(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "A method for calculating the lift and center of pressure of wing-body-tail combinations at subsonic, transonic, and supersonic speeds"

mi % 



(K/iliJi-IK-lOlzJ^) A StlECL iCf CAlCOUTIhG 
ILt Llk'l ANC CtMEE CI iklLilll Ct 
fciNG-tCDY-lAil CCt£If.fllICN£ £5 SUfcSCNIC, 
ii-Ah^Ci.iC, 6Nt ilEEESCNlC £EIIC£ aaticrial 
Advxsccy Ccniiitttc tot Aeictaitics. Aaes 0Uy02 



N8S-7CCJ0 



Uncias 
0U70Sd 



oc 

c 
C 

CO 

< 



< 

r ' 









V.;, TfSj t5 



ia%,.;:.ic?^Fi©Eis}iALsr 



"-• -— - m 



r"n-,- 



RM A53r 






NACA 



RESEARCH MEMORANDUM 



A IvIETHCD FCR CALCULATING THE LIFT AND CENTER OF 
PRESSURE OF V/ING- BODY- TAIL COMBINATIONS AT 



Is B 



SUBSONIC, TRANSONIC, AND SUPERSONIC SPEEDS 
and Robert F. Anastasio 



'^^mi 



-rtfy^ 



ss>*,: 






liJ r^ 



?&«* 



1.^ * ^ 



j^"^ . ^ -. r_- .^. iii.-U ^ ^^:^ct ^^'--^d.- L_ctUOl d-'JI > 

Lloffett Field, Calif. 
LJeRARV ! 



n,v 






^-jV 







NATIONAL ADVISORY COMMITTEE 
FOR AERONAUTICS 



WASHINGTON 



WW 

-iL 






CdNFlbENTIAL 



. t 



r v • v„ !-,» fcj 



■^^4l'^^ '- ^J *»*- ?»>' f 



It *■; 




IQ 



NACA RM A53G08 



NATIONAL 




RESEARCH MEMORANDUM 



A METHOD FOR CALCULATING THE LIFT AND CENTER OF 
PRESSURE OF WING -BODY-TAIL COMBINATIONS AT 



SUBSONIC, TRANSONIC, AND SUPERSONIC 

By Jack N. Nielsen, George E. Kaat jbari . 
and Robert F. Anastasio 



SUMMARY 



falsification Changed to 

UNCLASSIFIED^ 

" Authority 
DOD DIR. 5200.10 




A method is presented for calculating the lift and pitching-moment 
characteristics of circular cylindrical "bodies in combination with tri- 
angular, rectangular, or trapezoidal wings or tails throtigh the subsonic, 
transonic, and supersonic speed ranges. The method covers lonbahked 
wings, sweptback leading edges or sweptforward trailing edges, low 
angles of attack, and the effects of wing and tail incidence. The wing- 
body interference is handled by the method presented in NACA RM's A51J0l^• 
and A52B06, and the wing-tail interference is treated by assuming one 
completely rolled-up vortex per wing panel and evaluating the tail load 
by strip theory. A computing table and set of design charts are pre- 
sented which reduce the calculations to routine operations. Comparison 
is made between the estimated and experimental characteristics for a 
large number of wing -body and wing -body-tail combinations. Generally 
speaking, the lifts were estimated to within ±10 percent and the centers 
of press\ire were estimated to within ±0.02 of the body length. The 
effect of wing deflection on wing-tail interference at supersonic speeds 
was not correctly predicted for triangxilar wings with supersonic leading 
edges. 



INTRODUCTION 



In recent years the problems of the interference among the compo- 
nents of airplanes or missiles have received much attention because of 
their great importance in high-speed aircraft design. This increased 
importance is due to the current design trends toward larger fuselage 
radii and tail spans relative to the wing span. With, regard to wing- 
body interfere^e^oiif q^ tJu^jLi^able^ietl^^f ^^^ jll|^I^^MriWi^tak.at 

In 




J 




NACA RM A53G08 



subsonic speeds is that of Lennertz, reference 1; recent data supporting 
the vork of Lennertz are presented in references 2 and 3» Laborious 
methods are available (refs. k, 5^ and 6) for computing the interference 
load distributions of wing-body (or tail-body) combinations at super- 
sonic speeds, and simple engineering methods are available for estimat- 
ing the effects of wing-body interference on lift and pitching moment 
at these speeds (refs. T, 8, and 9)' With regard to wing-tail inter- 
ference, one of the notable methods for its calculation in subsonic 
aircraft design is that of Silverstein and Katzoff in references 10 
and 11. For supersonic speeds, Morikawa (ref . 12) has examined the four 
limiting cases of zero and infinite aspect ratio for wing and tail and 
has fo-und that the loss of lift due to interference can be as large as 
the lift of the wing itself for equal wing and tail spans. Using 
slender-body theory, Lomax and Byrd (ref. 13) have analyzed the wing- 
tail interference of a family of combinations having swept wings. Sev- 
eral authors have studied problems of the nonuniform downwash field 
behind wings in combination with a body at supersonic speeds; Lagerstrom 
and Graham (ref. 1^) present solutions for certain vortex models repre- 
senting the downwash field. Spahr and Dickey (ref. 15) have compared 
experimental measurements of downwash with the theoretical values and 
have found that the assumption of one fully rolled-up vortex per wing 
panel provides a good prediction for low-aspect -ratio triangular wings 
at small angles of attack. However, for large aspect ratios or high 
angles of attack more than one vortex per wing panel is needed to pro- 
vide agreement between theory and experiment. With regard to the prob- 
lem of determining the tail loads due to the nonuniform downwash field, 
Lagerstrom and Graham (ref. ik) advocate the use of strip theory. Alden 
and Schlndel (ref. l6) have developed a method based on linear theory 
for determining the tail load in certain cases. With regard to over-all 
lift and moment for wing -body-tail combinations, Grigsby (ref. 17), 
Edwards (ref. l8), Edelman (ref. 19), and Rainey (ref. 20) have compared 
experiment and theory on the basis of one fully rolled-up vortex per 
wing panel and have usually obtained good eigreement for the specific 
configiirations they have analyzed. 

The present report can be considered an extension of references 7^ 
8, and 9 to include subsonic speeds and wing -body-tail combinations. 
Its piorpose is threefold: first, to present a unified procedure for 
calcvilating interference effects and to examine the assumptions under- 
lying the procedvirej second, to compare the predictions of the method 
with experiment to estimate the accviracy of the predictions and the 
range of application; and third, to make suggestions for future research 
to improve the accuracy and increase the scope of the method. 



MCA RM A53G08 



(•=0. 



'T 



SYMBOLS 



Arp tail-alonei aspect ratio 

Ay wing-alonei aspect ratio 

Cp chord at wing -body juncture or tail-body junctiore, in. 

c-t^ tip chord of tail or wing, in. 

Cl lift coefficient based on wing-alone area 

C-^ lift-ctirve slope, per deg (unless otherwise specified) 

lift-curve slope of tail based on tail-alone area 



Cm pitching-moment coefficient based on wing-alone area 

frp wing vortex semispan at tail position, in. 

fy wing vortex semispan at wing trailing edge, in. 

f„ wing vortex semispan for large downstream distances, in. 

F('n) Alden-Schindel influence coefficient at spanwise distance t] 

image vortex semispan at tail position, in. 

image vortex semispan at wing position, in. 



hij. height of wing vortex above body axis at tail center of pres- 
sure, in. 

i tail interference factor 

k ratio of lift component to lift of wing alone or tail alone for 
variable wing or tail incidence 

K ratio of lift component to lift of wing alone or tail alone for 
variable angle of attack 

K-K, ratio of lift of body nose to lift of wing alone 



-■•The wing alone or tail alone is defined to be the exposed panels of the 
wing or tail joined togeth^ 




NACA RM A53G08 

Z length of wing -"body-tail combination, in. 

Zy distance from most forward point of body to wing leading edge and 
body intersection, in. 

Zjyj distance from most forward point of body to center of moments, 
in. 

ZjT distance from most forward point of body to shoulder of body 
nose, in. 

Zm distance from most forward point of body to tail leading edge and 
body intersection, in. 

Z distance from most forward point of body to center of pressure 
of combination, in. 

Zr moment reference length, in. 

L lift force, lb 

^T(V) lift on tail section due to wing vortices, lb 

Irg/yx lift on body section between wing and tail due to wing vortices, 
lb 

m cotangent of leading-edge sweep angle 

Mq free -stream Mach nvmiber 

q free -stream dynamic presstire, Ib/sq. in. 

r^j body radiiis at shoulder of nose, in. 

ry body radius at wing, in. 

rm body radius at tail, in. 

R Reynolds number based on mean aerodynamic chord of exposed wing 

Srp semispan of tail in combination, in. 

Sjf cross -sectional area of nose at maximum section, sq in. 

Sp reference area of combination lift coefficient, sq in. 

Srj tail-alone area, sq in. 



^4^ 



NACA EM A53G08 

Sy wing -alone area, sq in. 

Vq free-stream velocity, in. /sec 

Vjj vol-ume of tody nose -up to shovilder, cu in. 

ic distance to center of pressure measured from wing leading edge 
and "body intersection for wing quantities and from tail lead- 
ing edge and body intersection for tail quantities, in. 

Xjj distance from leading edge and body intersection to wing hinge 
line, in. 

a angle of attack of body center line, deg 



P JW- l| 

Fj^ circulation at wing -body juncture of combination, in.^/sec 

r circulation, positive co\interclockwise facing upstream, in.^/sec 

Sep tail incidence angle, deg 

8y wing incidence angle, deg 

At tail taper ratio, (c-^/cj.) 

Ay wing taper ratio, (ct/cj.) 

-^L.E. sweep angle of leading edge, deg 

Pq free -stream density, slugs /cu in. 

Subscripts 

B body alone 

C combination, either body-wing or body -wing -tail 

F forebody 

N body nose 

T tail alone 

V wing vortex 




NACA RM A53G08 



W wing alone 

AS Alden-Schindel theory 

B(t) "body in presence of tail 

B(w) body in presence of wing 

ST strip theory 

T(B) tail in presence of body 

W(B) wing in presence of body 

a a variable, 5 constant 

5 6 variable, a constant 



LIFT THEORY 



The lift theory as developed is for the angle -of -attack range over 
which the lift and moment curves are linear and is equally applicable to 
subsonic and supersonic speeds unless otherwise noted. The methods 
developed in references 7 and 9 for determining the various components 
of the lift have been substantiated for supersonic speeds. These methods 
are summarized and their applicability to subsonic speed shown. 

Attention is focused on pointed bodies having wings and tails 
mounted on body sections of uniform diameter. For the sake of being 
specific, the forward lifting surfaces are termed the wings, even in 
cases of canard configurations. Both wings and tails may have variable 
incidence, but cases of differential incidence are beyond the scope of 
this paper. 

The terminology used is indicated in figvire 1. The nose is that 
part of the body in front of the wing. However, when the wing is 
mounted on an expanding section of the body, the nose is taken to be 
the entire expanding part of the body. The principal lift components 
are (neglecting wing-tail interference): 

1. Lift on nose including forebody, Lj^ 

2. Lift on wing in presence of body, Iy(B) 

3. Lift on body due to wing, I'-gfy) 

h. Lift on tail in presence of body, Lipfg) 
5. Lift on body due to tail, Lj 




NACA RM A53G08 

The additional lift components due to the wing trailing vortices are: 

6. Lift on tail section due to wing vortices, Lrp/y\ 

7. Lift on wing afterbody due to wing vortices, L^/y-) 

All lift coefficients, except those for the tail alone, are based 
on the wing -alone area. All lift components are referred to experimen- 
tal or theoretical values of Cx^ or Cl , through vhich Mach number 

effects enter. Experimental valiies of CjVr or Cj^^ should be used when 

these are available, otherwise any discrepancies between experiment and 
theory for these component parts of a combination will also csLrry over 
to the characteristics of the complete configuration. The lift resiolts 
for tail -body interference are identical to those for wing-body inter- 
ference, except for a term to refer the tail-body interference lifts to 
the wing area and, therefore, will not be treated separately. 

Lift on Body Nose 

The method given in reference 7 for specifying the lift on the nose 
makes use of the equation 



wherein the coefficient K-^ is defined as 

Ly 

for equal angles of attack of wing and nose. For many applications it 
is sufficiently accurate to evaluate L^ by use of slender -body theory 



Lj, = 2rtr/ ag q (3) 

Lf = (k) 




8 l^^^^^Km ^ACA RM A^3G08 



so that 

It is known that slender-hody theory is Tisiaally not sviff iciently accu- 
rate to determine tocly-alone lifts in cases such as nonslender "bodies, 
hypersonic speeds, or large angles of attack. Itiese effects are dis- 
cussed in references 21, 22, and 23, respectively. HoveTer, for com- 
hinations vhich are not predominantly "body, the nose lift is not a 
large part of the total lift, and slender-hody theory giyes satisfactory 
results in most instances. 



Lift on Wing in Presence of Body 

The lift on the wing in the presence of the "body is given in refer- 
ence 9 as 

^LW(B) = [^W(B) ^ + Mb) ^J (cLaX ^^^ 

The factor %(b) is defined as 

Ky(B) » M^ with 8y = (7) 

and is greater than unity "because of hody upwash. The factor ky(B) is 
defined as 

lt-^/^\ a , with a « (8) 

and is less than unity because of the effects of interference on wing 
lift in the absence of body upwash. The lift ratios Ky/g) and ky(B^ 
have been determined from slender-body theory and are presented in fig- 
ure 2 as taken from reference 9. The use of slender-body values of K^rg) 
and ky(5^ for combinations employing wings of large aspect ratio has 
been justified in references 7, 9, and 2k for supersonic speeds. 

It might be surmised that the present method of determining the 
lift on a wing in the presenQe^^vt^i,fe^bfidK»is applicable at subsonic 




NACA RM A53G08 



speeds since the slender-body-theory veilues of %(b) ^^'^ %(b) °^ 
which it is based are not dependent on Mach number and the effect of 
Mach nvanber enters only through T Cl ) . This supposition will sub- 
serviently be shown to be borne out by experimental data. Spreiter 
made the observation in reference 25 that the loading on the minimum 
drag wing -body combination of Lennertz (ref . l) is identical at low . 
speeds to that of a slender wing -body combination with a body of \mi- 
form diameter. The division of lift between wing and body based on 
this loading is shown in figvire 3« Since the present method is based 
on the division of lift as given by Spreiter, the equality of the 
results of Spreiter an d Lennertz is further evidence of the applicabil- 
ity of the present method to subsonic speeds. 

At this point, it is desirable to consider the effects of spem 
loading on the division of lift between wing ajid body because this 
information has bearing on the validity of the vortex model used in 
determining some later results. Besides his resvilt for minimum drag, 
Lennertz also determined the division of load between wing and body for 
uniform span loading. This result, which corresponds to replacing each 
side of the combination by a horseshoe vortex, is shown in figure 3f 
wherein the part of the lift carried by the body is shown as a function 
of the ratio of body raditis to vortex semi span. For the same value of 
the abscissa there is not much difference between the fractions of the 
lift acting on the body for the two cases. Generally, the span of a 
horseshoe vortex replacing a wing is less than the wing span. If 
account is taken of this fact in the comparison, the existing differ- 
ence would largely disappear. Thus, the representation of the wing- 
body combination by a horseshoe vortex on each side is compatible with 
the present method of determining the division of lift between wing and 
body. 



Lift on Body Due to Wing 



The same general scheme used to compute the lift on the wing in the 
presence of the body is vised to con^jute the lift on the body due to the 
wing. In fact, the eq.uation analogous to equation (6) is 

^I-BCW) - [^B(W) ^^^W 5w] (cLa)^ (9) 

The factors Kb/^\ and k-g/y\, defined so that equation (9) is valid 
under the assumptions of linearity, are 

Kb(w) ' -T"^ ^i*b 8W = (10) 




10 ^^^^^^^V NACA RM A^3G08 



^ Lb(w) 



^B(W) = -T^ ^^^'^ ^ = (11) 



Generally, the valioes of K^/y) based on slender -body theory are xxsed, 
and these values are given in figure 2. Hovever, for the high -aspect- 
ratio range at supersonic speeds, a special design chart was developed 
in reference 7 by use of the planar model shovn in figure h. This 
design chart is presented in f igxire 5(a) . 

The case of no afterbody behind the wing or tail is investigated 
in Appendix A for the high -aspect-ratio range at supersonic speeds. 
The analysis is based on the planar model of figure h, and the lift is 
assumed to carry over onto the body only back to the wing (or tail) 
trailing edge. The design chart based on this assTjmption is presented 
in figure 5(b) . The difference between the afterbody and no-afterbody 
cases for the low-aspect-ratio raage at supersonic speeds has not been 
considered. 

A comparison of K£(y\ as determined from figure 5(a) vith that 
from figure 5(b) gives an indication of the inqportance of the afterbody 
for any particiilar configuration. For small values of the ratio 
2p(r/cx.) there is very little effect of the afterbody on Kg/y) but, 
for large values, the effect cem he as large as several hundred percent. 
At subsonic speeds no distinction will be made between the afterbody 
and no-afterbody cases. GSie difference between the two cases, which is 
usvially small in terms of total lift at supersonic speeds, is further 
reduced at subsonic speeds because of the lesser tendency of lift to be 
carried downstream. 

Slender-body theory is the only general means available for the 
determination of kB(w)* ^® values of kB(w) ^° determined are pre- 
sented in figure 2 (see ref. 9). Oliese values are used for both sub- 
sonic and supersonic speeds. 



Lift on Tail Section Due to Wing Vortices 



Wing-tail interference results from downwash in the region of the 
tall caused by the wing vortices, "nie problem of determining wing-tail 
interference breaks down into the problems, first, of detennining the 
number, strengths, and positions of the wing vortices at the tail and, 
second, of determining the reaction of the tail section to the nonunifccrm 
flow field induced by the wing vortices. This component of the combina- 
tion lift is the most laborious to calciaate . Ohe same method will be 
tised for subsonic and si^>ersonlc speeds. 



NACA KM A^3G08 IHBW 11 

Line -vortex theory is used in the solution of the ving -tail- 
interference problem following the general lines of other investigators. 
The model to "be used is illustrated in figure 6. This model of the 
ving is the same as the Lennertz model for uniform loading previously 
disctissed and is thas compatible vith the method used here for calctilat- 
ing wing -body interference. Only one trailing vortex per wing panel is 
considjered althovigh more vortices per panel could be used to obtain 
greater accuracy at the expense of greater complication. The wing 
trailing vortices stream backward but undergo lateral and vertical 
deflections as a result of the body cross -flow field and the interaction 
between vortices. Image vortex lines are introduced inside the body at 
the i ma ge position of the trailing vortices to satisfy the boxindary con- 
dition for a circxilar body. Sufficiently far downstream the external 
vortices approach an asymptotic spacing. 

Nvmiber of vortices per panel. - For ease of calculation it will be 
assumed that one fully rolled-up vortex is discharged from each wing 
panel. While this model simulates the flow behind the wing panels of 
many combinations, there are cases where it does not. For instance, 
the work of Spahr and Dickey, reference 15, shows that for panels of 
high aspect ratio the flow behind the panel can consist of a flat sheet 
or several vortices, and for high angles of attack body vortices appear 
in the flow. Ihiis, it is a fact that the simplified model of one vortex 
per wing panel is not always an adequate basis for computing downwash. 
However, seversil investigators, such as Grigsby, Edwards, Edelman, and 
Rainey, (refs. 17, l8, 19, and 20) have successfully applied this sim- 
plified model to the computation of tail loads. These results indicate 
that the total tail load of each of the configurations investigated is 
insensitive to the details of the vortex flow although the downwash and 
spanwise distribution of tail load are not. This conjecture is substan- 
tiated in part by the theoretical work of Morikawa, reference 12, who 
has calcvilated the tail lifts of slender wing -body- tail combinations 
using one fully rolled-\ip vortex per wing panel and using a flat vortex 
sheet. Only for fully rolled-up vortices in the immediate vicinity of 
the tail tip does any appreciable difference between the two cases occur. 
The resiilts of Lomax and Byrd, reference 13, for a family of swept wing- 
body-tail combinations are in accord with the findings of Morikawa. It 
was on the basis of this evidence and because of its great simplicity 
that the use of one wing vortex per panel was adopted. The accuracy of 
this assumption and its range of application will subseqLuently be deter- 
mined by comparison between experiment and theory. 

Vortex strength. - The circulation distribution at the wing trailing 
edge determines the strength Fm and the spanwise position fy of the 
vortex at the trailing edge. The actual circulation distribution is 
replaced by an equivalent horseshoe vortex corresponding to the Lennertz 
model for loniform loading. Figure 7 illustrates this model. Note that 
figure 7 contains the tacit assumption that the maximum value of the 




12 



NACA RM A53G08 



circulation is at the wing -body JTxncture. Since the lift of the bound 



vortex is Po'V'oI'm Per tmit span, the value of 
from the following series of equations: 



'•m 



can be estimated 



rm = 



Lw(b) 



i^(w) 



2PoVo(%-^w) 2PoVo(r^-gw) 2PoVo(fw-gw) 



(12) 



f w Sw 



= ri 



W 



(13) 



to satisfy the boundary condition that the body is circular. The first 



form of the equation will be used for determining 
tions (6) and (12) it follows that 



Fm. From eqiia- 



rm = 



Vo[%(B) °^ + %(B) M 



(^4 



Sw 



(ih) 



Vortex lateral position. - The problem of determining the lateral 
positions of the wing vortices must be solved before the foregoing equa- 
tion can be used to evaluate Tm. The assumption is made that the vor- 
tices of the wing in combination are discharged at the center of vortic- 
ity of the panels of the wing alone as determined by lifting-line theory 
or linear theory. This assumption is necessary because the circtilation 
distribution is not generally known for the wing-body combination. Hie 
validity of this assumption can be examined for slender wing-body com- 
binations for which the span loading is known and from which the lateral 
position of the vortex can be determined. In fact, the lateral vortex 
position on the basis of slender-body theory is given as 

n2 ^ / \2 _, 






(il 



1+ \ - 




- + 



f-r 
s-r 



-'aj 



sm 



-1 



1 - 



W 



1 + 



(f^ 



Aii- 



(15) 



[' -(=).] 



