1、IIE_ODUCEO 8YNATIONAL TECHNICALINFORMATION SERVICEil.S. DEPARTMENT OF COMMERCESPRINGFIELD, YA. 22161Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPO
2、RT No. 738GROUND EFFECT ON DOWNWASH ANGLESAND WAKE LOCATIONBy S. KATZOFF and HAROLD H. SWEBERGLangley Memorial Aeronautical LaboratoryLangley Field, Va.477390-43Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTI
3、CSHEADQUARTEI_S. LS00NEW HAMPSHIRE AVENUE NW WASHINGTON. D. C.Created by act of Congress approved March 3, 1915, for the supervision and direction of the scientific study of the problemsof flight (U. S. Code, title 50, sec. 151). Its membership was increa.qed to 15 by act approved March 2, 1929. The
4、 members areappointed by the President, and serve as such without compensation.JEROME C. HUNSAKER, Sc. D., Chairman,Cambridge, Mass.GEORGE J. MEAD, Sc. D., Vice Chairman,Washington, D. C.CHARLES G. ABBOT, So. D.,Secretary, Smithsonian Institution.HENRY H. ARNOLD, Lieutenant General, United States Ar
5、my,Commanding General, Army Air Forces, War Depart-mentLYMAN J. BRIGGS, Ph. D.,Director, National Bureau of Standards.W. A. M. BURDEN,Special Assistant to the Secretary of Commerce.VANNEVAR BUSH, So. D.,Director, Office Scientific Research aDd Development,Washington, D. C.WILLIAM F. DURAND, Ph.D.,St
6、anford University, Calif.O. P. ECHOLS, Major General, United States Army, Com-Inanding General, The Mat6riel Command, Army AirForces, War Department.SYDNEY M. KRAUS, Captain, United States Navy, Bureau ofAeronautics, Navy Department.FRANCIS W. REICHELDERFER, Se. D.,Chief, United States Weather Burea
7、u.JOHN H. TOWERS, Rear Admiral, United States Navy,Chief, Bureau of Aeronautics, Navy Department.EDWARD WARNER, Sc. D.,Civil Aeronautics Board,Washington, D. C.ORVILLE WRIGHT, Sc. D.,Dayton, Ohio.THEODORE P. WRIGHT, Sc. D.,Assistant Chief, Aircraft Branch,War Production Board.GtOR6E W. LEwis, Direct
8、or of Aeronautical Research JoHlq F. VICTORY, SecretaryHENRY J. E. REIn, Engineer-in-Charge, Langley Memorial Aeronautical Laboratory, Langley Field, Va.SMITH J. DEFRASCE, Engineer-in-Charge, Ames Aeronautical Laboratory, Moffett Field, Calif.EDWARD R. SHARP, Administrative O_cer, Aircraft Engine Re
9、search Laboratory, Cleveland Airport, Cleveland, OhioTECHNICAL COMMITTEESAERODYNAMICS AIRCRAFT MATERIALS INVENTIONS A DESIGNSPOWER PLANTS FOR AIRCRAFT AIRCRAFT STRUCTURES OPERATING PROBLEMSCoordination of Research Needs of Military and Civil AviationPreparation of Research ProgramsAllocation of Prob
10、lemsPrevention of DuplicationConsideration of InventionsLANGLEY MEMORIAL AERONAUTICAL LABORATORYLANGLEY FIELD. VA.AMES AERONAUTICAL LABORATORYMOFPETT FIELD. CALIF.AIRCRAFT ENGINE RESEARCH LABORATORYCLEVELAND AIRPORT, CLEVELAND. OHIOConduct, under unified control, for all agencies, of scientific rese
11、arch on the fundamental problems of flight.OFFICE OF AERONAUTICAL INTELLIGENCEWASHINGTON, D. C,Collection, classification, compilation, and dissemination ofscientific and technical information on aeronauticsProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS
12、-,-,-REPORT No. 738GROUND EFFECT ON DOWNWASH ANGLES AND WAKE LOCATIONBy S. KATZOFF arid HAROLD H. SWEBERGSUMMARY,4 theoretical study has been made of the reduction indoumwash and the upward displacement of the wake inthe presence of the ground, and some verification of thetheory has been obtained by
13、 means of air-flow measure-ments made with a ground-board and image-wing com-bination. ,lethods are given for estimating the effects andnumerous examples are included to illustrate the nature ofthese effects and to show their order of magnitude.INTRODUCTIONAn important consideration in tile analysis
14、 of thehandling characteristics of an airplane is the large re-duction of dow_lwash in take-off or in landing occa-sioned by the proximity of the ground. A related con-sideration is that the wing wake, which under normalflight conditions generally passes below the tail, is dis-placed upward by the g
15、round and may envelop the tailjust as a landing is about to be made.The basis for the calculation of downwash angles andwake characteristics for the normal condition (withoutground effect) is discussed at length in reference l ; ar6sum6 of the theory is given in reference 2, togetherwith numerous ch
