SECURITY INFORMATION

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. .* copy 210RM L52K20

RESEARCH MEMORANDUTW

SUMMARY OF PITCH-DAMPING DERIVATIVES OF COMPLETE AIRPLANE

AND MISSILE CONFIGURATIONS AS MEASURED IN FLIGHT

AT TRANSONIC AND SUPERSONIC SPEEDS

By Clarence L. Gillisand Rowe Chapman, Jr.

Langley Aeronautical LaboratoryLangley Field, Va.

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NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS.

WASHINGTONJanuary 22, 1953

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https://ntrs.nasa.gov/search.jsp?R=19930087384 2020-06-20T07:15:44+00:00Z

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NACA RM L52K20

NATIONAL

.-—- .-

TECH LIBRARY KAFB, NM

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ADVISORY COMMITTEE FOR AERONAUTICS

RESEARCH MEMORANDUM

SUNMARY OF PITCH-DAMPING DERIVATIVES OF COMPLETE AIRPLANE

AND MISSILE CONFIGURATIONS AS MEASURED IN FLIGET

AT TRANSONIC AND SUPERSONIC SPEEDS

By Clarence L. Gillis and Rowe Chapman, Jr.

Longitudinal-damping

SUMMARY

data in the form of the pitching-moment dampingderivatives

(%+ c~

)are presented and sumnsrized from NACA flight

tests of rocket-propelled models and full-scale airplanes. The experi-mental data are compared with calculations and a discussion of each con-figuration is given. Detailed conclusions are precluded by the lack ofsystematic configuration changes and the relatively unknown effects ofvarious factors. A general comparison of the resuits revealed the fol-lowing trends and general conclusions. The contribution to the pitch-damping derivatives of wings having 45° or less sweepback is erratic inthe transonic region and may be either positive or negative, leading topossible dynamic instability of tailless configurations using such wings.No satisfactory method of calculating the damping of such,wings in thetransonic region is available and a smoothly faired curve between sub-sonic and supersonic calculated values will probably be unconservative.Configurations having triangular and swept wings with approximately60° leading-edge sweep and rounded airfoil sections exhibited less vari-ation in damping in the transonic region. Calculated values of the pitch-damping derivatives for configurations with horizontal tails are more con-

.-

servative and give better agreement with experimental results if thedistance from the trailing edge of the wing mean aerodynamic chord (instead ‘-of from the center of gravity) to the tail is used to calculate the down-wash lag effect. The damping caused by downwash effects arising from lifton a forward surface due to pitching velocity and rate of change of singleof attack may be appreciable if the forward surface is at a large distancefrom the center of gravity.

.

*

2*-= -. NACA RM LZK20

INTRODUCTION

Successful accomplishment of aircraft flight at transonlc andsupersonic speeds has served to place increased emphasis on the dymmicbehavior of aircraft. The type of behavior referred to here concernsmotions of the aircraft as a whole as compared to motions of componentparts usually referred to as flutter. Dynamic instability of the lat-eral and directional modes of motion is a pr”oblemthat has occupied thedesigner’s attention for some time. A trend toward det-eriorationofthe damping of the longitudinal motion of aircraft operating in thetransonic region has also been experienced. This decrease in damping,as measured by cycles to damp, occurs because of the high altitude atwhich such flights are usually conducted and because of an actualdecrease in the dimensionless aerodwamic damping-in-pitch derivativesat transonic speeds for some aircraft configurations (refs. 1 and 2).

The present paper summarizes the available experifientaldataobtained by the National Advisory Committee for Aeronautics on pitch-damping derivative measured in flight at transonic and low supersonicspeeds. Most of the data contained herein were obtained from rocket-propelled models of airplane or missile configurations flown at theLangley Pilotless Aircraft Research Station at Wallops .lsland,Vs..Some data are also shown for several piloted=irplanes .obtainedfromflights at Ames Aeronautical Laboratory md”the NACl”High-Speed Fli&tResearch Station at Edwards, Calif.

Some of the damping information presented herein has been publishedpreviously as parts of general longitudinal-stabilityifivestigationsandsome is, as yet, unpublished. In the present paper the–damping data ar~...compared with each other and with values calculated by the usual methods.

SYMBOIS—

CL lift coefficient, L/qS

Cm pitching-moment coefficient, ‘itchim momentqsE

A aspect-ratio

c constant in stability equation

Iy mass moment of inertia about Y-axis,

ky radius of gyration in pitch, @y/mj

w’-u-Wg!g!x%$i==

Slug-ftp

ft

s

“i “.-

.—.

~=—.

.-

●

-m..{

.’

—+

. ,-

NACA RM L52K20

.

.

L

M

s

St

v

w

b

b

c

.m

. P

q

t

Y

lift

Mach number

wing area (including

horizontal-tail area

area enclosed within fuselage), sq ft

(total included area), sq ft

forward velocity, ft/sec

weight of body, lb

wing span in equation for 5, ft

damping constant in stability equations

local chord, ft

L

b/2mean aerodynamic chord, : c=’dy, ft

acceleration due to gravity, ft/sec2

tail length, measmed from center of grevity of confi~a-tion to center of pressure of tail,-ft -

~SS Of body, W/g, Shl&3

free-stream static pressure, lb/sq ft

dynamic pressure when used in ;quations forand equations (2) and (3), ~ YPM2, lh/sq

time, sec,,

reference axis through center of gravity ofperpendicular to plane of symmetry

angle of attack, radians

specific heat ratio (1.40)

control-surface deflection, deg

xi~ .’. . . . .

CL and Cmft

configuration

—

4

0.)

angle of downwash, radians —

angle of pitch, radians-. =-—

rate of change of angle of attack, da/dt

phase angle, radians —

frequency of oscillation, radians/see

—

..

dCLc%== —

Subscripts:

f

r

t

T

NACA RM L52w0

-.

-.

—

forward surface, based on its own area and chord

rear surface, based on its own area and chord

tail .

trinmed, or mean value

-

.

.- — F

—

—

.

NACA RI!L%3Q0 . . ... ... . . . 5

TEST AND ANALYSIS PROCEDURE

Experimental data presented were obtained in free flight by thefree-oscillation technique. In this test method, the aircraft is dis- “turbed from a trimmed condition, usually by means of a rapid elevatordeflection and the resulting short-period oscillation is recorded asthe elevator is held fixed. The method of analysis of these oscilla-tions to obtain the static and dynsmic stability derivatives is ade-quately covered in several references (such as ref. 3). For thepresent purpose, only that portion of the procedure dealing with thepitch-damping derivatives is of interest.

Making the usual assumptions of constant velocity, level flight,and linear aerotQnuamicderivatives, a solution of the two-degrees-of-freedom equation of longitudinal motion of an aticraft can be obtained.For any appropriate quantity such as normal acceleration or angle ofattack, the solution is of the form

a= Cebtcos(ti + q) + ~

The constant b in equation (1) defines the dampingand in terms of the aerodynamic derivatives is given

Equation (2) maybe solved for the sum ofgive

(1)

of an oscillationby

(2)

the damping derivatives to -.

Sq cm d

(3)

From the flight tests, therefore, the sum of the damping derivatives -_c% and C% may be determined if the damping constamt b is measuredand the lift-curve slope CL is known. The damping factor b is gen-

erally determined from the envelope of the curve defined by equation (l).This envelope is determined from the flight record of the appropriatemeasured qusmtity which, for rocket models, is angle of attack. Theequation for the damping factor is

b= loge ~/bltz - tl

(4)

6

where @al and @a,2 are the amplitudes measured fromof u at times t~ and t2. For rocket-model tests,

NAM RM LZ3C20

—>he mean value .: b=normal acc”elera- .

tion and angle of ;ttack were measured to provide thel#t-curve slopes.In some cases for the fuil-scale airplane tests reliable angle-of-attackinformation was not available from the flQht test so the lift-curve

r

slope was obtained from wind-tunnel tests and equation- (1) and (h)would be written in terms of the lift coefficient. The.test and analy-sis method described does not permit separation of the derivatives Cqand CW. This is not a severe limitation, however, be-causethe damping

is always proportional to the sum of the two derivatives regardless of —

the flight conditions or mass characteristics.

In free-flight tests, accurate measurement of the Ging deriva-

—

tive (C% + Cm) is difficult for several reasons. Firs%, as shown by ‘- _ – -

equation (2), t“hetotal damping is composed of the damping-derivativeterm and the lift-curve slope term, the relative magnitudes of which

--

depend on the radius of gyration in pitch. The inaccuracies in

Cmq+ CM, as obtaihed by solution of equation (2), are proportional to —

the relative contribution of the C~ term to the tota~damping, b.---

As an example, the c~ term contributed as much as two-thirds of the— —total damping in some ;f the rocket models, and in a f~l-scale test ofan airplane (ref. 1) the CL term contributed about on~-half of the -

total damping. Present design trends indicatethat the proportion ofdamping contributed by the c~ term on future airplanes will more ___

nearly approach the proportion for the rocketmodels.—

Other factors.-

which may contribute to inaccuracies in measuring C% + Cm are non-

linear aerodynamic derivatives, disturbances due *O gustg, md any other -- .effects on the oscillation peaks which define the envelope of the curve.Gusts and nonlinear~erodyn~c derivatives usually”appe= “asapparent “-changes in the damping coefficients.

CALCULATION METHOD

The experimental damping derivatives presented herein are.comparedwith calculated values from theoretical investigationswherever appli-cable, or experimental test data where such are available. It has fre-quently been assumed that all the damping on conventiona~airplaneconfigurations is caused by the tail. A damping moment derivative

c%results from the additional angle of attack at the tail caused by thevelocity of pitching about an axis through the center of -gravity. Adamping moment derivative C% results from the lag in downwash at thetall surface due to the finite time required for the downwash discharged .at the wing to reach the tail surface (ref. 4). The damping derivatives

“

NACA RM LZK2Q

. arising from these concepts are given by the

.