This equation gives the lateral position of the vortex as a fraction of 
the semispan of the exposed wing panel and as a function of the radius - 
semispan ratio. The maximum deviation between the values given by this 
equation and the wing -alone value of O.786 (or jt/ij-) is about 3 percent. 
This result is independent of the plan form of the wing or body in front 
of the maximum span position since in slender-body theory the potential 
and, hence, the circulation depend only on the cross -flow plane under 
consideration. 




NACA RM A^3G08 VHBHB 13 

For nonslender wing-body combinations the lateral position can 
easily be determined if the ving lift coefficient and the loading at 
the root chord are known. The necessary equation is 

fw = — ^ (16) 

2(c^c) 

In this equation (cjc) is the product of the section lift coefficient 
at the center line of the wing and the chord at that position. Inherent 
in the equation is the assumption that the maximum circulation occurs 
at the center line of the wing. 

A series of charts has been prepared for wings of unswept leading 
edges, midchord lines, and trailing edges to give the vortex location 
as a fraction of the wing-alone semispan and as a function of the effec- 
tive aspect ratio with taper ratio as parameter. The charts for sub- 
sonic speeds, shown in figure 8, are based on the lift charts of De Young 
and Harper, reference 26. It is noteworthy that for low aspect ratios 
the lateral positions of the vortices all tend toward the slender-body 
value of s^jh. No systematic set of lift charts similar to those of 
De Young and Harper is available for supersonic speeds. However, where 
linear-theory results were available, they were used to obtain the 
c\irves shown solid in figure 9> which is the supersonic analog of fig- 
ure 8, To complete the charts the solid lines have been continued as 
dashed lines toward the slender-body value of Tt/^f at zero aspect ratio 
for the cases in which it was felt that the extrapolation could be made 
safely. For the A = case with no leading-edge sweep, there is a 
possibility that the circulation distribution does not have its maximvim 
at the center line of the wing as assumed in eqTiation (l6). The linear- 
theory solution for the load distribution for the reversed triangular 
wing is unknown for pA^ < U. 

While the foregoing charts give the vortex lateral position at the 
wing, the lateral position at the tail, f^, is required for calculating 
wing-tail interference. The simple assumption can be made that fry is 
equal to fy. The determination of fy has been discussed by Spreiter 
and Sacks in reference 27. Also fy can be set equal to foo, the asymp- 
totic vortex lateral position, as determined from reference lU. (A 
step-by-step calculation of frp using the graphical aids of reference 28 
can be made, if desired.) To determine which of the approximations 
to ffji, fy, or foo, is more accurate, the experimental lateral positions 
are compared with fy and foo in figures 10, 11, and 12 for three tri- 
angvilar wing and body combinations reported by Spahr and Dickey in 
reference 15. As the angle of attack increases, the vortices become 
more rolled up at a given downstream station and are spaced closer 
together. Grigsby, reference Yl , has also found similar results. How- 
ever, the data of figures 10, 11, and 12 exhibit certain behavior that 
must be considered if accuraflHHHHHHHfttions at the tail are to be 




1^ ^BHHBP ^^'^^ ^^ A^3God 



predicted. In the first place, more than one vortex per wing panel 
sometimes occurs in the field for the higher aspect ratios. Secondly, 
at high angles of attack body vortices appear in the flow and affect 
the positions of the wing vortices. Further work is required before 
accurate predictions can be made of the vortex positions at the tail. 
On the basis of the compeirison between theory and experiment, neither fy 
nor f„ is superior for predicting the vortex spacing at the tail because 
of the appearance of other vortices in the flow. Until more data are 
available on vortex positions to Justify a more elaborate estimate, the 
value of fy will be used. 

Vortex vertical positions. - The vertical position of the vortex at 
the tail can be estimated by the step-by-step calculative procedure des- 
cribed in reference 15, but the process is generally too lengthy. Two 
alternate methods are considered. In the first method, the vortex is 
assumed to stream backward in the free -stream direction from the wing 
trailing edge. The second method, suggested by Lagerstrom and Graham, 
reference 1^1, is to ignore the effects of the image vortices, which are 
nearly equal and opposite, but to consider crossflow and the mutual 
effects of the external vortices. A comparison between the two positions 
predicted by these methods and the positions measured by Spahr and Dickey 
are shovn in figures 10(b), 11(b), and 12(b). Because of the occurrence 
of more than one wing vortex per panel and of body vortices, neither 
theoretical method appears superior. Therefore, it seems best to use the 
simpler of the two methods which ass-umes that the vortices stream back 
from the trailing edge in the free-stream direction. This assumption 
leads to the following eqtiation for vortex vertical location: 



h^ = - (cp - xjj)^ sin 5y + 



h(B) - h - (cr)y 



sin a (IT) 



The height is measured above the body axis and normal to it at the center 
of pressure of the tail panels. 

Lift due to wing vortices . - The load transmitted to the tail section 
because of the wing vortices depends on the vortex positions at the tail 
and the vortex strengths. For estimating the loads on the tail section, 
strip theory is generally applicable but the method of Alden and Schindel, 
reference l6, can be applied when the necessary theoretical span loadings 
are known. In specifying the tail load, use will be made of a tail inter- 
ference factor 

Lt(v)/(Lt)„ 

i = Ll 2 (18) 

57.3 rm/2jta Vo(sr[,-rT) 




NACA RM A^Ji08 ■^^^■^p 1^ 

vbere (Lt)„ i^ "t^® lift of the tail alone at angle of attack a. The 
interference factor represents a nondimensional quantity usefxol for 
computing tail loads. The factor i depends on the parameters Arp, 
(r/s)fj,, (cr/ps)vp, (f/s)ip, and (h/s)rp. For a fixed hody-tail configura- 
tion, the factor depends only on the vortex positions in the cross-flov 
plane of the tail. 

Whether the factor i is calculated hy strip theory or by the 
Alden-Schindel technique, several simplifying assunrptions are required 
regarding the wing -tail interference. The first assimption is one 
already used in determining Kg/y^% for large aspect ratios at supersonic 
speeds - that the nonplanar tail section can be reduced to an equivalent 
planar model similar to that shown in figure h. The body is assumed to 
be flat and to act at zero ajigle of attack, while the tail angle of 
attack ociji varies spanwise. The second assumption is that the lift on 
the tail section due to wing-tail interference is all developed by the 
tail panels, even though part of it is transferred to the body.. In the 
application of strip theory to determine this lift, Lagerstrom and 
Van Dyke in reference 29 have shown that an exact value (within the 
realm of linear theoiry) will be obtained for the over -all lift of the 
planar model if the leading edge is supersonic and the trailing edge is 
straight, as for a triangular wing of effective aspect ratio greater 
than k. It is to be noted that the second assumption circumvents the 
question of whether an afterbody occurs behind the tail. Generally, the 
lift acting on the body is only a small fraction of that acting on the 
tail section due to wing-tail interference, so that no precise considera- 
tion of the tail afterbody is usually required. 

Strip theoiy has been used to calculate a series of design charts 
for the estimation of i. The details of the calc\ilations are given in 
Appendix B, and the charts are presented in flgore I3. The charts of 
this figure show contours of constant values of i in the cross-flow 
plane of the tail with the parameters T^rp and (r/s)rji varying from 
chart to chart. It is to be noted that strip theory is independent of 
the chord-span ratio (c/ps)ip. In fact, strip theory represents the 
limiting case of linear theory as (c/Ps)qi — >0. The charts give an 
immediate idea of the regions wherein wing-tail interference is most 
important. For triangular tails (A^, = O) it is to be noted that the 
interference is a finite maximum when the vortex is in the plane of the 
tail and slightly inboard of the tip. For all other taper ratios, how- 
ever, an infinite meiximum effect occurs when the vortex is at the tail 
tip. Strip theory is, thus, not accurate for positions of the vortex 
near the tail tip, except in the case of triangular wings with supersonic 
leading edges, in which case it is accvirate to the order of linear theory. 

An alternate method for the determination of i is the method of 
Alden and Schindel, which will serve as a basis for assessing the accu- 
racy of strip theory. The essential result of the method is that the 



16 ^^^^^^^B MCA RM A^3C>08 



lift of a lifting surface with supersonic edges in a non-uniform flow 
field that varies spanwise can be evaluated to the accuracy of linear 
theory hy the equation 

L = r w(y)F(y)dy (19) 

•^span 

where w(y) is the vertical velocity at the spanwise position y and F(y) 
is proportional to the span loading of the tail at uniform angle of 
attack in reversed flow. Heaslet and Spreiter in reference 30 have 
extended the range of equation (19) to include surfaces with subsonic 
edges. For triangular tails with supersonic leading edges, the reversed 
tail is uniformly loaded so that F(y) is proportional to the local 
chord. Thus, strip theory and the Alden-Schindel method give identical 
res\ilts for this case. Generally speaking, the Alden-Schindel technique 
is not suited for an analytical determination of i because, in some 
cases, the necessary function F(y) is not known or leads to complicated 
integrations. (A clever electromagnetic device for performing these 
integrations has been described by Hill in ref. 31- ) The Alden-Schindel 
method leads to results in closed form for rectangular tail and body 
combinations, and the calculation has been carried out in Appendix C. 
The values of i for the vortex in the plane of a rectangular tail and 
for a radius-semispan ratio of 0.2 are given in figure lU for four values 
of (c/(3s)iji. For a value of (c/ps)ij. = the Alden-Schindel technique 
and strip theory are identical. Thus, a comparison of the curves for 
other values of (c/3s)rp with those for zero gives an indication of the 
error due to the use of strip theory for large chord-span ratios. The 
first result is that the infinity at (f/s)rp = 1 (for values of (c/ps)iji 
not equal to zero) has been eliminated by using the Alden-Schindel tech- 
nique. For vortex positions outboard of the tail tip, the effect of 
(c/ps)iji is very small. However, for vortex positions inboard of the 
tip, a larger effect of (c/ps)rr, is indicated. To obtain an idea of 
where the discrepancy due to the use of strip theory is large and where 
small, a figure has been prepared showing the ratio of (i^ - ^St) Aas 
as a measure of the error incurred in using strip theory for (c/ps)rjn=0.5. 
This ratio is shown as a function of vortex position in figure 15- For 
positions of the vortex outboard of the tail tip, the error is generally 
very small except in the immediate vicinity of the tip. For positions 
of the wing vortex inboard of the tail tip, a maximum error of about 
35 percent can be incurred by the use of strip theory. This error 
decreases with distance from the tail. The reason that larger errors 
are incurred for positions of the vortex inboard of the tail tip is 
that here the net effect of the vortex is the small difference of large 
positive and negative lifts, while for outboard positions the vortex 
induces negative lift across the entire tail. It is believed that the 
use of strip theory is more accurate for tapered wings than for rectan- 
gular wings since it is known to be exact for triangular wings with 




I^ACA RM A^3(K)8 I^IHIJ^^B ^7 



supersonic edges. Despite the fact that strip theory does not possess 
the accioracy of linear theory for purposes of estimating tail loads, it 
has several decisive advantages over the linear theory (exemplified at 
supersonic speeds by the Alden-Schindel method) . First, the necessary 
theoretical information is not available for using linear theory in 
some cases at supersonic speeds. Second, separate determinations would 
be required for different (c/^s)^J, values and for subsonic and super- 
sonic speeds, making the construction of design charts extremely diffi- 
cult. For these reasons and because of its great simplicity, strip 
theory is used in this report for computing the tail interference fac- 
tors except for rectangular tails at supersonic speeds. 

The contribution of wing-tail interference to the lift coefficient 
is now derived. The contribution is by definition 



Clt(v) = —^ (20) 



With the aid of equations (ik) and (l8) there is obtained 

^"^•3 (Ci^) (Clc,) [%(b) a + kw(B) 5^ KsT-r^) 

Cl = ^^ (21) 

^^ 2« AT(f„ - rw) 

The values of Ky^gS or ^^(-q) are obtained from figure 2, the value 
of i from figure 13, and the value of fy from figures 8 or 9. For 
rectangular tails at supersonic speeds the value of i calculated by 
use of the Alden and Schindel technique is recommended. 



Lift on Wing Afterbody Due to Wing Vortices 



In the previous work it was assTuned that no change in lateral vortex 
spacing occurred between the wing and tail because, for the pvirposes of 
this report, the extra work to compute the change is usxially not war- 
ranted. However, if for some reason a step-by-step calculation of the 
vortex path is made, the lift on the wing afterbody can be estimated. 
The model shown in figure 6 is used in the estimation. The lift repre- 
sented by a horseshoe vortex is P-Vorm per unit span. The lift repre- 
sented by the vortex system at the wing trailing edge is thus 
2PoVorm(fw-gw) and at the tail location is 2PoVoriii(fT-gT) • The net lift 
retained on the body between the wing and the tail is thus 



Lb(v) = - 2PoVorm[(fw-gw) - (^t-st)^ (22) 




18 



NACA RM A53G08 



With the aid of the relationships 



% = 






(23) 



g-T = 



rrp 



y%^ + V 



(21^) 



equation (22) hecomes in lift coefficient form 



Cl- 



'B(V) 



hr^ 


fw 


rm 


Sw^o 


I.J_, 1 

-/ f rp^ + hj^ 



(25) 



Lagerstrom and Graham (ref . ik) have derived this same result using a 
different method. Generally, the change in f between wing and tail 
is not known unless the step-hy-step solution mentioned in reference 15 
is performed. In this case hoth the total lift and distrihution of lift 
on the hody due to the trailing vortices is known. However, if only an 
upper bound on the value of C^ . . is desired, then the val\ie of foo 

can be used for ftp in equation (25) • 



Simmxary of Lift Components of Wing -Body-Tail Combinations 



The seven components of the lift acting on a wing-body-tail com- 
bination are outlined as follows: 



1. Lift on body nose, 

(Cl)n =%(cLa)^ ^B 

2. Lift on wing in presence of body, 

(^l)w(b) =[%(B) ^+ %(B) SwJ (CLa)^ 

3. Lift on body due to wing, 

(^l)b(W) ^[''Bi^) '^-^ ^B(W) Sw] (Cl^\ 



(26) 



(27) 



(28) 




NACA RM A53G08 




19 



k. Lift on tall in presence of tody (neglecting ving vortices). 



(Cl) 



T(B) 



Kt(b) a -H kT(B) 5t] (cLa)^(l^) (29) 



5- Lift on "body due to tail (neglecting wing vortices). 



(Cl) 



B(T) 



Kb(t) a + kB(T) St 



](^i-X(l) 



(30) 



6. Lift on tail section due to wing vortices. 



(Cl) 



5^-3 (cLc,) (Cl^) |_%(B) a + kw(B) 5w 



i(sT-rrp) 



T(V) 



27tAT(fw-ry) 



(31) 



7. Lift on wing afterbody due to wing vortices. 



(Cl) 



hr, 



m 



B(V) 



SwVc 



(fw^-r/) 



f T + 



^W 



y^v 






(32) 



A calculative form for determining the lift and moment characteris- 
tics of wing-body-tail combinations utilizing the foregoing res\ilts will 
subsequently be presented. However, the last lift component will not be 
incorporated into the form since it is only of importance in rare 
instances, and since it can only be computed after a step-by-step com- 
putation of the type discussed in reference 15- A chart summarizing 
the lift-curve slopes of wings at supersonic speeds as determined from 
linear theory is included as figure l6 for use with these formulas. 

CENTER-OF-PRESSURE THEORY 



In the section on lift theory the differences between subsonic and 
supersonic speeds were given only passing attention since the lift theory 
as developed applies in the same form to both speed ranges. The primary 
effect of Mach number was manifest through the quantities (Cj^ and 

{ Ct \ . However, in the center-of -pressure theory the Mach number has 
\ <^/T 

a direct effect on the centers of pressure of several of the lift com- 
ponents, and a definite distinction must be made between the subsonic 
and supersonic cases for these components. 




20 ^^^^^^^^ NACA RM A^3G0d 



Several conventions are adopted vith regard to center -of -pre sstire 
position in this report. All positions for the complete configuration 
are xiltimately given in fractions of the tody length behind the most 
forward point of the hody. The design chart for the centers of pres- 
sure of Lgf^^, %(b)' ■'^T(B)' ^^^ Lb(T) ^^^ given in fractions of the 
root chord (at the juncture vith the hody) behind the juncture of the 
leading edge with the hody. All length symbols having bars over them 
represent center-of -pressure lengths. 



Center of Pressure of Body Nose 



For most purposes the center of pressure of the body nose can be 
estimated vith s\ifficient accuracy by slender-body theory. The result 
is obtained that 

h-h(^'-^) (33) 

wherein Vjj, rjj, and l-^ are the voltnne, radius, and length of the body 
nose. For bodies with noses of small fineness ratio or even for bodies 
with slender noses at high Mach numbers, some lift is carried over onto 
the body behind the nose, tending to make l^ greater than the value 
given by equation (33)- If the lift on the nose is a substantial frac- 
tion of the total lift, the effect can be significant. In such cases 
linear theory is better than slender -body theory, although experimental 
values of 2jj are always to be preferred. In this report, slender-body 
theory will be used when theoretical values are used. 



Center of Pressure of Wing in Presence of Body 



The center of pressure of the wing in the presence of the body 
depends slightly on whether the lift is developed by varying the body 
angle of attack at fixed wing incidence or varying the wing incidence 
at constant body angle of attack. The difference in centers of pressure 
for these lift conrponents, determined experimentally for triangular all- 
movable wings and reported in reference 9, amoTmts at srjpersonic speeds 
to about 2 percent of the root chord or 3 percent of the mean aerody- 
namic chord. If account is taken of the difference, the center of pres- 
sure for the wing in the presence of the body is 

''«(B)<tX(B)a * ■'>'(=) *« (^X(B)B 
\ *^r/w(B) Ky(B) a + ky(B) By 



NACA RM A^3G08 ^^HIBJJiB 

Generally speaJcing, the theoretical valties of (x/cr)T,/-r,N and (x/cr)TT/-o\g 
are not known so that some approximate method of estimating them is 
required. In reference 9 the valixes of (x/cp) / x and i^/^r)-^(-n)^ ^or 
triang-ular vings in combination vith a rovmd body are given as computed 
on the basis of slender-body theory. Also, the values of (x/cr)y/-B\c 

for rectangular vings of effective aspect ratio 2 or greater are reported 
as determined by linear theory. For other cases the following approxi- 
mate resiiLt is recommended in lieu of more specific information: 



(±) = (f) (35) 

^ ^r >'w(B) ^ ^^W 



KB) 

The distance of the center of pressure of the wing in the presence of 
the body measiired from the most forward point of the body is, then 



Mb) = iw+ (cr)w {§;) ^36) 



/W(B) 



At subsonic speeds the charts of DeYoung and Harper, reference 26, 
may be used for estimating (x/cr)y for a wide range of aspect ratios, 
taper ratios, and sweep angles. A chart presenting the results is 
shown as figure 17- The results have been extrapolated from values 
of PA = 2 to the slender-body values at PA = 0. Cross -plotting 
aided in the extrapolation. A set of charts for supersonic speeds is 
presented as figure l8. These charts are based on linear theory and 
have been extrapolated to the slender-body val\ies at zero aspect ratio 
when linear theory was not available for the low-aspect -ratio range. 
The cixrve for A «= and no leading-edge sweep could not be extrapo- 
lated with any degree of assurance. 



Center of Pressvire of Body Due to Wing 



The center of pressure acting on the body due to the wing is deter- 
mined by different methods, depending on whether subsonic or supersonic 
flow is considered. For the supersonic case the method of reference 8 
is used. In this method the planar model of figure k is used with the 




22 ^^^^^^^^ NACA RM A^3G08 



assumption that the wing is at a uniform angle of attack. Generally- 
speaking, the model is applicable only if the tip Mach cones do not 
intersect the wing-hody j\incture, thereby influencing the wing -body 
interference. For this high-aspect-ratio range two cases are distin- 
guished: that of an afterbody behind the wing and that of no afterbody. 
The afterbody case is approximated by integrating the pressure field on 
the body to the trailing-edge Mach waves, as shown in figure k, and the 
no afterbody case is approximated by integrating only up to an exten- 
sion of the wing trailing edge. Based on these models, charts for 
determining i^/^r)-Q(^\ for the afterbody and no afterbody cases are 

presented in figures 19(3') and 19(b), respectively. 

While the charts of figure 19 can be used for an approximation to 
(x/cj.) / » even for the low-aspect-ratio range, as indeed was done in 

reference 9f nevertheless, a somewhat more accurate method can be 
derived for this range. In the more accurate method the independent 
variables are taken to be aspect ratio and taper ratio, with radius- 
semispan ratio as parameter. The values of (x/cr)^/„\ for pA = 

are those given by slender-body theory, and the valioes for (r/s)y = 
are those for the wing alone as given by linear theory. On the basis 
of this information it is possible to extrapolate the high-aspect-ratio 
theory to pA = 0, as has been done in figure 20 for the afterbody case. 
These charts are to serve as design charts for the aspect-ratio range. 
Similar charts can easily be formulated for the no afterbody case by 
use of the resiilts of figure 19(b) . In establishing the slender-body 
values at pA = 0, it was assumed that no lift was developed downstream 
©f the maxim\im wing span. The extrapolation was not attempted for A = 
and no leading -edge sweep. 

