national advisory committee for aeronauticsu upwash theory analysis cbservations conkerning...

DUM

METHOD FOR ESTIMATING LIFT INTERFERENCE OF WING-BODY

COMBINATIONS AT SUPERSONIC SPEEDS P

By Jack N. Nielsen and George E. Kaattari

Ames Aeronautical Laboratory Moff ett Field, Calif.

NATIONAL ADVISORY COMMITTEE l

FOR AERONAUTICS WASHINGTON

umv-~~ December 31, 1951 -

https://ntrs.nasa.gov/search.jsp?R=19930086955 2020-06-17T13:28:17+00:00Z

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

RFSEARCHMEMORANDUM

METHOD FOR ESTIMATING LIFT I:NTERFERE NCE OF WING-BODY

COMBINATIONS AT SUPERSONIC SPEEDS

By Jack N. Nielsen and George E. Kaattari

The modified slender-body method used by Nielsen, Katzen, and Tang in RM A5OFO6, 1950, to predict the lift and moment interference of triangular wing-body combinations has been adapted to cozibinations with other than triangular wings. That part of the method for predicting the

.effect of the body on the wing has been retained, but a new method for predicting the effect of the wing on the body has been presented. These methods have been applied to the prediction of the lift-curve slopes of nearly 100 triangulsr, rectanguler, and trapezoidal wing-b- configurations . The estimated and experimental values for the lift-curve slopes agree for most of the cases within f10 percent. Same of the higher- order effects that must be taken into account in a theory that is to give greater accuracy than the present one are discussed. A numerical example illustrating the method is included.

INTRODUCTION

By properly designing supersonic aircraft and missiles to teke advantage of ,the effects of aerodynamic interference, it may be possible to obtain large increases in performan ce end efficiency. For this rea- son, much effort has been expended in trying to predict-and control interference effects. -One of the most important problems is that of interference between wing end body, and a number of methods have been developed for predicting the characteristics of wing-body combinations at supersonic speeds. These methods generally fall into two categories. The first includes those theories attempting to solve mathematically the complicated boundary&.lue probleme .of wing-body interference, and the second category includes those approximate methods based on highly sim- plifying assumptions. In general,' the mathematical theories of the first category are-too difficult or time consuming to be useful in ordi- nary design work. The approximate theories of the,second category are

2 _,',,_ WA RM A5lJO4

.restricted in scope or are based-on assumptfons the -validity of which is Llnknown. As a consequence of these shortcomings, there is a -lack at the present time of a simple, reliable'method of calculating wing-body interference applicable to a wide range of wing-body c&inations. It. is the purpose of this report to supply such a method for predicting lift.

One of the first attempts to solve one of-the ~thematic~ally cam- .-I plicated boundary-value problems of wing-body interference is that of Ferrari (reference 1). By assuming the wing to be actipg..in the field of the body alone, Fcrrari was able &obtain-a-first approximation to _- the pressure field acting on the wing of a'rectangular wing-body co~&i; nation. By assLuning the body to be acting in the field of the wing alone, Ferrari also obtained the~appr&&,&e pressure field acting o!n thebody. In reference 2, Nielsen'and Matteson present a calculative---.-. technique for solvingwing-body problems -of symmetrical configurations. In reference 3, MoskoGitz and Masien.have applied the method to determining both thickness and lifting pressure distributions of a triangular wing-body combination and a rectangu%r wing-body conibination, and they have found-goodagreement with experiment except in the wing-b&y j.unc- ture, where boundary-layer effects are important: Two other mathemati-. cal attempts to solve boundary-value problems associated with.rectangu-. lar wing-body combinations are contained in references 4 and 5. In -. reference 4, Morikawa solves approximately the problem of a rectangular wing on a circular body both at the same angle of attack. In reference 5, Nielsen presents a general methodof solving wing-body problems for which the interaction between upper and loygy wing surfaces has no effect on the wing-body interference, The case of a rectangular i&.ng mounted at incidence on a body -at zero angle of attack is studied in detail.

_.- . ..- ~ ,.-.. --*

.-

-c* -Z

. s

Several approximate theories exist which illustrate important .~ -7-n interference effects. For instance. the m of-Stewart and - __---. Sieghrebli~-in- e-6. accountsfor&& increased wing lift of the exposed yings due.$~body upwash. --- The authors, however, take no account .,. of ,l&s:of lift beh&nd %Xach cone from the leading edge of the juncture nor of the.lift carried over o~~.e_.thebod~-~~-~~~- Another approximate theeis that presented by Morikawa (reference 7') for tri- - - I-_ angular, rectangular, and trapezoidal wings with no afterbody. while the limitation to no afterbody is unnecessarily restrictive, the valid-

.-_

ity of Morikawa's assmtions for various combinations aFits.experimental verification. . . --

An approximate method for triangular wing-body combinations that has been substantiated by experiment is that of Nielsen, &&Zen, and Tang (reference 8). Thepossibility of extending this method to ccatlbi- nations-with wings o? other plan forms mounted on bodies of revolution is investigated in this report.

_. o--

__

.

RACA RM A51J& 6 3

.

. A

CL

%

=r

=t

=Y d

E

K

KB

L

2,

lf M

m

Q

l r

R I

SYMaOLS

aspect ratio of exposed wing panels joined together

mean aerodynamic chord

c

L; \ Cy2W

$ i

, inches

CYG,

lift coefficient based on exposed wing area

lift-curve slope based on exposed wing area

chord at wing-body juncture, inches

wing tip chord, inches

wing chord at spanwise distance y from body exis, inches

body diameter, inches

complete elliptic integral of second kind

ratio of lift of co&ination to that of wing alone

ratio of lift carried by body of combination to lift acting on wing alone

ratio of lift karried by wing of cdination to lift acting on wing alone

lift force, pounds

afterbody length, inches

forebody length, inches.

free-stream Mach number

cotangent of leading-edge sweep angle

free-stream dynamic pressure, pounds per square inch

body radius, inches

Reynolds number based on mean aerodynamic chord

.

4 A NACA RM A5lJO4

S

%u

XIYIZ

%

5

area of wing alone formed by joining exposed wing panels together, square inches

semispan of wing-body combination, inches

streamwise, epanwise, and vertical coordinates, reepectively

angle of atea?& of body, radkns

local angle of attack at-spanwise distance y fkxabody axis, radians

effective aepect ratio

-. effective diameter, root-chord ratio

AL.X. leading-edge sweep angle, degrees

A. ct taperrEcM0 c ( > r

P

cp potenkial of perturbation velocities

Subscripts

W wing alone

C a-body c&fnat.ion

N _..

nose of conibination

C-N wing-body combination mkus nose

B body&one

W(B) wing in presence of body

NW) b&y fn presence of wing minus body n&e _ . .._ ".

.

