1、,.b 0.INATIONALADVISORYCOMMITIEEAFML TECHNiCALpffa AFBTECHNICAL NOTE 3956 “ (,*T-*,LIFT AND MOMENT RESPONSES TO PENETRATION OF SHARP-EDGEDTRAVELING GUSTS, WITH APPLICATION TOPENETRATION OF WEAK BLAST WAVESBy Joseph A. Drischler and Franklin W. DiederichLangley Aeronautical LaboratoryLangley Field, V
2、a.WashingtonMay 1957Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-L NATIONAL ADVISCRY KMCTEE InllllulmlililaillmAERL. OOL71W3OF SHARP-mTRAWUNG GUWES,WIEt APPIICCATIONTOPENETRATION OF WEAK BLAST WA Joseph A. Ikrischlerand FraziklinW. DiederichSUMMAR
3、YThe lift and moment responses to penetration of sharp-edgedtraveling gusts sre calculated for w5ngs h incqressible and supersonic*-dimensional flow, for wide delta and rectangular -s in supersonicflow, and for very narrow delta wings. By using the two- thus, the lsrge peaks which exist in the lift
4、response atsnbsonic speeds sre duplicated in the acceleration response.The relation between gusts traveling at supersonic speeds aad blastwaves is indicated, and the mnner in which the calculated lift andmoment responses can be used in a linearized approach to the blast-loadproblem is outlined.INTRO
5、DUCTIONThegrowth of theldftand mcment on a wiq entering a stationeryshsrp-edged gust has been the subJect of numerous investigations sinceit was first calculated for incompressibletwo-dimensional flow in Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-
6、,-2 m m 3956references 1 and 2. However, very little work appears to have been doneon the subject of lift and mment responseto traveling s-edged guststhe only published results being those presented for incompressibletwo-dimensional flow tn reference 3.The reason for this shortage of Infmmation is p
7、robablydue to the factthat gusts (ti the Ilteral sense) trs,vellng“athigh peeds sae not likelyto be encountered in practice. However, the lifts and moments due topenetration of traveling gusts can be used tocalculatethe loads andmotions of an airplane or missile dropped from another airplane, of ana
8、irplane crossing the wake of or flying paqt another airplane, of a _helicopter blade traversing the wake produced by itself and the otherblades of the rotor (a problem whdch furnished the motivation for ref. 3),of an airplane flying through a sonic “boomfl”and of an airplane encoun-terln.gor being o
9、vertaken by a blast wave.In the first section of this paper the unsteady lift and momentpursuaut to penetration of a traveling sharp-edgedgust e calcu-lated by linear theory for incompressibletwo-dimensionalflow (by amethod different from the one employed in ref. 3), for two-dimensionalsupersonic fl
10、ow, for delta whgs with supersonic leading edges, forrectangular tings in supersonic flow, and for very narrow delta -sIn .incompresslbleW compressibleflow. The unsteady-liftfunctionspresented here may be consideredto be generalizedunsteady-liftfunctionsin the sense that they include as special case
11、s the two previously calcu-lated unsteady-lift functions: namely, the”“gust-penetration(Iwhich are of first order, sre not taken into account entirely and myrequire sepsrate treatment and neither are the effects of the discon-thuities In density and teqerature taken into account. However, these “eff
12、ects are of higher order andj hence negligible for a weak blast wave.B-a71 .- .-.-:y:-.-.-R.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-llMA m 3956 3a71a15a15 General relations between the lift or moment responses to shsrp-edged gusts (traveldng
13、or stationary) and the responses to Indicial.flapdeflectiom! ere given in the appendix. These relations ham been usedto calcuhte the unsteady-ldft and unsteady-moment functions given hereinfor incompressibletwo-dimmsional flow and to check the results obta3nedfor sane other conditions.Aab(x)C(k)CLCL
14、cm(s)%cclcla%dhKkaspect ratiospeed of soundlocal spanSYMBOISof undisturbed streemTheodorsen functionlift coefficientslope of lift curvepltchimg-mment coeffIcient (steady-statevalue)instantaneousvalue of pitching-mmentpressure coefficientchord, root chord h case of delta wingsection U.ft coefficients
15、ection slope of LKt curvesection pitthing-moment coefficientdis%nce behind wave frontlocal effective stiing speed of wingalleviation factor for sharp-edged gustreduced frequency, m:ccoefficientProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4k(s)k5(s
16、E)kl(E)q(s)1(X)MMe%m%34“%qssttvgwunsteady-liftedged gustsunsteady-llftunsteady-liftunsteady-liftlift per unitMach nmiber,NACA!I!N3956 -” :function for penetration of travelhgfunction fcm indiciaifunction for indicialflap deflectionchange of anglea71sharp- .-*-=-=nof attack =function for penetration
17、of stationarygustlength along chord._ .-.V/aequivalentMach nuniber, M+%Mach nurribercorrespondingto gust propagation speed =slope of leadimg edge, b(x)/2xmass of airplane +.-:=.-.-.l$p)#z=w (xc+M. when it is negative but.speed is positive, theless in magnitude than a71Provided by IHSNot for ResaleNo