7

equation

(%+ c%).=-P+%)(’%lJw’ (5)

where the downwash lag contribution is represented by the d~/da factorin equation (5). A factor such as this assumes that the downwash lagterm is characterized by downwash discharged at the center of gravity ofthe configuration. It appears that this downwash lag term might be morerepresentative if it is assumed that the downwash is discharged at thetrailing edge of the mean aerod~amic chord of the wing rather than atthe center of gravity. I@dification of formula (5) in accordance withthis concept gives

(~+%)t=-p H)(’ ‘%)%%)2 (6)

where 11 is the length from the trailing edge of the mean aerodynamicchord to the center of pressure of the tail.

For airplanes in which the tail contributes the largest part of thedamping, equation (6) is satisfactory for an approximate calculation.It obviously falls for a tailless airplane. For airplanes with sweptwings the damping contributed by the wing may be of appreciable magnitude

. at all speeds, and in the transonic region the wing damping may be ofprimary importance for wings of any plan form. Theoretical studies(refs. 5 to 8) and experimental data (refs. 9 and 10) show that, at

. transonic and low supersonic speeds, the wing itself maybe dynamicallyunstable. Calculations of the damping derivatives should thereforeinclude the wing even though the damping due to the tail may be themajor factor.

Additionalof the downwashforward surface

change of angle

this effect may

increments in dam~ing-moment coefficients arise becauseon a rear lifting surface resulti from the lift on a

7)produced by the pitching velocity c~ and the rate of

(k)of attack C . .

be calculated as

The damping coef;ic;~nts caused by

)Zr SrF—Cs

(7)

(8)

8

where S and ~ are the quantities on whichexpression can be derived for AC%. The sum

coefficients is then:

NACA RM ~2K20

cm is based. A similar .—+.of the two damping-moment--

As will be shown later this increment in the-damping d~rivativessmall for conventional airplane configurationsbut can be fairlyfor canard configurations. If the forward lifting surface is at

distance from the center of gravity, the quantity dc --

77

can be

to a close approximation by the expressiond%

2Zf d~*=__

L)d= Zda

The theoretical results used to calculate the pitch-dampingtives for subsonic smd supersonic speeds sre given in references

.

(9)

is very .—largea large

obtained

—

deriva-5 to 8,

11, and 12. References 5 and 11 consider only untapere.dwings but the ~ “.results were assumed to apply to tapered wings also. Wherever possible,wind-tunnel measurements of tail effectiveness and downwash were used tocalculate the dsmping caused by the tail.

In calculating the derivative c= the simple downwash lag coricept ,

as given in equation (5) and modified in equation (6) was used at allspeeds. Several refinements to these calculations have-been consideredin references 13 and 14 but for the present purpose thege refinements

●

were neglected because of the uncertainties in the experimental resultscaused by lage possible experimental errors.in some cases and the rela-tively unknown but important effects of oscillation amplitude.

RESULTS AND DISCUSSION

The results of-the flight measti.emenf%siidthe”calcuiations areshown in figures 1 to.= for airplane and mis”sileconfigurations. Allinformation pertaining to one configuration @ given in-one figure;break lines on the drawings of the nmdels indicate wedge and hexagonal “-airfoil sections. The details of the airfoil section for each modelare given in table I. For consistency, damping coefficients in all fig- -ures are based on the total area and mean aerodynamic chord of the wingand are given for the rate terms (q and &) in radians yer second.This method of presentation does not correspond to that of the references ‘“-

——

from which the data were taken for some cases.

.

2JL NACA RM L52K20.- “

9

Scales to which the derivatives. (C% + C%) are plotted vary con-

siderably between figures. It is important to note, as pointed out inreference 15, that a comparison of the absolute values of dsnping coef-

. ficients for different configurations has little significance. Whenpresented, the curve designated “calculated (tail)” is ‘thevalue obtainedfrom equation (6), using wind-tunnel values of C& and d~/du. The

~alculated (tail) curve thus includes the downwash lag effect which isan indirect effect of the wing but acts on the tail. The direct dampingof the wing, calculated from theoretical results for the conventicmal air-plane configurations was added to the calculated (tail) curve to give thecurve designated “calculated (tail plus wing).” For the canard configu-rations, the calculated curve includes the damping increments given byequation (9) and the theoretical values of Cm given by references 5

and 6. There are insufficient data available to permit estimation of theeffects of airfoil shape, oscillation amplitude, or oscillation frequency.Reference 16 shows some effects of oscillation smplitude and frequency onthe damping derivatives (C% + C~) for a 45° delta wing at subsonic sPeeds

For reference, table II giv;s the reduced-frequency rsnge for all models,and it may be noted that the frequency ranges for most of the data dis-cussed herein are below the ramges investigated in reference 16.

Rocket-~opelled Models

Model l.- The experimental data for model 1 are contained in

-.—

refer----. ence 17 and, as-shown-in figure 12 exhibit a smooth variation t~ough

the transonic region. Theoretical values of ~+% and c% ‘e. also shown in figure 1 for the pertinent supersonic speeds. The positive

value of C% at supersonic speeds decreases the Cm damping of the

wing by approximately one-third. Although the experimental curve is con-siderably higher than the theoretical curve, the variations with Machnumber are similar. The effect of the fuselage was investigated by theuse of reference 18, which does not include the effect of the afterbody,and was found to be negligible. No data are available on the effects ofthe afterbody.

Model 2.- Figure 2 shows the experimental data for two models of atailless airplane configuration. The data for model 2 were taken fromunpublished rocket-test results. No curve is faired since the data wereat isolated Mach numbers amd were obtained from sustained low-amplitudeoscillations (zk= ~o.25°) at M = 0.91 and 1.24. The oscillationamplitude for the points at M = 1.34 was LcL% *l.O”.

Model 2B (data previously unpublished) contained pulse rockets to. disturb the model and, therefore, higher angles of attack were obtained

in the test. The data obtained at higher singlesof attack (h% *l.OO)

10

confirmed the data for modelof-attack variations. ~del

NACA RM L52K20,,

A at M = 1.34, which was for similar angle-B also exhibited a continued oscillation of

.

low amplitude (t0.25°) similar to that which gave the positive dampingcoefficients for model A. Analysis of these low-amplitude oscillations,assudng time to damp to one-half amplitude‘azinfinitei..gavevalues

.,

of c% + cm as varying from.1.98 to 2.25. The yalues-_ofd~pingobtained at higher amplitudes shown by the data points fir--modelB andlow amplitudes shown by positive data points for model A.are in realityboundaries for the damping coefficients where the coefficients for the _system depends with certainty on the amplitude of the oscillation andpossibly on the value of the mean angle of attack. -.

In order to calculate the theoretical damping it was necessary toapproximate the actual wing plan form by one more amenable to calcula-tion. Three approximationswere tried: a swept tapered”wing obtainedby extending the leading and trailing edges to the root and tip, atri-

.

angular wing having the same aspect ratio as the actual wing, and a tri-angular wing having the same leading-edge sweep as the actual wing. Thecalculated curves are shown for all three approximationsand best agree--meritwas obtained between the calculated 52.5° triangul= wing and theflight data.

.-

Model 3.- Data are presented in figure 3“for two tailless models ““designed to have different wing flexibilities. These data me from aprogram instituted to investigate the effects of wing flexibility onlongitudinal stability. The solid.line (model A) in fi&e 3 is experi-mental data for a 9-percent-thickwing of hminated wood”and metal con- .struction having medium rigid characteristics and is labeled “least

-—

flexible wing.” The dashed line is for a wing having the ssme geometricshape and thickness but with thinner metal inserts, hence, model B had a“- -~

more flexible wing and is labeled “flexible wing.” The least flexiblewing had a stiffness of approximately one-half that of a-solid aluminumwing of the same thickness and the flexible wing had a stiffness ofapproximately one-third that of a solid aluminum wing of the same thick-ness. These stiffness”ratios were determinedly comparison of the fnflu-ence coefficients for the solid aluminum wing and the l~nated wing.

A calculation of the C!% damping of the wing was made.at M = 0.7

by the method of reference 11. The subsonic calculation=gavethe value.—

of c% as approximately -I-6,which is far too high and unconsenative “j. ““,.._

when compared with the experimental data. It is possible.that the disa-greement between calculation and experiment at subsonic sneeds mav bedue to a positive ~ for

computation. A computationreferences 7 and 8 and goodobtained.

the wi~ which is not accou&d for i; the

of damping at M = 1.414 was made by usingagreement with the experimental data was

,,.

.

b“

●

Model 4.- Unpublished data for a 45° swept-wing tailless configu-ration are shown in figure 4. ,The wing was a 6-percent-thick sectionconstructed of solid dural. Qualitatively, the shape of the curves for

g damping of models 3A, 3B, and 4 show remarkable similarity for Mach num-bers from 0.90 to 1.15 with dsmping for both models exhibiting a charac-teristic drop in this region. The wing on model 4 was comparable instiffness to the flexible wing of model 3. Data for model 4 were not

.—

obtained ’belowa Mach nuniberof 0.88; hence, it is not known if the dampingdecreased in a manner similar to that for model 3. One calc~ated Pointfor the wing alone is shown at a Mach number of 1.38. The calculated valueis conservative but shows poor agreement with the experimental data. Acalculation of body damping by the use of reference 19 showed the body con-tribution to be small at supersonic speeds because of the ai’terbodyshape.