NACARM A5lJO4 A 5

Superscripts

3 slender-body theory

U upwash theory

ANALYSIS

Cbservations Conkerning Slender-Body Theory

The linearized equation of supersonic wing theory (or wing-body theory) is the wave equation for the velocity potential

CM2 - 1) ‘p,-Cpyy-‘p,, = 0 (1) For slender wing-body co&inations, Spreiter (reference 9) has shown that the first term of this equation can be ignored so that it reduces to Laplace's equation in the y, z plane. Using this stiplification, Spreiter has obtained simple, closed expressions for the lift-curve., slopes of many wing-body combinations. '

It is well-known that for wing-body combinations which are not slender the lift-curve s$opes are overestimated by slender-body \ theory (reference 8). However, this fact does not preclude the use of \ slender-body theory for nonslender configurations since, in certain \ Instances, the ratio of the lift of the wing-body combination to that of !L the "wing alonen may be adcurately @edicted by slender-body theory, even though the magnitude of the lift-curve slope may be incorrect. From the foregoing.ratio and a good estimate of the wing-alone lift-curve slope, the lift-curve slope of the combination can be obtained. This was essentially the method used by Nielsen, Hatzen, and Tang in reference 8 to predict the lift and moment characteristics of triangular wing-body

x combinations. Good agreement between expertient and theory was obtained. The method..& limited in principle to those configurations for whi&

The success of this method with triangular wing-body cozibinatkms was the result of two fortunate circumstances. First, the assumptions of slender-body theory are best met for ccxnbinations in which the lateral dimensions expand slowly, as for triangular wing-body ccmbinations. Also, because the aspect ratio of the wing alone is the same whether the wing alone is defined as the exposed half-wings joined together or as the triangular wing that includes the area of the wing blanketed by the body, the method of reference 8 gives identical results for the

.:.;-- ..’

6 -=Jbme NACA RM A51JO4

lift-curve slope using either definition. However;for wing-b.ody combinations employing other than t.riangular w&&, the wing+lone aspect ratio depends on the wing-alone definit.ion.. Thus the application of the method of reference 8 to rectangular wing-body ccrmbinations was found to give significantly different reeults, depending on whether the wing alone was taken as the &posed half&in& Joined together or a8 the expoaed half-wings plus the blanketed area. Although an attempt to determine a percent effective blanketed area was partially successful, .: thi6 quantity depended on PA and pd/cr, -and for other wing plan forG3: would depend -on additional parametere; Thie difficulty made It neceb- sary to attack the problem from an entireiytifferent poitit of view from that of reference 8. The method of Morikawa (reference T) for presenting lift interference was adopted. .-

In presenting the lift results use is made of a nuniber of wing-body parameters~. A wing plan form with trapezoidal panels of unlform taper can be specified entirely by aspect ratio, taper, and cotangent of the leading-edge sweep angle. For supersonic flow, the effective values of these parameters are :.PA, h, and @n. An additional parameter relating body size to some characteristic wing dimension is required to character& ize completely the geometry of a wing-body combination. The parameters r/sm and Bd/cr are both used..for thi.8 purpose.

In the method of Morikawa for presenting lift interference, the wing alone is defined as the exposed half-wings joined-together. The lift of the wing-body combination exclusive of the forebody is related -. to the l$ft of the.wing alone by the -factor K which ia to be determined. .

LC-N =KLW

The .factor K is decomposed into two factors KB and KW which represent the ratios of the.body lift and wing lift of the combination _ to that of the wing alone.

K= KB + KW

LB(W) KB = - -. --- .--

Lw

b(B) Kw=y-q-

(3)

So far, the scheme is only a way of representing lift results. The solution of the problem requires a determinstion of values of KW and KB that are reliable for all wing aspect ratios. In his paper,

.s-

I

-7 I I,

_ _ ---’ .d

::

: -_.:

-. ,

/.

f

_- : .- . --.-.

I-..

.-- .._

.L

.

I

RACA RM A51J& 7

Morikawa has given the slender-body values of K, I$, and KR which will be indicated here by a superscript.

i . . (6) :

-_. -. where r is the body radius and Sm is the maXiMum wing semispan. (The assumption. is made that no negative lift is developed'behind the maximumwing span. R. T. Jones (reference 10) has pointed out that for wings, at least, the negative lift predicted on these sections by slender-body theory is prevented by separation.) The value of Q(s) gfven by the slender-body theory is

The value of Kg(') is obtained by subtraction. and Kg(s) as determined b

A plot of K(6), Q(s), y slender-body theory appears in figure 1. In

the limiting case of r/sm = 0 the combination is all wing and the value of IQ(s) = 1 and Kg(s) = 0. As r/sm approaches unity, there is a very small exposed wing. For this small wing, the body is effectively a vertical reflection plane snd the angle of attack is 2~6 due to upwash (as will be discussed later). This makes q(s) = 2. The wing produces an equal amount of lift on the body.

It is clear that the values of KB(~) and w(s) should be satis- factory for slender wing-body canibinations. However, they cannot be used for large aspect ratios for which slender-body theory is inapplicable without further investigation. Independent methcds of det rmining Kg and m will now'be presented, and the applicability of and K&)willb

9) Kg s e inferred by comparison. ,

8 - . NACA RM A5lJO4

Increase 3nWingLift Due to Body-wash

Az.approxTmate method for evaluating KW is to suppose that the exposed wing8 are operating in the upwash field of the body alone and __ then to calculate the resultant wing Uft. Neglecting any effect of the nose, it has been pointed out (reference 11) that the upflow angle due to the body varies spsnwise on the horizontal plane ,of symmetry as

. _-

.

.-

”

where y is the lateral distance from-the body axie. The wing fs thus effectively twisted by the body-alone flow. If now the upwash angle given by equation (8) is taken into account by using strip theory, sn approximate value of- KW is obtained-as follows:

s s,

Q(U) = r ay % *

Grn (9)

Equation (9) does not include tip effects. The followhg expression is obtained in terms of r/sm and taper for wingsof uniform taper.

qp) = 3 (1+X) - $ - @&-,"A 2n $

0 1 5 ( >

s (1+x) (10)

It is notable that. Kw(~) d oes not depend on aspect ratio.

Equation (10) was used to determLne Kw(~) for A = 0, 6, and 1, and these results are compared to those of slender-body theory in figure 2. It is seenthatthe effect.& taper is small compared to the. effect of r/Q. Both theories give nearly the same values'at both'high asd 1OW values Of r/Sm, greater than KJ&s).

but the values -of KW(u) are in all instances Nowhere is the difference of great signi.ficance.

Although account has been taken of the upwaah induced along the wing span by the bcdy in the determination of .Kw(~), ngacco&has-&eg taken of the loss of lift due to interactionbetween the wing an the body of the winged part of the co&ination. For th&rea&n, KW u) 4- ii%lL be too- large. Ther:efore; iT=-decided to use ..KW(8) for all,

-

.c

.