18、 reproduction or networking permitted without license from IHS-,-,-10 NACATN 3956the speed of the wing, the wing overtakes the gust. When the gust speedIs negative but greater in magnitude than th of the wing, the gust over-takes the wingj that is, It approaches the wing from the rear. KU thesepossi
19、bilities till be considered in this paper.IncompressibleTwo-Dhnensloml FlowFor incoqressible two-dimensionalfloir,eqpation (1) becomes thetwo-dimensionalplace eqmtion, and its direct solution for the unsteadyboundsry condition representedby equation (3) constitutesa difficultproblem. This problem ha
20、s been solved in reference 3 by an indirectapproach,which consists in using the known results for the llft responsedue to an infinite train of travellng sinusoidalgusts and in obtainingthe respome for sharp-edged gusts by means-of the ireil-khuwnsuper- “ “”position Integral given in reference 5. How
21、ever, in order to effectthis transformation,the results for sinusoMal. gusts have to be andedin a series; thus, the results for the s-edged,travel gust con-.tain a certain degree of approxhatloa. The same function had been obtainedby an altogether differentmethod In connectionwith the present paper.
22、before reference 3 becameavailable. This method is based on the aroach outllned in the appendixand consists in relating the lift or mment response to penetration of astationary or travellng sharp-edgedgust to-indlcial LLfts and momentsdue to flap deflectionby means of superpositionintegrals. Its app
23、li-cation to the case of incompressibletwo-dimensionalflow Is outlinedin the following paragraphs. Although thisaro.ach.alsocontains anapproximation,a comparison of its results with those of reference 3should furnish an indication of the validity of the two approximations.Equations (Al) and (A2) of
24、the appendix.serveto express the desiredunsteady-lift function k(s) for traveling gusts in terms of the unsteady-lift function for indicial flap deflection k8(s,) for the wing withthe given plan fomg and Mach number; for incompressibletwo-dimensionalflow this function ka is given by equation-(A8). T
25、hus, upon substi-tuting this function into equation (Al), the fold.owingexpression isobtained for traveling gusts which ass-mer”thewing-frbut it is not constant as it was before-.The solution of the problem cannot, therefore, be obtained readily byconical-flowmethods; but theused conveniently,that i
26、s,O(x,o,t) = -+c*.*.-=-source-superpositionmethod can still be -. -JJMach K t -tl)2- (X-X1)2. .forecone . The resulting expressions for the loading functionary given intable 3, and the cclrrespbndingvues of k. d- Cm(s) e gfven in “-Provided by IHSNot for ResaleNo reproduction or networking permitted
27、 without license from IHS-,-,-NACA TN 3956*tables 4 and 5.values of .and are shown in figures 6Again, the functiontions kl(s)- and k2(s) (see ref. = O, respectively. The behaviorbe similar to that of the functions(See fl.gs.4 and 5.)The pressureof the Mach conesa two-dlmensionalMach cones cannotk(s)
28、17and7 for M= 2 and severalreduces to the known func-9, for hstance) for = m andof these functions may be seen tofor supersonic two-dimensional flow.In Supersonicdistributionh the region of aemanating frcmlthe wing tips isFlowrectangular wing aheadidentical to that ofwing. Although the pressure dist
29、ribution wlthln thebe calculatedreadily, the chordwise loading and thetotal lift and moment contributedby tse regions can be det however, if Vg = -Mm (VO + e) (the case of a gwt travelimg at the same velocity“e+oas the airfoil and with its leading edge just ahead of the trailing edge .-of the wing),
30、 thenThe functions k(s)from either direction meof A.k(s) = 1(S) and (s) for ts approaching the wingshown in figures 17 and 18 for severalvalues -The behavior of the response functlons”is similsr to that of the functions for incompressibletwo-dhensional flow. Again, large peaks . .associatedwith the
31、noncircukkory contributionto the lift exist at low values of s for gusts approaching the:wing or overtakingthe -jand, again, the value of the response function at all finite values of . . NO such calculationshave been made. However, theunsteady-lift functions given here can be sh the other value rep
32、resents a fighter or boniberairplane at lowaltitudes, or the tramwrt a- at tlt*s a71 me 8ts e _shown in figures 19 to 22. -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-24 NACA !ni3956In using response functions for two-dimajsional.flow to represen
33、t those for an actual tapered wing, basically two approx-tlons are made,inasmuch as both the steady-statelift and the manner Inwhlch it isapproached as a function of time differ for they canbe expected to do so to an gven greater extent forlsrger values of the mass ratio. The conclusion can, therefo