Mbdel 5.- The data for model 5 (fig. 5) are from reference 20.This nmdel was a wingless fuselage-tail configuration that has been usedfor tests of a number of wing plan forms for supersonic airplanes(models 6 to 12). The damping coefficients in figure 5 are based on thewing area and chord of model 6 for comparison purposes. The theoreticalvalues of C + cm agree fairly well with the experimental values,

.-

%!

.

.

particularly at supersonic speeds, as does the calculated values ofc%

of the tail surface (curve labeled “calculated C% (tail)”). The agree-

ment of the theoretical and experimental values is somewhat fortuitous,however, because, as shown in figure 5, the theoretical values of Cqare considerably higher than those calculated from measured values oftail effectiveness. The theoretical values of C%, which are those for

the isolated tail uninfluenced by downwash, are positive throughout thesupersonic speed range considered and become rapidly larger as the Machnumber decreases below about 1.2.

Model 6.- The data for model 6 (fig. 6) are from reference 20. TWOgeometrically identical models were flown; model B having a steel wing(designated “rigid wing” in fig. 6) and model A, having an aluminum wing(designated “flexible wing” in fig. 6). At transonic Mach numbers ratherlarge changes in the experimental damping data occurred as contrasted tothe smooth variation with Mach number of wing-off data (fig. 5) and calcu-lated tail contribution. As indicated by the calculated curve includingthe direct wing effects, part of the loss in dsmping near M = 1.0 canbe explained by a lsrge positive value of c% + c% for the wing. This

large destabilizing effect of the wing is caused by the positive valueof C% being much lager than the negative value of ~. Another

—

reason for the large damping changes near M = 1.0 can p~obably befound in unaccounted-for downwash changes in this region. In calcu-lating the C% portion of the tail contribution to damping it was

. assumed, in the absence of appropriate data, that the downwash variationwith l.kchnuuiberwas similar to the variation of lift-curve slope, which

.

12 NACA RM L52K20

did not show large changes (ref. 20). Since large ch&ges in staticstability for this configurationtook place in the transonic region(ref. 20), it is probable that the downwash variation with Mach numberwas considerably different from that assumed.

‘e i:em:t‘n r’mq+ % caused by the downwash resulting from

the CL%

on the wing was calculated for model 6 and is sho~-

Jn fi~qe 6. This contribution to the damping is very small because thete~ CLq and CM are very small and, at least for-supersonic speeds,are of opposite sign. Since this condition shouldbe approximately thesame for all configurationshaving the forward surface near the centerof gravity, this contribution to the damping was neglected for all othersuch configurations herein.

Model 7.- Model 7 was identical to model 6 except that the winghad an IW!A 65(o~)A004.5 airfoil section instead of $he sharp-edgehexagonal section on model 6. Data for model 7 are sh~@wnin figure 7and were taken from unpublished data. Model 7, which had an aluminumwing, showed less damping than does model @ and a larger disagreement_between the low-lift experimental curve and the calculated curve for thetail. The reason for the disagreement in the three sets of experimentaldata has not been established.

Model 8.- TWO experimental curves (fig. 8) were obtained for model 8(ref.~one at low lift coefficients and one at high lift coefficientsThe calculated tail damping shows a large decrease at Mach nunibersnear0.93, as did the test data, and &his is caused by the large decrease indownwash at these Mach numbers (ref. 22). The direct effect of the wingwas fairly small in the region where it could be calculated. The directcontribution of the wing (as computed) is destabilizing at the supersonicspeeds of the test. ‘lt is perhaps significant that when the effect ofthe wing is included, the variations with Mach number ox the experimentaland calculated curves are, in general, similar at supersonic speeds.

Model 9.- The damping data for two 45° swept-wing-mdels are pre-sented in figure 9 and are not previously published. Model A had asteel wing and is denoted as “rigid wing” in the figure. Model B hadan aluminum wing and the curve is labeled “flexible wi#’ in figure 9.Calculated values of the damping shown for models A and B are based onexperimental tail effectiveness. An additional curve labeled “calcu-lated (tail, theoretical)” is shown in the figure and is based on theo-retical tail effectiveness. The direct wing contribution to damping atpertinent supersonic Mach numbers was small and is notficluded in thecalculated curves. It is noted that the difference in the experimental_damping curves for models A and B is in the opposite directionto thatdifference “inthe calculated curves for the twocenter-of-gravity effect. A difference such as

—

—

.

..—

.

-.

models, which is a .this might possibly be

L

NACA RM L52K20 -%imaiiizsi%%m”;-= 13

explained by a higher dc/du for the more rigid wing. Severe changesin downwash for the flexible wing might explain the high peak and rapidchange that occurs between Mach nunibersof 0.93 and 1.03 for the flexiblewing. Peak values and severe changes such as these occur on a swept-wingairplane which is discussed in a subsequent section.

Model 10.- The data for a 600 swept wing model are shown in fig-ure 10 as obtained from reference 23. The direct contribution of thewing to the total damping is illustrated by the increment between thetotal damping curve and the tail-damping curve (includes dowmrash lag).Two additional curves are shown in the figure to illustrate differenttechniques of computation. The curve labeled “calculated (tail, theo-retical)” uses theoretical tail effectiveness plus a downwash lag termfrom estimated ’downwash. The peak value of damping which occurs atM = 0.85 is not predicted by the calculations but is similar to a peakthat occurs in the data of model 11.

Model 11.- The experimental data presented in figure 11 for model l.1are reported in reference 24. This nndified triangular-wing model exhib-ited damping characteristics that showed a msrked change between Machnumibersof 0.84 and ‘0.88where the damping derivatives alnmst doubled invalue in a manner similar to model 10. Calculated values for the tailand for the tail plus wing are also shown in the figure and show a smoothvariation over the Mach number range. The difference in variation betweenthe experimental and calculated curves and a comparison with the data formodel 5 indicate that the rise in daqping between M = 0.80 and M = 0.90can be attributed directly to the wing or to increased downwash from thewing.

Model 12.- The data presented in figure 12 for the 60° triangular-wing model are from reference 25. Two experimental curves are shown inthe figure: one for the low-lift-coefficientrange and the other forthe high-lift-coefficient range. This difference in damping for highand low lift coefficients is primarily attributed to the nonlinesr down-wash behind the triangular wing. The calculated (low lift, wing plustail) curve shown is for dc/dcf”evaluated at zero lift and for experi-mental tail effectiveness. Calculated damping coefficients, shown infigure 12, for the wing-plus-tail (high lift) configuration indicatethat the increased dsmping at high lift canhe primarily attributed tothe increased downwash.

Model 13.- Damping data for a supersonic airplane configuration areshown in figure 13. Experimental data are shown for two models; model Adata were at high lift and model B data were at low lift. Curves fortail damping and total damping for model B are also shown in the figure.No computations were made for the high-lift model. The disagreementbetween the two sets of experimental data at subsonic speeds is believedto be due to the changes in downwash for high and low lift coefficients.

..

—

—

—.

14 NACA RM L52K20

Good agreement was obtained between the computed and ex~erimental data—

at low lift. From the experimental curve and the fact--fiatit fairs~:

into the calculated (tall plus wing) curve, it appears that the directwing contribution to damping approaches zero at Mach numbers of approxi- ,mately 1.17 and 0.90 lmt generally does not &-ivemuch destabilizingeffect. It is noted that if the calculated (total damping) curve wereextended to lower supersonic Mach nunibers,the unstable contribution ofwing cm& would make the agreement between calculation“andexperiment _..

—

worse. .

Model 14.- Data for a 45° swept-wing airplane model from reference 26are presented in figure 14. Calculated curves are shown for the taildamping using both ”themodified and unmodified tail length for the down-wash lag term. Flight data vary unpredictably througA the transonicregion and a comparison with the calculated curve for the tail indicatesthat the wing contributes both positive and negative damping over the -region. A single data point (unpublished)for a similar tailless con-figuration shows the wing to have a positive (unstable)-damping coeffl-cient at M = 0.79. The calculated curve using the modified tail-lengthconcept gives bettem average agreement with the experimental data and ismore conservative than the unmodified formula. No t0t81i damping calcu-..lated curve is shown since the wing contributionwas small at the higherMach numbers where it could be computed and could not be computed overthe ~ch number range where data were obtained.

—

Model 15.- The experimental data shown in figure 15_for model 15were taken from reference 27. A curve of calculated tail damping shows s.

fairly good agreement with the experimental data, both as to magnitudeand general variation with Mach number. At subsonic speeds the calcu-lated wing damping was appreciable, being about one-third of that con-

.-

tributed by the tail.. For the supersonic speed range below a Mach numberof 1.28 the calculated wing dsnping coefficient is positive and the cal-

—

culated damping of the complete configuration indicates a greater varl-. ._

ation with Mach number than is shown by the experimental data.

Model 16.- Reference 28 and figure 16 coutain the e~perimental data”for model 16. Data are presented for models A and B, id~ntical modelsexcept for center-of-gravitylocation. The effect of the center-of-gravity location on the damping is small. In”contrast to most other”-swept-wing configurations included herein.,the variation-with Mach num-

-.

ber of the experimental damping coefficients is smooth and the dampingincreases as the Mach number increases. The significance of thesephenomena and whether they axe related to the inverse taper are notknown. At subsonic speeds, the calculated wing damping ~s about 50 per-cent of that calculated for the tail. Because of the inverse taperratio on the wing, the methods of references 7 and 8 =e not wplicableto this model.

