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Aerodynamic Shape of the Wing Tlips 52'752

(None)Hoerner, SihardEngineering Division, Air Materiel Command I3-458 -3-ZTAir Materiel Command, Wright- Patterson Air Force Base, Dayton, 0.

AFTr%-5732

one) Unclass. U.S. English 9 photo

itudy was made of the aerodynamic characteristics of h wing tips, as well as experimonted Investigationsncerning the mecauuswm of the tip vortices and the lift/drag ratio of a wing fltt4d with differently ¶_p~Irng tips. Results show there are two ways in which the wing tips affect flow and lurces on a ,-zog: con-tering the tip vortices the effective span, of a wing does not coincide with the geometrical gnan, i.e., thOometrical location of the tip vortices depends upon the shape of the wing tips; ard that some paramig dragLginates t the wing tips, its amount also depending upon the shape of the wing tiM. Using these ren.uts,optimum wing-tip shape is described. This wing tip has a sharp side edge, its plane form shows a-er at the trailing edge and its upper surface extends approximately straight to the end. Emplyin, thisid of wing tip the climbing speed is Increased in the order of I ft/sec and the range by 1 or 2%, In compaxi.-i tu disadvantageous ip shapes.

Copies of this rf.port obitnabie from CADO

Aer'odynaamics (2) Wing tipq - Aerodynamics character-Wings and Airfoils (8) Istics (99147.193); Vortex Thaory (9731O)

-l -

I.

"ATI No. 52732

ulna AERODYNAMIC SHAPE OF THE WI6G TIPS

UNITED STATES AIR -

AIR MATERIEL

Wright-Patterson %ir For. r -o

Datn *i'°I"

NOTM

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prmpl notified of any apparent conflict between the Govern.m t roIetary interests and t.ose of others.

ZAploage ActNotic: '11his document contains information affecting the

national defense of the United States within the meaning of theEspionage Act, 50 U. S. C., 31 and M2, as amended. Its transmissionor the revelation of Its contents in any manner to an unauthorizedpenon is prohibited by law."

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The U. S. Government Is absolved from any litigation whichMy enaue from the contractor's infringing on the foreign patentights which may be involved.

UNITED STATES AIR FORCEAIR MATERIEL CCOMMA1W

'URIGHT-PATTMON AIR FORCE BASEDAYTON, OHIO

T±ECHNICAL Mr?ORT

No.- 5752

AERODYNAMIC SHAPE OF~ THE WING TIPS

Dr. Sigbard Hoerner

Approvedt

Chief, Aircraft laboratory

For thm Coin~zzx Gonmra1:

Yn. R. WDENT 4

Ohibfj, Wriqin@@ring 04ýA'tlorr

~. ~8in33TP 1iirkwring Dlivig o n

W.A.. JUL 41 In

TAMWCOM

Page •m'•-"r

1. Xweaton of the Wing-Tip Vortices ..... .... I

TJI er,,aits Wing-Tip Drag. . . . .......... 2

IUl Foere Measueremnts on Wig . . . . . . . . .*. . 3

ITV Effect on Flight Performames ... . . . .

V. Practical Design of the Wing-ip cape ...... 4i

References . . . . . . . . ... . . . . . . . .. .

r752 ±

ABSTRACT

The author studied the aerodynatic characteristics of wing tipa, and bedid, and had Gmrman research institutions do, experizntal invectigationsconcerning the mechanism of tbs tip vortices and the lift/drag ratio of a wizWfitt*d with several differently shaped tip caps@

There are two wqs in which thvi wing Uips affect flow and forces on awireS (a) Gonsidering the tip vortices the effective span of a wing doesnot coincide with the geometrical span; that is, the geometrical location of Whwtip vortices depends upon the shape of the wing tips. (b) Sore. parasitedrag originates from the wing tips, its amount also depending upon the shapeof tha tip caps.

The main results of the toots as mentioned, are presented in this roport,and the optimum wing-tip shape (No. 5) is described in Figure. 9. This tip caphas a sharp side edge, its plane form shows a corner ot the trailing Adge andits upper surface extends approximately straight to the :-nd, Mxploying thiskind of wing tip the climbing speed is increased in the crder of 1 ft/sec andthe range by 1 or 2%, in comparision to disadvantageous tip shapes.

' - - ii

AuR ODYNLIC SHAP%" OF THW WING TIPS

I. Location of The Wing-Tip Vortices

From each tip of a wing a sharply determined vortex is origirvting. Thesetip vertices must not be confusod with the vortex sheet originating from thetrailing edge of the wing. This sheet transforms itself very soon into thepair of tip vortices. Fig. 1 shows the formation of one of the tw.o . ip vortices,made visible when releasing gasoline through an ersrgeny, outlet at the 1fftwing t*p. The two vortices form a stable system (horseshoe vortex), the inherantmomentum of which is the equivalent of the induced drag. Like this drag, thevortices cannot 1hP. avoided in practical airplane construction.