-7

. -..

EEA RM A5lJO4

combinations. with the wing

This procedure corresponds to the method of reference (8) alone defined to be the exposed half-wings joined together.

.-- 9 -.

.

Lift Carried Onto Body From Wing

While the.upwash theory represents a simple method for estimating the effect of he body in increasing the wing lift, no general, simple method, othe

P han slender-body theory, exists for estimating the lift.

carried ont$ the body by the wing. Morikawa, in reference 7, has estimated KB for combinations with no afterbody using various assumptions for various plan forms. A method using uniform assumptions and includ-. ing afterbody effects will now be given. I

;j On the basis of slender-bodytheory, nonexpanding se&I-o-&of a b .-.ip a Unix -P

orm-flow develop--~~-l~.'~~erore, the lift on a s raight portion of b & -nn'--&~yc&-' a-iiing is mounted is due prticf- paJLy to lift csrried over from the wing onto the body?A>.oi_nt on the wing is thought of asaource.of. lifting disturban~ces.w~.ch move in aU. dE6ctiops in the downstream Mach cone from the point. Some of these -.*---_. -22. -- -- disturbances are carried over onto the bod~.--~The assum&,ion is made that the sole effect of the body (regsrdless'of cross section) is to dis- _i - ^.-_ -. 1 place these pulses.d- own~%~esm w2thou-t d$minishing their-g poten- t-is iSyi=o-called delayed reaction of Lagerstrom and Van Dyke in-reference 12, which was substantiated for a particular family of rec- tangulsr wing-body combinations by Nielsen in reference 5.. Downstream of the wing, the flow returns to the free-stream direction, The effect of this change in flow direction is felt on the surface of the afterbody behind the Mach helix originating at the trailing-edge, root-chord juncture . In this region, the reaction tends to cancel the lift carried over from the wing onto the--body. The effective resultant lifting area on the body for one half-wing can thus be approxFmated by the shaded area shown in figure 3(a).

While a nonplanar model has been set up to represent the lift carried over onto the body by the wing, further stiplification to as equivalent planar case is desirable before calculations can be performed. The body is imagined now to be collapsed to a plane snd the Mach helices of figure 3(a) become the Mach lines of figure 3(b). The lifting srea of the body is the shaded area of figure 3(b) at zero angle of attack. This area is equal to the horizontal projection of the lifting area of the actual body surface (fig. 3(a)). The lift on the body.can be. c&cu- l&edaimply.by integrating pressures dato the half-wing ova-the . shadedsea tiXi?Crihg t-t *~ -- * -.= -

In determining the pressure field of the half-wing on the planar area, both subsonic and supersonic leading edges are c'onsidered. Tip

. . . -

10 Y ,- NACA RM A5lJ-04

effects are not considered, and the analysis is confined to the case in which the Mach line emanating from t&..lead,fng.edge of the wing tip falls behind the regionof lift carry-over,'&o%h.e~body; _ ThJs Condii .. - 'k--L tion imposes the-faming restriction: _ - 1: .:' l--:5

BA (1+x)(-& + l)t4

on the wings for which the method is to apply.

The value of 3Jf-t carried over onto the bodyby ahalf-wIng with a supersonic leadi@ e@e is given (us* the solution of reference 13).as . .__

with the coordinate.syatem of figure 3(b). This result is doubled to account for the lift of two half-wings and dikided by the lift of the wing alone to obtain Kh. For -all Mach numbers Kg is'

--

KR = 8pm

2

Pm (@a+l)&k%I

I[ 1 ( > cr-

I+Bm m

co&-l (1 + $) - +&- COS-l

I- .- 03)

where m@ >‘I. ,f.. -.. ._ I

c

NACA RM A5lJO4 11

Similarly, for subsonic leading priate conical lifting solution

edges there is obtained, using the appro- from reference 14,

.

Kg =

where @Cl.

04)

The effect of body upwash in increasing the lift of the exposed wing has notihmW30 a .- ccount ;tn cal&Latingthe effect of.th~ wings the

It is to be note& that KB in nkber of parameters, of which four

tity K~(l+x)

equations (13) and (15) depends on a are independent. However, the quan-

a function of-only mp and e.

The quantity ie presented as a function of @d/C, for constant values of @ Fn figure 4 which is to serve,as a design chart in determining KB subject to the restriction of equation (ll). The values

can be obtained from the charts of Lapin in reference 15

or those of Lagerstrcm and WaU in reference 16.

For the purpose~of~illustrating the beha equations (13) and (15) with alender-body

or of Kg. and comparing KB s), figure 4 has been used i?

together tith.reference 15 to obtain figure 5,.which presents Kg: as a .- function of SA and r/sm for -X = 0,-i/2, and 1 and for no trailing- edge sweep. The case.of .X = 0 corresponds to triangular wings (fig. 5(a)), L = 1 to rectangular wings (fig, 5(b)), and X =-l/2 to.- trapezoidal wings-.(fig. 5(c)). For lx+ngular wings, the curve of Kg by the present theory for. /3A = b is slightly greater~than KB(~) as given by-slender-body theory,. _ and ha8 not been included in the' figures, For such small values of j3A slender-body theory is the more.vitlid. Incidentally, the restriction of equation (11) is met by all triangular wings with no trailing-edge sweep. An examination of figure 5(b),for rectangukr wings sh?s good agreement between slender-body theory and the present theory at PA = 2, the loweet aspect ratio for which the we- sent theory is applicable to rectsngular wings. In the case of the trapezoidal wings (fig. 5(c).> the-restriction of equation (11) imposes the condition that j3A>4/3. For a value of 6 4 of 4/3 there is no appreciable difference-between slender-body Kg s) and the value of Kg by the present theory.

.

? .-

- y- L

On the basis of figures 5(a)-, 5(b), and 5(c), the following selec- --f--

tion rule is given:

theory KB(S);

tain caina ions Kg>% s). 1

of taper andlow aspec ratio it may turn out that In,such cases, use Kg s) 1 since it is more accurate than Kg for small aspect ratios. Although this rule has been derived by compar-lson between-the present theory and slende-r-body theory.for unswept trailing edges, it has also~~'~ed vaUd experimentally for ._~ swept-forward trailing edges. '

Since rectangular and triangular wings are very common, and

since is lmown in closed form-for these plan forms, special-

_. --

ized reklts &II readAly be obtained from eqU.ations (13) and (15) for' Kg. For reCtaX@b?2 wing-body CORibtitiOD.8, Kg 18 given as

I

.._: -

. ..-

-.-. _

.