Hitherto, no method seems to have been available for estimating 

(x/cj.) , , at subsonic speeds. For this purpose, the lifting-line 
B^wj 

model shown in figure 21 has been used. The lifting line is placed 
along the quarter-chord line of the wing and its image is introduced 
inside the body. The external lifting line is divided into a number of 
bound vortices, the strengths of which are proportional to the circula- 
tion distribution. The lifting line is not uniformly loaded although 
the horseshoe vortices are. The external vortices have their internal 
images which produce the lift on the body, this lift being produced at 
the bovmd part of the horseshoe vortex. Since the lift on the body 
due to each elemental image horseshoe vortex is proportional to the 
product of its strength times the length of its bound element, and 
since its lift acts at the bound element, it is easy to determine the 
center of lift of all the image horseshoe vortices. The formulas 
for the calcTilation are presented in Appendix D and the results are 
presented in figure 22 as a series of design charts for {x/Cj.) , •. 

at subsonic speeds. In Appendix D, the lifting line was assumed to be 




NACA HM A^3G08 ^BJIIIJH 

elliptically loaded. This assumption should "be valid for most cases 
since the calciilation is not sensitive to the span loading and since 
efficient wings tend to be elliptically loaded. No difference between 
(x/cr) , . and (^Ar)B/y\8 ^^^ been considered since any such differ- 
ences will be small and are beyond the scope of available theory. 

The charts of figure 22 give results for unswept leading edges, 
midchord lines, and trailing edges as a function of pA and (r/s) . 
The results for PA > 4 represent the results of lifting-line theory. 
It is to be noted that no dependence on aspect ratio is found on the 
basis of lifting-line theory. It is known that at low aspect ratios 
the loading on the wing-body combination approaches the slender-body 
loading for which the center of pressure on the body is known. The 
value from slender-body theory is plotted on the charts of figure 22 
at PA = 0. Furthermore, for r/s =0 it is clear that (x/cr)^/„\ 

equals the center of pressure of the loading at the root chord of the 
wing alone. For rectsmgular and triangular wings of low aspect ratio 
this quantity has been obtained from the work of reference 32. The 
resiilts for r/s = at low aspect ratio agree with good accuracy with 
the lifting-line-theory results for r/s = at about pA = 4. There- 
fore, lifting-line theory has been adopted for PA > if, and for pA < i|- 
the curves have been extrapolated to the slender-body values at pA = 
with the r/s = results used as a guide. The extrapolated curves 
are shown dotted in figure 22. The distance of the center of pressure 
from the body point is given as 

Center of Presstire of Tail in Presence of Body 

The center of press\ire of the tail in the presence of the body 
(wing-tail interference being neglected) is given by the same procedure 
as that for the wing. For supersonic speeds the value of (x/cp)„ as 

determined from figure l8 is used as an approximation to (x/cr)m/iD\ • 

For subsonic speeds the charts of reference 26 or those of figure 1? 

are available for estimating (x/cr)m' The distance from the most forward 

point of the body to the tail center of pressiore is thus given as 



T(B)-JT-(<=r), (^) '^' 



'T(B) 



2k ^tKtt/ttm ^^^^ ^^ A^3G08 

Center of Pressure on Body Due to Tail 



The center of pressure on the body due to the tail, wing-tail inter- 
ference being neglected, is determined by the same procedure as that due 
to the ving. For supersonic speeds the charts of figures I9 and 20 are 
used for cases of afterbody and no afterbody. For subsonic speeds the 
charts of figure 22 are used in estimating (x/cj.) / v . From these values 

the distance from the point of the body to the center of press\ire is 
given 



h{T) = ^T + (cr)^ (■£) , , (39) 

1 \ ^^B(T) 



Center of Pressxire of Tail Section Due to Wing Vortices 



The flow over the tail due to the wing vortices varies greatly as 
the position of the vortex varies with respect to the tail. It follows 
that the center of pressure of the lift due to the effect of the vortices 
on the tail section is also dependent on the position of the vortices 
with respect to the tail. It is possible on the basis of strip theory 
to take accoTjnt of this effect. However, the refinement is hardly war- 
ranted in view of the fact that the distance from the center of moments 
to the tail is usually large so that great precision in the location of 
the center of pressure of the load on the tail section due to the wing 
vortices is unnecessary. A good approximation is to take the center of 
pressure as that for the tail panels in combination with the body. Thus 



^T(V) = ^T(B) (^) 



Sianmary of Center-of -Pressure Positions 
of Wing -Body-Tail Combination 



The components of the lift, with the exception of the lift on the 
wing afterbody due to the wing vortices, have center -of -pressure posi- 
tions estimated as follows: 



1. Center of pressiire of body nose. 






NACA RM A53G08 




25 



2. Center of pressure of wing in presence of body. 



Mb) = ^w + (^L^. (-r)^ 



vith 






W(B) 



%(B) «(^) + Mb) ^w(|:) , ^ 



%(B) 



^ + J^W(B) ^W 



(1^2) 



(J^3) 



3. Center of pressure on body due to ving. 



^B(W) = ^W+ (cr)^ (^) 



B(W) 
k. Center of pressxire of tail in the presence of body. 



Zrp(B) » ^T + M^ (^) 



T(B) 



5. Center of pressvtre on body due to tail. 



^B(T) = iT+ (cr)T (^) 



(H) 



(^5) 



B(T) 
6. Center of presstire of tail section due to wing vortices, 

^T(V) = ^T(B) 
The center of pressure for the entire combination is thus 



(i^6) 



(^7) 



Zn(Cl)n+Mb) (Cl)w(b)+^b(w) (Cl)b(w)+^B(T) (Cl)b(t)+^t(b) (Cl)t(b)+"^t(v) (Cl)^(y) 





26 ^^^^^^^ NACA RM A^3(>08 



COMPUTATIONAL TABLE FOR DETERMINING LIFT COMPONENTS AND 

CENTERS OF PRESSURE 



To organize and illustrate the calcvilations of the lift and center- 
of -pressure characteristics of ving-body-tail combinations, a computa- 
tionsil table, based on the eq,^lations and chsirts already presented, is 
presented as table I- A numerical example is included in the table, 
•which is self-explanatory. The reference area and moment reference 
point and length are arbitrary. Angular measiires are always to be taken 
in degrees. 

A possible confusion in the use of the computing table is the maa- 
ner of using figure 13 vhen interpolations must be made with respect 
to A and r/s. Normally, one can interpolate at constant values of the 
vortex lateral and vertical positions. However, for positions of the 
vortex near the body, interpolating in r/s may carry the vortex inside 
the body. Under such circumstances, it is recommended that the interpo- 
lation be made at constant values of {f\i- rrp)/(sy - rij), the vortex 
lateral position as a fraction of the span of the exposed wing panel. 

Again, it is advocated that experimental values of the lift-curve 
slopes (Ct ^ , (Ci^\ , and ('CL^^ be used if available. If the 

experimental values of fCLa) ^°^ V^) ^'^'^ unavailable and if the 

theoretical values are not obtainable from the material at hand, then 
references 26, 33, or 3^ should be consulted. It is to be noted that 
in the calculative form, the body radius can be variable since the quan- 
tities rjj, ry, and rrp are all considered separately. If the body- 
radius is varying at the wing or tail location, sua average radixis should 
be used at each location. Ihe assumption has been used in determining 
the lateral vortex position at the tail that the wing vortex streams 
back in the free-stream direction. For variable body radius the assump- 
tion is made that in the plan view, the ving vortex streams back parallel 
to the side of the body. Ihis assumption is incorporated into the com- 
puting table. A speeiail figure to aid in determining the center of 
pressure of ogival noses is presented in fig\are 23 and used in the com- 
puting table. 



RESULTS AKD DISCUSSION 



To test the method of this report, a series of calcxLLations have 
been performed to estimate the characteristics of a number of combina- 
tions, and these characteristics have been compared with experiment. 
The geometric and aerodynamic characteristics of those combinations for 





NACA RM A^JiOQ ^HVH^P 2? 



which the comparisons have been made are sTjmmarized in table II for 
wing -body combinations and in table III for wing -body-tail combinations. 
The experimental data have been taken from references 35 to 6^, inclusive. 

In summarizing the aerodynamic data, little difficiilty was experi- 
enced with wing -body combinations because their lift and moment charac- 
teristics, being usually linear at low angles of attack, are well repre- 
sented by lift-curve slope and center of pressure at a = 0. However, 
these quantities are not sufficient to describe the nonlinear character- 
istics exhibited by many wing -body -tail combinations- Some of the moment 
characteristics were so nonlinear that it was impossible to determine 
the center-of -pressure position at ag = accurately, and in these 
cases the information was not entered in table III. Curves of the non- 
linear characteristics will subsequently be presented. 

The discussion of the main lift and center-of -pressure correlations 
between experiment and theory is for no deflection of wing or tail. The 
effects of wing deflection on wing-body interference were discussed in 
reference 9- Some effects of wing deflection on wing-tail interference 
are discussed after the main lift and center-of -pressure results. 



Lift 



In presenting the lift resiolts attention is fi^-st focused on sub- 
sonic wing -body combinations. No results are presented for supersonic 
combinations since it has already been shown in reference 7 that the 
present method is applicable to combinations employing rectangular, tri- 
angiolar, and trapezoidal wings at supersonic speeds to within an error 
of about ±10 percent for lift. 

Wing -body combinations . - In figure 2k the experimental values 
of 3(dCL/da)c for subsonic wing -body combinations are plotted against 
the estimated values. A i<-5° line of perfect agreement is shown in the 
figure together with lines of ±10-percent error. Certain of the correla- 
tion points have flags to indicate that they represent the Mach number 
range 0.9 to 1.0. It is apparent that the present method of predicting 
(dCL/da)Q is accurate to within about ±10 percent for wing -body com- 
binations at subsonic speeds, as well as supersonic speeds, except for 
certain combinations in the transonic range. 

Figure 25 is presented to show how the present method predicts the 
trend with Mach number of the lift-curve slopes of wing -body combinations. 
In general, the trends are well represented by the theoiy and the magni- 
tudes are within the expected accuracy, except for certain combinations 
in the transonic range. For these combinations the wing-alone lift-curve 




28 ^^^^^^^M ^ACA EM A^3G08 



slopes in the transonic range are greater than the value given by linear 
theory "because of nonlinear transonic effects. McDevitt (ref . 66) has 
shown that for rectangular wings having NACA 65A0XX sections, good 
agreement between linear theory and experiment is obtained near Mq = 1 
for lift if the transonic similarity parameter A(t/c) ' is less than 
unity. No well-defined dependence of the agreement between experiment 
and theory on this parameter was noted for the various plan forms repre- 
sented in figure 25- 

For some combinations the theory shows a peak in the lift- 
coefficient variation at Mq = 1, while for other combinations the peak 
occurs on the supersonic side. For Mq = 1, the effective aspect ratio 
is zero, and the slender-body value of the lift-curve slope, (n/2)A, 
has been used in the theory. On the supersonic side of Mq = 1 the 
values of pA are small and the wing lift -curve slope has been obtained 
from low-aspect -ratio lineajr theory. If the lift-curve slope so obtained 
is greater than that obtained from slender-body theory, then the maximum 
lift-curve slope occurs on the supersonic side of Mq = 1. The behavior 
of the lift variation with Mach number around Mq = 1 thus depends on 
the low-aspect-ratio lift characteristics of the wing alone. 

While the agreement between the estimated and experimental lift- 
c\irve slopes for the large n\imber of combinations compared is evidence 
suggesting that the division of lift between wing and body is correctly 
given by the present method, nevertheless, more direct evidence is 
needed to prove the point. Such evidence has been obtained for super- 
sonic speeds and is available in reference 67. At subsonic speeds data 
in references 2 and 3 give the same division of lift between wing and 
body as a function of diameter-span ratio as the present method. The 
comparison of the data of these reports is with the theoretical division 
as given by the Lennertz theory which, as previously pointed out, is 
numerically the same as that given by slender-body theory on which the 
present method is based. 

Wing -body-tail combinations . - The values of p(dCL/da)c at a = 
obtained from experiment are plotted against the estimated values in 
figure 26 for subsonic speeds and in figure 27 for supersonic speeds. 
To illustrate the importance of wing-tail interference, the points are 
shown as squares for no wing-tail interference and as circles for wing- 
tail interference included in the estimated values. It is apparent 
that effects of wing-tail interference can be very large on a percentage 
basis, 30 to kO percent. However, after the effects of wing-tail inter- 
ference have been included in the theory, the errors are generally 
within ±10 percent. Therefore, the accuracy of prediction of the wing- 
tail interference in the worst cases must be within about ±25 to 30 
percent. 



MCA BM A^3G08 ^^^^^^HB 29 

Sufficient data tiave "been analyzed to present some effects of 
angle of attack and Mach number on the lift characteristics of wing- 
body-tail combinations. The nonlinear variations of Cl with a for 
subsonic wing -body-tail combinations are shown in figure 28. The 
theory with and without wing-tail interference is shown. The theory 
including wing-tail interference is in good accord with the experiment. 
As expected, in the high-angle -of -attack range the measured lift tends 
to be greater than the estimated lift, probably as a result of body 
cross flow. Comparison has been made between experiment and theory for 
supersonic speeds in figure 29- Again, in the low-angle -of -attack 
range the agreement between the experimental and theoretical values of 
the lift coefficient is good. The variations of lift-curve slope for 
zero angle of attack and of lift coefficient for several angles of 
attack with Mach number are shown in figures 30(a) thro\igh 30(j) for a 
ntmber of combinations. It is clear that the trends with Mach nijmber 
are well predicted for the combinations considered. Where the theory 
has not been extended to Mq = 1 from the subsonic or supersonic range, 
the wing-alone or tail-alone lift-curve slopes could not be predicted 
accurately for the low effective aspect ratios involved. The large 
transonic effects exhibited by some of the combinations are predicted 
by the theory. Unfortunately, the wing-body-tail characteristics were 
not available for any wing-body combination exhibiting nonlinear tran- 
sonic characteristics, so it was impossible to see the effect of adding 
a tail in such a case. 

Center of Pressure 

Wing -body combination .- The center-of -pressure locations for 
wing-body combinations at supersonic speeds are not considered since 
the problem is discussed in reference 8, where it was shown that the 
center of pressure of wing -body combinations employing triangular, rec- 
tangular, or trapezoidal wings could be estimated to within about ±0.0l6Z 
or less at supersonic speeds by the present method. 

The center-of -pressure positions for subsonic wing-body combina- 
tions as determined experimentally have been plotted as a function of 
the estimated positions in figure 31« Lines of ±0.02Z error have been 
included in the figure. Generally speaking, the configurations corre- 
lated lie within the ±0.02Z error limits. It is to be noted that the 
errors are randomly distributed about the line of perfect agreement. 
Comparison is made between theory and experiment for subsonic and super- 
sonic speeds in figure 32 in which the variation with Mach number of 
the centers of pressure is presented for a number of wing-body combina- 
tions. The theory for supersonic speeds has been presented in two 
manners. The solid line represents the theory without correction, while 
the dashed lines represented the theory with the corrections advocated 
in reference 8. Generally speaking, the variation with Mach number of 



30 1^^^^^^^^ MCA BM A^3G08 



the center of pressure is not large so long as the transonic range is 
not traversed. However, through the transonic range, changes in center 
of pressure of appreciable magnitude can occior. The magnitxides of the 
shift are fairly well predicted by the theory when the correction of 
reference 8 is made . It should he remembered that the correction 
applies only to wing -body combinations at supersonic speeds. 

Wing -body- tail combinations . - A correlation of the center-of- 
pressure positions for a = as determined experimentally and as 
estimated are presented in figure 33 for subsonic *^ing -body-tail com- 
binations. It is clear that including the effects of wing-tail inter- 
ference is svLfficient to move the points into the correlation band for 
almost all cases. 

The re stilts corresponding to figure 33 are shown in figure 3^ for 
supersonic wing -body- tail combinations. The effects of wing-tail inter- 
ference are larger generally than for the subsonic wing-body combina- 
tions. The correlation is accizrate to within ±0.02Z for nearly all the 
combinations . 

The effects of Mach nxanber and angle of attack on the center-of- 
pressure position of wing -body-tail combinations can be very large. 
The effects of angle of attack are illustrated in figure 28 for sub- 
sonic combinations and in figure 29 for supersonic combinations. In 
figure 28 the theory with and without wing-tail interference is shown. 
The effects of wing-tail interference are generally large for the com- 
binations illustrated and the effects are generally predicted to 
within O.02Z- One important observation is that some large rearward 
changes in center -of -pressTore location with angle of attack are observed 
and predicted for combinations such as number 101, changes that are 
comparable in magnitude to the effects of wing-tail interference itself. 
The rearward shift is due to a decrease in the tail download caused by 
the wing vortices as the angle of attack increases. An examination of 
figure 29 for supersonic speeds discloses resiilts similar to those of 
figure 28. The most significant difference is that the supersonic con- 
figurations exhibit more drastic angle -of -attack effects than the sub- 
sonic combinations. 

One of the important problems of aircraft and missile design, the 
center -of -pressure travel in the transonic range, is considered in fig- 
ure 35. The wing -body-tail combinations shown in this figure exhibit 
very small to large rearward shifts in center-of -pressure position. 
Another important effect shown is the large rearward shift due to chang- 
ing the angle of attack. The changes due to angle of attack are in one 
instance greater than those due to Mach number. With regard to the 
comparison between experiment and theory, it can be said that the trends 
with angle of attack and Mach nvmiber are well predicted and that the 
absolute values of the center -of -pressure position are within the +0.02Z 
given as the accuracy of the m^jrj^Jijjih^correlation c\irves. 




NACA RM A^JiOQ (^^^^^^^M -^-^ 

Effects of Wing Incidence 



Varying the incidence of the wing affects the wing-body and wing- 
tail interference, while varying the tail incidence affects only the 
tail-body interference. The effects of wing and tail deflection on 
wing-body and tail-body interference have already been considered in 
reference 9, wherein it was shown that the present method predicts the 
effects with engineering acc\iracy. Thus, there remain to discuss only 
the effects of wing deflection on wing-tail interference. 

Deflecting a wing positively will normally cause an upload on the 
wing, but the resulting wing vortex causes a download on the tail. As 
a resiilt, a considerable pitching moment is developed. For slender wing- 
body-tail combinations with tail spans greater than the wing span, 
Morikawa, in reference 12, pointed out that the lift on the tail due to 
interference is equal and opposite to that on the wing. Under these 
circumstances a pure couple is developed on the airplane due to wing 
deflection so that the center of pressure moves forward. The forward 
movement can be large. 

To determine the validity of the present computational method for 
estimating the effects of wing incidence on the lift and moment inter- 
ference of complete configurations, estimates are made of the lift and 
moment characteristics of those combinations for which data for variable 
wing incidence are available. The estimated and experimental character- 
istics are compared in figures 36 to hO, inclusive, for several combina- 
tions differing widely in Mach nimiber and wing and tail plan form. All 
combinations exhibit the forward movement of the center of pressure. In 
the low-angle -of -attack range where the theory applies, the agreement 
between theory and experiment is good except for the combination of fig- 
ure 39- This combination, which was tested at supersonic speeds and 
which has a triangular wing with supersonic leading edges, exhibits a 
behavior which is not explainable In terms of the theoretical model with 
one fully rolled-up vortex per wing panel. 

A closer examination of figure 39 reveals that the predicted lift 
due to wing deflection is in good agreement with experiment, but the 
predicted moment is not realized. Since the predicted moment is due 
primarily to tail download, it follows that the tail download is not 
developed. This behavior is explainable in terms of span loading. As 
yet unpublished experimental results and theoretical resiolts (ref . h) 
indicate that for rectangular wings of sufficiently large aspect ratio, 
the span loading at the juncture of the wing and body is considerably 
below the maximum span loading on the wing for variable wing Incidence 
at zero angle of attack. This means that the shed vortlcity Inboard 
has the opposite sense of rotation of that shed outboard, and upwash 





32 ^^^^^^Bi ^-^^^ ^ A^3G08 



is generated inboard. Under these circumstances it appears that two 
vortices per ving panel are the least number that can adequately repre- 
sent the trailing -vortex system. The combination of figure 39 possesses 
a triangxilar rather than a rectangtilar wing, but its effective aspect 
ratio is 6.8 so that the foregoing effect may be anticipated. A compli- 
cating factor is that the shock vave is detached from the wing for all 
angles greater than about 3° so that the flow is, in part, transonic. 
Also, the tail span is considerably less than the wing span so that the 
tail is located largely behind the inboard portions of the wing. For 
these reasons it is felt that the theoretical model of one vortex per 
wing panel is inapplicable and that two vortices per wing panel is the 
minimum number that can describe the gross effects of the phenomenon. 
However, more experimental work must be done before aji accurate theory 
can be developed to cover this case. 



Limitations and Extensions of the Method 



In the application of any method such as the present one, the 
important question of its limitations arises. Because of the very large 
n-umber of variables specifying a wing -body- tail combination, it is not 
practical to present correlations covering all possible combinations. 
For this reason the limitations and possible extensions of the method 
are best determined by an examination of the assimrptions made with regard 
to configuration geometry, angle of attack, and Mach number. 