.

b

NACA RM L52K20 ...m*~ti ,=_:_ 15

Model 17.- The damping data for model 17,.shown in figwe 17, arefrom unpublished test results.‘This model had the ssme wing as the tail-less model 3 and had the same characteristic loss in damping near a Machnumber of 1.0. Comparison of the experimental curve for model 17 withthe calculated damping of the tail indicates that the wing contributed apositive (unstable) damping coefficient near M = 1.0 as did model 3,although the quantitative values of wing damping for models 3 and 17 are?ot directly comparable because of the different center-of-gravity loca-tions. The agreement of the total calculated damping with the experi-mental values is very good at subsonic speeds. The wing dsmping couldnot be calculated over the supersonic speed range of the tests.

Model 18.- T,heresults shown in figure 18 for a 600 triangular-wingmissile configuration are from reference @. Damping data are presentedfor both the inltne- and interdigitated-tailpositions. As pointed outin reference 30 the marked difference in the characteristics for theinline and interdigitated tail can be attributed to the difference indownwash at the tail by considering the rolled-up vortex sheet. Theexperimental curve for the inline-tail model has a variation with Machnumber that is, in general, similar to that for the modified-triangular-wing model (model il.). A calculated curve for the tail is shown as wellas a calculated curve for total damping coefficient (both curves beingfor the inline-tail configuration). Estimates of downwash and taileffectiveness based on experimental data were used and good averageagreement with the flight data were obtained. A theoretical curve isshown and is generally nonconservative at the higher mch numbers but

. shows good agreement with experimental data in the region near a Machnumber of 1.1.

. ~del 19.- The damping data for a cansrd missile model shown infigure 19 are unpublished. The calculated damping is considerably lessthan the experimental damping, but the variation with Mach number of thetwo curves is remsrkahly similsr. The increments in dsmping coefficientscaused by the downwash resulting from the canard lift effects CL

and CM were calculated and found to be appreciable as shown inqfig-

ure 19. This was true for all the cansrd configurations consideredherein. The reason isths.t the value of CLq depends upon the distance

of a lfiting surface from the center of gravity (refs. 5 and 6) and, forthe canard surface, becomes fairly large and of the same sign as c~,

resulting in an appreciable effect on the damping.

Models 20 and 21.- The data for models 20 and 21 were taken”fromreferences 31 and 32 and are shown in figure 20. ~dels 20 and 21 weregeometrically identical except that the cylindrical portion of the bodybetween the wing and the canard was ~ inches longer for model 21 thanfor model 20. All the experimental curves in figure 20 show similar

—

NACA RM L521C20

variations with Mach number near a Mach number of l.O,”Xhich differ con-”.,.

siderably from the variations indicated by the calculated curves..

For.

model 21 neither the theoretical damping nor~that calculated from exper~--—.-

mental data predicted the variation with Mach number of the measyre~—

damping at supersonic speeds.r .-

The calculated-valuesf= model 20-were ~ ‘ “:considerably lower than the experimental valtiesat supersonic speeds butshowed a similar variation with Mach nuniber.

Model 22.- The experimentalvalues for xiiodel22 (fig. 21) were——-

taken from unpublished results. lbdels A and.B were identical except.-

for center-of-gravitylocation and the different lift-coefficientranges-.

covered by each model. Calculated values exhibit fair agreement withmeasured values only at supersonic speeds a@ low lift _coefficients.The difference between the calculated values for models”LAand B was

—.

caused partly by the different center-of-gravity locations and partlyby different values of downwash (shown by wind-tunnel data) over the twolift-coefficientranges. Also shown in figure 21 are the values ofdamping contributed.bythe downwash resultimgfrorn the canard lifteffects c~q and C “7

%0—.

Full-Scale Airplanes-.--. —

Airplane l.- Dsmping data from flig,ht.testsof the~-1 research-air-plane are shown in figure 22. These data were obtained~rom reference 33,and reference 22 was used to obtain the calculated curves shown on thefigure. The calculated damping agrees well with the exp~~imental data ___ { ~“.both as to magnitude and variation with l@ch number. T~e calculatedtotal damping curve is somewhat lower and agre~s betterwith the experi-’~mental data than the calculated curve given irireference 33. This iS

—.

probably caused by the use herein of the modified tail @@h for corn- “-puting the downwash lag effect (eq. (6)). Model 8, previously discussed,was equipped with the X-1 wing. The Iow-lift:experimentzldata formodel 8 show a variation with Mach number very similar to that for the

.-

flight-test data of the X-1 airplane. —

Airplane 2.- The data for the x-k airplaqe are show= in figure 23,as obtained from reference 2. Measured values_are considerably lowerthan the calculated values and, for the highest altitude--test,becamezero at a Mach number of about 0.85. At a Mach number of 0.88, a sus-tained oscillation of small amplitude was obta”~ed in the flight testwhich yielded a large positive value of C% + ~. Because this oscil-

lation was of small amplitude, the value shown can be cotiidered valii ‘.only for small-amplitudemotions. The measured values showed an effectof altitude, which, as stated in reference 2, inayfindicatethat aero-elasticity has a large effect on the damping i_Rthis case~ ,

3H NACA RM L521C20 17

Airplane 3.-. The results for the F-86 airplane in figure 24 weretaken from reference 1. The sharp drop in the experimental curve atM = 0.92 was confirmed by a number of separate test points and corr&-

- spends to a similar irregular variation in the static stabilityparameter C%. Definite reason for these fairly sharp changes was not

established in the preliminary investigation of reference 1 but they aresimilar to those for other swept-wing configurations (models 3> 4) 9>●nd 15).

The estimated damping contributed by the tail and the tail pluswing are shown in figure 24. Tail contributions were calculated fromlift-curve slopes and downwash values obtained from transonic bump testsof 35° swept wings. Although reference 34 contains tail effectivenessdata (a~ait) these were not used in calculating the damping because

—

the values measured were about 25 percent lower thsm would be obtainedby using the lift-curve slopes of an isolated 35° swept-tail swface.This is probably primarily caused by the fact that the inboard portionof the adjustable stabilizer (approximately 10 percent of the span) doesnot rove. The lift contributed by the entire surface, however, iseffective in producing damping. The damping contributed by the wing wasappreciable at subsonic speeds for this configuration and a comparisonof the calculated and experimental data indicates that the dsmping dueto the wing is approximately zero at Mach numbers near 1.0.

Airplane 4.- The dsmping data shown in figure 25 for the D-558-II air-plane were tsken from reference 35. The calculated damping agrees fairly

, well with the experimental data at Mach nunibersup to about 0.75, but as sthe Mach number increases, the experimental data show, first, a more rapidincrease, and, then, a more rapid decrease than the calculated values..The more rapid decrease maybe attributed, at least partially, to a proba-ble dynamically unstable contribution of the wing as shown by model 3 andairplane 2.

GENERALIZATION OF RFSULTS

A generalization of results on damping derivatives is limited bythe nuniberand types of configurations and the continuity of the experi-mental flight data available for summary. Some general trends are notedfor each type of configuration and a discussion is presented on the com-putation of damping. The general trends noted are limited for some ofthe cases by inconclusive evidence.

18 NACA RM L52K20

Tailless Configurations

‘“Four of the five tailless configurations (models 2,L3, and 4, andairplane 2) exhibited either very small negative values or positivevalues of C

%+ c= in the transonic region. The fifth configuration

(model 1), with a 600 triangular wing, showed a fairly smooth variationthrough the transonic region with no indication of a decrease in dampingsimilar to that encountered on the swept-wing configurations. On model 2and airplane 2 the positive (unstable) damping coefficientswere obtainedfrom small-amplitude sustained oscillations and the.evidence indicatesthat the damping is nonlinear with amplitude, being less..a~the smalleramplitudes. The data shown for model 1 were obtained from fairly large-amplitude oscillations but other models having the same wing on a slightlydifferent fuselage have been flown with no pitch disturbtice applied(unpublished) and no sustained oscillations were encountered.

Examination and comparison of the data for models ~, 3B, and 4show that the damping of swept wings is dependent on the.fkxibility.Also, these data show that similar swept wings exhibit similar varia-tions of damping with Mach number, characterizedby a ra~id decrease indamping above M = 0.85 which would not atie~ to be a“critlcal Mach ~number effect. This same decrease in damping is evident’’forairplane 2.

.

.

.

—

Wingless Configurations —

Data are shown for only one wingless configuration (model 5) and”” _ “-indicate little variation in the damping coefficients with Mach nuniber.It is reasonable to expect that the damping contributed hy any liftiu”surface having a large moment arm from the center of gravity shonld vsry

.

with Mach number in 8, manner similar to its lift-curve slope if it isnot operating in the flow field from a forward--surface.-

tive

Wing-Plus-Tail Configurations

None of the configurationshaving tail surfaces exhibited any posi-values of Cmq + C% through the Mach ntiber range~tested, although

several experience~ large changes in the transonic region resulting insome fairly small negative damping coefficients. The contribution of anunswept wing to the damping derivatives of the-total cofiiguration is –usually erratic and may be either positive or negative in the transonicregion. In the ma~ority of the cases the damping of the unswept-wi~configurationswas nonlinear with lift coefficient.

—

In general the swept-wing configurations having 45° or less sweep .also showed erratic changes in damping in the .t.ransonicregion although

b

.

NACA FM L52K20 19

such changes were not as severe as those for the tailless swept-wingconfigurations because of the stiller contribution of the wing to thetotal damping. The one 60° swept-wing configuration discussed had afairly smooth vsriation with Mach nunlbernesr M = 1.0. The triangular-wing configurations generally had a somewhat smoother variation with Machnumber than those with unswept or swept wings. Modifying or thickeningthe airfoil sections of the triangular wing (nmdels I.1and 18) seems toresult in somewhat less smooth variations in damping with Mach number.

