorly with angular velocity until a limiting value of the maximum lift coefficient Is reached which le unaffected by further Increases in angular velocity.

CCMFfflENTIAL

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commjüüri'iAi NACA KM No. L6I1D

COHCLOSIOHS

Tren the flight testa of the P-51D airplane It nay be oonolnded that:

1. The maximum lift coefficient attainable In abrupt stalls decreases rapidly with Mach number until a minimum value Is reached at a Mach number of 0.U8, and then Increases until a secondary peak la reached at a Mach number of O.56, aftor which the maximum lift coefficient decreases with Mach number. The maximum lift coefficient attainable in abrupt stalls appears to be independent of Reynolds number within the limits of the test. data.

2. The variation of maximum 15ft coefficient with Mach number obtained in gradual stalls la somewhat similar to that obtained in abrupt stalls at Mach numbers above O.ltO. However, the maximum lift coefficients obtained in gradual stalls are lower than those obtained In abrupt stalls.

3. The maximum lift coefficient obtained in abrupt stalls also defines the buffeting boundary up to a Mach number of 0.6U. Above a Mach number of 0.61t there is a rapid, almost linear, decrease in the buffeting lift coefficient which approaches zero lift at a Mach number of about O.83. The actual maximum lift coefficient is above the buffeting boundary at Mach numbers greater than 0.6k.

Langley Memorial Aeronautical laboratory National Advisory Committee for Aeronautics

langley Field, Va.

COMflUHRFIAL

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XACA BM »0. L6I10 CONFIDENTIAL 11

REFERENCES

1. Novby, C. T.: Discussion of Critical Boundary for Tail Buffeting at High Speeds. Struc. Project Rep. No. 21, S«r. NO. 35, Bur. Aero., July 29, 19^3«

2. Paine, M. G. V., and Dickinson, 0. R. H<: on Dive and Recovery Characteristics. m, 37th Part (BritiBh), June IB, 19^.

Effect of Mach Number Rep. No. AAA.E.E./692,

3. Kramer, Max: Increase in the Maximum Lift of an Airplane Wing Due to a Sudden Increase in Tts Effective Angle of Attack Resulting from a Gust. HACA TM No. 678, 1932-

U. Farron, W. S.: The Reaction on a Wing WhoBe Angle of Incidence is Changing Rapidly. Wind Tunnel Experiments vith a Short Period Recording Balance. Report R. &. M. No. 16W3, British A.R.C., 1935-

5. Rhode, Richard V.: Correlation of Flight Dr,ta on Limit Pressure Coefficients and Their Relation to High-Speed Burbling and Critical Tail Loads. NACA ACR No. LUI27, 19AU.

6. Spreiter, John R., and Steffen, Paul J.: Effect of Mach and Reynolds Numbers on Maximum Lift Coefficient. NACA TH No. 1(M, 19W.

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Mayer, John P.

AUTHOB(S)

€©Cs3PIISaK17llßlL •• - - .= , DIVISION: Aerodynamlce (2) SECTION: Porfomianco (2) CROSS REFERENCES: Lift - Mach number effect (^ö?1»);

Alrplanee - Flight characterletlco (08VU3)

1AT0° 7»3 OalG AGENCY NUMBEO

RM-L6I10

REVISION

AMER. TITLE: Effect of Mach number on the maximum lift and buffeting boundary determined In flight, on a Kurt.h American P-5H> airplane

FOBG'N. TITIE,

OBIGINATING AGENCY: National Advisory Committee for Aeronautlce, Waehlngton, D. C. TRANSLATION:

I LANGUAGE |FORG'N.CLAS.*| "• S.CLAS5. COUNTRY U. S. Confd'l

DATE PAGES IUUS. FEATURES Jun'lt7 19 8 photos, graphs

ABSTOßE? Abrupt and gradual etalls were made in Mach ranges of 0.21-0.63 and O.ltl-0.65 reepec-

tlvely. Abrupt pull-ups were made through Mach range of 0.21-0.30. Mach number greatly affected maximum lift coefficient and buffeting boundary line. Buffeting boundary was defined Sy maxizus lift coefficient only up to M • 0.6*t. Alwre M- 0.12, calculations loat their agreement with flight data. Gradual etalle showed same effect of Mach number as abrupt stalle.

HOTE: Request for copies of thia report must be addressed to: H.A.C.A., Vaehington, I>. C.

T-2. HP, AIR MATERIEL COMMAND AIR TECHNICAL ONDEX WRIGHT FIELD. OHIO. USAAF KtKO-V HAH 47 |M