With regard to configuration effects, the assumption was made that 
the leading edges are not swept forward nor are the trailing edges swept 
back. For sweptforward leading edges or sweptback trailing edges, the 
solution of slender-body theory used to determine Ky/-g\ and Kg^y^ is 
not applicable because no account is taken of the trailing -vortex system 
that passes through the cross -flow planes of the wing -body combination. 
The use of the correct cross -flow solution, determined by the method of 
Lomax and Byrd in reference 13, should circumvent this difficulty. How- 
ever, some successful preliminary correlations between data on swept 
wing -body combinations and the estimates of the present method (ignoring 
the sweep of the trailing edges) indicate that the effect may not be 
large. While the present method is worked out only for unbanked con- 
figurations with two wing panels, it seems possible by use of the appro- 
priate slender-body-theory solution to extend the method to banked con- 
figurations with any number of wing panels. For interdigitated or high 
tails the method can be easily generalized. For differential incidence 
of the wing panels, the method is still applicable if a step-by-step 
calculation of the type mentioned in reference 15 is used to determine 
the vortex position at the tail. The model on which the present method 
is based corresponds to the case of the maximum circiilation of the wing- 
body juncture. A violation of this assTmiption invalidates the model. 





MCA RM A^3(}08 ^^^^^^B^m 33 



Such a condition coiold conceivably arise through the use of inverse 
taper, sweptforward wings, high-aspect-ratio deflected wing panels with 
supersonic leading edges, or wing panels having large gaps "between wing 
and body. 

With regard to angle-of -attack effects, it has already been stated 
that the assumption of linearity in the present method limits the useftil 
angle -of -attack and wing-deflection ranges of the theory. Body vortices 
and more than one vortex per wing panel can occur in flow at high angles 
of attack, as shown by reference 15- With regard to Mach ntunber effects 
in the transonic and hypersonic ranges, the present method will fail 
where nonlinear effects become important. However, since the division 
of lift is not sensitive to span loading, the lift ratios may be appli- 
cable in the nonlinear range . 



CONCLUSIONS 



On the basis of the comparison between predicted and measured lifts 
and center-of -pressure positions of a large number of wing-body and 
wing -body-tail combinations, the following conclusions can be drawn: 

1. It was determined that the present method predicts lift-curve 
slope to within ±10 percent for most combinations through the speed 
range. However, in the transonic range nonlinear effects may reduce the 
accuracy of the lift prediction. 

2. For wing -body and wing -body-tail combinations at subsonic 
speeds, the center-of -pressure positions are predicted to within ±0.02 
of the body length. At supersonic speeds the same accuracy is obtained 
for wing -body-tail combinations. 

3. The effects of wing-tail Interference may change the combination 
lifts by as much as 35 to kO percent and may change the center-of -pressure 
positions by as much as 10 to 20 percent of the body length. 

k. The nonlinear effects of angle of attack on center-of -pressure 
position and lift may be as important as those of Mach number. 

Ames Aeronautical Laboratory 

National Advisory Committee for Aeronautics 
Moffett Field, Calif., July 8, 1953 




3i^ 




NACA RM A53G08 



APPENDIX A 
DETERMINATION OF Kg/^^ AND Kg(r[i) FOR NO BODY 
BEHIND WING OR TAIL TRAILING EDGE 



The method for determining %(y) or Kb(t) for the case of no 
afterbody parallels closely the method used in reference 7 for the 
afterbody case. Referring to figure kl the pressiire distribution acting 
on the top of the plan-form area of the body is 



P = 2 



aym 



"/ 



cos 



-1 



m2p2_i 



T] + m5 



(Al) 



for supersonic leading edges and 



P = 



ha^ipmf^' 



P - ^ 



7t3(m3 + l) V m|+ J] 



(A2) 



for subsonic edges, where P is the pressure coefficient and Oy is 
in radians. These results have been taken from references 68 and 69. 
The lift acting on the body due to using both panels is then 



L = 4q 



dT] 



P d5 



^'PTI 



(A3) 



where d is the body diameter. Carrying out this integration and 
dividing by the lift of the wing alone yields 



KB(W)[p(cLa)J(A+l)(f -1) 



8 



n/ 



mp 



P^m^-1 



(f) 



(-fj 



cos 



-If !^ ^-m-pY-^y cos 
mc / \pd/ 



1 4- 



\mpy 



2 

(^) ym^p^-lsin-^f -ym^p^-l cosh'^ ^ 




;pm>l,p >d (Ak) 



NACA RM A53G08 




35 



K- 



B(W) 



[.(c,jJ(A.l)(f-l). 



Tt(mp+l) 



(^){(-f)y(^-)(f-) -ar <-'=''^ 



mp 



(^/(^.i) 



tan' 




t-)/(^^^) 



(m(3 + 1) 
-/mp" 



tanh" 



TK^^W^)}^ ^ 



im < 1, 



f>- 



(A5) 



The restriction that "S ^ ^ 



is not a serious one. For 



d > p it is 
c 



clear that the lift transmitted to the body is the same as for d. = -g 



so that Kg/^) is constant. The value of the parameter %(w) P( ""La, 1 
(A + 1) ff - l) is a function only of mp and pd/c, and has "been 
plotted as a function of these two variables in figure 5(a). The fig- 
ure is so constructed for pd/c > 1 that K-g(y) is constant for a 
given wing panel. 





36 ^^^^^^^^ NACA RM A^360d 



APPENDIX B 
DETEEMTMTION OF TAIL INTERFERENCE FACTOR BY USE OF 
STRIP THEORY AND SLENDER -BODY THEORY 

The tail interference factor to te eval\iated is 

i "m!!^ (Bi) 

57.3 rni/2na Vo(st - rj) 

The lift ratio is readily evaluated by a combination of strip theory 
and slender-body theory. The model \ised to obtain the vertical velocity 
at the tail induced by the ving vortices is the slender-body model given 
by figure k2. From the Biot-Savart lav for an infinite line vortex, the 
vertical velocity dtie to the right external vortex is 

w « (B2) 

2n [h^ + (f-n)^] 

In this equation Pm is positive counterx:lockwise facing upstream, and 
V is positive upvard- The tail is effectively twisted because of the 
variation of w across its span. All geometric qiiantities in the deri- 
vation are understood to be those of the tail rather than the ving so 
that no subscript will be used. 

The application of strip theory to obtain the load on the tail due 
to the vortex involves an integration across the exposed part of the 
tail. As previously discussed, the lift eval\xated by this procedure 
appears partly on the tail panels and partly on the body. If the section 
lift coefficient is taken as k/^, the lift diie to the right external 
vortex on the right external panel is 

The veiltie of Li obtained by integrating equation (B3) is obtained with 




NACA EM A53G08 



37 



the aid of the following ftmction: 



<^.i'l'l)={ 



(s-rA)- f(l- A) h^+ (f - s)' 
In 



2(s - r) h2+(f -r)2 



(1-A) 
(s-r) 



(s - r) + h tan'^f J - h tan"! -y" • ]■ 



(Bif) 



as 



Li = 



2«pVo 



r f h 



/ , r r h v 



(B5) 



The lift on the right panel dtie to the left vortex is 



^2" 2jtpVo 



/ ^ r f h \ 



(B6) 



Consider the image vortices having coordinates f^ and h^ given hy the 
following equation: 



- ^^ 
^^ ^ f^ -h h^ 

hr^ 



hi = 



f 2 + h^ 



(B7) 



The lifts of the right and left image vortices are then given, respec- 
tively, by 



SitpVo \ s s s / 



L4- 



- ^ ^a^r 



2nmn 



(^'P-^^^) 



(B8) 
(B9) 




38 



NACA RM A53G08 



The total lift due to the wing vortices and their images is 



^T(V) 



8qr. 



m '-r 



2jt(3Vc 



^(l)-<4)-K^)^K-^)](-) 



To obtain the tail interference factor, i, requires a determination 
of the lift of the tail alone by strip theory to nondimensionalize the 
foregoing lift quantity. 



(Lt) = 



2qa 



<^ 57.3 



- ) Ct] dT) 



(Bll) 



Integration gives 



(Lt) = 
-^ a 



l4-aq(s-r)cj,(l+A) 
57.3 P 



(B12) 



Forming the ratio given by equation (Bl) yields the following resiilt 
for i: 

1+K L\sssy Vsss/ \ s s s J \ s ss/J 

(BI3) 




NACA EM A53G08 




39 



APPEHDIX C 
DETERMINATION OF TAIL INTERFERENCE FACTOR FOR RECTANGULAR 
TAILS USING ALDEN-SCHINDEL TECHNIQUE 



The technique of Alden and Schindel described in reference l6 can 
be used for estimating the load on the tail section due to wing vortices. 
Figure ^3 shows the model which is analyzed. The assumption is made 
that the lift due to the vortices originates on the exposed tail panels 
even thoiigh some of this lift may be carried over onto the body. Thus, 
an integration across the exposed wing panels gives all the lift. This 
assumption is the same as that made in evaluating the tail interference 
factor by strip theory and has been previously discussed. The analysis 
is carried out with P = 1 to simplify the algebra, and the P' s are 
reintroduced into the final charts. The essential idea of the Alden- 
Schindel technique is that the total lift acting on a wing of arbitrary 
twist can be evaluated by a strip technique wherein the weighting factor 
for the local strip corresponds to the span loading at the strip for the 
same plan form at imiform angle of attack in reversed flow. In mathe- 
matical form this result is stated as 



L = / w(ii) F(ti) dT] 
'span 



(CI) 



wherein F(ti) is the weighting factor and w(t)) is the vertical component 
of velocity. With reference to figure k3 for model and coordinates, the 
weighting factor is given for the three regions as 



Region I . : 



F(ti) = 



kqc 



(C2) 



Region II. : 



F(ti) 



Region III. 



ffqc 



F(ti) = 



- cos ^ ^ 



c c y jt,v 



i<-qc 



(C3) 



^e.-^(..^.^>|y(|.i)_(|.aj] 



(ck) 



ko 



NACA RM A53G08 



The vertical velocity component due to the right external vortex is 

rm(f-Ti) 



v(ti)= 



2«[h2 + (f-Ti)2] 



(C5) 



To evaluate the lift due to the right external vortex the following 
integration must he performed: 



Li = / F(ti) w(ii) dTi + r F(ti) w(ti) dri + 

^-s -'-s+c 

f F(^) v(ti) dTi + I"^ F(ti) v(ti) dTi (C6) 



Performing the integrations presents some algebraic difficulty. Hoirever, 
the answer was obtained in closed form in terms of the following func- 
tion: 



\ c c c c / 



^1 2c 






2^^ 



iln 



8.^ + (fT+73-H /Ti82i/^;;^+y^(f) ^n^Tf^ 



V^5i(fi) V-ai + 7i aiSiy^^TTTI a/2 82 ( ^) ^ -cxg + 7^ 



7i 



-/slsi 



7i 



0^282 -s/ 0^2 + 72 1 

— + 



a/2 [62 1 



72 



2 L h^,+ (f- 



s+c)^ 



h^ +(f+r)^ 
Lh^ + (f+s-c)^ J 



(C7) 



NACA RM A53G08 



1^1 



vhere 



5i = — - — +1 



52 = 



c C 



= 51.2^- 1 



O'l^a = Oi^2' 



(fT 






71,2 = 



5l,2" 



(fT-il ^^a.,.= (fyj 



(C8) 



In terms of the f ■unction X, the lift is 



Li = 



«V. 



V ( f h s r 
c c c c 



(C9) 



The contribution of the image vortex to the lift must now be determined. 
The coordinates of the image vortex to the right are 



f i = 



hi = 



r^f 
f^h^ 



r^h 
f^+h^ 



(CIO) 



In terms of these coordinates the lift due to the image vortex, taking 
into acco\int the change in the sign of the circiilation, is 



L - ^=^^%^fiM sr>) 
itV_ \ c c c c / 



(Cll) 



The X function is determined in terms of the following parameters: 




h2 



NACA RM A53G08 



ft 2fi 2s 

8 -_i£i_££ + 1 

■* c c 



> (C12) 



'3,4 



,,..(i^)=.xl...3,/ (¥T 



The lift due to the two external vortices and the two internal vortices 
is thus 



.(u.L.).2Mi[, (£,-!).. (a,^-)] ,cx3) 



The lift so determined is exact within the limits of linear theory. 
It is necessary to ohtain the lift of the wing alone, as given by linear 
theory, to form the ratio given hy the tail interference factor i. 



1 = 



g(Ll+Lg)/(Lrp)^ 

5T.3rni/2nVoa(s-r) 



(Cl4) 



The lift-curve slope of a rectangular tail per radiaji is 



dC^ 
da 



= U 1 



2An 



so that 



(LtI = 



2c(s-r)qa 



Ki-D-f] 



a 



57.3 (,.|) 



(C15) 



(ci6) 



The lift ratio is obtained hy division 



2(Li+L2) 



(Lt) 



5T.3rr 



m 



a 



L aVo(s-r) 






-X 




f i hi 



(CI?) 



NACA RM A53G08 



h3 



or 






a.iiL 



(C18) 



APPENDIX D 

DETERMINATION OF CENTER OF BODY LIFT DUE TO WING 

AT SUBSONIC SPEEDS 



Hitherto, no subsonic method has been available for estimating the 
center of the lift transferred by a wing or tail to the body. An 
approximate method for accomplishing this, based on lifting-line theoiy, 
is now presented. It is known that a good approximation of the lift 
and moment characteristics of swept wings at subsonic speeds can be 
gained by placing a lifting line of variable loading at the wing quarter 
chord and satisfying the tangency conditions at the three-quarter chord. 
See, for instance, reference 26. An extension of this model to include 
the body is shown in figvire 21. The image of the quarter-chord line 
inside the body is obtained by reflecting each point of the quarter- 
chord line into the body in its cross-flow plane. Since the quarter- 
chord line is not imiformly loaded, trailing vortices will stream back- 
ward from the line proportional in strength to the gradient of the 
span-loading curve. A series of three horseshoe vortices representing 
the span loading is shown in figure 21 Image vortices inside the body 
are also illustrated. In the mathematicaJ. treatment that follows, the 
number of vortices increases without limit. 

Consider the qioarter-chord line with an elliptical loading 



r =r^ 



j^-c~r <-' 



The strength of the boimd vortices is proportional to P , for both the 
external flow and the internal flow. The lift due to the bound part of 
an elementary horseshoe vortex is proportional to the product of its 
strength times its length 



dL -rdTii ^ r d(^£^)~-rr^ ^ 



(E2) 



The lift due to any horseshoe vortex is concentrated at its bound vortex 
so that the moment about the leading-edge quarter-chord intersection is 

rr^ldTi rr ^(Ti-r)tanAi/4dTi 
dM ~ 5 ~ 5 V-^j^ 



NACA KM A53G08 



^5 



tan A 



^b(w)-T"l 



1/4 



r(Ti-r) 



dn 






dTl 



(Dl^) 



y(s-r)2-(ri-r)^ 



(Ti-r) dT] 



^B(W)-ir=*^^ V* 



^s y(s-r)2 - (Ti-r)2 



dT| 



(D5) 



The value of %(y\ as determined by integrating equation (D5) is 



^B 



(W) = if + (s-^) ^^'^ ^1/4 



r-s 



ys(s-2r) cosh-^(^)- (s-r) + iHl 



(s-r)r ^-i/ s-r^ ^ (s-r)2 „. . 
cosh (— )+ — 2^^"^^ 



'/s(s-2r) 



<^) 



j s > 2r 



(d6) 



k6 ^^____^ ^^^^ ^ A^3G08 



REFEEENCES 



1. Betz, A.: Applied Airfoil Theory. Airfoils or Wings of Finite Span. 

Vol. IV of Aerodynamic Theory, div. K, ch. Ill, sec. 1, W.F. Durand, 
ed., Jiilius Springer (Berlin), 193^^ PP- 152-157- 

2. Hopkins, Edward J., and Carel, Hubert C: Experimental and Theoreti- 

cal Study of the Effect of Body Size on the Aerodynamic Character- 
istics of an Aspect Ratio 3,0 Wing-Body Combination. NACA RM A51G24, 
1951. 

3. Hopkins, Edward J., and Carel, Hubert C: Experimental and Theoreti- 

cal Studies of the Interference at Low Speeds Between a Slender 
Body and Triangular Wings. NACA RM A53Allf, 1953. 

k. Nielsen, Jack N., and Pitts, William C: Wing -Body Interference at 
Supersonic Speeds with an Application to Combinations with Rectan- 
gular Wings. NACA TN 2677, 1952. 

5. Ferrari, Carlo: Interference Between Wing and Body at Supersonic 

Speeds - Theory and Numerical Application. Jovir. Aero. Sci., 
vol. 15, 19^, pp. 317-336. 

6. Morikawa, George K.: The Wing -Body Problem for Linearized Supersonic 

Flow. Calif. Inst, of Tech., Doctoral Thesis, 19k^9. 

7. Nielsen, Jack N., and Kaattari, George E.: Method for Estimating 

Lift Interference of Wing-Body Combinations at Supersonic Speeds^. 
NACA RM A51J0lf, 1951- 

8. Kaattari, George E., Nielsen, Jack N., and Pitts, William C: Method 

for Estimating Pitching-Moment Interference of Wing-Body Combina- 
tions at Supersonic Speeds. NACA RM A52B06, 1952. 

9. Nielsen, Jack N., Kaattari, George E., and Drake, William C: Com- 

parison Between Prediction and Experiment for All -Movable Wing 

and Body Combinations at Supersonic Speeds - Lift, Pitching Moment, 

and Hinge Moment. NACA RM A52D29, 1952. 

10. Silverstein, Abe: Toward a Rational Method of Tail-Plane Design. 

Jour. Aero. Sci., vol. 6, 1939, pp. 36I-369. 

11. Silverstein, Abe, and Katzoff, S.: Design Charts for Predicting 

Downwash Angles and Wake Characteristics Behind Plain and Flapped 
Wings. NACA Rep. 6h8, 1939. 

12. Morikawa, George: Supersonic Wing -Body-Tail Interference. Jour. 

Aero. Sci., vol. I9, na. 5. 1Q'5P. -nrL. 333- 3^. 




MCA RM A^3G08 ^^^^^HH 

13. Lomax, Harvard, and Byrd, Paxil F.: Theoretical Aerodynamic Charac- 
teristics of a Family of Slender Wing-Tail-Body Combinations. 
NACA TN 255^, 1951. 

ik. Lagerstrom, Pace A., and Graham, Martha E.: Aerodynamic Interfer- 
ence in Supersonic Missiles. Douglas Aircreift Co., Rep. No. 
SM-137l^3, 1950. 

15. Spahr, Richard J., and Dickey, Robert R.: Vortex Wake and Downwash 

Field Behind Triangular Wings and Wing-Body Combinations at Super- 
sonic Speeds. NACA RM A53D1C, 1952. 

16. Alden, Henry L., and Schindel, Leon H.: The Calculation of Wing 

Lift and Moments in Nonuniform Supersonic Flows. M.I.T. Meteor 
Rep. 53, 1950. 

IT. Grigsby, Carl E.: The Use of the Rolled-Up Vortex Concept for 

Predicting Wing-Tail Interference and Comparison with Experiment 
at Mach Number of 1.62 for a Series of Missile Configurations 
Having Tandem Cruciform Lifting S\irfaces. NACA RM L52H05, 1952. 

18. Edwards, Samuel S.: Experimental and Theoretical Study of Factors 

Influencing the Longitudinal Stability of an Air-to-Air Missile 
at a Mach Number of l.k. NACA RM A52J19, 1952. 

19. Edelman, Gilbert M.: Wing -Body and Wing -Body-Tail Interaction at 

Supersonic Speeds for Generalized Missile Configurations at High 
Angles of Attack. U. S. Navy Sympositmi on Aeroballistics, 
May 13-14, 1952. 

20. Ralney, Robert W.: An Investigation of Several Supersonic Missile 

Configurations Directed Toward Minimizing Center-of -Pressure 
Travel. NACA RM L52G01, 1952. 

21. Tsien, Hsue-Shen: Supersonic Flow Over an Inclined Body of Revolu- 

tion. Jour. Aero. Sci., vol. 5, no. 12, Oct. 1938, pp. k80-kd3. 

22. Canning, Thomas C, and Denardo, Billy Pat: Investigation of the 

Lift and Center of Pressure of Low-Aspect -Ratio, Cruciform, Tri- 
angular, and Rectangular Wings in Combination With a Slender 
Fuselage at High Supersonic Speeds. NACA RM A52C2li-, 1952. 

23. Allen, H. Julian, and Perkins, Edward W. : Characteristics of Flow 

Over Inclined Bodies of Revolution. NACA RM A50L0T, 1951. 

2lf. Nielsen, Jack H., Katzen, Elliot D., and Tang, Kenneth K.: Lift 
and Pitching-Moment Interference Between a Pointed Cylindrical 
Body and Triangular Wings of Various Aspect Ratios at Mach 
Numbers of I.50 and 2.^^^Ua^tL^50F06, 1950. 




hQ flll^^^^Bl ^A<^A RM A^3G08 



25. Spreiter, John R.: Aerodynamic Properties of Slender Wing -Body 

Combinations at Subsonic, Transonic, and Supersonic Speeds. 
NACA Rep. 962, I95O. 

26. DeYoung, John, and Harper, Charles W.: Theoretical Symmetric Span- 

Loading at Subsonic Speeds for Wings Having Arbitrary Planform. 
NACA TR 921,' I9I+8. 

27. Spreiter, John R., and Sacks, Alvin H.: The Rolling -Up of the 

Trailing Vortex Sheet and Its Effect on Downwash Behind Wings. 
Jour. Aero. Sci., vol. 18, no. 1, 1951> PP. 21-32. 

28. Edvards, Sherman, and Hikido, Katsimi: A Method for Estimating 

the Rolling Moments Caused by Wing-Tail Interference for Missiles 
at Supersonic Speeds. NACA RM A53H18, 1953- 

29. Lagerstrom, Paco A., and Van Dyke, M. D.: General Considerations 

About Planar and Non-Planar Lifting Systems. Douglas Aircraft 
Co., Rep. No. SM-13'14-32, 19i*-9- 

30. Heaslet, Max. A., and Spreiter, John R.: Reciprocity Relations in 

Aerodynamics. NACA TN 2700, 1952. 