The results for model 17 show that the orientation in roll of thecruciform wings and tails with respect to each other had a significanteffect on the damping. It has previously been shown in reference 36that the tail bending of a configuration similer to model 18 appreciablyaffected the damping in roll. It is probable that tail flexibilityeffects also influence the pitch dsmping. .

Canard Configurations

It appears that for the canard configurations shown, the experimentaldata are less amenable to accurate prediction, probably because of largeinterference effects and in the case of model 22 by nonlinemities in allthe aerodynamic characteristics. Practically no experimental data areavailable at transonic speeds on the downwash and interference effectsapplicable to canard configurations.

The contribution to the damping coefficients of the downwash causedby the canard lift increments C~

qand C% was appreciable for all the

canard configurations considered ad it appears that this effect shouldnot be neglected for any configuration in which the forward lifting sur-face is at a large distance (either forward or rearward) of the centerof gravity.

Agreement of Calculations qd Experiment

It has been generally shown that a computation of the danq?ingcon-tributed by the tail can be made and it will agree reasonably well withthe experimental damping. If it is assumed that the downwash lag effectof the wing on the tail Is that effect caused by the change in downwashin the finite interval of time required for air to travel from thetrailing edge of the mean aerodynamic chord to the tail rather than fromthe center of gravity to the tail, then the damping due to the tail willexhibit better agreement with experimental data and will be a more con-servative estimate.

20

—-.NACA RM L52K20

There exists no suitable means of calculating the.wing contributionto damping in the Mach number region from 0.80 to l.~.and a smoothlyfaired curve through this region from subsonic to supersonic speeds isof no value except possibly for triangular wings having rounded airfoilsections and which are not in the presence of a wake from a canardsurface.

The means of calculating the isolated surface con~ribytion to”’ .hamping by using references 5 to 8, 11, and 12 general~y give valuesthat are nonconservativebut are in reasonable agreemefitwith experiment ‘“if used within the limitations imposed by the theory.

It should be noted that for computatio~of wing damping at super-sonic speeds, acceptable results are obtained only if TC% and C~

are both used since the effects are generall-yin opposite directions.Computations of the damping derivatives for swept wings at lower super-sonic ~ch numbers by use of references 7 and 8 are extremely limited bythe theory.

—..-—

—.-

——

——

—.-

CONCLUSIONS

From a study of the pitch-damping derivatives mea=med in flight o~about 33 models and full-scale airplanes of widely differing configura-tion and geometric characteristics,the folltiing genera”lconclusionsare offered.

.- -.

2. No suitable means exist for calculati~ the wi~ damping in thetransonic region and a smoothly faired line between the subsonic and

.

supersonic values will, in most cases, not conform to the experimentald’ataand will probably give an unconservative result.

2. The damping contributio~ of unswept and swept wings of 45° or “--”--less sweep is erratic in the transonic regio~”and may be either positiveor negative, leading to possible dynamic instability for tailless .configurations.

3. Cofii~ations with triangulw ~d sw~pt w~gs having approxi- .mately 600 sweep of the leading edge and rounded airfoil.sections exhibitfairly smooth variations of damping in the transonic region.

4. Calculations of the damping for configurations that have a hori-.-=

zontal tail surface appear to give the best agreement with the experi-mental data i.fthe distance from the trailing edge of the mean aerodynamicchord of the wing to the tail is used for computing the downwash lag.

NACA RM L52K20 21

5. Damping moments resulting from the downwash on a rear liftingsurface caused by the lift increments on a forward surface proportionalto the pitching velocity and the rate of change of ~gle of attack maybe appreciable if the forward surface is at a large distance from thecenter of gravity, as on a canard configuration.

It is believed that no detailed conclusions are warranted because.afthe unsystematic nature of the data and the effects of relativelyunknown factors such as experimental accuracy, nonlinesrities with liftcoefficient and oscillation sarplitude,and the effects of oscillationfrequency.

Langley Aeronautical Laboratory,National Advisory Committee

Langley Field, Va.for Aeronautics,

22 NACA RM L52K20

REFERENCES

—

1. Triplett, William C., and Van Dyke, Rudolph D., Jr.: F&eliminaryFlight Investigation of the Dynamic Longitudinal-Sta.bilityCharac-teristics of a 35° Swept-Wing Airplane. NACA RMA50JOgal 1950.

2. Sadoff, Mel~in, Ankenbruck, Herman O., and O’Hsre, William: Stabilityand Contfol Measurements Obtained During USAF-NACA CooperativeFlight-Test Program on the X-4 Airplane (USAF No. 46-677). NACARMA51H09, 1951.

3. Gillis, Clarence L., Peck, Robert F., andVitale, A.,J~es: Prelimi-..—

nary Results From a Free-Flight Investigation at Transonic andSupersonic Speeds of the Imgitudinal Stability and Control Charac-teristics of an Airplane ConfigurationWith a Thin Straight Wing ofAspect Ratio 3. NACA RM L9X25a, 1950. —

.

—

-—

4. Jones, B. Melvin: Dynamics of the Airplane. Symmetric or PitchingMoments. Vol. V of Aerodynamic Theory, div. N, ch. II, sees. 37-44,W. F. Durand, cd., Julius Springer (Berlin), 1935, PP. 48-54.

5. Harmon, Sidney M.: Stability Derivatives at Supersonic Speeds ofThin Rectangular Wings With Diagonals Ahead of Tip Mach Lines.NACA Rep. 92.5,1949. (SupersedesNACATN 1706.)

6. Ribnerj Herbert S., and Malvestuto, Frank S., Jr.: Stability Deriva-tives of Triangular Wings at Supersonic Speeds. NACA Rep. 908,1948. (SupersedesNACATN 1572.)

7. Malvestuto, Frank S., Jr., and Hoover, Dorothy M.: Supersonic Liftand Pitching Moment of Thin Sweptback Tapered Wings Produced byConstant Vertical Acceleration. Subsonic Leadi~g Edges and Super-sonic Trailing Edges. N4CA TN 2313Y 19%.

8. Malvestuto, Frank S., Jr., and Hoover, Dorothy M.: Lift and PitchingDerivatives of Thin Sweptback Tapered Wings With Streanndse Tipsand Subsonic Leading Edges at Supersonic Speeds. NACATN 2294,1951.

9. Tobak, Murray, Reese, David E., Jr., and Beam, Benjamin H.: Experi- -mental Damping in Pitch of 45° Triangular Wings. NACA RMA50J26,1950.

10. D’Auitolo, Charles T., and Parker, Robert N.: preli~nary Investi--gation of the Iow-AmplitudeDamping in Pitch of Tailless Delta-and Swept-Wing Configurations at Mach Numbers From 0.7 to 1.35.NACARM L52G09, 1952.

.

a#!mk@t&tRwQ i

NACA RM L521C20 23

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

Toll, Thomas A., and Queijo, M. J.: Approximate Relations and Chartsfor Low-speed Stability Derivatives of Swept Wings. NACA TN 1581,1948.

Fisherj Lewis R.: Approximatepressibility on the SubsonicNACATN 1854, 1949.

Jones, Robert T., and Fehlner,

Corrections for the Effects of Com-Stability Derivatives of Swept Wings.

Leo F.: Transient Effects of theWing Wake on the Horizontal-Tail. NACA TN 771, 1940.

Ribner, Herbert S.: Time-Dependent Downwash at the Tail and thePitching Moment Due to Normal Acceleration at Supersonic Speeds.NACA TN 2042, 1950.

Mitchell, Jesse L.: The Static and Dynsmic Longitudinal StabilityCharacteristics of Some Supersonic Aircraft Configurations. MCARM L52A10a, 1952.

Beam, Benjamin H.: The Effects of Oscillation Amplitude and Frequencyon the Experimental Damping in Pitch of a Triangular Wing Having anAspect Ratio of 4. NACA RMA52G07, 1952.

-.

Mitcham, Grady L., Crabill, Norman L., and Stevens, Joseph E.:Flight Determination of the Drag and Longitudinal Stability andControl Characteristics of a Rocket-Powered Model of a 600 Delta-Wing Airplane From Mach Numbers of 0.75 to 1.70. NACA RM L51104,1951.

Henderson, Arthur, Jr.: Pitching-Moment Derivatives Cq and C%

at Supersonic Speeds for a Slender-Delta-Wing and Slender-Body Com-bination and Approximate Solutions for Broad-Delta-Wing andSlender-Body Combinations. NACA TN 2553, 1951.

Smith, C. B., and Beane, Beverly J.: Dsmping in Pitch of Bodies ofRevolution at Supersonic Speeds. Preprint No. 311, Inst. Aero.Sci., Feb. 1951.

Gillis, Clarence L., and Vitale, A. James: Wing-On and Wing-OffLongitudinal Characteristics of an Airplane Configuration Havinga Thin Unswept Tapered Wing of Aspect Ratio 3, As Obtained FromRocket-Wopelled Models at Mach Numbers From 0.8 to 1.4. NACARM L50D6, 1951.

Parks, James H.:Model AirplaneWing. NACA RM

Icmgitudinal Aerodynamic Characteristics of aConfiguration Equipped With a Scaled X-1 Airpl~eL51L10a, 1952.

24

22.

23.

24.

25.

26.

27.

28.

29.

30.

NACA RM L521C20

Mattson, Axel T., and Loving, Donald L.: Force, Static Longitudinal

Stability, and Control Characteristicsof a ~ -Scale Mdel of the

Bell X3-l Transonic Research Airplane at High Mach Numbers. NACARM 18A12, 1948.