34、re,be drawnfrom these curves that the accelerationresponse depends to a lsrge “extent on the magnitude and direction of the gust speed.h the preceding p=agraphs only sharp-edged gusts have been con-sidered. For traveling gusts, the intensity of which is a function ofthe distance behind the wave fron
35、t d, the accelerationresponse can bedeterminedly superpositionfrom the sharp-edged gust response obtained-”by solving equation (25). lksmuch asthe gust intensity can also be expressed as a function of s, nsmelv,w(s)= InK(s), theas.-“y- .-i*-.:A-.terms of this function %d the acceleration-respoe func
36、on ,.;normal accelerationfor a time-dependentgust cw be written .,-. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 3956.25(26).The convolution process indicated in thts eqyation msy tend toobscure some of the minor effects resulting from ch
37、anges in gust speed,but the maor conclusions reached concerning the effect of such chamgeson the acceleration response to sharp-edged gusts exe likely to be vaMdfor the acceleration response to other types of gusts as well.RELATION BETWEEN ELAST WAVES AND TRAWLING GUSTSWhen a blast wave strikes a st
38、ationary obJect, the Instantaneouspressures on the surface of.the obect =e proportional to the peak over-pressure of the blast, the constant of proportionality being a reflec-tion factor which depends on the geometric characteristics of the obJectsndl for strong shocks, on the shock strength as well
39、. (See ref. 13.)This overpressure is due not only to the fact that the object is i.nitialJ.ysed to the sW* fit -O to the fact that it arrests the propaga-tion of that shock or deflects it. Themanner h which the problem ofcalculs.tingthis overpressure (the diffraction problem) can be solvedis indicat
40、ed in reference 14, where the results of several.such caJ.cu-lations tie also given.When the obect is a wing fl.ylnghltia.lly through still air, its. response to the overpressure of the shock is similar, but in addition tothis effect it also responds to the velocity behind the shock. Theeffects of o
41、verpressure and velocity overlaand csnnot be divorced fromeach other readily. For instance, for a weak shock, which propagatesstistanti thus, consideration of either the overpressureOr velocity yiesa result for the initial response which includes the effects of the otherin tlds case. On the other ha
42、nd, after some time has elapsed, the over-pressure equalizes around the plate and, hence,produces no fiessureclifference directly, although in subsonic flow It can still influencethe lift through the yorticity shed while it was acting; thus, exceptfor this induction effect in subsonic flow, the pres
43、sure difference isthen due to the velocity effect alone.-.-+.=In this section ODJY the effects of the change in relative velocityoccasionedby entry into a weak blast are considered. In view of the preceding argument, these effects include at least some of the effects .of the overpressure associatedw
44、ith the given blast. Inasmuch as atten- tion is confined to week blasts, the effects of change in temperature(and hence speed of sound) and density acros the blast wave, which pro- Dduce only second-order effects on the lift of the wing) will be disregarded. .The relation between a blast wave and a
45、traveling gust is indicated -in the following sketches: ., -?-Blast wave .- !:.DISCUSSION .The lift and moment responses have beericalculatedherein for two-dimensionalwis incompressibleand supersonicflow, for tide delta _ _.and rectamguhr wings in supersonicflow, aiidfor vkry nekrow deltawings. The
46、reason for selectlng these cases was that for them the tic- - “.tions of interest could be readily calculated. For three-dimensional -_ _Incompressibleflow end for tmxlimensional compressibleflow the func- Qtions kl and have been calculated Inprevious investIgatlons,but .the uthds used do not lend t
47、hemselves to the calculationof the more dgeneral response functions of interest here; also no simple thods areavailable “forcalculating the desired respes of wings with subsonic “;-”-leading edges in supersonic flow. -. -The results of calculationsfor very nerrow delta wings have beenincluded despit
48、e the fact that the results Qf linear theary for thesewings are of llmlted practLcal utility, inammch as for even relativelylow angles of attack the wake of these wings,tends to curl up and intro-duce deviations from linearity in force and moment responses. Thereasons for including these results is that they are obtained very easilyfor incompressible-”flowand serve as the only Indicationof aspect-ratioeffects in subsonic flow available at present. In other words, theirsignificance stems pr-ily