NACA RM AglJ& .- 13

For triangulw -g-body combinations with subsonic leading edges, KB is given as

Kg= 83 ($99

x2 g2 0 4

2

0 PA 4 ‘2

,( ) 2 J.=+l 4

1+ 2 1+.y e

( 1

1 r --. %l

2 l+J= r ( ) 4 s,

1 r -- 8m

+

14 NACA RM A51JO4

and for ai1pSiiso3iIc leading edges -as.. -

--- '-. -. r I -- -__

I (18) . .

,

-. - - --

-.

mp = 6.64

Bd/cr = (?-69)(w) 3.878

NACA FM A51J& -- 15

- Numerical Example

To illustrate the use of the method developed in the foregoing sections, the determination of the lift-curve slope for a trapezoidal wing- body xzibination is now presented. Given that ct = 1.500, cr = 3.878, r = 0.850, sm = 3.790, M = 2.87, sd no midchord sweep, the following values of the parameters are obtained:

A=. 4(2 .g40)

1.5 -I- 3.878 = 2.19, aspect ratio, of wing alone '

p = JG = Q/ = 2.69 1-.”

$A = 5.89, effective aspect ratio'

r/sm 4 0.224, body-radius, semispan ratio ',

?b 1.500 = - = 0.387, taper ratio 9 3.878

2(2.94) m = (3.878 - 1.5) = 2.47

= 1.18

The value of the parameter

j3A (1+X)

in equation (ll) is

1 J = (5.89) (1.387)

The value of l$(s) from equation (7)

Now determine I$(s) frcm figure 1:

KBb) =

,

16 - --- ? NACA FM A5WO4

The value of Kg f*am figure 4-b parametricform is

Hg(PC&)w (l+h.) ($- ;: l)= 4;".

from the charts of referenke 16 is i '/ I

( > pcLa = 3.85 j,,/ w .- -‘I

The value of- Kg is thus >- ..: i

Kg = p4.41"- .p-

(3.85j(1.387)(3.46) = o.24

Since .KB< KB(~), the value of... Kg -is -to be.sTd:

K = s(') + Kg = 1.18 + 0.24 = 1.42

: ’

. . -...--’

- --

I c

The lift-curve slope of the comb~~~tibn.excluding.the effect of the nose 1. -;-I, is thm . . L.f.rTL

= (l-42)(3.85) = 5.46 per radiw ._ ' ...-;

For the lift-curye slope of-the comslete cmination,. *he l$ft due - 1 .-rz

to the nose must be added to If the nose is slender so

that slender-body theory is valid, then

( 1. PCLc, =gprrr' S

= (2.94)(1.%0 + 3:878)-Y o-77 per radian -' i,-y:

Finally, the lift-curve slope for the entire cmfiguration is given by

= 5.46 + 0.17 = 6.23 per ,radian ~

::

3E NACA RM A5lJO4

EXPEZUNFJRAL VERIFICATION

17

The results of the foregoing analysis have-been applied to the cal- culation of the lift-curve slopes of nesrly 100 wing-body configurations of widely varyLng plan forms. The same geometric configuration at two

. different Mach numbers has been counted t@ce. The results are compared with the experimental lift-curve slop&~ which were measured in vsrious

. windtunnels. The correlation between the experimental and estimated results is shown in figures 6, 7, and 8 which apply to triangular, rectangular, and trapezoidal wing-body combinations, respectively. Tables I, II, and III a ummarize the geometric and aerodynamic characteristics and the test conditions for the tr@ngular, rectangular, and trapezoidal tingaody combinations. A sketch of a wing-body co&ination defining the dimensions is given in figure 9, and rough sketches of the combinations are included Fn the tables. The sources of the test data are listed in references 17 to 38; some of the test data are unpublished.

Some difficulty was met in trying. to determine lift-curve slope from published curves since slight nonltiearities near a = 0 were present. In the several such cases encountered the curves were essentially linear for +2O, and the average over this range-was used. The values of the lift-curve slope for the bodies alone were in some instances also difficult to obtain accurately because of the,small slopes of the published curves. Furthermore, the reliability of the experimental lift- curve slopes was sometimes questionable. In one case, data on similsr configurations from different testing facilities (and at different Reynolds numbers) gave a difference of the order of 10 percent in the lift-curve slopes. Also, generally ape-, the data have not been corrected for any flow irregularities that may exist in the various wind tunnels.. In view of these difficulties, together with the approximations made in the method, it was felt that a correlation of f10 percent would be a realistic-accuracy to expect.

The actual lift forces developed by the winged sections of the combinations are not given directly by eqeriment, so that no direct comparison could be made between the method and experiment for this lift component. Instead, it was decided to perform the correlation on the basis of over-all lift-curve slopes of the combinations. The estimated over-all lift-curve slopes were determined by adding to the contribution due to the winged part of the combination, as determined by the present method, the contribution due to the b&y nose as determined by slender- body theory. The lift contribution of the nose for cotiinations having . relatively small wings is large. Consequently, the correlation reflects in part the ability of slender-body theory to predict the lift of the nose.

18 . * .- .IUCA RM A51J&

It shouldbe borne ti.mjlnd-that correl+.t+nbetween the method and experiment on the.bissis of-total lift does not-necessarily imjly.that the distribution of lift between body and wing has-been correctly predicted by the method. -To substantiate this-point will require more data on the lift.of components than is now available. _-

Included.on the-curves of figures 6, 7, and 8 are lines of perfect agreement, and dashed lin es indicating *lo-percent deviation from perfect agreement. Data for co&inati& wLth no afterbodyhave-been indicated.by flagged symbols.. It is~~readily appaiSit from these figures that the present method estimates the lift-curve slope within +lO.percent for most of the combinations, and thus properly accounts-for the first;. order effects of wing-body interference.1. .%!he scatter about the,wes ; of perfect agreement -is a~arently random and is due to second-order effects that wi-ll subsequently be,di.sEussed. The points--on the correlation curves for configu.ratJons with no afterbody have, onthe average,- higher estimated lift?curve sJo@s ths$ the eeerimentalj as would be ~ expected since the present method includes afterbody lift,.

With-regard-to triangular wing-body combinations the present methad is not substantially different from that of reference 8, which was found to be-valid for such combinations. Thus correlation for the triangular wing-body combinations was assured.

For the rectangular w&g-body ccmibinations, a pointof interest is furnished by the fact that slender-body theory should be inaalica;ble. Consider the slender-body combination tith the sxea OA'A in figure -10, According to alender-body theory the entire lift is developed on CM'. If A approaches A!, the.slender combination becomes nonslander and, on the basis of slender-body theory, the lift r&ins tichanged and ia concentrated on the lead&g edge of--the rectangular half-wing. This applicat$on.of slender-body theory to rectangular wing-body cauibinatious represents a degenerate-case of the theory. .-. It-2s thus interesting that the use-of IQ(s) produces correlatiosfor rectangul& wing-body con&f- nations. The good-correlation of.the trapezoidal wing-body combinations is more significant-than-that for t-he-.tr+angular or rectang&ar wing-b&y .- -. conibinations because generally four quant~ties~ are.necessaYy to describe the geometry of trapezoids&co@inations, whereas only two are necessary for the latter coaibinations. .-

'In this connecUon;-it ,is significant to ask how much error can be -' -- introduced by neglecting interference. For the triangular wings of

this report it was determined that the ,sums of t&tin@;-alone and body-alone lifttcurve slopes .were oqth~_aver+ge i6Jperc& greater thanthe corresponding experimental lift-curve slopesfor the cc%ibiira- tions when the wing alone is taken as the triangular wing that includes the blanketed.s,re%. -For very small w+gs the sum can~app?%ach twice the experimental value. _-.