Vitale, A. James, MeFall, John C., Jr., and Morrow, John D.: Lorlgi-tudinal Stability and Drag Characteristics at Mach Numbers From 0.75to 1.5 of an Airplane Configuration ~ving a 600 Swept wing of”Aspect Ratio 2.2&As Obtained From Rocket-Propelled Wdels.. NACARM L51K06, 1952.

— —

Chapman, Rowe, Jr., and Morrow, John D.: Longitudinal Stability andDrag Characteristics at Mach Numbers Frgrn0.70 to 1.37 of Rocket-l%opelled Models Having a Modified Triangular Wing. NAcA I?ML52431, 1952.

Peck, Robert F., and Mitchell, Jesse L.: Rocket-Model Investlgation”-of Longitudinal Stability and Drag Characteristics of am AirplaneConfiguration Having a 600 Delta Wing and a High Unswept HorizontalTail. NACA RM L52@k3, 1952.

Parks, James H., and Kehlet, Alan B.: Icu@tudinal Stability, Trim,and Drag Characteristics of a Rocket-l%opelled Model of an AirplaneConfiguration Having a 45° Sweptback Wi~ and an Unswept HorizontalTail. NACA RM L52F05, 1952.

D’Aiutolo, Charles T., and Mason, Homer P.: preliminary Results ofthe Flight InvestigationBetween Mach Nu?ibersof Q.80 and 1.36 ofa Rocket-Powered Model of a Supersonic Airplane ConfigurationHaving a Tapered Wing With Circular-Arc Sections and k(l”Sweepback~NACA RM L50H29a, 1950.

Mitcham, Grady L., and Blanchard, Willard S., Jr.: Summary of theAerod~amic Characteristics and Flying Qualities Qltained FromFlights of Rocket-~opelled Models of an Airplane configurationIncorporating a Sweptback Inversely Tapered Wing at Transonic andLow-SupersonicSpeeds. NACA RM L50G18a, 1950.

Hall, James R.: Free-Flight Investigation of LmgitMdinal Stabilityand Control of a Rocket-Propelled Missile Model Having Cruciform,Triangularj Inline Wings and Tails. NACA RM L51J17, 1952.

Edwards, Samuel Sherman: Experimental and Theoretical Study ofFactors Influencing the Longitudinal Stability of an Air-to-AirMissile at a Mach Nwiber of 1.4. NAcARMA51J19, 1952.

.

—

--

-.

.

-.

1

ML. liACARM L52K20

-!+.. *.

k-”” +fiir.

31. Moul, Martin T., and Wineman, Andrew R.: Longitudinal Stabilityand Control CharacteristicsFrom a Flight Investigation of aCruciform Canard Missile Configuration Having an Exposed Wing-

~ Canard Area Ratio of 16:1. NACA RM L5D2b, 1952.

32. Brown, Clarence A., Jr., and Lundstrom, Reginald R.: Flight Investi-gation From Mach Nuniber0.8 to Mach Numiber2.0 To Determine SomeEffects of Wing-To-Tail Distance on the Longitudinal Stability andControl Characteristics of a 60° Delta-Wing - Canard Missile.NACA RM L52C26, 1952.

33. Angle, Ellwyn E., and Holleman, Euclid C.: Determination of Longi-tudinal Stability of the Bell X-1 Airplane From Transient Responsesat Mach Nunibersup to 1.12 at Lift Coefficients of 0.3 and 0.6.NACARM L50106a, 1950.

34. Merrill, Charles P., Jr., and Boddy, Lee E.: High-Speed Stabilityand Control Characteristics of a Fighter Airplane Model With aSwept-Back Wing and Tail. NACA RMA7K28, 1948.

35. Holleman, Euclid.C.: Longitudinal Frequency-Response and StabilityCharacteristics of the IXmglas D-558-II Airplane AS DeterminedFrom Transient Response to a Mach Number of 0.96. NACARM L52E02,1952.

36. Hopko, Russell N.: A Flight Investigation of the Damping in Roll. and Rolling Effectiveness Including Aeroelastic Effects of Rocket-

Propelled Missile ~dels Having Cruciform, Triangular, Interdigi-tated Wings and Tails. NACARM L5H)16, 1951.

.

. . —

Bfa.lel

1

:9

10111.2

1314U

1617

18

19

2021

22

Airplane

TABIX I

AIRFOII 6EKT.UX CRARA~IC2

(Mee.eurfM pre.llel to free 6tream unless otherwise stated)

Type Bedim

m

EAcA

Round noee

HEm&nalHexa&mal

RAcA

RAcA

HAM

EACAIim4

MACA

Hexagonalmu

Circular F1l’C,

~cflRound nose

RACAImble vedge

HACA

EexagcmdHe.xa@nel

Dmble we3ga

Type section

lulx

MoAIwc4

MuiOer or prcenttbickmem at mot

65(@fM6.5

M07-63/3n-9.5° ma.

‘$ALp

4.54.5

62(06)Ac@.5

.&H&3

65Ao06

OLM, ma. to 3.5

65( 06~3

m4&?6

5

7.56

65M09

66(&02.64

3.1

;:.;

Rulnh- or percatthicknws at root

&LIL%

W1O-64

001.2-64 @.63-o1o

Rmber or percent

tbicknem at tip

L5

65(g4$.5

@Qo6

“m6

14$9,66-006

9.39.3>.0

mmhr or percentthickness at tip

L%-109

(K)1O-64

ml-at m%l.

631-01.2

R6a?ukM

Xfor!ml ta O.ya%

Radii at break llnea

Eonml i% O.&

R-kc

normal to 0.2%2

H- to 0.30C

.

1

.

NACA RM L52K20 ““‘“--“-i”iapiiFiMRw

TABLE II

RJZDUCED-FRE-CY RANGE

FOR DA!I!APRESENTED

Model . Range of w/ZV

1 0.0212 0.02582 .0287 .0455

.0186 .0217; .0118 .01265 .0046 .00536 .0119 .0135

.0081 .0108; ● 0050 .00729 .0081 ● 009710 .0122 :012$?11 .0161 .016912 .0165 .017813 .0054 .015614 .0168 .020715 .01.64 .024116 .0151 .027317 .0069 .013418 .0089 .010619 .0209 .029520 .0103 .01252i .0058 .008622 .0081 .0100

Airplane Range of w/2V

1 ---.-- ------2 0.0449 0.05393 .0155 .03104 .0SL7 .0162

27

NACA RM L52K20

-(

> &Jo .

/_ 7-—1- -45.69

.- --

-13.1

M,AC,

Y - 3

—

-.

—

Center-of-gravity lomtion

NOclelAwing

20 percent M.A.C.A

ldodel 8 25 percent M.A.C.s, aq ft

M.A.O., in.

8

6

4

%q+ %&)

2

- %&

o

-2

2.81

6.25 ‘

26.28

.

--

All dimensions are in inches.

.

.7 .8 .9 1.0 1.1 1.2 1.3 - 1.4” 1.5 - 1.6 1.7 1.8M

.

Figure 1.- Geometric characteristicsand d~pingcoeff~cient6for a- ““ “’”~““-600 tria.ngularwtigaircraft configuration (nmdel 1). .

.

N.ACARM L52K20

L10.894

E +----+-!

29

‘-’w)!)!:-:‘:Center-Of-gravity location K.A.C., in. 21.90

Model A 16.7 peroent M.A.C.

Model B 9.8 peroent )f.A.C.

I

2

.L

-(qq+ cm;)

o

-1

-2

All dimensions are in inches.

\Refa. 7 and 8 (swept-tapered wlng)- ~

t- ~ <Y..L~. -Ref. 6 (triangular A=2.01)

--—

. . I .7

[1

m

8

.-,. .

~Ref. 6 (52.5°trhngular wing)

c I

o =zS==-

Q—-—

G1 ———-—OModel A

EIKodel Bm

.7 .8 ●9 1.0 1.1 1.2 1.3 1.4 1.5 1.6M

Figure 2.- Geometric characteristics and damping coefficients for atailless aircraft configuration (model 2).

—

wing

A

s, aq rt

M.A.C., in.

16

12

e

-(cmq+c%) 4

0

-4

-8

-12

NACA RM L521G20

6.00

3.8S

9.s5 center-or-gravitylcmtlon

Model A -86.7 peraentu.A.C.

Modal B -*.7 pea-centMx. c.

~67.70

All Cllmenslonsare in bakes.

.

—

.

— —

Sxperlmntal (flexiblewing”II

EEEL----

.

./’ -.\ I I/1 t

v /“

\

I/

\ -.\

i’

/\

/ ‘\‘\ r

! ! I \ I / \! b

w I /! I

I I

1111 ~lJ!/\ -----Model BI ! I

w“’’’’ ”-;I I

t(

,, I i tII

I I I I I--’J%YY

,. /4 I I I / I I I f r

/“ ‘Experimental(hunt flexiblewins]

w II

.

.- .7. . .8 .9 1.0 1.1 ~ 1.2 1.3 1.4 1.6 1.6

Figure 3.- Geometric characteristicsand dam~ing coefficients for a —45° sweptback wing and body configuration (model 3).

.

NACA RM 152K20

/

-13.2550.72

~

28.16

)’ / I/ / -—-, ..I \

L\\‘4\.

MAG

12.25.

\ .\

Center-of-gravlt~ location u—————J—

-78.8 percent M.A.C. 45.3 &

6.8

—

1= 4 Ak 80”’0 ~

.(% + Cm&)

All dlmnstone are In i.nchea.

wing

A

s, Sq ft

H.A.C., In.

16

12

\

/ -

8

\, A -

- Experlmentnl

4 ,

DCalculated (wing m.lone)-~

0 ,.8 .9 1.0 1.1 1.2 1.3 1.4 1.5

M

31

5.5

3.27

9.84

Figure 4.- Geometric characteristics and damping coefficients for ak50 sweptback wing tissile configuration (nmdel 4).