,f fective Span

The distance bi bptween thm two vortices is a measure of the effectivespan of the wing. If measured along the trailing edge of the wing, bi isusually sml~fthan the actual span b by 10% or 20% of the wing chord. Thelarger the value of bi, the smaller is the induced angle of at'.ack And 41.hoinduced drag and the greater the lift curve slope. Th- induced drag is animportant property of the wing (f an airplane; the slope is of special interestwhen using the wing as a horizontal tail surface.

Pigure 2 shows the geomtric )ocation of the tip vortex core for sixdifferent tip shapes, as measured in Ref. 3. The tips No* 1, 2 and 6 presentthe largest effective spans bi. Evidently the trailing edge of the wing tipis important, dir-cting the vortex as far outward as possible.

Side !Ages

The tips 1 in comparison to 2. and h in comparison to 3, show larger biValues.* Obviously the sharp 6ide edges are advantageous; on the other hand,well rounded edges facilitate the flow around them, from the lower to theupper wing surface, as illustrated with tip No. 2 in Fig. .

Lift Curve Slope

Figure 3 shoaw the relation be~weon thp lift curve slope and th" distancebi of ,1-i vwtic...; for thi aspect ratio 3 as used with the expe•riw-nts in Rof. 3.Prom the lifting line theory

1f4YP ~~t'nt.+)~Influoncem of t'h. vitn, c'hrd ani cnnnvo-rtinc! 4thel anti.,'of attack inrto degrees, it is derived in hef. 8:

d C-

L~74'4

wit-. A.I., cnagon as to mnat~ch th- oxpi-rimental poinzts in Fig. 3 and Ai indicatingtJ,-i -tffctiv, aupect ratio = (b'/-)) - AA. in the present case AA=2y/c was

tak~- ~ Z as measured on thob prolongation of the wing trailing edge,

Fnd.Plate Ftffct

The points 1 and 5 lie below the calculated curve. It was leuirnp~d fromthe f-.orn trical measurements on this tip vortices, that these two tip 3hapeahave a vortex-cor* location which is approximatel~y 5% of the wing chord higherthan with thp other Prins. In effect this location means a formation of thevortex sheet leaving tho trailing edge, similar to that of a wing fitLted withsmall and plates.

Ref. h confirmq thina fftmet, A reircle wing with the up~per surface runningstraight from side edge to sids- edge,. shows a higher lift/drag .*atio than asymptrically designed wing. Tha.t means, the effective wing span is somewhati~nreajsed, owing to thp dihedral eff-ct.

Rolling Moment

The rolling mompnt of a wing due, to yaw, is affected by a wing tip similarto No. 5 in Yig. 1. With a wing of aspect ratio 6., a thickrinhes ratio t/c -12%and a trapezodial plan form having Ctip/ Ceent<v 0.6, the form No. 5 or thetip cap 43 recomm-nded in Part V, presetis an ntflct equivalent to approximtely1.50 of positive wing dihedral.

III Parasite Wing..Tip Drag

Figuro 4~ shows tbe side component of the flow at the wing tip As d#erivedfrom visual observations in a water tunnel (Ref 2). A larger or szaaller amountOf parasite drag is connected with this flow, owing to flow separation. It.magnitude was determined ba mome ntum loss measureiwnts within the vortex cw'e('ef 5); that ia, measurements were conducted in the wake of a wing model,employing a emill sphere (2-dimensional yaw head) far determining pressures andiargles of the loc.al flow* At zero lift the parasite* tip drag deponds on theshape of its ftnrward portion. Tips well rounded toward their leading edgepresent a small negative amunt of tip drag, obviously owing to thm fa~ct thatthe 2-dimensionaf-7l-n-g-7;ow is changed To a 3-diwensional ne-ar the tips.

Parasite Drag Depending !!pon Lift

At positive lift coefficionts Fig. 5 indicates rplatively small dragcoafficiontbi for all the sharp edges (vos. 4., 5 and 6). 7vidently thoy matcht-hp raturn-i fJlow shown on Fig. It much better than the square and blunt a!,L-Nos. I and 2. Accordinglyý the latter show a Darasito drag approx~imsat .1y i-uic f

'R,9 largA ai tive sharp-edged t orus.