16、arts to facilitate its application. Thepresent paper is essentially a supplement to thesepapers and extends the theory and tile methods of cal-culation to cov,r take-off or landing conditions. Itincludes also a sutficient numl)er of illustrative exam-pies to enable the d(,signer to estimate the effe
17、cts ofthe groun(l on the wake location and on the (Iow_lwashangles.A few wind-tunnel tests were made to provide some.verification of the theory and to indicate that noimportant fa(,tors had I)een neglected.SYMBOLS( lift coefficientCz_ lift coefllcient at a particular angle of attack,flaps upCL I inc
18、rease of lift coefficient, at same angle ofattack, on deflecting the flapc_o section profile-drag coefficientA aspect ratioa angle of attackdownwash angle_wbCCrZdmdownwash angle contributed by plain wingdownwash angle contributed by flapspanchordroot chordmean aerodynamic chordvertical distance from
19、 ground to wake origin atroot sectiondistance from wing aerodynamic center togrounddownward displacement of center line of wakefrom its origin at trailing edge, measurednormal to relative windvertical distance from elevator hinge axis towake origin at root section, measured normalto relative wind (p
20、ositive if hinge axis i_above trailing edge)longitudinal distance from elevator tfinge axis t,_quarter-chord point of root sectionlongitudinal distance from elevator hinge axis t_trailing edge of root sectionwake half-widthcorrection factor in formula for ground effect onangle of attackfree-stream d
21、ynamic pressureTHEORYIn the proximity of the groun(l, the wing vorte,:system is reflected in the ground and the resultiI_:downwash at the tail corresponds to tim coml)medfield of flow of the two symmetrically situated and op-positely rotating vortex systems. The superposition i._illustrated in figur
22、e 1. Figure l(a) shows the down-wash field in the plane of symmetry of a wing, undernormal flight conditions; the field is symmetrical abouttim wake, which is so curved that its slope at everypoint is the tangent of the (h)wnwash angle at thatpoint. The superposition of tim refleetcd downwashfield w
23、hen the wing is near the ground is shown infigure 1 (t); the downwash angle at every point is thealgebraic sum of the two downwash angles, and theslope of tim wake at every point is the tangent of theresultant downwash angle at that point. Tim resultantfiehl is shown in figure 1 ().IProvided by IHSN
24、ot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 REPORTNO.738- NATIONAL ADVISORY (t(IMMITTEE FOR AERONAUTICS4O0 _0 40 GO 80 I00 120 /40 /GOD/stonce behind quorfeF-cho_d poi_/, _rcent ._em#s_on(a) Normaldownwash field.(b) Sul)erpositioll of downwash fields of actual
25、 vortex system (full lines) and re-flected vortex system (dotted lines),(c) Resulianl downwash field.Fiotn_ L-Illustration of the ground effect on the do_nwash field behind an air-foil. Rectangular win_; A, 6; C#, 1.0; zf_, 1.0.The assumption, implied in this procedure, that thesystem of bound and t
26、railing vortices is independentof the distance from the ground does not strictly hold.First, since the field of the reflected bound vortex re-duces the effective airspeed at the wing, the averagestrength of the bound vortex must be correspondinglyincreased in order to maintain the given lift coeffic
27、ient.3.5_2This increase is about -_-f_ percent, and the resultsobtained by the proccdure given may, for better accu-racy, bc increased by this amount. Second, the dis-tribution of the bound vortex across the span of thewing will be altered by the presence of the ground with,usually, a slight concent
28、ration toward the center of thewing. Third, the trailing vortices shed from the tipsof the wings and the flaps do not extend straight backbut move laterally outward under the influence of theirown reflections. The last two effects are relatively543c_ZJ:o_c, I i! : i i _ tI-._0 (resultant of the actu