.

32

-- 8.09

3.23

———

1.55-

HorizontalCenter-of-gravity looation

52.8 peroent body length-— A

s, Sq ft ● 67

6.01”M.A.C., in.

7.00

t

~G:8*:. ;

,

---- -_=—. ---

..

.;

All dlaenslons are h lrmhes.—.—

Notes Coef~iclents are based on wln~ area and wing chord of model 6.

..?

32~,. .

ITheoretical (Cmq + C&)- \ !lheoretleal

%

\/ “

\ , “ ‘J \ \

- -t- -\ ~ — “-- -=

<.

-—-

:

\ \

-- ~ ‘ ---1—- ---

calculated c% (tull)~ - Experimen twl

=wi%=-

24

-(~ +C.d)

16

- Gmq

8

n

.7 .8 .9 1.0 1.1 1.$? 1.3 1.4 1.6 1.6

M

Figure 5.- Geometric characteristics and damping coefficients for awingless body and horizontal tail combination (model 5).

.

.x. .

+16.19+

.~

36.04

!.— —

“

O.zse 9Center-of-gravity location

Model A =.4 percent M.A. C.

Model E 12.4 percent M.A.c.

7.00

~, i

.

All dimensions are in inches.

33

wing

A 3*OO

s, Sq ft 2.68

M.A.C., in. 12.03

Horizontal Tail

Same as mcdel 5

40

—-7——s — Model-A

—-—, ——,—-- M~el B

32~ - Experimental (flexible wing)

/- -Experimental (rigid wing)

?.

r -Calculated (tail) I

24 - I \ I

t- -.+% --- _‘-=E=--

1/ -/ ‘

/ +- .— -16 , / . / <

— ~

\i \ \ \

L

0‘ 4

Inorement due to L . Oaloulated (tail plus wing)wing C and ~

%i kl Io , I I -- e.7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.6 1,9

K

Figure 6.- Geometric characteristics and damping coefficients for anaircraft configuration having an unswept tapered wing with ahexagonal airfoil section (mdel 6).

NACA RM L52K.20

L16019+~6.48~ - .-

1

~F

38.04 36.42—

I.—-—

\

3.11

0.25a Ywing

Center-of -gravl tg location -A 3.00

12.4 percent M.A.C. s, sq rt 2.66

M.A.C., In. 12.03

Horizontal Tail’

same as mdel 5

.(% + c%)

—

All dimenaiona are in inches

40I I I I I I I

● ✎✍✜

24

I

16 . I .~ I I 1X1 I I I I I I I

1! \‘Calculated (tail)

r

\ /aloulated (tall plus wing)

I / L \\

I 1 I

/ \8 1 t I

/f ‘

I

I I z Experimental (low lift) , ,~-

.7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.6

K

Figure 7.- Geometric characteristicsand damping coefficients foran aircraft configuration having an unswept wing with anNAC!A65(06)AOO~.5 airfoil section (model 7).

.

.

NACA F/ML52X20. .

0.250 -h‘1‘~

42 .77

.84-9

r

Center-o%gravlty looatlon

16.3 peraent H.A.C.

7.00

i

Ul dl=ensfons are in inohes.

1s4)

120

.(%+ CM) ~

40

0

Wing

A 6.02

s, sq rt 2011

M.A.C., in. 7.36

Horizontal Tall

Same aa model 5

I ~calculated (tail pluawlng)l ~Experimental (high llft)

v ./ —Hxperlmental (low 11.ft)

\ h.*

/ */

I I I

\\ I i’/ I

t-t-t

33

I -M--l’ I I I qcalc.late~(t~lDl~wfwl

.7 .8 .9 1.0 1.1

M

Figqre 8.- Geometric characteristicsaircraft configuration having

1.2 1.3 1.4 1.5

and damping coefficients for anthe x-1 wing (model 8).

--

Wi! yj~

36 NACA RM L52K20

+7.37+-k_ -,

1/1c/4

,/’v 4*

T::-

‘\

-9.5

Center-of-gravity locationt

Model A—

2X,9 percent M.A.C..—

Wing —

Model 3 4.6 percent M.A. C. A“ 4.00

s, aq rt 2.69

7.00 M.A.C., In.

t

10.05

-. — -. Horizontal Tail - ‘“ “. ‘.

# \\Same as model 5

90.26

80

64

48

-(qq+ Cmd)

32

16

0

All dimensions are in inches.w.

Experimental (flexible wing

q ‘ —“-—~— ._;_ Model A

/1II —---7- —--Model BI —.

{:1 Experimental (rigid wing)

t

Calculated (tall)r

/ I I4 Y

=E=?-----p \

7 - -/

/ -r

r- *

i \ ~.I ----

/ >

Calculated (tail)J/{

Calculated (tail, theoretical)~

.7 .8 .9 1.0 1.1 1.2 r.3 1.4 ‘1.5

.

—

.

M

Figure 9.- Geometric characteristicsand damping coefficients for”an~. .. ..

aircraft configurationhaving a 450 sweptback wing (model 9).

NACA RM L52K20 37

.

A

—18.63A

&- 31.19

.-~ f 28. S0

-..

-11.77

1\

iYlngCenter-of-gravity loohtion

A-4 percent E.A.C.

2.24

s, Sqft 2.58

M.A.C., In. 14.10

7.00 Horizontal Tall

i Same 6LS model 5

All dimensions are in inches.

32Calculated (wing plus tail)

Calculated (tail, theoretical) /

24 /- /

-Experimental\ /

— /_ -“ \ I

16\ /

/ —— — b . — --

/ “~

8 } ‘y ‘

Calculated (tall)~

~-

0.7 .8 .9 1.0 1.1 1.2 1.3 1.4 L 5 1.6

Figure 10.-aircraft

M

Geometric characteristics and danmiruzcoefficients for anconfiguration having a 600 sweptb=ck-wing (model 10).

—.

,, .J--%-.?.-

maE!E#kT+

2.46

&

33.52

- ~:-.

9.5-+M.A. C.

NACA RM L52K20

,..

.-j

Center-of-gravl~ location

13.2 percent M.A. C.

7.00

~,o=.

All dimenalans are in inches.

32

24

16

8

0

-.

-. :

Wlna

A 2.53

s, Sq I-t 3.14

kA.c., in. 16.40

Horlzontd Tall

game as model 5

I I I

=@=’-

Calculated (wing plus tall+ 7n J r/,

- — \7c > ~

-

Calculated (tall)J

●7 .8 .9 1.0 1.1 1.2 1.3 1.4 195

M

Figure 11.- Geometric characteristicsand damping coefficients for anaircraft configuration having a modified triangular wing (model 11).

.

.

.—

.:

.

.

●

NACA RM LZIC20 39

-----

Center-f-gravity loaation

20.5 percent M.A. C.

All dlrenelms are k inohes. Same as model 5

-(q+ C&)

Figure 12.-aircraft

16 -

.Oalmlated (low lift)(wing plus tall)

X2 -Experimental (high lift)

Oaloulated (high lift)

8(wing plus tail)

/

/“ -

-u

4 -calculated (tail) J

Experimental (low lii%)— —

0.7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5

M

Geometric characteristics and damping coefficients for amconfiguration having a 600 triangular wing (model 12).

—

—

-- ..

40.

-1.kwJf

j~~n(j i-“106.5 6.6

64. N.

11-8.0m

3.9

t

M.A. C.

2.8 ~..,—

7“— -—- ------ - 18.6 ““-

My

2 :..,.

Center-of-gravity Iaoation 20.3A

NAC!ARM L.52K20,

. ..-

—-m

.—

-. -...,— ;

Wing g

3.0Mode 1 A

10.4 percent M.A. C.

n r8”0 s, Sq rt 4.26Model B -15.0 peroent 16.A.C. .-

.LX.A.C., in. 15.1

-—

-~j~: :::::: “’”:

All dimensions are in inches.

.

50— -.

I — Model A

—-—40

,——,------ Model BExperimental (low lift)

//

30 /\ \

-(%q+ oma)/’

\\,Calculated (te,llplus wing)

/<-.

20

10 Calculated (tail}””

Experimental (high llft)–=E=

0

.7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5

M

Figure 13.- Geometric characteristicsand damping coefficients for asupersonic aircraft configuration (model 13).

.

.

t

6H

.

.

NACA RM L521S20 ‘“’ “A+&&f #j&$j$$j$_+

~12.E&.l-?6.63

1wing

Center-ofqavlty looatlon A 4.00

0 percent M.A.C. s, aq rt 2.77

K.A.C., in. 10.21

I Horizontal ‘Eail

s, sq rt .55H.A.C., In. 4.3s

All dimensions are in inahes.

*

b

40

Calculated (tail, unnmdifled formula)7

..

b

32

24

-(~+ f&)

16

I /.- /

/ - /\‘.- -~.lA

., , v

A I I [ I I A I I -. fl

II Exnn~%menkal 1 .I I_.r..-—....—_

I! I I I P A-

I I

Calculated (tail, modified formula) L /

8 I I I

~-0

.6

Figure 111.-aircraft

.7 .8 .9 1.0 1.1 1.2 J1.3 1.4

M

Geometric characteristics and damping coefficients for anconfiguration having a 45° sweptback wing (nmdel 14).

.

-...<

42

““””rNACA RM L52K20

I

,L__ ; ~“~’24.41 33.3840; ~oo /“ 7

/ -%. 22.50

\ --

d “k I

56. 56.

18.848.03.

\ 4.82\ \

‘“A”C”NLJ.H..wing

4.00

6.56

14.64~9.4+

—------ ,_ .-.