Th pav-asit^ tip-drag must not be contused with the induced drag. Howevemr,sismiiar to t11 s onem, it ir~rerasoas with a high poweor Of CL. From FIg. 5 1-t ý,an be.im'rivod f~n ar' LAir uf sharp-..dgedj tip caps that

Ill. F...em M.asur-ments on Wings

rei wr•tsn on a Wing Series

Fib. 6 shown the lift and drag coefficients for a wing with aspect ratio 3,fitted 4ith the 6 different tip caps as illustrated in Fig. 1. Neglecting No* 1,which naturally is the worst at small lift coefficients, the Nos. 5 and 6 areth@ best ones; that means they show the high-st lift/drag ratios. Applying theknowledge acquired in the Paragraphs I and II, the efficiency of the differenttips can be attributed to the following causess

i W Lift a Result Due to:

1 high Sharp side edge and complete trailing edge.2 low Round side edge, in spite of complete trailing edge.3 low Round side edge, cut-away trailing edge*4 low Cut-away trailing edge, in spite of sharp side edge.5 high Sharp side edge and rather complete trailing edge.6 high Sharp side edge, full trailing edge.

Shape No. 5 follows best the natural flow direction, as shown in Fig. h. Thisnumber and No. 1 show in addition a favorable end plate effect as explainedbefore. wvidently those tip forms are the beat which employ sharp side edgesand complete or full trailing edges. It can also be seen from Fig. 6 thattips 1, 5 and 6 have the highest C values, probably owing to the effect ofthe trailing edge. Considering prac cal application, tip No. 5 is preferreduver No. 6 because of simpler design and construction.

W!iai; Tanks

The worst form, as far as lift and drag is concerned, is the No. 2,because of its well rounded edge, which allows the flow to get around it fromthe lower to the upper side, as shown in Fig. l. In this connection Fig. 7furnishes further inforatton, presenting the infiui-nce of a wing-tip shapeainilar to a sm9 l drop tank. Owing to this tip form, the lift-curve slopeis decreased by 5 and 9% respectively as compared to conventional tip shapes.That means, the induced angle of attack (and accordingly the induced drag)is increased by approximately 11 to 20% in this case. However, differentex_-p•rintal results on a pair of tip tanks aro presented in Ref.6. Upon addingtne tanks to the wing the llft/drag ratio is somewhat increased above CL a O.9.Obviously in this case the tanks act like endplates, their din.nnions beingmuch larger than those in Figs. -4 and 7; d• 6 ttip and 1 0 3 5tip . In fact itis possible to compute a difference of induced drag as measured when taking intoAccount both the endplate effect and the wing span, which is sorpwhat omnlarg.'dby, th- tanks.

!Mr 1n .1 Data

In Fig. 8 general data arp givon, indicating the effectivp aspect ratioof various wing, farms. lnr addition to the systematic vpasvn_-nts of Ref. 3,To•w =or^ rxferincos hive bUn used, indicating especially thp valuos of•.UIptlcal and nwvpt wings. it is rismarkabl that tho elliptical plan form

-'rac*.ci±iy ao-i not present the smalst possible Amount of induced angle and.indic- arnp aR pr-ict-d by theory, especially not if the quartm chord points areLined -3 on Lhe latoral wing ads.. In tids case (see Fig. 8), not only a rearýorrnr i- missing, but the wing looks like a large portion of *iig area was cutoff at tho outer part of the trailing edge. Such a cutting of results in shiftingthe tip vortex inward, as shown - FVg. 2, and in reducing the effective wing aspct-ratio correspondingl*y

s.pt Wings

Considering swept wings from various sources (Ref 7), itb found that theminimum induced drag and the saxium lift curve slope are attained appromatel=

at an angle of sweep I 5 0 So; with ( measured on the quarter chord line.This mount of positive mue ,mans for the avorage trapesoidal wing almost astraight trtiling edge. Here again, the Importance of the trailing edge isobvious; according to Fig. 8 an effective aspect ratio is obtained which isslightly 5jMr tnhaf tho geomtrical ore.

IT, 'ffeet on Flight Perfor @aea

From Fig. 1 or 8 it can be seen that the advantageous tip shapes actapproximately as if thn aspect ratio of the wing was enlarged by AA = 0.3 overtbat Af some of tk disadvantageous wing forms In tha case of an averageamlitary airplane with W/S - 4O lb/ft 2 and CL)/Cý2 = 150 and A = 7, th-rfore,by changing the tip shape from No. 2 .'r 3 to No.0 , the climbing speed JAilereasod at the rate of 1 ft/sac. A•so concerning range, the shape of the wingtips has a certain bearing. Corresponding to UA - 0.3 tho range is incrrasedby i or 2%. Tbese imrovw nts are not large; but thq can be accomplished byproper design without any disadvantages or additional expenditures in conitruction.Of course, the effect on the flying qualities (rolling moment), as presented bya tip shape similar to No. 5 (Fig. 2), bas to be considered too.