31. Hill, J. A. F.: An Electrical Analog for Studying Wing-Tail Inter- 

ference on Guided Missiles. Description of Method. U. S. Navy 
Symposium on Aeroballistics, May 13-1^^ 1952 

32. Lawrence, H. R.: The Lift Distribution on Low Aspect Ratio Wings 

at Subsonic Speeds. Jour. Aero. Sci., vol. I8, no. 10, 1951^ 
pp. 683-695. 

33. Lagerstrom, Paco A., Wall, D., and Graham, M. E.: Formulas in 

Three -Dimensional Wing Theory. Douglas Aircraft Co., Rep. 
No. SM-11901, I9J+6. 

3if. Lapin, Ellis: Charts for the Computation of Lift and Drag of Finite 

Wings at Supersonic Speeds. Doxiglas Aircraft Co., Rep. No. SM-I3W0, 
191^9. 

35- Johnson, Ben H., Jr., and Rollins, Francis W.: Investigation of a 
Thin Wing of Aspect Ratio k in the Ames 12 -Foot Pressure Wind 
Tunnel. V. - Static Longitudinal Stability and Control Throughout 
the Subsonic Speed Range of a Semispan Model of a Supersonic Air- 
plane. NACA RM A9IOI, I9U9. 

36. Lauritsen, Chaxles H.: Wind Tunnel Tests at Transonic Speeds of 

the MX-770 Missile Without Ram-Jets. North American Aviation, Inc., 
Rep. No. AL-629, 19it8. 




NACA RM A^3G08 tRHHIB ^9 

37* Strohmeyer, William E.: Svtpersonic Wind Tvumel Tests at M » I.73 
of MX-7T0 Canard and ConventionEil Configurations. North American 
Aviation, Inc., Rep. Ho. AL-545, 19^*8. 

38. Magnus, R. J., Beal, R. R., and Kutschinski, C. R.: Sparrow 13-D, 
Analysis of Force emd Moment Characteristics from Subsonic Wind- 
Tunnel Tests of a 50-Percent-Scsae Model. Douglas Aircraft Co., 
Rep. No. SM-13632, 1950. 

39- Beek, Charles R., and Anderson, Arnold W.: Wind-Tunnel Tests of the 
XSSM-N-6 (Rigel) Pilotless Aircraft. Part II. - Longitudinal 
and Lateral Stability Characteristics of a l/lf-Scale Model with 
Single Booster. David W. Taylor Model Basin Rep. C-201, Aero. 76O, 
19l^9. 

kO. Heitmeyer, John C: Lift, Drag, and Pitching Moment of Low-Aspect- 
Ratio Wings at Subsonic and Supersonic Speeds - Plane Triangular 
Wing of Aspect Ratio 3 with KACA OOO3-63 Section. NACA RM A51H02, 
1951. 

kl. Reese, David E., and Phelps, E. Ray: Lift, Drag, and Pitching 
Moment of Low-Aspect-Ratio Wings at Subsonic and S\rpersonlc 
Speeds - Plane Tapered Wing of Aspect Ratio 3.I With 3-Percent- 
Thick Biconvex Section. NACA RM A50K28, I951. 

\2.. Cahn, Maurice S., and Bryan, Carroll R.: A Transonic -Wing Investi- 
gation in the Langley 8-Foot High-Speed Tunnel at High Subsonic 
Mach Numbers aaid at a Mach Number of 1.2 Wing -Fuselage Configura- 
tion Having a Wing with 0° Sweepback, Aspect Ratio 4.0, Taper 
Ratio 0.6, and NACA 65AOO6 Airfoil Section. NACA RM L51A02, I95I. 

if 3. Smith, Donald W., and Heitmeyer, John C: Lift, Drag, and Pitching 
Moment of Low-Aspect-Ratio Wings at Subsonic and Supersonic 
Speeds - Plane Triangxilar Wings of Aspect Ratio 2 With NACA OOO8-63 
Section. NACA RM A50K20, I951. 

hk. Heitmeyer, John C: Lift, Drag, and Pitching Moment of Low-Aspect- 
Ratio Wings at Subsonic and Supersonic Speeds - Plane Triangular 
Wing of Aspect Ratio k with 3-Percent -Thick Biconvex Section. 
NACA RM A51D30, I951. 

45- Weber and Kehl: Wind-Tunnel Measurements on the Henschel Missile 
"Zitterrochen" in Subsonic and Supersonic Velocities. NACA 
TM 1159, 19^. 

kS. Smith, Donald W., and Heitmeyer, John C: Lift, Drag, and Pitching 
Moment of Low-Aspect-Ratio Wings at Subsonic and Supersonic 
Speeds - Plane Triangular Wing of Aspect Ratio 2 with NACA OOO5-63 
Section. NACA RM A50I< 




^ ^^^^^^^m NACA RM A^3G0d 



kl . Heitmeyer, John C, and High tower, Ronald C: Lift, Drag, and 

Pitching Moment of Low -Aspect -Ratio Wings at Subsonic and Super- 
sonic Speeds - Plane Triangular Wing of Aspect Ratio k with 
3-Percent-Thick Rounded Nose Section. NACA RM A51P21, 1951- 

h&. Anderson, Adrien E.: An Investigation at Low Speed of a Large- 

Scale Triang\xlar Wing of Aspect Ratio Two. III. Characteristics 
of Wing with Body and Vertical Tail. NACA RM A9H0i^, 19^9. 

49. Polhamus, Edward C, and King, Thomas J. Jr.: Aerodynamic Charac- 

teristics with Fixed and Free Transition of a Modified Delta 
Wing in Combination with a Fuselage at High Suhsonic Speeds. 
NACA RM L50C21, I95O. 

50. House, Rufus 0., and Wallace, Arthur R.: Wind-Tunnel Investigation 

of Effect of Interference on Lateral-Stability Characteristics of 
Four NACA 23012 Wings, an Elliptical and a Circular Fuselage, and 
Vertical Fins. NACA Rep. 705, 19^1. 

51. McKay, James M., and Hall, Albert W. : The Effects on the Aerody- 

namic Characteristics of Reversing the Wing of a Triangvilar Wing- 
Body Combination at Transonic Speeds as Determined by the NACA 
Wing-Flow Method. NACA RM L51H23, I95I. 

52. Smalley, J. H.: Wind-Tunnel Investigation of a 3/l+-Scale Model of 

the XAAM-N-lf (Oriole) Guided Missile. David W. Taylor Model 
Basin Rep. C-305 Aero. 785, 1950. 

53. Payne, W. Randolph: Wind-Tunnel Tests of the XSSM-N-6 (Rigel) 

PilotlesE Aircraft. Part I - Longitudinal and Lateral Stability 
Characteristics of a l/5-Scale Model. David W. Taylor Model 
Basin Rep. C-161, Aero.760, 19kQ. 

^k. Niewald, Roy J., and Moul, Martin T.: The Longitudinal Stability, 
Control Effectiveness, and Control Hinge-Moment Characteristics 
Obtained from a Flight Investigation of a Canard Missile Con- 
figuration at Transonic and Supersonic Speeds. NACA RM L50I27, 
1950. 

55. Brown, Clai^nce A., and L\mdstrom, Reginald R.: Flight Investiga- 

tion From Mach Ntmiber 0.8 to Mach Ntimber 2.0 to Determine Some 
Effects of Wlng-to-Tail Distance on the Longitudinal Stability 
and Control Characteristics of a 60° Delta-Wing -Canard Missile. 
NACA RM L52C26, 1952. 

56. Spahr, J. Richard, and Robinson, Robert A.: Wind-Tunnel Investiga- 

tion at Mach Numbers of I.5 to 2.0 of a Canard Missile Configura- 
tion. NACA RM A5ICO8, 1951. 





NACA BM A^3G08 ^^^^^^^Bi ^1 



57- Rainey, Robert W. : Langley 9-Inch Supersonic Tunnel Tests of 
Several 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 and Less 
Than 1 and Some Static Rolling -Moment Data. KACA RM L5OG07, 1951- 

58. Ellis, Macon C, and Grigshy, Carl E.: Aerodynamic Investigation 

of Mach Number of I.92 of a Rectangular Wing and Tail and Body 
Configuration and Its Components. NACA RM L9L28a, 1950. 

59. Grigsby, Carl E.: Tests at Mach Number of 1.62 of a Series of 

Missile Configurations Having Tandem Cruciform Lifting Surfaces. 
NACA RM L51J15, 1952. 

60. Fischer, H. S.: Supersonic Wind-Tunnel Tests of a 0.0T5 Scale 

Model of the Nike kQ2 Missile. Douglas Aircraft Co., Rep. 
No. SM-13QkS, 1950. 

61. Harshman, J., and Uddenberg, R. C: Supersonic Wind Tunnel Tests 

of GAPA Models at a Mach Number of 1.28 in the Aberdeen Tunnel. 
Boeing Aircraft Company Document No. D-7817, 1914-6. 

62. Uddenberg, R. C: Supersonic Wind Tunnel Tests of GAPA Models at 

a Mach Number of 1.72 in the Aberdeen Tunnel. Boeing Aircraft 
Company Document No. D-7818, 19h6. 

63. Uddenberg, R. C: Supersonic Wind Tunnel Tests of GAPA Models at 

a Mach Number of 1.72 in the Aberdeen Tunnel Supplement A - 
Results From the Fourth Aberdeen Test Period. Boeing Aircraft 
Company Document No. D-7818A, 19ij-7. 

6k. Beal, R. R.: Analysis of Force and Moment Characteristics From 
Supersonic Wind-Tunnel Tests of a 13.5-Percent-Scale Model of 
the Sparrow ll^-B at Mach Niimber I.50 Including the Effects of 
Systematic Variations of Wing Planform. Douglas Aircraft Co., 
Rep. No. SM-20175, 1951. 

65. Mead, Merrill H.: Experimental Investigation of the Aerodynamic 

Characteristics of an Air-to-Air Missile Employing Cruciform 
Wings and Tails of Rectangular Plan Form at Mach Numbers ot l.k- 
and 1.9. NACA RM A52K11+, 1953- 

66. McDevitt, John B.: A Correlation by Means of Transonic Similarity 

Rules of the Experimentally Determined Characteristics of 22 Rec- 
tangular Wings of Symmetrical Profile. NACA RM A51L17b, 1952. 



52 



NACA RM A53G08 



67. Coletti, Donald E.: Investigation of Interference Lift, Drag, and 

Pitching Moment of a Series of Rectangular Wing and Body Combina- 
tions at Mach Numbers of 1.62, 1-93^ and 2. 1+1. NACA RM L52E26, 
1952. 

68. Jones, R. T.: Thin Oblique Airfoils at Supersonic Speeds. NACA 

TN 1107, 19^. 

69. Lagerstrom, P. A.: Linearized Supersonic Theory of Conical Wings. 

NACA TN 1685, 191*5 • 



NACA RM A53G08 



53 



^h 



NACA RM A53G08 




Eh 
I 

O 

I 

























H 














H 






S 








-H 




On 
H 


H 
O 


ITN 

OJ 

in 


O 

ir\ 


ITN 
O 






^ 


CC 


E 


g 


_g 


11 




•-i 


CU 


^ 


^ 


IT. 


'•O 




NACA RM A53G08 




55 















^ 














s 








































^Y 






8 






























~--^ 


fr-> 


o 


o 


o 


O 




9 










3 


s 


o 


■ 


' 


' 




(3 

+ 














©' 












^ 


si, 


■;*, 


•^ 




/-^ 








o 

H 




/ 


o 


o 


° 


o 




f|) 






c 




+ 

1^ 
















^ 


CM 


^ 




■-j:* 














I 


8 




m 


® 




o 










o 


9 




y 


® 










V 

c 

s 


®© 


©1® 




3 






cy 

8 
9 












' 




























^ 


© 


^ 




H 


® 






t 


° 


H 












3 


(55 






o 


o 


f ) 




+ 


® 


© 








O 


■' 


.* 


.■ 






@ 












3 

o 


^ 


(^ 


^ 




8 


J" 




is 


H 


IP, 




II 










+ 




o 




H 


H 




^ 


/ 


/ 






;^ 












a 
o 

1 

1 

o 
o 






O 


















CTv 


CM 
ON 


a\ 


g; 






o 








O 
II 












9. 


® 




OJ 








©^ 


































^ 


ITN 
O 


H 
O 


3 




f 








S 


O 
OJ 
H 






§ 

© 








'S* 




o 




H 


« 




o 


o 


















o 


a 












II 


II 




& 




to 


-:* 






■■ 






J 


i 


.f 


































O 


o 


o 




c^ 




°d 


O 


IPn 


o 

H 


in 


s 


® 


g 













^r> 


f- 


















^ 


^ 




^ 


s 


^^ 


fi 
















X 




































rfii 


s 


o 














4J 






■^ 












^ 


















1 




"■(-i 


^ 


d 


a\ 


R 


•^ 














H 


t ) 


(Vl 














'3- 
. O 


o 


O 






l 




So) 




















3 






O 




o 


^-. 












Md/ 






















^' 












o 




























H 


H 




OJ 


+ 




S 




LP, 
CT 


^ 


,^ 















^ 




o 






H 


































© 




























1 






5 


^ 






On 


© 






S 


S 
























1 


H 
l( 








■ o , 








1 


f-^ 
































a" 


+ 










'^ 








1 


■? 


^ 


, :^ 








snt' 




\n 


v,n 


\D' \d 


5 




•w 






r-\ 


3) 




-^ 


o 




o 
o 


*" 




^^ 












+> 


,? 


i 




u 


.'^ 




M 




























-=!■ 






























o 
o 


8 


1 g 

H 


S 
J 


H 






O 


8 

in 


S 


s 








































































tr\ 














































■H 




tVJ 


tu 


I 








& 


































S 








1^ 
















11 






■^^^ 














C 


D 








(B 


i 


OJ 

-4- 
o 


lTn 


-=h 














■^ 


© 


^ 










© 




























c5 


@ 




m 


© 
















®, 




iH 


(s5 




o 








Ol 


(^ 






^ 




t 












^ 










o 


































c* 










■"* 















rH O 










■P 




v-p 












































n> 




































§1 












iU . tJ ■ 


»l§ 










3 KC C- 
H CD 0) IP, 






















































f*^, 




OS J^ 




■3 ° !! " 




(d CO c 










■p 13 d ffl 
a a; ^ 9^ 


n 








■H 




H o 








M 




a^:;^.H 




















■H Xl r-l 




s §^ 














il 




















&?;ds 














n 


OJ <u a 
















■p 




























,§ 














CO 










_ 


_ 


__ 




__ 


„ 


_ 


[^ 


C\J 


ro 




J- 


IXN 


>o 









0\ 
































i 




9 




8 




3 


s*, 




S 


o 




t~ 




O 








o 


(^ 




O 
II 


(S) 






i 


(D 


© 


© 


CD 
® 




e 






© 
(!)■ 


(D 




® 










+ 


+ 


+ 


+ 






© 


® 


© 


® 


> 


IP, 


6 






. 


3 


o 
o 


(gfe 






6 


tH 


II 










+ 


& 








,© 


.©, 










OJ 












9 






§ 






X 






M 


- 


H 












6 


< 1 






>-l 


o 


o 


(K) 










© 


© 






g 


1 


+ 


© 


o 
o 


9 








® 

1 r 


© 


© 




*^ 


?s 








^ 


8 


Q 








>-l 


O 

© 


^2/ 


i 








o 


9 


o 








ft 


1$ 


s 


S 






i 


g 


^ 


^ 






o 


U 


o 


o 














-* 


IfN 


^ 


t_ 




















-^ 




H 




56 



NACA RM A53G08 



TABLE II.- SUMMARY OF GEOMETRIC AND AERODYNAMIC CHARACTERISTICS 
AND TEST CONDITIONS FOR WING -BODY COMBINATIONS 
(a) Geometric Characteristics 



No. 


Sketch 


«o 


B 


'N 


iR 


1m 


I 


Section 


h 


"c- 


'w 


3A 


^L.E. 


X 


ni 


(-a 


Ref. 


Facility 


la 


"*" 


0.2O 


l.B6<10O 


6.1.8 


18.67 


70.5 


iw; 


^tex. 


0-042 


17^40 


64.20 


3.43 


9-450 


0-546 


6.43 


0.179 


35 


Ames 

12 ft 


b 


.50 


l.S6<10'' 


6.48 


IS. 67 


70.5 


146 


hex. 


.042 


17^4o 


64.20 


3.02 


9.450 


• 546 


6.43 


.179 
.179 


35 


Ames 
12 ft 


c 


.70 


1.86<10« 


6.1.3 


18.67 


70.5 


11.6 


hex. 


.042 


17.40 


64.20 


2.49 


9.450 


• 546 


6.43 


35 


Ames 
12 ft 


d. 

e 


.80 


1.86<10'' 


6.1.S 


18.67 


70.5 


11.6 


hex. 


.042 


17.40 


64.20 


2.10 


9.450 


.546 


6.43 


.179 


35 


Ames 
12 ft 


■ 90 


i.e&io" 


6.1.8 


18.67 


70.5 


ll«S 


hex. 


.042 


17.40 


64-20 


1.52 


9.450 


.546 


6.43 


.179 


35 


Ames 
12 ft 


2a 


^ 


.80 


.78>clO= 


.8125 


1.625 


6.575 


13.075 


=b.c. 





2.91 


8-06 


1.03 


45O 


.401 


.812 


.258 


36 


OAL 


b 
c 
d 


.90 


- _ - 


.8125 


1.625 


6.575 


13.075 


h.c. 


. _ - 


2.91 


8.06 


.744 


45° 


.401 


.812 


.2» 


36 


OAL 


1.10 


.67x10^ 


.8125 


1.625 


6.575 


13.075 


b.c. 


_ _ . 


2.91 


8.06 


.782 


45° 


.401 


.812 


.258 


36 


OAL 


1.73 


i.eoxio" 


.8125 


1.625 


6.575 


13.075 


h.c. 





2.91 


8.06 


2.41 


450 


.401 


.812 


.258 


37 


OAL 


3a 
b 

d 


-^^ 


.80 


.36x10° 


.8125 


1.625 


6.575 


13-075 


h.c. 





1.34 


1-51 


1.18 


45O 


.341 


.546 


.308 


36 


OAL 


■ 90 


, _ . 


.8125 


1.625 


6.575 


13.075 


b.c. 


- _ - 


1.34 


1-51 


.856 


450 


.341 


.546 


.308 


36 


OAL 


1.10 


.31x10" 


.8125 


1.625 


6.575 


13-075 


b.c. 





1.34 


1-51 


.900 


45» 


.341 


.546 


.308 


36 


OAL 


1.73 


.7l.xl0° 


.8125 


1.625 


6.575 


13-075 


b.c. 





1.34 


,1-51 


2.77 


450 


• 341 


.546 


-308 


37 


OAL 




^4— 


.1.65 


1.95x10® 


2.0 


8^38 


36.1.6 


61.-41 


*d.w. 


.029 


8.38 


23-24 


2.06 


60O 





2.0 


-216 


38 


CAL 4 CWT 


■ 70 


l.33<10<' 


2.0 


8.38 


36.1.6 


61.-1.1 


d.v. 


.029 


8.38 


23-24 


1.66 


60" 





2.0 


-216 


38 


CAL & CWT 


■ 90 


1.05^10" 


2.0 


8^38 


36. i«; 


64.1.1 


d.w. 


.029 


8.38 


23-24 


1.01 


600 





2.0 


-216 


38 


CAL & CWT 


5a 


^-^ 


.1.65 


.91x106 


2.0 


8.38 


36.1.6 


64.41 


d.v. 


.030 


3.92 


57-53 


3-54 


450 





2.0 


.254 


38 


CAL A CTT 


b 


.70 


.6a<io6 


2.0 


B.38 


36.1^; 


64.41 


d.v. 


.030 


3.92 


57-53 


2-86 


450 





2.0 


.254 


38 


CAL & CWT 


c 


■ 90 


.i.9<io6 


2.0 


8.38 


36.1.6 


64.41 


d-v- 


.030 


3.92 


57-53 


1-74 


450 





2.0 


.254 


38 


CAL & CWT 


=6 


>^B 


■ Mil 


.3C6<106 


3.50 


7.00 


76.26 


80.41 


d-v. 


.05 


2.69 


11-14 


2-46 


26.60 


.500 


3.45 


.514 


39 


DTMB 


^ 


^«H^ 


.201. 


