1、SECURITY INFORMATIONf-%- * copy 210RM L52K20RESEARCH MEMORANDUTWSUMMARY OF PITCH-DAMPING DERIVATIVES OF COMPLETE AIRPLANEAND MISSILE CONFIGURATIONS AS MEASURED IN FLIGHTAT TRANSONIC AND SUPERSONIC SPEEDSBy Clarence L. Gillisand Rowe Chapman, Jr.Langley Aeronautical LaboratoryLangley Field,Va.cus91Fm
2、D DOCUMENTlM9n!aarmc0ntainmMamam0ntfracwtim FmlOmlmfanmcdlbudtedstawswlttiatb IcLmlr#04quations forand equations (2) and (3), YPM2, lh/sqtime, sec ,reference axis through center of gravity ofperpendicular to plane of symmetryangle of attack, radiansspecific heat ratio (1.40)control-surface deflectio
3、n, degxi . . . . .CL and CmftconfigurationProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-40.)angle of downwash, radians angle of pitch, radians -. =-rate of change of angle of attack, da/dtphase angle, radians frequency of oscillation, radians/seedC
4、Lc%= Subscripts:frtTNACA RM L52w0-.-.forward surface, based on its own area and chordrear surface,based on its own area and chordtail .trinmed, or mean value-.- F.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RI!L%3Q0 . . . . . . . 5TEST AND A
5、NALYSIS PROCEDUREExperimental data presented were obtained in free flight by thefree-oscillationtechnique. 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
6、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.Makin
7、g the usual assumptions of constant velocity, level flight,and linear aerotQnuamicderivatives, a solution of the two-degrees-of-freedom equation of longitudinalmotion of an aticraft can be obtained.For any appropriate quantity such as normal acceleration or angle ofattack, the solution is of the for
8、ma= Cebtcos(ti + q) + The constant b in equation (1) defines the dampingand in terms of the aerodynamic derivatives is givenEquation (2) maybe solved for the sum ofgive(1)of an oscillationby(2)the damping derivatives to -.Sq cmd (3)From the flight tests, therefore, the sum of the damping derivatives
9、 -_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 qusmtitywhich,
10、for rocket models, is angle of attack. Theequation for the damping factor isb= loge /bltz - tl (4)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6where al and a,2 are the amplitudesmeasured fromof u at times t and t2. For rocket-modeltests,NAM RM LZ
11、3C20he 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-attackinformationwas not available from the flQht test so the lift-curverslope was obtained from wind-tunnel tests and equ
12、ation- (1) and (h)would be written in terms of the lift coefficient. The.test and analy-sis method described does not permit separationof the derivatives Cqand CW. This is not a severe limitation,however, be-causethe dampingis always proportional to the sum of the two derivativesregardless of the fl
13、ight 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 magnitu
14、des of which-depend on the radius of gyration in pitch. The inaccuraciesinCmq + CM, as obtaihed by solution of equation (2), are proportionalto the relative contributionof the C term to the totadamping, b. -As an example, the c term contributedas much as two-thirds of the total damping in some ;f th
15、e rocket models, and in a fl-scale test ofan airplane (ref. 1) the CL term contributed about on-half of the -total damping. Present design trends indicatethat the proportion ofdamping contributedby the c term on future airplaneswill more _nearly approach the proportion for the rocketmodels.Other fac
16、tors .-which may contributeto inaccuracies in measuring C% + Cm are non-linear aerodynamic derivatives,disturbances due *O gustg, md any other - .effects on the oscillationpeaks which define the envelope of the curve.Gusts and nonlinearerodync derivativesusually”appe= “asapparent “-changes in the da
17、mping coefficients.CALCULATIONMETHODThe experimentaldamping derivativespresented herein paredwith calculatedvalues from theoretical investigationswherever appli-cable, or experimentaltest data where such are available. It has fre-quently been assumed that all the damping on conventionaairplaneconfig
18、urations 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 ti
19、me required for the downwash discharged .at the wing to reach the tail surface (ref. 4). The damping derivatives“Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM LZK2Q. arising from these concepts are given by the.7equation(%+ c%).=-P+%)(%lJw
20、(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 characterizedby downwash discharged at the center of gravity ofthe configuration. It appears that this downwash lag term might be morerepresentative if
21、it is assumed that the downwash is discharged at thetrailing edge of the mean aerodamic chord of the wing rather than atthe center of gravity. Idification 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 aerodynamiccho
22、rd 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 app
23、reciable 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 dynamicallyunstabl
24、e. Calculations of the damping derivatives should thereforeinclude the wing even though the damping due to the tail may be themajor factor.Additionalof the downwashforward surfacechange of anglethis effect mayincrements in daming-moment coefficients arise becauseon a rear lifting surface resulti fro
25、m the lift on a7)produced by the pitching velocity c and the rate of(k)of attack C . .be calculated asThe damping coef;ic;nts caused by)Zr SrFCs(7)(8)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8where S and are the quantities on whichexpression c