I

_ .

;;l.

.--

--- --- _ .._-

- .---

-.--.

.

NACA RM A51J&

ADDITIONAL FACTORS AZYZECTIRGLIFI'

19

The scatter that is exhibited by the correlation charts indicates the existence of a number of higher-order effects not fully accounted for by the present method, such as afterbody shape, forebody Shape, Reynolds number, angle of attack, and airfoil section.

Afterbcdy Shape

The length of afterbody behind the wing of a combination has an effect on how much lift is developed by the afterbody. The first few body diameters of afterbody length are the most effective in this res- pect. Lagerstra and Graham (reference 39) have studied flat afterbodles behind triangular wings. For the planar case, they find, on the basis of linear theory, that the lift force increases as the afterbody length increases up to a certain optimum length and decreases thereafter. Whether such considerations are also val3d in the case of cylindrical' afterbodies is not clear. Lagerstrom and Graham imply that theoretically an opt- afterbody length would be expected for the nonplanar case. Data are not yet available to indicate whether an optimum length of afterbody exists for nonplanar combinations when viscosity affects the flow.

Theoretically, boa-&ailing of the afterbody should have the effect of decreasing the lift-of the combination if the flow follows the body. Because of separation, it is expected that little, if any, lift will be lost.

Forebody Shape

The forebody shape can influence the lift of a wing-body ccxnbina- tion as predicted by the theory of this report in a number of ways. First, if the nose of the combination is not slender, the lift, as predicted by slender-body theory, will be inapplicable. If the w%ng is located close to the nose;the upwash field till vary chordwise and spanwiae instead offonly spanwise as assumed in equation (8). The wing of the combination will thus be effectively cambered as well astwisted, and the wing-body interference as well as the lift due to upwash will be altered.

An additional-effect of forebody shape is the marner in which it affects the boundary-layer phenomena of the winged part of the conibination. For instance, if the same wing were mounted near the base of a

20 NACA RM A51JO4

. given bw'rather than near the nose, the boundary,layer would be thicker n. ~.- and more serious boundary-layer interference could be anticipated.

.

Reynolds Number and Angle of Attack

The effect of Reynolds nuDiber onthe vortex and boundary-layer flows : ..:cti of .wing-body combinations is not well understood. While the effects may not be significant for lift at low angles of attack, they are of consid- erable- importance at high angles -of attack. Infact,. the piscous.cross flow of the type discussed by Allen and Perldns in reference 40 is auf- .--I ..A ficiently important to-invalidate at high angles of attack any theory of 1:

wing-bodycombinations based solely on frictionless flow considerations. ----==z

Airfoil Section L .-- - --

It is known that the airfoil section canhave-a large effect on the , .Z lift-curve slope of wings of identical plan -form, Such an effect is also .--...:;: to be anticipated for cccmbinations in which the wing furnishes most.of the lift.- It cannot be ascertained without experiment whether the addi- ,:. _ ..- -.-.-, ..,i ;"- tion of the body will alleviate or aggravate differences in lift-curve .c L slope due to airfoil section since these differences are not yet under.- .r- 7::-:. stood for wings alone. -. r ii----

CONCLUDING REMARKS

On the basis of the correlations between the estimated snd experimental lift-curve slopes presented in this report for--nearly 100 t&angular, rectangulsri and trapezoidal wing-body configurations, the leading edges of which are not swept .forwar d and the trailing e&es of which are. not swept back, it can be. concluded that, using the methods of this report, the lift-curve slopes of the combinations can be predicted in most cases within +lO percent. The scatter observed in the correlation is due to effects such as forebody and aft&body Shape,.Reynolds number, angle of-attack,endairfoil section which cannot be predicted at the present time. :. _.. . ..~...-. _ _...... .~ ..=I~.=~-l----~....=..~.T. : ~.

Ames Aeronautical Laboratory, National Advisory Committee for-Aeronautics,

Moffett Field, Calif. . .-- .- a

-.- ,- -.

NACA RM A5lJO4 21

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

SL.

ti:

REFERFlNms

Ferrexi, Carlo: Interference. Between Wing and Body at Supersonic Speeds - Theory and Numerical Application. Jour. Aero. Sci., vol. 15, no. 6, 1948, pp. 317-336.

Nielsen, Jack N., and Matteson, Frederick H.: Calculative Method for Estimating the Interference Pressure Field at Zero Lift on a Symmetrical Swept-Back Wing Mounted on a Circular Cylindrical Body. NACA RM AgElg, 1949.

Moskowitz, Barry; and Maslen, Stephen H.5. E&rfmental Pressure Distributions Over Two Wing-B&y Ccmbinations at Mach Nmiber 1.9. NACA RM E5OJOg, 1951.

Morikawa, George: The Wing-Body Problem for Linearized Supersonic Flow. GALCIT J.P.L. PR 4-116. Dec. 19, 1949.

Nielsen, Jack N;: Supersonic Wing-B&y Interference. California Institute of Technology, 1951.

Stewart, H. J., and Meghreblian, R. V.: Body-Wing Interference in Supersonic Flow. GALCIT J.P.L. PR 4-99, June 2, 1949.

Morikawa, George: Supersonic Wing-Body Lift. Jour. Aero..Sci., vd. 18, no. 4, 19%

Nielsen, Jack N., Katzen, Elliott D., and Tang, Kenneth K.: Lift and Pitching-Mament Interference Between a Pointed Cylindrical Body and Triangular Wings of Various Aspect-Ratios at Mach Nimibers of 1.50 and 2.CQ. NACA RM A5OFO6, 1950.

S$reiter, John R,: Aerodynamip Properties of Slender Wing-Body Co&inations at Subsonic,~Transonic, and Supersohic Speeds. NNA Rep. $2; 1948. (Formerly NACA TN's 1662 and 18%')

Jones, Robert T.: Properties of Low-Aspect-Ratio Pointed Wings at Speeds Below and Above the Speed of Sound. NACA TN 1032, 1946.

BeskIn, L.: Determfnation of Upwash Around a Body of Revolution at Supersonic Velocities. Rept. No. m-251, 1946.