V. Practical DNsign of thp WingM-Tip Caps

Tho +4- !... o pZ in4g a3 the most advantageous in Figs. 5 and 6 is thpNo. 5, besides No. 6. If, by imagination, ths end of a sufficiently longtrapezodial wing b•ec•s cut off from blo'r, in an oblique diraction, autcnmticallythe basic form of No. 5 13 obtained. This shapp has to b0 rounded in itsforwnrd part, apTroxi'ately up to the maximum span. Finall7, by fairini, thetransition from thp lcwr wing surface towarithp tUD and by r-placing pl.r-ut uirzlac. by a curvod onoi, thP shape as shown in Fig. .' ±5 obt22.iad.

T¶h span of th- tip cap is approximatply a.& (0.25 to 0.30) ctiD. TIV1i 1]ar-n ii W-ýt Y+ -ynjed up .o LUu- r-ar corrbr. The dpeigin ,as to b)e Adjuelt'dfaithfuliy to thicknroi ratios and noction shapes diffprent from the ayarivla

-.. hown In Fi•.ý o

'1nr-n. ccan.- lo-eignod ac.;Jr.±iZ• to the rulps outlined abov-, havo 'hon- - -.. T ~~ ý- s t, h as ti- si ! - r 26, 5 '6 h iuipr.l 5 )ind w-ith fho moro

recent vprsions of the Junkera 87 and 88. Frobably thmre are also AmericandPsln4s Incorporating s3iilir principles.

1. IAurner, Einflusa der Kantenabrundung ani Widerstand und Aukrieb, Influenceof Rornding the Side Edges of a Wing on Drag and Lift, G•rman Doct ZWB FB248 (DVL 1935).

2. Hoerner, Raemwlicia Untersuchungen in Wasserkanal, Three-DimensionalInvestigations in the Water Tunrel, Germam Doct Fieseler Wasserkanalbericht16 (1939).

3* K assalkaul, Dreikomoneutenuessungen und Strombilduntersuchungen an Fluegelnmit verachiedenen ErAkppen, Three-Component and Flow-Pattern 'xperiments onWirgs Fitted with Various Tip Caps, Geruan Doct Institute for AircraftDesign, Technical University Braunschweig, Rpt from 3) May 1941.

4. Zimraan, Characteristics of Several Airfoils of Low Aspect Ratio, NACAT. Note 539,

5e Hoernor, Vr-ittlung des schaedlichen Randwiderstandpms, Determination of theParasite Drag Originating from the Wing Tips, Gorman Doct Mosserschmitt TB92 or ZIN UM 7815 (1943).

6. Johnson, Development of the Lockheed P-80A Jet Fighter Airplane, J. Aeron. 5c.Vol. 12, 1947, p. 659.

7. Hoerner, Air Drag, Volume 2, Wing Drag Associated with Lift, UnpublishedGerman Report.

8. Hoprnpr, Berechnung des raeumlichen Tragfluegels Calculation of Wings mithLimited Span, German Doct Ilesserschmitt TB 45/19h.

9. Hoermer, Forugebung der Flumgetrandkappe, The Shapo of the Wing-Tip Cap,Lilit-nthal Conference Rpt 179a, 1944, p. 69 or Doct ZWB3 Ul 7819.

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C"5 e /,/ (.-/ NAU)- 52752

I TITLE Aerodynamic Shape of the Wing Tips `oAUTHOR(S) :Hoerner, Sighard " I C 0 . .ORIG. AGENCY :Engineering Division, Air Materiel CommandPUBUSHED BY :Air Materiel Command, Wright-Patterson Air Force Base, Dayton, 0. "

(Noel Unlap. U.. nalish 9photo(Z=one I 7.Z.". I, ,. =S" E ' I'9 1 -,,,,

ABSTRACT:A study was made of the aerodynamic characteristics of wing tips, as well as experimental investigationsconcerning the mechanism of the tip vortices and the lift/drag ratio of a wing fitted with differently shapedwing tips. Results show there are two ways'in which the wing tips affect flow and forces on a wing: con-sidering the tip vortices the effective span ofa wing does not coincide with the geometrical span, i.e., thegeometrical location of the tip vortices depends upon the shape of the wing tips; and that some parasite drag

.originates f ron the wing tips, its amount also depending upon the shape of the wing tip. Using these results,- an optimum wing-tip shape is described. This wing tip has a sharp side edge, its plane form shows a

corner at the trailing edge and its upper surface extends approximately straight o the end. Employing thiskind of wing tip the climbing speed is increased in the order of 1 ft/sec and the range by I or 2%,in compari-sop to disadvantageous tip shaas. . , /

4DISTRlBtTION: Copies of this report obltinable ftin D ) (1) -

DIVISION: Aerodynamics (2) / SUBJECT HEADINGS: Wing tips - Aerodynamic character-

SECTION: Winzs and Airfoils (6• istics (q0147.193); Vortex Theory (97380)

AD-A800 3 74i-