29、al andthe reflected vortex fiehls) in the wake at 0.20_ behindthe trailing edge._b. Calculate tile wake displacement at 0.45_ behindtile trailing edge as 0.45_Xtan _.20.c. Taking this displacement into account, find thedownwash angle to4,_ in the wake at 0.45ff behind thetrailing edge.d. Calculate t
30、he wake displacement at _ behind tiletrailing edge as _X tan _0_-The wake effect (fig. 2) is added as described in ref-erence 2 with consideration, also, of the reflected wakefor positions very close to the ground. For such posi-tions it may happen that the wake half-width, ascalculated by the metho
31、ds of reference 2, exceeds thedistance from the wake center to the ground. In thisW_e eric)inFIliIRE 11 ,-Illustration of the Nmpllfled method of determining the wake dk_pla_-merit at a distance _ behind the trailing edge. The average slope between the trail-ing edge and _ approximalely equals the s
32、lope at l).45 and the average slotc _etweenthe trailing edge and 0.4_ approximately equals tim slope at 0.2f)_.ease the ground effect will no longer be simply a reflec-tion of the normal wake; for the calculation ofdownwash angles, however, the assumption of simplereflection will give approximately
33、correct results though,physically, the corresponding concept of a wake imagepartly extending above the ground is obviously in-correct.The small correction for the variation of downwashacross the tail span (fig. 21 of reference 2) may be dis-regarded in these calculations.Ground effect on lift.-Altlm
34、ugh this paper is notprimarily concerned with the ground effect on the winglift, some remarks concerning it may be in order, inas-much as its magnitude must be known for any applica-tion of these results. For a given lift coefficient, theangle of attack decreases as the airplane approaches theground
35、; hence the corresponding increase in the angleof attack of the tail is, for a given lift coefficient, lessthan the decrease in the angle of downwash.The ground effect on the wing may be considered toconsist essentially of three parts: (a) A reduction inthe effective ab_peed at tile wing, due t_ the
36、 field of tllereflected hound vortex; (b) a change in the effectivecamber and airfoil section characteristics in general,due to the cllrVlillne alid ltle dist,orlion (if the, flow byI,he reflected wing; and (C) ii reduclinn in the inducedaiigle at llie wing, due lxi the uptlow assoeilited witii ther
37、ellecl.ed trailing vortices. All extensive theoreticalanalysis is given in referen(:es 6 and 7, and tile resultsare sumniarized in the appendix of reference 8. Asindicated in reference 8, however, (c) alone appears toacconnt approxinntteiy for the c .,erved groumi effecton lift, so that (a) an,l (b)
38、 nmy be considered to nullifyeach other fl)r most conditions of practical interest. Asimplified theory based on () alone may therefore betentatively re(ommended, at least for stability and(:ontrol calculations. The reduction in the angle ofattack for a given Jill coefficient is then given by theequa
39、tionc_Aa=-57.3 _ ain which, by reference 8,ff _ (_zi_(2d/b)O .768For the landing attitude, a may be of lhe order of 0.5,wllich corresponds to the effective doubling of the aspectratio.R_:SUM_:OF METHOi)For the calculation of downwash angles and wakelocation in the proximity of the ground, the proced
40、uregiven in reference 2 is revised as follows:Plain wings.-1. Determine x,/_, m, and z in semispans. (Considerthe wake origin to coincide with the trailing edge.)2. Determine the do_-nward displacement h of thewake center line at the elevator position in the followingsteps:a. Determine _020 from the
41、 downwash charts ofreference 2._._0=C_(x-0.8_, 0)-_(z-0.8_, 2z)(The term _(x-0.8_, 0) is the doualwash angle readfrom the appropriate chart of reference 2 at the pointwhose abscissa is x-0.8_ and whose ordinate is 0.Similarly, the term _(x-0.8/_, 2z) is read at the pointwhose abscissa is x-0.8_ and
42、whose ordinate is 2z. Itwill be noted that the ordinates in the charts are thusconsidered as“ vertical distances flom the wake center“;the present label, “vertical distance flom quarter-chord point,“ which applies only to the “undisplaced“downwash-angle contours, has given rise to someconfusion.)b.