■ 8a<io° 


3.50 


7.00 


76.26 


80.41 


hex- 


.06 


7.45 


50-69 


2.86 


14° 


.462 


3.50 


.250 


39 


mMB 


da 


^ 


.60 


i.-lxio" 


2.38 


11. .39 


28.11 


46.93 


NACA 
0003-63 


-03 


12.27 


20-50 


2.40 


53.1° 





2^38 


-147 


40 


Ames 
6(6 ft 


t 


.90 


1.-1x106 


2.38 


^■39 


28.11 


46.93 


MCA 
0003-63 


-03 


12.27 


20-50 


1-31 


53.10 





2.38 


• 147 


40 


Ames 
6x6 ft 


c 


1.20 


1..1X106 


2.38 


1I..39 


28.11 


46.93 


NACA 
0003-63 


-03 


12.27 


20.50 


1^99 


53.10 





2.38 


-147 


40 


Ames 

6x6 ft 


d 


1.1«3 


1..IXI06 


2.38 


11.. 39 


28.11 


46-93 


NACA 
0003-63 


.03 


12.27 


20-50 


2^94 


53 •lo 





2. 38 


.147 


40 


6<6 ft 


e 


1.53 


l..l;{106 


2.38 


lit. 39 


28.11 


46.93 
46.93 


NACA 
0003-63 


.03 


12.27 


20-50 


3-47 


53^10 






2.38 
2.38 


.147 


40 


Ames 
6k6 ft 


f 


1.70 


V. 1x106 


2.38 


11..39 


28.11 


NACA 
0003-63 


.03 


12.27 


20.50 


4.13 


53-1° 


.147 


40 


Ames 
6x6 ft 


9a 
■b 

d 


"*■ 


.60 


2.22X10° 


2.38 


11.32 


23.88 


46.93 


b.c- 


.03 


10-50 


20-29 


2.26 


19.1° 


.427 


2.38 


.145 


41 


6x6 ft 


.70 


2.2a<io6 


2.38 


U.32 


23.88 


46.93 


b.c- 


.03 


10.50 


20-29 


2.02 


19-10 


.427 


2.38 


.145 


41 


Ames 
5<6 ft 


.80 


2.2a<106 


2.33 


11..32 


23.88 


46.93 


b-c- 


-03 


10.50 


20-29 


1.69 


19-1° 


.427 


2.3a 


-145 


41 


Ames 

6x6 ft 


.90 


2.2^106 


2.38 


11.32 


23-88 


46-93 


b-c- 


• 03 


10.50 


20.29 


1.23 


19-1° 


• 427 


2.38 


.145 


41 


Ames 
6<6 ft 


e 


1.20 


2.22x106 


2.38 


11.32 


23.88 


46-93 


b.c- 


• 03 


10-50 


20.29 


1.87 


19-1° 


.427 


2.38 


-145 


41 


Ames 
6x6 ft 


f 


l.UO 


2.2a<106 


2.3B 


11.32 


23.88 


46-93 


b-c. 


.03 


10.50 


20.29 


2.77 


19-10 


.427 


2.38 


.145 


41 


Ames 
6x6 ft 


g 


1.60 


2.23<106 


2.38 


11.32 


23.ee 


46-93 


b.c. 


• 03 


10.50 


20.29 


3.53 


19 -lo 


.427 


2.38 


-145 


41 


Ames 
6x6 ft 


h 


1.90 


2.2a(106 


2.38 


11.32 


23.88 


46.93 


b.c- 


• 03 


10.50 


20.29 


4.56 


19.10 


.427 


2-38 


.145 


41 


Ames 
6x6 ft 




MCA RM A53G08 



57 



TABLE II.- SUMMARY OF GEOMETRIC AND AERODYNAMIC CHARACTERISTICS 
AND TEST CONDITIONS FOR WING -BODY COMBINATIONS - Continued 
(Td) Aerodynamic Characteristics 



No. 


Mo 


K„ 


Kw(B) 




Kb(W) 


Theoretical 


Experimental | 




«Llft 


Center of pressure 1 


®Lift 1 


c.p. 


^s, 


^^% 


^^ 


In 


Mb) 


hW 


'c 


(a 


POi^ 


^I-oc 


a)c 


la 


0.20 


0.077 


I.l4 


0.24 


3.47 


0.27 


5.05 


33.4 


70.76 


70.05 


68.67 


0.470 




4.70 


0.471 


b 


.50 


.072 


1.14 


.24 


3.16 


.23 


4.59 


33.4 


70.76 


69.99 


68.78 


.471 




4.35 


.468 


c 


■ 70 


.067 


1.14 


.24 


2.83 


.19 


4.10 


33.4 


70.76 


69.82 


68.87 


.472 




3.94 


.470 


d 


.80 


.063 


1.14 


.24 


2.51 


.16 


3.62 


33.4 


70.76 


69.60 


68.94 


.472 




3.56 


.470 


e 


.90 


.057 


I.l4 


.24 


2.02 


.12 


2.90 


33.4 


70.76 


69.23 


69.02 


.473 




3.08 


.475 


2a 


.80 


•'{.2llt) 


1.22 


.38 


1.43 


.194 


2.60 


2.52 


9.73 


9.39 


8.80 


.673 


(0.305) 


2.51 


.690 


b 


■90 


(.232) 


1.22 


.38 


1.04 


.l4l 


1.90 


2.52 


9.70 


9.32 


8.71 


.667 


(.242) 


1.82 


.695 


c 


1.10 


(.17^) 


1.22 


.38 


1.26 


.147 


2.24 


2.52 


10.10 


10.25 


9.39 


.718 


(.221) 


2.49 


.710 


i 


1^73 


{■130) 


1.22 


.29 


3.29 


.457 


5.40 


2.52 


10.39 


11.22 


9.92 


.759 


(.427) 


5.44 


■ 730 


3a 


.80 


(.SlU) 


1.26 


.46 


1.56 


.81 


3.95 


2.52 


2.35 


2.17 


2.38 


.182 


(1.27) 


4.17 


.187 


b 


.90 


(.855) 


1.26 


.46 


1.18 


.59 


3.04 


2.52 


2.35 


2.16 


2.38 


.182 


(1.01) 


3.40 


.195 


c 


1.10 


(.615) 


1.26 


.46 


1.50 


.62 


3.» 


2.52 


2.55 


2.69 


2.57 


.197 


(.92) 


3.75 


.187 


d 


1.73 


(.520) 


1.26 


.34 


3.42 


1.91 


7.25 


2.52 


2.65 


3.23 


2.71 


.207 


(1.78) 


7.56 


.180 


Ita 


.1*65 


.109 


1.18 


.31 


2.25 


.25 


3.60 


11.6 


30.18 


28.74 


28.62 


.446 




4.00 


.460 


b 


.70 


.lOlt 


1.18 


.31 


1.90 


.20 


3.03 


11.6 


30.20 


28.86 


28.71 


.448 




3.39 


.462 


c 


.90 


.094 


1.18 


.31 


1.28 


.12 


2.03 


11.6 


30.39 


29.09 


29.00 


.452 




2.22 


.465 


5a 


.1*65 


.206 


1.21 


.37 


3.14 


.65 


5.61 


11.6 


60.74 


60.03 


55.00 


.854 




5.65 


.835 


b 


.70 


.187 


1.21 


.37 


2.78 


.52 


4.91 


11.6 


60.76 


60.08 


55.44 


.864 




4.46 


.878 


c 


■ 90 


.162 


1.21 


.37 


1.97 


.32 


3.43 


11.6 


60.80 


60.20 


56.05 


.875 




3.25 


.925 


« 


.204 


1.578 


1.47 


.82 


2.82 


4.45 


10.91 


7.21 


13.05 


12.37 


10.54 


.131 




11.40 


.122 


7 


.201* 


.163 


1.21 


.36 


3.08 


.50 


5.35 


7.21 


53.71 


53.34 


49.26 


.613 




5.15 


.609 


8a 


.60 


.045 


1.11 


.20 


2.49 


.11 


3.37 


12.23 


30.62 


28.01 


29.64 


■ 632 




3.68 


.634 


b 


■ 90 


.038 


1.11 


.20 


1.59 


.06 


2.14 


12.23 


30.88 


28.69 


30.04 


.640 




2.42 


.648 


c 


1.20 


.036 


1.11 


.18 


2.58 


.09 


3.42 


12.23 


32.77 


31.36 


32.03 


.684 




3.34 


.678 


d 


i.to 


.041 


1.11 


.17 


3.36 


.14 


4.45 


12.23 


32.77 


32.09 


32.05 


.684 




4.28 


.676 


e 


1.53 


.OW* 


1.11 


.17 


3.72 


.16 


4.92 


12.23 


32.77 


32.55 


32.06 


.685 




4.55 


.675 


f 


1.70 


.048 


1.11 


.16 


4.00 


.19 


5.28 


12.23 


32.77 


33.10 


32.07 


.685 




5.15 


.672 


9a 


.60 


.038 


1.11 


.20 


2.65 


.10 


3.58 


12.23 


24.68 


23.83 


24.21 


.508 




3.82 


.510 


b 


.70 


.037 


l.U 


.20 


2.46 


.09 


3.32 


12.23 


24.68 


23.75 


24.21 


.508 




^.80 


.510 


c 


.80 


.035 


1.11 


.20 


2.17 


.06 


2.92 


12.23 


24.68 


23.64 


24.21 


.508 




^.50 


,510 


d 


.90 


.032 


1.11 


.20 


1.71 


.05 


2.30 


12.23 


24.62 


23.43' 


24.15 


.507 




=3.30 


.461 


e 


1.20 


.028 


l.U 


.19 


3.04 


.09 


4.05 


12.23 


26.68 


29.13 


26.73 


.561 




3.74 


.558 


f 


l.ltO 


.036 


1.11 


.17 


3.48 


.13 


4.60 


12.23 


26.99 


30.20 


27.00 


.567 




4.51 


.565 


e 


1.60 


.044 


1.11 


.16 


3.64 


.16 


4.81 


12.23 


27.10 


30.96 


27.08 


.569 




4.97 


.570 


h 


1.90 


.054 


1.11 


.16 


3.78 


.20 


5.01 


12.23 


27.14 


31.90 


27.10 


.569 




5.05 


.575 




58 



NACA RM A53G08 



TABLE II.- SUMMARY OF GEOMETRIC AND AERODYNAMIC CHARACTERISTICS 
AM) TEST CONDITIONS FOR WING-BODY COMBINATIONS - Continued 
(c) Geometric Characteristics 



No. 


Sketch 


Ho 


R 


'N 


'e 


■m 


1 


Section 


't 


''c 


>» 


0A 


-^L.E. 


X 


iw 


(0„ 


Ref. 


Facility 


10a 
b 

d 




0.60 


1.66<10» 


1.667 


6.125 


20.0 


33.33 


NACA 
65AOO6 


0.06 


5.89 


18.23 


2.85 


3.6° 


0.635 


1.667 


0.139 


42 


Langley 
8 ft 


.70 


1.75^10"^ 


1.667 


6.125 


20.0 


33.33 


NACA 

65A006 


.06 


5.89 


18.23 


2.55 


3.6" 


.635 


1.667 


.139 


42 


Langley 
8 ft 


.8c 


i.8a<io= 


1.667 


6.125 


20.0 


33.33 


NACA 
65A006 


.06 


5.89 


18^23 


2.14 


3.6" 


.635 


1.667 


.139 


42 


Langley 
8 ft 


• 90 


1.9X10" 


1.667 


6.125 


20.0 


33^33 


NACA 
65A006 


.06 


5.89 


18^23 


1.56 


3.6° 


.635 


1.667 


.139 


42 


Langley 
8 ft 


1.20 


1.86x10'' 


1.667 


6.125 


20.0 


33^33 


NACA 
65A006 


.06 


5.89 


18.23 


2.37 


3.6= 


.635 


1.667 


.139 


42 


Langley 
8 ft 


b 

d 

e 


^ 


.21* 


2.l46<10® 


3.06 


22.67 


38.12 


6o^44 


NACA 
0008-63 


.08 


18.60 


27.24 


1.94 


63^4'> 





3.06 


.180 


43 


Ames 
12 ft 


.60 


2.46x10" 


3.06 


22.67 


38.12 


60.4* 


NACA 
0008-63 


.08 


18.60 


27.24 


1.60 


63.4" 





3.06 


.180 


43 


AmeE 
12 ft 


.80 


2.WK10" 


3.06 


22.67 


38.12 


60.4* 


NACA 
0008-63 


.08 


18.60 


27.24 


1.20 


63.4= 





3.06 


.180 


43 


Ames 
12 ft 


• 90 


2.l4&<10" 


3.06 


22.67 


38.12 


60.44 


NACA 
0008-63 


.08 


18.60 


27^24 


.87 


63.4° 





3.06 


.180 


43 


Ames 
12 ft 


.95 


2.46K10" 


3^06 


22.67 


38.12 


60.44 


NACA 
0008-63 


.08 


18.60 


27^24 


.62 


63.4" 





3.06 


.180 


43 


Ames 
12 ft 


f 


1.30 


2.1*^10" 


3.06 


22.67 


38.12 


60.44 


NACA 
0008-63 


.08 


18.60 


27.24 
27.24 


1.66 
2.S 


63.4° 





3.06 


.180 


43 


Ames 
6<6 ft 


g 
h 


1.53 


2.l;6xl0" 


3.06 


22.67 


38.12 


60.44 


NACA 
0008-63 


.08 


18.60 


63.40 





3.06 


.180 
- 
.180 


43 

43 


Ames 
6x6 ft 

Ames 
5<6 ft 


1.70 


2.46<10« 


3.06 


22.67 


38.12 


6o.4li 


NACA 
0008-63 


.08 


18.60 


27.24 


2.75 


63.4" 





3.06 


1012a 
to 

d 

f 


H- 


.60 


3.6>aD" 


2.38 


12.46 


27.40 


46.93 


"i.e. 


.03 


10.90 


20.43 


3.20 


45" 





2.38 


.127 


44 


Ames 
(X6 ft 


.80 


3.6X10' 


2.38 


12.46 


27.40 


46.93 


b.c. 


.03 


10.90 


20.43 


2.40 


45° 





2.38 


.127 


44 


Ames 
6x6 ft 


.90 


3.65<10" 


2.38 


12.46 


27.40 


46.93 


b.c. 


.03 


10.90 


20.43 


1.74 


45° 





2.38 


.127 


44 


Ames 
6x6 ft 


1.20 


3.65<10" 


2.38 


12.46 


27.40 


46.93 


b.c. 


.03 


10.90 


20.43 


2.65 


45° 





2.38 


.127 


44 


Ames 
6x6 ft 


1.40 


3.6X10® 


2.38 


12.4* 


27.40 


46.93 


b.c. 


• 03 


10.90 


20.43 


3.92 


45° 





2.38 


.127 


44 


Ames 
6c6 ft 


1.70 


3.6X10° 


2.38 


12.46 


27.40 


46.93 


b.c. 


• 03 


10.90 


20.43 


5.50 
1.73~ 


45° 
26:5° 





2.38 


.127 


44 


Ames 


13a 
b 
c 
d 

e 


^ 


• 50 


li.29<10' 


.50 


1.00 


9.79 


9.79 


b.c. 


• 063 


2.08 


3.723 





.50 


.243 


45 


German 


• 70 




.50 


1.00 


9^79 


9-79 


b.c. 


• 063 


2.08 


3.723 


1.43 


26.5" 





.50 


.243 


45 


Genmin 


.90 


6.5aclO» 


.50 


1.00 


9.79 


9.79 


b.c. 


.063 


2.08 


3.723 


.872 


26.5° 





.50 


.24, 


45 


German 


l.>>5 


2.76<10° 


.50 


1.00 


9.79 


9.79 


b^c. 


• 063 


2.08 


3.723 


2.10 


26.5° 





.50 


.243 


45 


German 


1.99 


2.31©<10" 


.50 


1.00 


9.79 


9.79 


b.c. 


• 063 


2^08 


3.723 


3.45 


26.5° 





.50 


.243 
• 327 


45 
45 


German 
German 


Iks. 
b 


"•■ 


.50 


5.6OCI0" 


.50 


1.00 


9.79 


9.79 


b.c. 


• 037 


2^74 


3.475 


.866 
.714 


4^ 





.50 


.70 




• 50 


1.00 


9.79 


9.79 


b.c. 


• 037 


2.74 


' 3.475 


14:^ 





.50 


• 327 


45 


Germaji 


d 


.90 


8.67X10' 


• 50 


1.00 


9.79 


9.79 


b.c. 


• 037 


2.7l> 


3-475 


.436 


1*5" 





.50 


• 327 


45 


German 


l.M 


3.64x10" 


• 50 


1.00 


9.79 


9.79 


b.c. 


• 037 


2.74 


3.475 


1.05 


4:^ 





.50 


.327 


45 


Genian 


1.99 


3.08x10= 


• » 


1.00 


9.79 


9.79 


b.c. 


• 037 


2.74 


3.475 


1.72 


45° 





.50 


• 327 


45 


German 


^5a 
b 

d 

e 


^ 


.2lt 


2.U6<10« 


3.06 


22.67 


38.12 


60.44 


. NACA 
0005-53 


• 05 


IB. 60 


27.24 


1.94 


63.4= 





3.06 


.180 


46 


Ames 
12 ft 


.60 


2.1«6xlo« 


3.06 


22.67 


36.12 


60.44 


NACA 

0005-53 


.05 


18.60 


27.24 


1.60 


63.4° 





3^06 


.180 


46 


Ames 
12 ft 


.80 


2.46<10" 


3.06 


22.67 


38.12 


60.44 


NACA 
0005-53 


.05 


18.60 


27.24 


1.20 


63.4° 





3^06 


.180 


46 


Ames 
12 ft 


.90 


2.46x10" 


3.06 


22.67 


38.12 


60.4* 


NACA 
0005-53 


.05 


18.60 


27^24 


.37 


63.4° 





3^06 


.180 


46 


Ames 
12 ft 


1.30 


2.46<10" 


3.06 


22.67 


38.12 


60.44 


NACA 
0005-53 


.05 


18.60 


27^24 


1.66 


63.4° 





3^06 


.180 


46 


Ames 
&6 ft 


f 


1.53 


2.146x10" 


3.06 


22.67 


38.12 


60.44 


NACA 
0005-53 


.05 


18.60 


27.24 


2.32 


63.4° 





3.06 


.180 


46 


Ames 
6x6 ft 


g 

1 


1^70 


2.46(10" 


3.06 


22.67 


38.12 


60.44 


NACA 
0005-53 


.05 


18.60 


27.24 


2.75 


63.4° 





3^06 


.180 


46 


Ames 
6x6 ft 




MCA RM A53G08 




59 



TABLE II.- SUMMARY OF GEOMETRIC AND AERODYNAMIC CHARACTERISTICS 
AND TEST CONDITIONS FOR WING-BODY COMBINATIONS - Continued 
(d) Aerodynamic Characteristics 



No. 


Mo 


% 


%(B) 


'^B(W) 


Theoretical 


Experiment 


°Llft 


Center of pressiire 


°Llft 


c.p. 


^S, 


^w 


^-"c 


h 


^W(B) 


hw 


\ 


® 


^-^B 


^S 


G). 


10a 


0.60 


0.038 


1.11 


0.19 


3.07 


0.11 


l*.ll 


7.88 


20.02 


19-93 


19-66 


0.590 




''U.Ol 


0-575 


b 


.70 


.036 


1.11 


.19 


2.88 


.10 


3.85 


7.88 


20.02 


19.89 


19-68 


.590 




^3-72 


-577 


c 


.80 


.03"* 


1.11 


.19 


2.58 


•09 


3.1*5 


7.88 


20.02 


19.82 


19.68 


.590 




^.73 


.572 


d 


.90 


.031 


1.11 


.19 


2.07 


.06 


2.75 


7.88 


20.02 


19.65 


19.69 


■591 




S3. 12 


.601 


e 


1.20 


.030 


1.11 


.18 


3.28 


.10 


l*.33 


7.88 


21.27 


22.98 


21.20 


.636 




"3-77 


.617 


11a 


.ZK 


.068 


1.15 


.25 


2.15 


.15 


3.15 


12.1*1* 


1*2.71* 


39-28 


1*0-75 


.671* 




3.30 


.676 


b 


.60 


.066 


1.15 


.25 


1.81* 


.12 


2.70 


12.1*1* 


1*2.88 


39-62 


1*0.95 


.678 




2-79 


.681 


c 


.80 


.061 


1.15 


.25 


1.1*7 


.09 


2.15 


12.1*1* 


1*3.02 


39.93 


1*1.21 


.682 




2.21* 


.685 


d 


.90 


.058 


1.15 


.25 


1.13 


.07 


1.65 


12.1*1* 


1*3.33 


1*0-20 


1*1-56 


.688 




1.78 


.691 


e 


.95 


.05"* 


1.15 


.25 


.87 


.05 


1.26 


12.1*1* 


1*3.75 


1*0-1*6 


1*2.01 


-695 




1.36 


.706 


f 


1.30 


.055 


1.15 


.22 


2.26 


.12 


3.22 


12.1*1* 


1*5.81* 


1*1* -02 


1*4.26 


-733 




3-27 


-723 


g 


1.53 


.061 


1.15 


.21 


2.87 


.18 


1*.07 


12.1*1* 


1*5.81* 


1*5-11* 


1*1*. 30 


-733 




l*.Ol* 


.723 


h 


1.70 


.061t 


1.15 


.20 


3.22 


.21 


l*.56 


12.1*1* 


1*5.81* 


1*5-75 


1*1*. 31 


.733 




l*.l*8 


.723 


12a 


.60 


.036 


1.10 


.17 


2.96 


.11 


3.86 


9.65 


29.1*0 


26.63 


28.50 


-598 




l*.2l* 


8.606 


b 


.80 


.032 


1.10 


.17 


2.1*9 


.08 


3.21* 


9.65 


29.1*3 


26.92 


28.62 


.601 




3.1*7 


«.612 


c 


• 90 


.030 


1.10 


.17 


1.97 


.06 


2.55 


9.65 


29.50 


27.33 


28.76 


.601* 




2.92 


8.620 


d 


1.20 


.028 


1.10 


.15 


3.11* 


.09 


1*.01 


9.65 


31.29 


30.38 


30.71 


.61*5 




3.78 


.61*5 


e 


i.iw 


.033 


1.10 


.11* 


3.96 


.13 


5.01* 


9.65 


31.29 


31-03 


30.70 


.61*5 




l*.6l 


.61*5 


f 


1.70 


.01*6 


1.10 


.15 


1*.00 


.18 


5.17 


9.65 


31.29 


32.11* 


30.62 


.61*3 




5.17 


.61*1* 


13a 


.50 


.11(2 


1.20 


.35 


1.97 


.28 


3.31* 


1.00 


■'(l*.19) 


1*.1*2 


3.97 


.1*05 




3.36 


.1*08 


■b 


.70 


.136 


1.20 


.35 


1.70 


.23 


2.86 


1.00 


(l*.19) 