Johns Hopkins Univ. Applied Physics Lab.,

Lagerstram, P.-A., and Van Dyke, M. D.: General Considerations About Planar a& Non-Planar Lifting Systems. Douglas Aircraft Co., Inc., Rept. No. SM-13432, 1949.

22 .- v NACA RM A5lJ&

13. Jones, R0bert.T.: Thin.ObU.qm Airfoils at NACA Rep.. 851, 1946.. (Formerly NACA TN llO7

14.. Lagerstrom, P-A.: Linearized Supersonic Theory of C&Cal Wings. NACA TN 1685, 1948.

.

,.

.- T---

15. Lapin, Ellis: Charts for the Computation of-Lift and Drag of Fini;e Wings at Supersonic Speeds. Douglas Aircraft Co., Inc.; Rept. No. SrJr-13480, 1949.

;.- ,-- - 1

_I

J 16-c

17.

Lagerstrom P--- A:, Wall, D., DFmensiokal'Wing Theory.

and Graham, M. E.: Formulas in Three- Douglas Aircraft Co., Inc.,

Rept. No. SM-ll901, 1946. -.

- -,I=

Spahr, J. Richard, and Robinson, Robert A.: Wind-Tunnel Investi@+- tion at Mach Numbers of 1.5 and 2.Caf a Canerd~Missile Configura- tion. NACA RM A51CC8, 1951. : ': --

i -y--

..-+i& --

._

18. Jevon, R. W.: Data Report for Supersonic Wind Tunnel Tests on XSEM-~a-6 Models #3C and #6A. Fifth Daingerfield Test &rid, M = 2.0. Grumman Aircraft Engineering Corp., Rept. No. 3147.20, Mfwch, 1950.

19-m

20.

21*

22.

23.

Jevon, R. W-;-s&l Bastedo,.W. Jr.: Data Report for Supersonic Wind Tunnel Tests on XS%-N-6 Model#3A. First Daingerfield Test Period, M = 2.0. Grumman Aircraft Engineering Corp., Rept.. No. P/A 3128.20, April 1949.

-- :

I _-

Jevon, R. W.: Data Report for Supersonic'Wind Tunnel ‘&St8 on XSM-N-6 Models #3B and &A. end-&h Daingerfield Teat Periods,

. . ,: &,.&&& tic&&t Esl&neering cmpm, .

= 2.0, 2.25, 1.73. fept. No. P/A 3141.20, Sept. &g.

. - _ _ _x

.--,.. Basted--W. Jr.: Data Report for Superstic Wind Tunnel Test% on

XSSM-~-6 Model #6, -2nd Aberdeen Test Period, M =-l-.72. Grumman Aircraft Engineering Corp., Rept. No. P/A 3107.21, .-- ..- July 1949.

-.- Katzen, Elliott.D., and Kaattesi, George E.: Drag Interference ~ --.

Between a Pointed Cylindrical Body and Triangulsr Wings of-Various -

Aspect Ratios.:at Mach Numbers of 1.50 +d 2.02. NACA RM A5lC27,~ ' 'I' 1951.. -:I='

-. ----- ..-. -_ . .%. -. - - __ --..- - Peters, R. G.: Data Report for Supersonic:.Wind Tunnel Test8 on

GAPA Model ~~~87. Sixth and Seventh Aberdeen Test Periods, ' M= 1.72 and. M :.1.28.. Bqeing_Airglane Co., ~-8788, (Tech. Rept. No. ill-g), Feb. 1948. --Y----

-u^-.

--- ;

NACA RM A5lJO4 ,,L,,,,,,,. 23

24. Peters, R. G.: Data Report for Supersonic Wind Tunnel Test8 on GAPA Model ~~-87. Fifth Aberdeen Test Period, M = 1.72. Boeing Aircraft Co., D-8397, (Tech. Rept. No. Ill-7), Aug. 1947.

25. Rainey, Robert W.: Langley g-Inch‘ Super%on&Tunnel Tests of Sev- era1 Modifications of a Supersonic Missile Having Tandem Cruciform Lifting Surfaces. Three-Component Data Results of Models Having Ratios of Wing Span to Tail Span Equal to 1. NACA RM LgL30, 1951.

26. Rainey, Robert W.: Langley g-Inch Supersonic Tunnel Tests of SeV- era1 Modifications of a Supersonic Missile Having Tandem Cruciform Lifting Surfaces. Three-Component Data Results of Models Having Ratios of WFng Span to Tail Span Less Than 1. NACA RM L50I29a, 1950.

27. Rainey, Robert W.: h.Y&ey g-I&h S’UperiOniC ?kUInel TeBtB Of SeV- era1 Modifications of a SupersOniC Missile Having Tandem &XCifOITn Lifting Surfaces. Three-Component Data Results of Models Having Ratios of Wing Span to Tail Spsn Equal to end Less Than 1 and Some Static Rolling-Moment Data. NACA rjM L50307, 1951.

28. Speth, Robert F.: ReBIiLtB of Rascal Supersonic Wind Tunnel Tests at M = 1.72. .Bell Aircraft Corp., Rept. No. 56-980-001, vol. 1, Dec. 1948.

29. Speth, Robert F.: Resuits of Rascal Supersonic Wind Tunnel Tests at M = 1.28. Bell Aircraft Corp., Rept. No. 56-980-001, vol. 2, Dec. 1948.

30. Har~hman, J. D., and uddeziberg, R. C.: Supersonic Wind Tunnel TeBtB of GAPA Models at a Mach Eu&er of-l.28 in the Aberdeen Tunnel. Boeing Aircraft Co., Rept. D-7817, Aug. 2, 1946.

31. Uddenberg, R. C.: Supersonic Wind Tunnel Teats of GAPA Models at a Mach Number of 1.72 in the Aberdeen Tunnel. BoeFng Aircraft Co., Rept. ~-7818, Dec. 1946.

32. Flake, H. M.: Supersonic Wind Tunnel TeBtS of a 0.020~Scale Model of the NA-705 mssile at Mach Number 2.87 to Determine,Effect of Aspect Ratio and Plsnform of Wings on the Aerodynamic Character- is++ics of Wing Plus Body. North American Aviation, Inc., Rept. No. AL-l.l56, Oct. 1950.

33. Hall, Albert W., and Morris, Garland J.: Aerodynamic Characteristics at a-Mach Number of 1.25 'of a 6-Percent-Thick Triangular Wing and 6- and Sj-Percent-Thick Triangulax Wings in Co&ination With a Fuselage-Wing Aspect Ratio 2.31, Biconvex Airfoil Sections. NACA RM L5ODO5, 1950.

NACA RM A5LJO4 24

34.

35.

36.-

37.

38.

39.

40.

Fischer, H. S.: Supersonic Wind-Tunnel.Teete of a O-075-Scale Model of the Nike 482 Missile. Douglas Aircraft Co., Inc., Rept, No. SM-13848, Nov. 19%.