Center-o f-gmvity location ~

1o.9 percent M.A.C.

7.00 Horizontal

Figure 15.-aircraft

All dinensfona nre in inches.

Tall

3.72

.938

6.27

12.

, , I

d \ Calculated (tail plus wing)8 . — -—

Calculated(tail) -7- - . \ /

4 L /

4- -

2xperlmental - J

\. / - — —- .

0. t

●7 .8 .9 1,0 1.1 1.2 1.3 >.4 1.s

M

Geometric characteristicsand damping coefficients ofconfiguration having a 40° sweptback wing (model 15).

an

.

—

4

—.-

. .

4

N/WA RM LZIC20

+23.18,+0.60C

414.2 /

~~~

7.72

/

1-

it-_ – !{

69.4440 T

t / 30.00

~L-y\

\ \

1

!56.40@

U.A. C. \

\

5.s

43.44 M.A.C .\\

Center-of-gravity locatlon

Model A 12.5 percent M.A. C.

Model B 5.6 percdnt M.A.C./7

wing

A

s, Sq rt

M.A.C., in.

Horizontal

A

s, aq ft

M.A. C., in.

43 “-

3.07

7.20

19.08

Tall

3.98

1.57

7.72

All diuenslons are h inches.

—.— 9 Model A------ Model B

24

Calmlated (tall plus wing)

.7 .8 .9 1.0 1.1 1.2 1.3

M

Figure 16.- Geometric characteristics and damping coefficients of anaircraft having a k(l”sweptback wing that incorporates inversetaper (model 16).

&35.11

.— . .

F13.82

Center-of-gravity location

25.0 percent M.A.C.

7.00

~’o*’’”-” ‘““

.(C% + c%)

All cilmensions are in inches.

40

I I

Measured (1OW lift)

32r —

I~ “ Meastc”od (hi@ lfft)J

fCalculated (ball)

124 ,0

--

/ ‘

/

/ y16 \

.

r ‘ --- – - -

u

8 ~- calculated (tall PIUS ~in6)

o I I.7 .; .9 1.0 1.1 1.2 1 ●3

A

Wine

6.Oil

.

—

.-9, Sq I-t S*I38

—=.

M. A.C., in. 9.85.-

Horizontal tall

A 4.00

S, sq ft (h chordplane ) .90

.

M. A.C., in. 6.05 —

Dihedral -zoo

—.

.-

‘-35= ““-””-

M

Figure 17.- Geometric characteristicsand dsmping coefficients for “an~ .._aircraft configurationhaving a 45° swept}ack wing~model 17).

-. .,.-

.

N.ACARM L52K20

64

48

-(Cmq+ Cm&) 32

16

0

1,/ I-—-

Wing

2.31

z, Sq rt 5.23

Center-of-gravity location M.A.C., in. 24.10

Model A S3.6 percent K.A.C.Horizontal Tall

Model B 60.8 percent K.A.C.A 4.00

s, Sq ft 2.19

M.A.C., in. 11..S3

All dimensions are in inches.

. .. . ~ Experimental (lnterdlgltated tall)

// t

\ wing plus tail/ \ ~ OeIculated ( theoretical\ )

\ - ---- w ---—.

I Y —

Calculated (wing plus tail)

~ Experimental (inline tall)\-

-

I‘\

Calculated (tail) 1>

— #—. _ ,—-–,— --Model A

-------heel B ‘--+@=-L II

.6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

Figure 18. - @ometjric

600 triangu~r

K

characteristics and damping coefficients of awing missile configuration (model 18).

Center-of-gravity looatlon

Station 56.98

I

40.56

8

6

4

2

All dimensions are in inches

NACA RM L52K20

—

KlnG

.b.—

A 1.87 —

s Sq I-t..

6.12

M.A.C., in. 26.94

Canard

A (in chord plann) 1.R7

8, sq ft. (in chord ‘“ -plane) 1.08

M.A. C., in. 11.s3

D!hedral ~~o

-. :

.

II I

- Experimental

/ ‘

i“— _

/ ‘

/ — — “

J —Inorement due- to oanard C

%“ind cL&

- . I —- 1 I

0.8 .9 1.0 1.1 I.e 1.3 1.4” 1.5 i.lj 1.7

b

-. .. ..—,

M.

Figure 19.- Geometric characteristics and damping coefficients for amissile configuration having a modified 600 triangular wing andcanard surface (model 19). %

N.Am RM L52K20

.

ad ..2 ~-—13.00-— —~ —-.-

31*IM.

- 9.02~ ‘ M.A.C.I wing

w~Model 20 Model 21 A

Dimension a 29.S0 69.343 S,sq ft

Dlmermlon b 114.20 154.20 M.A.C., in.

Center-of-gravity station ~.00 91.s0 Oanard

7.00

i AA

S,sq St

2.s1

2.S455

17.62

2.31

.s0

M. A. C., in. 7.50

f

+

b~Ml dImensl@ns are L! inches.

48

\

40 1 \ I 1 1 I 1 t I \

v 4- /

1-+

L .Experimental ~~-~:$ _’

\ ,-

321

\/r

-—

\ Y _-.

k /.

Wdel 21 \ .

24 Theoretical — ~ r\

G&) \ ~ ‘O.slculated /

16 + — — — — — — y - - - — -\ ~ - +

// /

8 / 2 -Model 20

/{Ex erlmental— ~/

=@@=-C!z~culated

0.8 .9 1.0 1.1 1.2 1.3 1.4 1.6 1.6 1.7 1.8 1.9

M

Figure 20.- Geometric characteristics and damphg coefficients for twomissile configurations having 600 triangular wings and canard surfaces(nmdels 20 and 21).

-.

- 8.23 -~12.s9

z12.e8- 37.44 + 3.s

?16.60 t

v\

Center -Of-gFavity location

Model A Station 38.6

Model B Station 40.4

5.68

/n t7-

—-— -

!

200

160

120

-(c% + c%)

20

40

0

NACA RM L52K20

.

wing

K “aqft

it. A.C., in.

.-Canmd

A

s; Sq rt

M.A.C., in.

All dimensions are in inches.

Madel A (law lift)CalculatedExperimental .

{

J\

- -& \

\ -

/ /f . .---- #/-..- \

R> -.=

/ ,-.

Inorement due to Oanar~ CL

3.02

1.422

9.20

.7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

M

Figure 21.- Geometric characteristicsand damping coefficients fora missile configuration having essentially unswept wings andcanard surfaces (nmdel 22).

“3.i4

.682 - —

5.S6

...

k

.- -_

—

.

.

*

—

—

L-”

‘7H

.

●

.55+

Center-of-gravity locatlon

23 peroent K.A.C. 3.0=UL n

wing

A 6.0

s, aq ft 130.Q

M.A.C., ft 4.76

Horizontal Tail

A 5.0

s, Sq rt 26.0

All dimensions are in feet.

.

.

~I J Calculated (wine DIUS tail)

.

.

-(c%+%)

Experi.mental(reference 33OL

16I 1% I /1 11/

m-. [ [/1

I t I 1t

8\,~ I I

‘b -Calculated (tail) .

n I II

.7 .8 .9 1.0 1.1 1.2 1.3

M

Figure 22. - Geometric characteristics and damping coefficients for theX-1 airplane (airplane 1).

50

-+

-41.570

5.21i

4.674~k

Center-of-gravity looation

19’.5 peroent M.A. C./7

All dimensions are in

-(%q+ C&)

2

1

0

-1

.2

NACA RM L52K20

— —— -.

.

feet.

------- .

c1 El [3r

c) E1 r El9 El

●

Calculated EXp . +–Ill

.3 .4 .6 .6 ●7 .8

M

Figure 23.- Geometric characteristicsand d~>ingX-4 airplane (airplane 2).

~~’ “

.9

wing

A 3.8

s, aq rt 200

M.A.C., ft 7.81

..

,

.

—

—

,

. .*-co”efficientsfor the ‘-” “-””—

—

.

.

NACA RM L521C20 ““’’””E@--

0.25c

350 14 f * 3.80

Tf 12.eg\\

K1

37. 10

1.71 + ~

Center-of-gravity location 45.28~

22.5 percent M.A. C.

-(cmq+ c%)

All dkenslons are in feet.

51

wing

A 4.79

S, eq ft 287.9

M.A.O., f% 8.09

24

— Calculated (tail PIUZ wing)16

/ -Experimental1 rir

~ . .

8

!

~ — — — —

L -Calculated (tall)\

o

Horizontal Tail

A 4.6S

S, eq ft 3s.0

U.A.C., ft 2.89

Tail length, ft 18.12

.6 .7 .E1 .9 1.0 1.1 1.2

M

— —.—

Figure 24.- Geometric characteristics and damping coefficients for theF-86 airplane (airplane 3).

-. .-7.,.

52

-9.04

* 25.00

,/

(-\\

0.25u

Center-Of-~avity location

25.o peroent M.A.C.

~-

-(.C% ~+C. )

““oo~

All dimensions are in feet

—

Experimental

“21,000 to_25,000 ft

43,000 ft4>~

29,Om

r-37,.S30ft

f 1 1 1 r --,-”- . .

‘Calculated (tall DIUS wing) I

.6 .7 .8 .9 1.0 1.1

M

NACA RM L52K2C)

4

= lrfn.g

A 3.57

s, Sq ft 175.0

M.A.C., ft “7.27

Horizontal Tail

A- 3.59

S,sq ft 39.9

M.A.C., ft. 3.48

Figure 25.- Geometric characteristics and damping deriv~tives for theD-558-II airplane (airplane 4).

—

NACA-Langleg-l-2%5L!-S25

.

--.-

--

.

.