1*.38 


3.97 


.1*05 




3-0I* 


.1*08 


c 


.90 


.125 


1.20 


.35 


1.13 


.16 


1.89 


1.00 


Cl*.19) 


1*.32 


3.98 


.1*06 




2-18 


.1*08 


d 


1.1*5 


.127 


1.20 


.35 


2.69 


.31* 


l*.50 


1.00 


(1*.67) 


5.93 


l*.66 


.1*76 




1*-1*0 


.1*28 


e 


1.99 


.151 


1.20 


.35 


3-71 


.55 


6.31 


1.00 


(1*.67) 


6.19 


l*.66 


.1*76 




5.95 


.1*28 


lUa 


.50 


.27 


1.28 


.1*9 


1.22 


.33 


2.1*8 


1.00 


l*.l*6 


1*.25 


3.96 


.1*01* 




2-1*9 


.l*lS 


b 


• 70 


.26 


1.28 


.1*9 


1.02 


.27 


2.08 


1.00 


l*.l*l* 


1*.21 


3.91* 


.1*02 




2.05 


.1*08 


c 


.90 


.25 


1.28 


.1*9 


.65 


.16 


1.32 


1.00 


l*.36 


l*.15 


3.89 


.397 




1.50 


.1*08 


d 


I.U5 


.20 


1.28 


.1*9 


2.01 


.1*0 


3.96 


1.00 


1*.63 


5-1*6 


kM 


.1*57 




3-35 


.1*1*1* 


e 


1.99 


.23 


1.28 


.1*9 


2.83 


.65 


5.66 


1.00 


l*.8l 


5-96 


l*.66 


.1*75 




5-12 


.1*1*9 


15a 


.21* 


.068 


1.15 


.25 


2.15 


.15 


3.15 


12.1*1* 


1+2.71* 


39-28 


1*0.75 


.671* 




3.33 


.679 


b 


.60 


.066 


1.15 


.25 


1.81* 


.12 


2.70 


12.1*1* 


1*2.88 


39-62 


1*0.95 


.678 




2.79 


.682 


c 


.80 


.061 


1.15 


■ 25 


1.1*7 


.09 


2.15 


12.1*1* 


1*3-02 


39-93 


1*1.21 


.688 




2.26 


.689 


d 


• 90 


.058 


1.15 


.25 


1.13 


.07 


1.65 


12.1*1* 


1*3.33 


1*0.20 


1*1.56 


-695 




1.77 


.695 


e 


1.30 


.055 


1.15 


.22 


2.26 


.12 


3.22 


12.1*1* 


1*5.81* 


1*1*. 02 


1*1* -26 


-733 




3.2I* 


.728 


f 


1.53 


.061 


1.15 


.21 


2.87 


.18 


l*.07 


12.1*1* 


1*5.81* 


1*5.11* 


1*1*. 30 


-733 




l*.Ol* 


.728 


g 


1.70 


.061* 


1.15 


.20 


3.22 


.21 


l*.56 


12.1*1* 


1*5.81* 


1*5.75 


1*1*. 31 


-733 




l*.l*8 


-727 




60 




NACA RM A53G08 



TABLE II.- SUMMARY OF GEOMETRIC AND AERODYNAMIC CHARACTERISTICS 
AND TEST CONDITIONS FOR WING-BODY COMBINATIONS - Continued 
(e) Geometric Characteristics 



No. 


Sketch 


«o 


R 


'!( 


'» 


»K 


1 


Section 


H 


^c- 


h 


PA 


Al.E. 


X 


^w 


ca 


Ref. 


Facility 


^^I6a 


-4- 


0.60 


3.65<10« 


2.38 


12.1.6 


27. uo 


1*6.93 


^'b.C. 


0.03 


10.90 


20.43 


3.20 


45° 





2.38 


0.127 


47 


Ajnes 
4<6 ft 


t 


.80 


3.6^10® 


2.33 


12. U6 


27.'tO 


1*6.93 


b.c. 


.03 


10.90 


20.43 


2.40 


45° 





2.38 


.127 


47 


Ames 
6x6 ft 


c 


■90 


3.6J<10° 


2.38 


12.1.6 


27.1*0 


»*6.93 


■b.c. 


.03 


10.90 


20.43 


1.74 


45° 





a. 38 


.127 


47 


Ames 
6<6 ft 


d 


1.20 


3.63<10= 


2.38 


12.1.6 


27.J*0 


1*6.93 


b.c. 


.03 


10.90 


20. k} 


2.65 


45° 





2.38 


.127 


47 


AjneE 
6x6 ft 


e 


i.i*o 


3.6>10® 


2.38 


12.1.6 


2T.'tO 


1*6.93 


b.c. 


.03 


10.90 


20.43 


3.92 


45° 





2.38 


.127 


47 


Ames 
6<6 ft 


f 


1.70 


3.6i<10' 


2.38 


12.1.6 


27. 1+0 


1*6.93 


b.c. 


.03 


10.90 


20.43 


5.» 


450 





2.38 


.127 


47 


Ames 
(x6 ft 


17 




.13 


2.7X10® 


26. git 


196.1.0 


358.6 


673.9 


■*d.w. 


.01*8 


161.20 


264.1 


2.00 


63.0° 





26.94 


.196 


48 


Ames 

toxso ft 


l8a 
b 
c 
d 


'*' 


.ko 


2.8l*<10® 


3.10 


1I..20 


27.0 


51.8 


NACA 
61*2 A012 


.12 


12.80 


20.02 


2.51 


35° 


.352 


3.10 


.160 


49 


Langley 
7X10 ft 


.60 


3.67x10" 


3.10 


11..20 


27.0 


51.8 


NACA 
61tiA012 


.12 


12.80 


20.02 


2.19 


35° 


.352 


3.10 


■ 160 


49 


Langley 
7x10 ft 


.80 


li.6»<lo« 


3.10 


11.. 20 


27.0 


51.8 


NACA 
61*j^A012 


.12 


12.80 


20.02 


1.64 


35° 


.352 


3.10 


.160 


49 


Langley 
7x10 ft 


.90 


U.BSKIO" 


3.10 


1I..20 


27.0 


51.8 


NAcA 
61t-3_A012 


.12 


12.80 


20.02 


1.19 


35° 


.352 


3-10 


.160 


49 


Langley 
7X10 ft 


19 


« <^^ 


.100 


.57x10= 


3.hh 


9.1.0 


13.0 


ltO.31 


NACA 
20312 


.12 


9.1.0 


10.5 


5.62 


0° 


.88 


3.44 


.115 


» 


Langley 
7X10 ft 


20 


« ^-^ 


.100 


.6a<io* 


3.Wt 


9.85 


13.0 


1*0.31 


KACA 
20312 


.12 


10.20 


7.47 


5.52 


18.3° 


.38 


3.44 


.115 


50 


langley 
7X10 ft 


21 


• i^ 


.100 


.6a<io« 


3.W 


9.85 


13.0 


1*0.31 


NACA 
20312 


.12 


10.20 


8.98 


5.52 


9.3° 


.38 


3.44 


.115 


50 


Langley 
7x10 ft 


22 


m ^M. 


.100 


.6a<io* 


3.1.1. 


9.85 


13.0 


1*0.31 


NACA 
20312 


.12 


10.20 


10.51 


5.52 


0° 


.38 


3.44 


.115 


50 


Langley 
7X10 ft 


23a 


^^ 


■ Til 


1.2TXloe 


.583 


1..07 


8.1*9 


ll*.0 


b.c. 


.06 


3.1.0 


5.43 


1.49 


60° 


° 


.572 


.158 


51 


Wing Flow 
(langley) 


b 


.851 


1.31x10® 


.583 


1..07 


8.1*9 


lU.O 


b.c. 


.06 


3.IK) 


5.43 


1.18 


60° 





■ 572 


.158 


51 


Wing Flow 
(Langley) 


c 


1.067 


1.2>10« 


.583 


1..07 


8.1*9 


ll*.0 


b.c. 


.06 


3. to 


5.43 


.834 


60° 





.572 


.158 


51 


Wing Flow 
(Langley) 


2i*a 


"^ 


.7117 


1.31X10« 


.583 


3.67 


8.92 


ll*.0 


b.c. 


.06 


3.66 


6.99 


1.60 


0° 





.502 


.139 


51 


Wing Flow 
(Langley) 


b 


.851 


l.Wixlo" 


.583 


3.B7 


8.92 


1I..0' 


b.c. 


.06 


3.66 


6.99 


1.26 


0° 





.502 


■ 139 


51 


Wing Flow 
(Langley) 
Wing Flow 
(Langley) 

D.T.M.B. 


c 


1.067 


1.25X10« 


.583 


3-87 


8.92 


11..0 


b.c. 


.06 


3.66 


6.99 


.90 


0° 





.502 


■ 139 


51 


25 


i 


.183 


.74xlO« 


4.125 


8.25 


66.15 


106.5 


d.v. 


.04 


7.09 


47.73 


2.53 


24° 


.272 


4.125 


.333 


52 




NACA RM A53G08 




61 



TABLE II.- SUMMARY OF GEOMETRIC AND AERODYNAMIC CHARACTERISTICS 
AND TEST CONDITIONS FOR WING-BODY COMBINATIONS - Concluded 
(f) Aerodynamic Characteristics 



No. 


Mo 


K„ 


Kw(B) 


Kb(w) 


Theoretical 


Experiment 


«Llft I 


Center of pressure 1 


^Ift 1 c.p. 


^S 


^S 


^\ 


h 


h(B) 


h{v) 


h 


(0 


^lo^ 


^W 


(ft 


I6a 


0.60 


0.036 


1.10 


0.17 


2.96 


0.11 


3.86 


9.65 


29.I10 


26.63 


28.50 


0.598 




1*.30 


0.608 


b 


.80 


.032 


1.10 


.17 


2.1*9 


.08 


3.21* 


9.65 


29.1*3 


26.92 


28.62 


.601 




3M 


.612 


c 


•90 


.030 


1.10 


.17 


1.97 


.06 


2.55 


9.65 


29.50 


27.33 


28.76 


.60V 




2.89 


.617 


a 


1.20 


.028 


1.10 


.15 


3.11* 


.09 


1*.01 


9.65 


31.29 


30.38 


30.71 


.61*5 




3.78 


.61*7 


e 


l.ltO 


.033 


1.10 


.11* 


3.96 


■ 13 


5.0l* 


9.65 


31.29 


31.03 


30.70 


.61*5 




l*.6l 


.61*6 


f 


1.70 


.Oli6 


1.10 


.15 


u.oo 


.18 


5.17 


9-65 


31.29 


32. ll* 


30.62 


.61*3 




5.17 


.61*1* 


17 


.13 


.069 


1.15 


.25 


2.19 


.15 


3.22 


139.1 


398.5 


368.2 


381.0 


.566 




3.38 


.567 


"l8a 


.Uo 


.052 


1.13 


.22 


2.72 


.11* 


3.81 




28.02 


26.19 








3.81* 


.522 


t 


.60 


.050 


1.13 


.22 


2.51 


.13 


3.51 




28. Ol* 


26.16 








3.61* 


.522 


c 


.80 


.01*5 


1.13 


.22 


2.07 


.09 


2.88 




28.06 


26.21 








3.15 


.522 


d 


• 90 


.da 


1.13 


.22 


1.63 


.07 


2.26 




27.99 


26.26 








2.63 


.509 


19 


.100 


.11*5 


1.09 


.155 


1*.13 


.60 


5.30 


k.oh 


12.85 


12.97 


12.62 


.315 




5.81 


.323 


20 


.100 


.iia 


1.09 


.155 


1*.12 


.58 


5.27 


l*.0l* 


13-62 


11.68 


13.12 


.328 




1*.83 


.323 


21 


.100 


.iin 


1.09 


.155 


1*.12 


.58 


5.27 


V.Ol* 


13.1*6 


12.72 


13.11 


.328 




1*.83 


.323 


22 


.100 


.11*1 


1.09 


.155 


1*.12 


.58 


5.27 


l*.0l* 


13.09 


13.73 


12.92 


.323 




1*.83 


.323 


23a 


.7^7 


.052 


1.13 


.23 


1.76 


.092 


2.1(8 


3.0!* 


8.29 


7.67 


7.98 


.570 




2.1*0 


.560 


b 


.851 


.01*9 


1.13 


.23 


1.1*6 


.072 


2.06 


3.0I* 


8.33 


7.73 


8.05 


.575 




1.95 


.561* 


c 


1.067 


.01*2 


1.13 


.21 


1.22 


.051 


1.68 


3.0l* 


8.83 


8.18 


8.56 


.611 




1.53 


.589 


2l^a 


.747 


.01*8 


1.11 


.188 


1.81* 


.090 


2.1(8 


3.0I* 


7.81 


7.92 


7.66 


.51*6 




2.38 


.502 


■b 


.851 


.01*6 


1.11 


.188 


1.53 


.071 


2.05 


3.01* 


7.78 


7.81* 


7.63 


.51*5 




2.19 


.503 


c 


1.067 


.038 


1.11 


.188 


1.31 


.050 


1.71* 


3.0I* 


7.51* 


8.09 


7.1*9 


• 535 




1.76 


.538 


25 


.183 


.366 


1.285 


.50 


2.72 


1.00 


5.85 


10.8 


51.09 


50.63 


1*1*. 13 


.1*11* 




5. 71* 


.391* 



■"■- denotes nonuniform or unknown t/c, thiclmese -chord ratio 

hex, indicates hexagonal 

^b,c. indicates biconvex 

■*d,v, indicates double wedge 

^ CJonf iguration tested with extended tail boom coaxial vith body 

®3Ct per radian based on exposed wing area 

''^O denotes experimental value used in theory for combination 

^Experimental data nonlinear near a=0° 
9 
Nos, 11 and 15 identical except wing thickness 

^°Nos, 12 and 16 identical except wing thickness distribution 

^■^Ho experimental or theoretical value available for Zjj 

12 

c based on exposed wing area 




62 



NACA RM A53G08 



TABLE III.- SUMMARY OF GEOMETRIC AKD AERODYNAMIC CHAEIACTERISTICS 
AND TEST CONDITIONS FOR BODY-WING-TAIL COMBINATIONS 
(a) Geometric Characteristics 



No. 


Sketch 


«o 


'b 


^ 


^R 


1m 


I 


Surface 


Section 


2t 


"c 




0A 


Al.E. 


\ 


r 


• 


Ref. 


Facility 


101 


. a 


0.183 


0.79>:10® 


hr.123 


8.25 


66.15 


106.5 




^d.w. 


0.042 


7.09 


47.73 


2.53 


241 


0.272 


4.125 


0.333 


52 


DIMB 


B ■ 


tall 


d.w. 


.042 


7.W 


93.40 


2.55 


24" 


.270 


4.125 


.321 


102 


1 1 


.184 


.71x10® 


2.815 


5.63 


34.18 


56.37 


wing 


*hex. 


. . _ 


3.72 


14.60 


2.64 


13.9° 


.500 


2.815 


.369 


53 


mMB 


tall 


hex. 


.06 


6.69 


37.74 


2.64 


14= 


.499 


2.815 


.246 


103 


A 


.l8lt 


.71x10" 


2.815 


5.63 


34.18 


56.37 


vln« 


hex. 


. - - 


2.6k 


15.30 


2.68 


13.8° 


.500 


2.815 


.448 


53 


DTOB 


— 1 B — 


tail 


hex. 


.06 


6.69 


37.74 


2.64 


14° 


.499 


2.815 


.246 


lOl. 


t 1 


.l8k 


.71x10* 


2.815 


5.63 


34.18 


56.37 


vlng 


hex. 




6.1.7 


10.54 


1.43 


70» 





2.815 


.443 


53 


DTWB 


tail 


d.w. 


.06 


6.69 


37.74 


2.64 


140 


.it99 


2.815 


.246 


105a 


^ 


.20 


1.66cl0* 


6.48 


18.67 


70.50 


146 


ving 


hex. 


.042 


17.38 


64.20 


3.1.3 


9.450 


.546 


6.43 


.179 


35 


Ames 
12 ft 


tall 


hex. 


.042 


8.72 


130.71 


3.43 


9.450 


.54a 


3.16 


.176 


b 


.50 


1.86(10° 


6.k8 


18.67 


70.50 


146 




hex. 


.042 


17.38 




3.02 


9.45° 


.546 


6.43 


.179 


35 


Ames 
12 ft 


tall 


hex. 


.042 


8.72 


130.71 


3.03 


9.45» 


.548 


3.16 


.176 


c 


.70 


1.86x10° 


6.1*8 


18.67 


70.50 


146 


vlng 


hex. 


.042 


17.38 


64.20 


2.49 


9.450 


.546 


6.43 


.179 


35 


Ames 

12 ft 


tall 


hex. 


.042 


8.72 


130.71 


2.50 


9.450 


.548 


3.16 


.176 


d 


.80 


l-aftcio" 


6.U3 


18.67 


70. 3D 


146 


vln« 


hex. 


.042 


17.38 


64.20 


2.10 


9.450 


.51^ 


6.43 


.179 


35 


Affles 
12 ft 


tail 


hex. 


.042 




130.71 


2.10 


9.'.5" 




3.16 


.176 


e 


.90 


l.86<10® 


6.h& 


18.67 


70.50 


146 


WitKt 


hex. 


.042 


17.33 


64.20 


1.52 


9.450 


.546 


6.43 


.179 


35 


Amee 
12 ft 


tail 


hex. 


.042 


8.72 


130.71 


1.53 


9.450 


.51^ 


3.16 


.176 


106a 


-^^ 


.89 


6.CK10'' 


3.50 


17.89 


60.0 


114.2 


vlnR 


hex. 


. . _ 


4.62 


25.87 


1.05 


60O 





3.50 


.467 


54 


Flight 


tall 


hex. 


. - - 


13.87 


68.20 


1.05 


600 





3.50 


.226 


■b 


1.25 


9.2xl0« 


3.50 


17.89 


60.0 


114.2 




hex. 




I..62 


25.87 


1.73 


600 





3.50 


.467 


54 


Flight 


tail 


hex. 


_ - - 


13.87 


68.20 


1.73 


600 





3.50 


.226 


107a 


-^^ 


.83 


3.^10* 


3.50 


17.57 


91.3 


154.2 


tfin« 


hex. 


_ _ _ 


3. '.7 


26.70 


1.29 


600 





3.50 


.538 


55 


Flight 


tall 


hex, 
hex. 




13.60 


108.20 


1.31 


59.30 





3.50 


.226 


t 


1.38 


8.ie<io® 


3.50 


17.57 


91.3 


154.2 




s.w 


26.70 




600 





3.50 


.538 
.226 

.308- 


55 
36 


Flight 


tall 


hex. 


y~ 


13.60 
2.90 


108.20 




59.30 





3.50 


108a 


^ 


.80 


.7a<lo'' 


.8125 


1.525 


6.575 


13.075 


ulng 


Sb.C. 


1.51 


1.18 


450 


.341 


.546 


OAL 


tall 
wing 


b.c. 
b.c. 


. . _ 


1.35 


8.06 


1.03 


450 


.401 


.312 


.253 


■b 


■ 90 




.8125 


1.625 


6.575 


13.075 


- - . 


2.90 


1.51 


.856 


45" 


.341 


.546 


.308 


36 


OAL 


tall 


b.c. 


_ _ _ 


1.35 


8.06 


.744 


45O 


.401 


.312 


.258 


c 


1.10 


.67x10° 


,3125 


1.625 


6.575 


13.075 


wing 


b.c. 


_ _ . 


2.90 


1.51 


.900 


450 


.341 


.546 


.306 


36 


OAL 


tall 


b.c. 


- . - 


1.35 


8.06 


.732 


450 


.401 


.812 


.2» 


d 


1.73 


1.6cl0° 


.8125 
2.00 


1.625 
8.38 


6.575 


13.075 


wing 


■b.c. 


_ . _ 


2.90 


1.51 


2.77 


450 


.341 


.546 


.303 


37 


OAL 


tail 


b.c. 


. . _ 


1.35 


8.06 


2.41 


45O 


.401 


.812 


.253 


109a 




.165 


1.95<10® 


36.46 


64.41 


wing 


d.w. 


.029 


8.38 


23.24 


2.06 


600 





2.00 


.216 


38 


CAL&CWT 


tall 


d.w. 


.030 


3.92 


57.53 


3.54 


450 





2.00 


.254 


b 


.70 


1.3^10° 


2.00 


8.38 


36.46 


64.41 


wing 


d.w. 


.029 


8.38 


23.24 


1.66 


600 





2.x 


.216 


38 


OALiCWT 


tall 


d.w. 


.030 


3.92 


57.53 


2.86 


"45^ 





2.00 


.254 


c 


.90 


1.0>;io° 


2.00 


8.38 


36.46 


64.41 


wing 


d.w. 


.029 


a. 38 


23.24 


1.01 







2.aD 




38 


CAL&CWT 


tall 


d.w. 


.0,30 


3.92 


57.53 


1.7I. 


450 





2.00 


.254 


d 


1.15 


i.26<10° 


1.80 


7.54 


29.14 
29.14 


"57.97 


wing 
tall 


d.w. 


.029 


7.54 


20.92 


1.31 


60O 





1.80 


.216 




Ames 
69<6 ft 


d.w. 


.030 


3-53 


51.77 


2.27 


450 





1.80 


.254 


e 


l.ltO 


1.26x10° 


1.80 


7.54 


57.97 


wing 


d.w. 


.029 


7.54 


20.92 


2.26 


600 





1.80 


.216 




AjDes 
6<6 ft 


tall 
wing 


d.w. 
d.w. 