- - . I --

Grigsby, Csrl E.:. 'Investigation at a Mach Number of 1.93 to Deter- mine Lift, Drag; .Pitching Moment, and Average Downuash Character- istics for Several Missile Configurations Having Rectangular Wings and Tails of Various Spans. NACA RM L50108, 1950.

Zllia, Macon C., Jr., and Grigsby, Carl E.: Aerodynmnic Investiga- tion at Mach Number 1.92 of a Rectangular Wing and Tail and Body ' - Configuration and Its Ccmrponents. NACA RM LW8a, 1950. lL

Jaeger, B. F., and Brown, A. E.: The .Aerodymmic Characteristics at Mach Nn&er 2.0 of 14- and -18~Caliber Fin-Stabilized Rockets With Varying Body and Fin Parametera. U. S. Naval Crdnance Test Station, Inyokern, Calif., NAVCRD Rept. l2ll, Jan. 1950.

Dorrance, W. H.:-' Body-Tail Interference in.Supersonic Flow Includ; ,. -' .- z,T ing an Example Application. University of Michigan, UMM-38, Aug._ 199. ,-- .a

Lagerstrom, P. A., and Grahem, M. E.: Aerodynmic Interference in. .:- ..z-. Supersonic Missiles. DOU&ELB Aircraft Co., Inc., I Rept. No. SM-13743, 1950. ---- '. 77

Allen, H. Julian, and Perkins, Edward W.: Characteristics of Flow . . ..-.'._I. Over Inclined BDdieB of Revolution. NACA RM A5OLO7, 1951.

4E NACA RM A5lJ04

.

25

26 NACA RWl5uC!

TABLE I.- SUMMARYOFAEBODYNAMIC ANDcrM)ME'sRI~ CHAqACqSmCS AND TEST CONDImC?NS FoR~IITII@XLATj WING-BODY-COmINAnONS

._ .,.__ --

., .--__

.-

-7 1

a..- .-

._ I,

. ..L

I

---- -

-

.

.

‘

NACARMA5lJO4 27

TABLE I.- CONCLUDED

,3A(l+X) & cl

() I

Kg

1 4.7 0.97 1.56 1.13 2.63 5.48 2.56 6.35 2 ;:: .94 1.5 1.67 4.08 8.25 5.38 10.02

.60 1.38 2.07 1.32 5.41 1.29 1.38 2.88 2.04 7.52 2.69

.41 1.29 2.83 .88 5.69 .86

.37 1.29 3.73 1.36 7.54 1.79

B 8.7 .32 .30 1.23 1.23 4.00 3.42 1.02 .66 5.95 1.35 St ;*g 9 .26 1.19 3.86 053 a-;; 5:69

10 ;*i 8:5 .26 1.19 4.00 .82 6162 1.08 XL .23 1.16 4.00 6.01 .43 ;-z; 12 10.9 .23 1.16 4.00 6.24 .90 7:09 13 ;:a -34 1.23 2.08 .33 3.59 -- 3.63

14 .20 1.17 2.33 3.29 -25 1.18 2.49 22 3.78 .

;-:z

lE .24 1.18 3.61 .39 -47 5:05

17 10:8

.20 1.14 4.00 .77 2% .91 6.74 18 l 25 1.14 4.00 -77 6.32 ,.91 6.55

19 10.2 .22 1.18 4.00 .77 .91 20 2:; -31 1.18 4.00 2% .91 22 21 1.25 3.33 6:04 -91 22 2.9 1.25 3.33 6.35 .91

;:fi

23 2; -27 1.18 1.86 :z

2.84 3:01 24 .26 1.18 2.u .18 3.22 . 3.39 25 z-z .25 1.18 2.51 .23 3.83 -- 3.95 26

617 -25 1.18 2.83 .27 4.31 4.41

27 025 1.18 3.17 4.84 XI 4.88 28 2:; ' .24 m-8 3.53

A-8

?28 -- 5.36

29 29 1.21 3.10 7.9 .27 ;.;; 2.:: .71 6:58 -1 2:: . 29 1.00 .42 1133 3192 2 29 .44 1.33 3.39 1.77 7.77 1.72 7.66

I'TACA RM A51JYO4

!llABix II.- SUMMARY QF..AEZ3ODYNAMIC AND GEKMFERIC CHApACTlZRISTTCS - ;.-.. ANO TEST COKDI!XONS FOR,RECTANGULAR~mG-BODYCOMBINA~ONS

_ - . 4

1.l2xlo= hex. 2.60 1.07 .265 7.6 12.2 30 ~lberaeen

,1.12xlae hex. 2.60 1.87 .% 7.6 1.2.2 31 AberdBen I I I I I I I I

.56x10e 1 hex. 1.30. 7.48 .I53 8.8 13.1 31 Aberdeen

.Lj.OXy --- 1.25 1.66 .35Q 6.8 9.8 $Y?

.we --- 1.25 2-J-4 .350 6.8 9.8 LanglG 9 In- I I -

.4~~j3 - -- 1.25 2.84 .350 6.8 9.8 9 in.

.5oxlde ad.w. 1.47 1.86 .384 0.0 14.5 38 Mich. u.

I I I I I

--- --- 1.32 1.73 .333 0.0

--- --- 1.32 3.46 200 0.0

--

-- ..- -

-

, .

.--- -

3.a.o. indicates blwnvex %x. indicates hexagonal ‘d.w. tidlcatee double wedge

NACA Fit4 ASJO 29

i 9

10 ll I.2 13 14 15 16 17 la 19 20 -

TABLE II.- COXCLUDED

0.12 1.14 '3.79 .64 .64 5.40 5.40 5.44 5.44 .16 1.17 3.73 .a2 .a2 5.76 5.76

"12 "12 5.47 5.47

.22 1.23 3.62 1.15 1.15 6.41 6.41 1.15 1.15 6.69 6.69 A0 1.33 3.37

1:g 7.73 1.90 7.16

.= 1.~ 3.65 4.71 .23 4.37

.14 1.12 3.53 22 4.67 .19 5.08

.3a .3a 1.22 1.22 2.13 2.93 22 .3a 3.63 5:07 .19 .40 4.70 3.46

.l2 1.12 3.73 .3a .40 33 1.33 '2.93 1.09

Ei. 1.14

.52 1.30 2.79

.44 1.30 3.07 12 5.84 .a0

1.05

.3a .59 1.30 1.33 '2.92 3.30 1.29 1.13 2.g 6:74 1.34 1.48 6.51

.08 1.06 3.58 .06 4.14 -- 4.l.l

.og -40 1.33 1.06 3.37 3.35 .04 3.89 --

2.04 4.05 7.93 .45 1.33 3.18 249: ;:g 1.53 6.97 30 .20 1.2a 1.16 3.42 2.84 :g z:g :$f 4:aa 548

L8.a 14.7 10.5

6.3 11.3 a.5 ;::

15.0

Z

613 ii*25 4.9 2:;

30

T#!J3LE III.- TEST

coNFImAL

SUMMARYOFAERODYmAMIC~AllDGEQMETRIC CONDITIOI'JS FUR TRAPEZOIDAL WING-BODY

NACA RM A5lJ09

cHARAcTEBIs~cs AND COMBlIlNAlTONS

. . .