43、Determine _o._nfrom the do_alwash charts._o.,_=C_(,-o.55_, o)-_x-0.55_, 2(z-0.45_ tan _o.o)3. Determine the downwash at the hinge line as_=CL_(X, m+h)-_(_, 2Z+m-D)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-GROUND EFFECT ON DOWNWASH ANGLES AND WA
44、KE LOCATION 11Flapped wings.-1. Determine x, _, m, and z as before, but measure mand z fiom the wake origin rather than from the trailingedge.2. Determine h in the following steps:a. _o.2o=CL_,x-.S0L 0)-_(x-0.8_, 2z)+CLflg(z-0.86 0)-_Ax-0.SL 2z)where the subscripts of _ and ,y signify that thesevalu
45、es are to be read from the downwash charts for theplain wing and for the flap, respectively.b. _0.4_= CL_ _,(x- 0.55L 0) - _x-0.55_,2(z-0.45_ tan _o.2o)+ CLs_Az- 0.55_)-_ix-0.55L 2(z-0.45_ tan c0.:0)c. h = _ tan _o.453. _=CL_(x, m+h)-_x, 2(z+m-h)_-Cc/_t(x, m+h)-_Ax_ 2z +-m-h)4. Add the wake correcti
46、on (fig. 2). This correctionis a function of c%, _ (measured in root-chord lengths),and m+h (measured in root-chord lengths).5. Add the correction for the reflected wake, which isa function of ca0, _, and 2z+m-h.EXAMPLESThe specimen calculations of reference 2 will be re-peated here for the case in
47、which the trailing edge orwake origin is 0.2 semispan from the ground (fig. 12).W_ke _dqeWoNe(a) “-x =.C8 _ i z =2bt2 G- our_dP/oNe ec1_eZ=.21._I 2 - Wnhe _d(b) -c_o_,-,d. . . ( . . J Ol Flap till(h) Flap down.FIGIRE 12. -111l_tratil)ll fifflheSlIe(!ili!lllVallllali ollsOtdwnw;k_h:tlI( %_ake.For the
48、 flap-u l) condition, the reduction in angle ofatta(k for the given lift coeiIi(ient is al.)l,t 0.7; for thelap-down (.ondition, the reduction is about 1.2 .These changes corresl)nnd to an increase in ,n of about0.0lb/2. The steps just outlined are:Flaps up.-1. x=0.68, _=0.43, m=0, z=0.22. a. _o20=0.9_(0.34, 0)-_(0.34, 0.4)=0.9 (7.5-3.27=3.9 (An extrapolation of the downwash-angle charts wasnecessary to find these values of _.)b. _0.4._-0.9E(0.44, 0)-E(0.44, 0.37)=0.9(6.60-3.5 ) =2.8 c. h=0.43 tan 2.8 = 0.023. ,=0.9,(0.68, 0.02)-_(0.68, 0.38)1=0.9(5.80-3.3 )=2.3 The wake half-width is abo