26、an be derived for AC%. The sumcoefficients is then:NACA RM 2K20cm is based. A similar .+.of the two damping-moment-As will be shown later this increment in the-damping drivativessmall for conventionalairplane configurationsbut can be fairlyfor canard configurations. If the forward lifting surface is
27、 atdistance from the center of gravity, the quantity dc -77can beto a close approximationby the expression d%2Zf d*=_L)d= ZdaThe theoretical results used to calculate the pitch-dampingtives for subsonic smd supersonic speeds sre given in references.(9)is very .largea largeobtainedderiva-5 to 8,11, a
28、nd 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 effectivenessand downwashwere used tocalculate the dsmping caused by the tail.In calculatingthe derivative c= the simple downwash
29、 lag coricept ,as given in equation (5) and modified in equation (6) was used at allspeeds. Several refinements to these calculationshave-been consideredin references 13 and 14 but for the present purpose thege refinements a71were neglected because of the uncertainties in the experimentalresultscaus
30、ed by lage possible experimental errors.in some cases and the rela-tively unknown but important effects of oscillation amplitude.RESULTS AND DISCUSSIONThe results of-the flight measti.emenf%siidthe”calcuiationsareshown in figures 1 to.= for airplane and mis”sileconfigurations. Allinformationpertaini
31、ng to one configuration given in-one figure;break lines on the drawings of the nmdels indicatewedge 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 ae
32、rodynamic chord of the wingand are given for the rate terms (q and s the reduced-frequencyrsnge 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 ModelsModel l.- The experimental data f
33、or model 1 are contained in-.refer-.ence 17 and, as-shown-in figure 12 exhibit a smooth variation toughthe transonic region. Theoretical values of +% and c% e. also shown in figure 1 for the pertinent supersonic speeds. The positivevalue of C% at supersonic speeds decreases the Cm damping of thewing
34、 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 investigatedby theuse of reference 18, which does not include the effect of the afterbody,and was found to be ne
35、gligible. 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 we
36、re 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 obtainedin the te
37、st. The data obtained at higher singlesof attack (h% *l.OO)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10confirmed the data for modelof-attack variations. delNACA RM L52K20 ,A at M = 1.34, which was for similar angle-B also exhibited a continued
38、oscillationof .low amplitude (t0.25) similar to that which gave the positive dampingcoefficients for model A. Analysis of these low-amplitudeoscillations,assudng time to damp to one-half amplitudeazinfiniteigavevalues .,of c% + cm as varying from.1.98 to 2.25. The yalues-_ofdpingobtained at higher a
39、mplitudes shown by the data points fir-modelB andlow amplitudes shown by positive data points for model A.are in realityboundaries for the damping coefficientswhere the coefficientsfor the _system depends with certainty on the amplitude of the oscillationandpossibly on the value of the mean angle of
40、 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 ha
41、ving the same aspect ratio as the actual wing, and a tri-angular wing having the same leading-edgesweep as the actual wing. Thecalculated curves are shown for all three approximationsand best agree-meritwas obtained between the calculated52.5 triangul= wing and theflight data.-Model 3.- Data are pre
42、sented in figure 3“for two tailless models “designed to have differentwing flexibilities. These data me from aprogram institutedto investigatethe effects of wing flexibility onlongitudinal stability. The solid.line (modelA) in fi theof damping at M = 1.414 was made by usingagreementwith the experime
43、ntaldata was ,. b“Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-a71Model 4.- Unpublished data for a 45 swept-wing tailless configu-ration are shown in figure 4. ,The wing was a 6-percent-thicksectionconstructed of solid dural. Qualitatively,the sha
44、pe of the curves forg 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 no
45、t.obtainedbelowa Mach nuniberof 0.88; hence, it is not known if the dampingdecreased in a manner similar to that for model 3. One calcated Pointfor the wing alone is shown at a Mach number of 1.38. The calculatedvalueis conservativebut shows poor agreement with the experimental data. Acalculation of
46、 body damping by the use of reference 19 showed the body con-tribution to be small at supersonic speeds because of the aiterbodyshape.Mbdel 5.- The data for model 5 (fig. 5) are from reference 20.This nmdel was a wingless fuselage-tail configurationthat has been usedfor tests of a number of wing pla
47、n 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 comparisonpurposes. The theoreticalvalues of C + cm agree fairly well with the experimentalvalues, .-%!.particularly at supersonic speeds, as does the calculatedv
48、alues of c%of the tail surface (curve labeled “calculated C% (tail)”). The agree-ment of the theoretical and experimentalvalues is somewhat fortuitous,however, because, as shown in figure 5, the theoretical values of Cqare considerablyhigher than those calculated from measured values oftail effectiveness. The theoretical values of C%, which are those forthe 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 refer