,

-.

---/ .-

---.

-.

. -tl

v--

CONTIDENTIAL .

NACARM A5lJO4

,

I 1

I d

I

1

,

I d

;

1

No<

- 1 2

2

65

i 9

10 li I2 13 14 1-5 16 17 I.8 1-9 20 21 22 23 24 25

g

ig

;"1

;i

;z

3: 39 +o Cl -

fM( J-+X I(.. +$

6.5 8.9

2:;

86': 819 7.7

10.1

9.6

;:2 4.7

2:; 5.4

;::

462

?k 6:9 3.8

z:i:

Z:; 4.3

::2

;*f3 7:4

55:: 4.7

TABLE III.- CONCLtiED

3.56 :Z -27 .41 .32

;g

.34

.33

.26 -32 -31 .61 .39 -33 .26 -23

:?i 043 .23 -67

2; .37

:g .28 033 .37 033 030

::; .24 -33 .42 -52 0%

1.44 1.44 1.21 1.21 1.27 1.27 1.4-4 1.44 1.44 1.27 1.27 1.21 1.27 1.27 1.41 1.22 1.22 1.19 1.19 1.41 1.31 1.31 1.19 1.41 1.41 1.41 1.34 1.31 1.19 1.19 1.25 1.25 1.22 1.22 1.22 1.22 1.18 1.19 1.24 1.33 1.33

3.72 3.77

zz 3:06 - 2.64 3.68

;:g 2.58 3.m 2.62

2%

?",;r 3:73 3.27 3.73 . 3.27

3.85

3.05

more ti ca

Y > %

4.8 7. 42

2; .98

1.51 7.48 6.09 8.70 1.22 1.23

.89 1.51 1.76 2.48

.22

.38 22 -38

2.42 1.01

076 .38 a

1.87 2.42 2.01 1.99

A9 0% 29

LO8 .62 .22 ;38 22 .38

:Z

1:$! 1.19

U.81 14.72

Z*E 6:86 7.42 -4.72 L3.24 ~6.00 7.05 7.02 6.45 7.42

E 3.51

?:$ 5.61 8.60 6.37 5.25 5.61

2% 8:01 8.27 4.08 5.89 5.10 6.98 5.92 3.27 4.85

6.89

31

ExpChL3nt31 ‘I f 3 c 0 %

11.05 16.29 6.10 7.15 7.15 8.20

B % 0 B

4.98 9.20

-59 1.09 1.01 1.86 7.93 6.55 9.10 1.44 1.30

.94 * 1.60

1.85 3.20

-27 .44 .27 .44

2.79 1.38

.9Q

.44 2.15 2.91 2.41 2.39

::' .3-o

1.12 .66 .28 A-6 .28 .46 .91 . .91 .91

1.67 1.16

I:

15942 12.21 16.95 7.19

227; .

2% 8:67 3.53 4.18 4.03 5.36 8.69 6.16 4.87 5.14 6.~ 7.78

iK$ 3:90 5.71 4.42 7.38 5.68 3.21 4.64 3.36 4.77 6.30

kg

i-2 .

c / .

.

.

.

.

5E NACA IIM A5lJO4 33

.

,

1

,

L

i *

3.6

2.8

/.6

/.2

I

.8

0 .2 4 .6 .8 LO

Body-rut?7us~ wing -semispan f&-O, f/G

Figure /. - V&es of flKE/ and $’ from s/end+-body theory.

34 NACA RM A51304

S/endef - -T- body theory

- -. -.-

--. -..-

.-

.2 .4 4s .8 i.0 Body -rodiuS, wing-son&pan rafio, r/s-

F/gure 2. - Comparison of K,, deiermined by slender-body and upwash fbeories.

.

NACA FM A51J04 35

tl

04 \ \ QL

cr ‘\/’ /\ / \

‘\ \ .

-Region of influence of whg on body

Mach lines - - -

“t l!!l

\<’ CR --/ \ / \ / \ \

(a) Afonplanar case. (b) Equivalent planar case-

Figure 3. - t?egion of influence of ha/f -wing on body.

6

.I

.P

.I

.B I.2 Lb 2.0 2.4 2.8 Effective bo+diamfq roof-chtwd ratio, /de

.;a I

NACA RMA5lJOk v

.8

.6

K, .4

J .2 .3 .4 Body -radius, wing- semispan ratios r/s,

(a) Tricmgu/af whg -body comb/nations.

37

BA /

2

3 4

&gum 5. - Comparison of K, deiefmined by slender -body theory and present theory for ivings wifh no fraihhg-edge sweep.

38

.8

.7

.6

.5

K, .4

.3

.2

./

0

EACA FM A5WO4

./ .2 .3 .4 Body-rodiis~ wing-semispan mfla, v%

/b) Rectangufur wing -body combhutions , Figure 5. - Continued

.5

_. -

NACA RM A51JOk

.a

.6

K, .4

.3

.2

./

0 .I -.2 :3 .4 Body-radius, wing - semlspan ra fro, r/s,

(8) Trapeoidal wing-body combinations. Figure 5 - Concluded.

d

39

#A 4/3

2

4

NACAFMA51304

2 4 6 8 a

.

figure 6 - Coffehfion between experimentd and esfimuted lift -curve slopes for friunguhr wing - body combinofions.

SE

.

NACA BM A5lJO4

/’

/ .

he of perfecf /

/

ugfeemenf a a 2 k/ffJ

,/ GO%

/f/’ /XL2

d no ufferbody

2 4 6 8 Esfimufed l/f f - curve dope, fl($$

41

figure Z - Correluflon befwe,en exper/menfu/ and esfimafed //ft-curve slopes for ret funguhr wing -body com@inufions. + c-

NACA RM A5lJO4

Line of perfect

2 4 6 8 10 I2 14 ! Estimated /if# curve - dope, ,&(2d

Figure 8. - Goir&afion befween experimenio/ and eshmoted liff - curve dopes for trapezoida/ wing -body combinutions.

7E NACA RM A5lJO4

d-t LE. Sm

4-d Lcr-4 - - -3 -'I -

f

Lr

lzzl wing done

-

Figure 9. - Plan form dimensions for wing -body combinations.

‘\\ \

\ \’ ’ 4\

F/gure IO.- Formation of ret fangular wing-body combinofion from a slender combination.

43

NACA-Langieg - la-al-63 - a?5

national advisory committee for aeronauticsu upwash theory analysis cbservations conkerning...

Documents