.030 


3.53 


51.77 
20.92 


3.92 

3.18 


45O 





1.80 


.2* 


f 


1.70 


1.26<10^ 


1.80 


7.54 
7.00 


29.14 
76.27 


57.97 


.029 


7.54 


66° 





1.80 


.216 




Ames 

6<e ft 


tall 


d.v. 


.030 


^ ^-3 


51.77 


5.50 







l.SO 


.254 




.204 


.92x10° 


3.50 


30. 41 


wing 


d.w. 


.05 


2.69 


11.14 


2.46 


26.60 


.500 


3.45 


.514 


39 
56 






tall 


hex. 


.06 


7.45 


50.69 


2.89 


140 


.461 


3.50 


.250 
.436 


b 


1.50 




.50 


1.00 


5.75 


11.49 


wing 


d.w. 


.06 


.39 


1.72 


2.98 


26.60 


.500 


.46 


Ames 
1x3 ft 


tall 


hex. 


.06 


1.06 


7.24 


3.30 


i4» 


Ml 


.50 


.250 


c 


2.00 




.9J 


1.00 


5.75 


11.49 


wing 


d.w. 


.06 


■ 39 


1.72 


4.62 


26.6° 


.500 


.16 


.486 


56 


fines 

L<3 ft 


tall 


hex. 


.06 


1.06 


7.24 


5.11 


l4o 


.461 


.50 


.250 


111 


^ _ 


1.93 


.3>1C^ 


.1*16 


.832 


4.747 


9.10 


ving 


hex. 


. . _ 


1.02 


4.42 


1.69 


600 


.323 


.416 


.465 


57 


Langley 
9 in. 


^■■^p^ 


tail 


hex. 

hex. 


.01+9 


.85 
1.02 


7.91 


2.03 


600 


.305 


.416 


.465 


112 


c ; 


1.93 


.3>clO° 


.ltl6 


.832 


5.135 


9.49 


wing 


4.81 


1.69 


60O 


.323 


.416 


.465 


57 


Laogley 

9 10. 


tall 


hex. 


.06I4 


■ 50 


S.9} 


5.51 


00 


1 


.416 


.333 


U3 




1.93 


.3><io^ 


.lvl6 


.832 


5.135 


9.49 


wing 


hex. 




1.02 


4.810 


1.69 


600 


.323 


.416 


.465 


57 


Langley 
9 in. 


tall 


hex. 


- -^ 


.74 


8.476 


3.16 


45° 


.352 


.416 


.383 


114 


m ^ 


1-93 


.8>10« 


.416 


.832 


5.135 


9.49 


wing 


hex. 


.86 


2.757 


1.69 


60° 


.323 


.416 


.508 


57 


Langley 

9 m. 


tall 


hex. 


_ - - 


2.57 


6.037 


1.03 


700 


.400 


.416 


.356 


115 


<^h4 


1.93 


.3>LlO® 


.416 


.832 


5.135 


9.49 


ving 


hex. 


- _ _ 


.35 


3.834 


3.31 


60O 





.4l6 


.579 


57 


Langley 

9 m. 


tall 


hex. 


- - - 


2.57 


6.037 


1.03 


700 


.400 


.416 


.356 


116 


-H 


1.93 


.83.10° 


.416 


.832 


5.135 


9.49 


wing 


hex. 


. _ - 


.52 


3.573 


3.81 


60" 





.416 


.479 


57 


Langley 

9 m. 


tall 


hex. 





2.57 


6.037 


1.03 


70O 


.400 


.416 


.356 


117 


-^ 


1.93 


.8J<10° 


.416 


.832 


5.135 


9.'t-9 


wing 


hex. 


. . - 


■ 70 


3.311 


3.81 


feo 





.4l6 




57 


Langley 
9 In. 


tail 


hex. 





2.57 


6.037 


1.03 


700 


.400 




.356 


118 


■ 


1.92 


.ita<io° 


.35 


1.25 


4.177 


8.75 


wing 


b.c. 


.06 


1.25 


3.569 


5.64 


oo 


1 


.350 


.140 


53 


Langley 
9 In. 


tall 


"b.c. 


.06 


.616 


8.054 


5.14 


qo 


1 


.285 


.228 


119 




1.92 


.iK5xl0° 


.35 


1.25 


4.927 


8.75 




b.c. 


.06 


1.25 


4.319 


5.64 


oo 


1 


.350 


.140 


58 


Langley 
9 in. 


tall 


b.c. 


.06 


.616 


8.054 


5.14 


00 


1 


.285 1 .228 




NACA RM A53G08 



63 



TABLE III.- SUMMARY OF GEOMETRIC AND AERODYNAMIC CHARACTERISTICS 
AND TEST CONDITIONS FOR BODY-WING-TAIL COMBINATIONS - Continued 
(b) Aerodynamic Characteristics 



No. 


St 


h 


'V(B) 


"bW 


tT(B) 


Tb(t) 


Theoretical 


Experimental 


"'Lift 


Center of pre 


SBure 


'Lift 


c.p. 


BOk^ 


»v 


Ki^ 


'^^ 


PCi^ 


Ig 


'w(B) 


hM 


hm 


'b(t) 


\ 


h 


m 


CDc 


""^ 


*^^"C 


Q-l 


101 


1.115 


0.338 


1.29 


0.50 


1.28 


0.48 


2.95 


2.97 


1.00 


10.87 


8.17 


10.83 


51.05 


50.56 


96.90 


96.39 


69.59 


60.46 


0.653 


0.568 




8.45 


0.576 


102 


3-227 


.I181 


1.32 


.56 


1.21 


.35 


2.94 


2.94 


.44 


6.76 


5.86 


5.05 


16.07 


15.89 


40.39 


40.04 


31.84 


30.49 


.565 


.541 




4.90 


.545 


103 


6.286 


.930 


1.40 


.70 


1.21 


.35 


2.96 


2.94 


.44 


6.03 


5.52 


5.05 


16-35 


16.24 


40.39 


40.04 


33-76 


33.14 


.599 


.588 




4.68 


.575 


loit 


3.21*9 


.8I12 


1.39 


-70 


1.21 


.35 


1.69 


2.94 


.44 


6.08 


5.52 


5.05 


16-00 


15.34 


40.39 


40.04 


33-45 


32.74 


.593 


.581 




4.75 


.565 


105a 


.252 


.077 


1-14 


.24 


1.14 


.24 


3.47 


3.48 


.27 


6.45 


5.56 


33.43 


70.76 


70.05 


134.00 


133.63 


81.23 


76.10 


.557 


.521 




5.20 


.505 


b 


.252 


.072 


1.14 


.24 


1.14 


.24 


3.16 


3.16 


.23 


5.T1 


5.16 


33-43 


70.76 


69.99 


134.00 


133.61 


91.23 


75.71 


.557 


.519 




4.65 


.500 


c 


.252 


.067 


1.14 


.24 


1.14 


.24 


2.83 


2.83 


.19 


4.70 


4.21 


33.43 


70.76 


69.82 


134.00 


133-52 


82-50 


76.66 


.565 


.525 




4.25 


.493 


d 


.252 


.063 


1.14 


.24 


1-14 


.24 


2.51 


2.51 


.16 


4.» 


4.02 


33.43 


70.76 


69.60 


134.00 


133.42 


81.48 


75.13 


.558 


.515 




3.87 


.489 


= 


.252 


.057 


1.14 


.24 


1.14 


.24 


2.02 


2.02 


.12 


3.60 


3.17 


33.43 


70.76 


69.23 


134.00 


133.23 


81.65 


74.48 


.559 


.510 




3-11 


.483 


106a 


9.00 


.957 


1.42 


.74 


1.19 


.32 


1.32 


1.32 


.14 


2.51 


2.06 


11.88 


29.82 


29.32 


80.06 


78.00 


68.77 


66.33 


.602 


.581 




1-97 


.583 


b 


9.00 


.890 


1-42 


.62 


1.19 


.27 


2.34 


2.34 


.23 


4.17 


3.40 


11.88 


30.49 


32.04 


82.07 


81.51 


71.63 


69.29 


.627 


.607 




3.38 


.603 


107a 


15.69 


1.762 


1-49 


.87 


1-19 


.32 


1.56 


1.59 


.18 


2.81 


2.46 


11.83 


29.65 


29.31 


U9.75 


118.01 


105.08 


102.90 


.681 


.667 




2.62 


.650 


b 


15.69 


1.690 


1.49 


.72 


1.19 


.26 


2.77 


2.31 


.30 


4.7» 


4.14 


U.83 


30.17 


32.47 


121.81 


122.01 


107.66 


105.36 


.698 


.683 




4.23 


.678 


108a 


I..I6 


^.8lU) 


1.26 


.46 


1.22 


.38 


1.56 


1.43 


.19 


3.20 


2.78 


2.52 


2.35 


2.17 


9-73 


9.39 


7.47 


7.14 


.571 


.546 


(0.30) 


2.65 


■ 555 


b 


It. 16 


(.855) 


1.26 


.46 


1-22 


.38 


1.18 


1.04 


.14 


2.67 


2.35 


2.52 


2.35 


2.16 


9-70 


9.32 


7.32 


7.01 


.560 


.536 


(.24) 


2.27 


.553 


c 


lt.l6 


(.615) 


1.26 


.46 


1-22 


.38 


1.50 


1.26 


.15 


2.86 


2.36 


2.52 


2.55 


2.69 


10.10 


10.25 


7.85 


7.39 


.601 


.565 


(.22) 


2.34 


■ 577 


d 


It. 16 


(.520) 


1.26 


.34 


1.22 


.29 


3.42 


3.29 


.46 


6.72 


5.91 


2.52 


2.65 


3.23 


10.39 


11.22 


8.50 


8.20 


.6» 


.627 


(.43) 


5.96 


■ 599 


109a 


.381 


.109 


1-18 


.31 


1.21 


.37 


2.25 


3.14 


.25 


5.53 


4.26 


11.6 


30.18 


28.74 


60.74 


60.03 


39.90 


33.70 


.620 


.523 




4.35 


■ 505 


b 


.381 


.lolt 


1.18 


.31 


1.21 


.37 


1.90 


2.79 


.20 


4.66 


3.56 


11.6 


30.20 


28.86 


60.76 


63.08 


40.19 


33.95 


.624 


.526 




3.63 


■ 509 


c 


.381 


.091 


1.18 


.31 


1.21 


.37 


1.28 


1.97 


.12 


3.22 


2.34 


11.6 


30.39 


29.09 


60.80 


60.20 


40.71 


34.01 


.632 


.518 




2.24 


■ 503 


c 


.381 


.084 


1.18 


.27 


1.21 


.22 


1.86 


2.84 


.16 


4.39 


2.99 


10.4 


28.46 


27.64 


55.29 


55.55 


37.03 


28.54 


.639 


.496 




2.86 


.516 


e 


.381 


.095 


1.18 


.25 


1.21 


.17 


2.83 


3.9<; 


.27 


6.46 


4.72 


10.4 


28.46 


28.44 


55.29 


55.20 


36.40 


29-59 


.628 


.509 




4.49 


.522 


f 


.381 


.lU 


1.18 


.24 


1.21 


.14 


3.4l 


4.00 


.38 


7.33 


5.91 


10.4 


28.46 


29.18 


55.29 


55.20 


35.18 


30-20 


.606 


.521 




6.15 


.535 


noa 


8.81t 


1.578 


1.47 


.82 


1.21 


.36 


2.82 


3.08 


.50 


6.06 


5.67 


7.21 


13-05 


12.37 


53.71 


53.34 


44.77 


44.11 


.558 


.549 




5.25 


■ 514 


b 


8.83 


1-503 


1.44 


-56 


1.21 


.29 


3.49 


3.56 


.58 


6.73 


6.28 


1.03 


2.01 


2.44 


7.89 


8.51 


6.69 


6.61 


.583 


.575 


.60 


6.45 


■ 557 


c 


8.83 


2.591 


1.44 


.50 


1.21 


.27 


3.73 


3.78 


.89 


7.54 


7.25 


1.03 


2.02 


2.66 


7.92 


8. 76 


6.40 


6-33 


.557 


.550 


1.09 


7.96 


i°567 


111 


.839 


(.819) 


1.41 


.63 


1.41 


.26 


2.94 


3.12 


2.01 


12.77 


8.70 


(1.50) 


5.22 


5.82 


8.63 


8.70 


5.78 


4.44 


.635 


.488 


2.41 


8.39 


10 


112 


.931 


( .819) 


1.41 


.63 


1.29 


.057 


2.94 


3.64 


2.01 


12.87 


11.73 


(1.12) 


5.61 


6.22 


9.23 


9.32 


6.14 


5.85 


.647 


.616 


2.41 


11.15 


.599 


U3 


1.01 


(.619) 


1.41 


-63 


1.34 


.14 


2.94 


3.67 


1.99 


13.81 


10.31 


(1.12) 


5.61 


6.22 


9.10 


9.15 


6.29 


5.33 


.662 


.561 


2.39 


10.72 


.555 


lilt 


5.7lt 


(1.155) 


1.46 


■ 69 


1.31 


.54 


2.94 


1.94 


.49 


4.98 


4.26 


(1.12) 


3.43 


4.09 


7.88 


3.24 


6.32 


5.93 


.666 


.625 


-59 


'"3.90 


'".595 


115 


23.10 


(3.479) 


1.54 


.70 


1.31 


.51. 


3.91 


1.94 


.49 


4.54 


4.16 


(1.12) 


4.18 


4.79 


7.88 


8.24 


6.82 


6.69 


.718 


.705 


.59 


3.77 


.683 


116 


30.30 


(1.554) 


1.43 


.54 


1-31 


.54 


3.91 


1.94 


.49 


4.92 


4.16 


(1.12) 


4. 10 


4.67 


7.88 


8.24 


6.62 


6.40 


.698 


.675 


.59 


3.82 


.663 


117 


5.79 


(.873) 


1.36 


.44 


1.31 


.5* 


3.91 


1.94 


.49 


5.39 


4.26 


(1.12) 


4.09 


4.57 


7.88 


- 8.24 


5.38 


5.97 


.672 


.629 


.59 


4.00 


".604 


118 


.221 


( .067) 


1.11 


.12 


1-19 


.069 


3.65 


3.60 


.23 


5.73 


5.45 


(■317) 


4.12 


4.78 


8.35 


8.47 


4.79 


4.63 


.548 


■ 529 


.23 


5.24 


.527 


119 


.221 


(.067 


l.U 


.12 


1.19 


.069 


3.65 


3.60 


.23 


5.73 


5.45 


(.317) 


4.92 


5.53 


8.35 


8.47 


5.38 


5.21 


.615 


.595 


.23 


5.31 


■ 599 




6k 



NACA RM A53G08 



TABLE III.- SUMMARY OF GEOMETRIC AKD AERODYNAMIC CHARACTERISTICS 
AND TEST CONDITIONS FOR BODY-WING-TAIL COMBINATIONS - Continued 
(c) Geometric Characteristics 



No. 


Sketch 


Mo 


'■R 


^ 


'r 


^M 


I 


Surface 


Sect ion 


_^ 


*=^c 




SA 


Al.e. 


X 


•■ 


r 


Ref. 


Facility 


120 




1.92 


O.UoxlO^ 


0.350 


1.25 


5-677 


8.75 


winR 


""l-.c. 


0.06 


1.25 


5.673 


5.64 


0° 


1 


0.350 


0.140 


» 


Langiey 
9 In. 


tail 


b.e. 


.06 


.616 


6.05V 


5.14 


0" 


1 


.255 


.228 


121 




1.62 


.2>10e 


.350 


.1<X> 


1^.375 


9.;>o 




■•hex. 


- - _ 


.667 


3.20 


3.31 


00 





.350 


■ 350 


59 


Lsuigley 
9 in. 


— w r 


tail 


hex. 




.667 


7.92 


3.31 


0° 





.350 


.3» 


122 


> i 


1.62 


.2>10* 


.35C. 


.IOC 


''.375 


9. CO 


«ing 


hex. 




.667 


I..70 


3.31 


0° 





.350 


.350 


59 


Langiey 
9 In. 


tail 


hex. 


- - - 




7.92 


3.31 







.350 


.350 


123 


g 1 


1.62 


.2^10* 


.35c 


.130 


1^.375 


9.x 


vlr.g 


hex. 




.667 


3.20 


3.31 


57° 





.350 


■ 350 


59 


Langiey 

9 m. 


^■^^^^ 


tall 


hex. 




.667 


7.92 


3.31 







.350 


■ 350 


12ll 




1.62 


.25<10^ 


.350 


.700 


1..375 


9.00 


wing 


hex- 




.667 


4.70 


3.31 


57° 





.350 


■ 3» 


59 


Langiey 
9 in. 






hex. 




.667 


7.92 


3. .31 







.350 


■ 350 


125 




1.62 


.2>:10^ 


.350 


.700 


1^-375 


9.00 




hpx. 




.667 


3.20 


3.31 


57° 





.350 


■ 350 


59 


Langiey 
9 In. 


tail 


hex. 




.667 


7.92 


3-31 


57° 





.350 


■ 350 


126 


A 


1.62 


.2>10® 


.3^ 


.700 


i..375 


9.00 


wing 


hex. 




.667 


4.70 


3.31 


57° 





.350 


■ 350 


59 


Langiey 
9 in. 


■^^^^ 


tail 


hex. 




.667 


7.92 


3.31 


57° 





.3» 


■ 350 


127 


1 1 


1.62 


.3^10® 


.350 


.730 


'*.375 


9.0c 


wing 


'^ex. 


.06 


1.00 


3.20 


1.66 


0° 


1 


.350 


■ 350 


59 


Langiey 

9 m. 


tall 


hex. 




06 


1.0c 


7.91 


1.66 


0° 


1 


.350 


■ 350 


128 


."^^^^i 


1.62 


. 3>:10* 


.350 


.700 


It. 375 


9.00 


wing 


hex. 




06 


1.00 


It. 70 


1.66 


0° 


1 


.350 




59 


Langiey 
9 m. 


tail 


hex. 






1.00 


7-91 


1.66 


0° 


1 


.350 


■ 350 


129 




1.62 


.52x10^ 


.350 


.700 


"+■375 
It. 375 


9.00 
9.0' 


wing 


hex. 




01 


l/jO 


2.''k 


1.11 


0° 


1 


.350 


.350 


59 


Langiey 
9 in. 


tail 
wing 


hex. 




O'i 


1 . "o 


7.91 
It. 1.1. 


iTt?i 

1.11 


0° 
0° 


1 
1 


.350 


.350 


130 


M 1 


1.62 


.5a<io^ 


.350 


.350 


.350 


59 


Langiey 
9 In- 

BRL 




hex. 




:i 


l.Oi" 
" 1.0 i 


7.91 


1.66 




1 


.350 


.350 


131 


t ^ 


1.72 


1.2i.xio« 


.1^50 


1^.12 


10.68 


19 -O?"] 




hex. 




073 


1.96 


2.24 


63.2° 
75° 

0° 




6" " 

1 


.308 
.4» 


.331 


60 


tail 


hex. 




025 


3.00 


10. J9 


1.50 


.272 


132 


1 t 


1.23 


i.ia<io^ 


.625 


1.25 


9.125 


15.0c 
15. OG 


wing 


hex. 


... 


2.60 


8.021 


1.07 


".^25" 


.265 


61 
61 


BRL 
BKL 


tail 
wing 


hex. 
hex." 


-^l-'r- 


1.71 
2.39 


12. ^j 








.625 
" V625" 


.379 


133 


-«H 


1.28 


1.2'wlO* 


.625 


1.25 


9.125 


6.69 


■ 1.07 


60° 


.268 


.265 


tail 


hex. 




1.71 


12.58 


1.07 


60° 


.268 


.625 


.379 


134 


-%H 


1.28 


.79x1:?® 


.625 


1.25 


9.125 
9.125 


15. AT 
15.00 




hex. 




1.81. 


a. 34 


1.07 


0° 


1 


.625 


.3,38 


61 
61 


BFL 

BRL 


tail 


hex. 




1.71 


12. ;« 


1.07 
1.07 


£0° 
60° " 


.268 
.268 


.625 
.625 


.379 
■ 338 


135 


^ 


1.28 


.87x10^ 


.625 


1.25 


ving 


hex. 




2.02 


7.40 


tail 


hex. 




1.71 


12.5= 


1.07 


60° 


.268 


.625 


■ 379 


136 




1.72 


1.11^10® 


.625 


1.25 


9.125 


15.00 


wing 


hex. 


. - . 


2.57 


6.69 


i.31 


59.40 





.625 


■215 


62 


BRL 


tall 


hex. 


. - - 


1.68 


12.61 


2.& 


50° 


.253 


.625 


■ 294 


137 


-m irf 


1.72 


.56x10^ 


.625 


1.25 


9.125 


15.00 

15.00 


wing 


hex. 


. - - 


1.30 


8.60 


7.48 




1 


.625 


■ 153 


62 


BRL 


tail 
wing 


hex. 




1.68 


12.61 


2.80 


50° 


.253 


.625 


■ 294 


138 


-« ^ 


1.72 


1.3l<xlO* 


.625 


1.25 


9.125 


hex. 




3.11 


6.69 


1.87 


60° 


.130 


.625 


■ 265 


62 


BRL 


tail 


hex. 




^rsr 


12.51 


2..?0 


50° 


.253 


.625 


■ 29l 


139 


<« ^ 


1.72 


1.17x10* 


.625 


1.25 


9-125 


15.00 




. _ . 


2.73 


7.53 


1.87 


30° 


.444 


.625 


.265 


62 


BEL 


tall 


hex 


_ _ - 


1.68 


12.61 


2.80 


50° 


■ 253 


.625 


.294 


ito 


^ -4 


1.72 


1.12x10* 


.625 


1.25 


9.125 


15.00 


wing 


hex. 




2.60 


6.02 


1.87 


0° 


1 


.625 


.265 


62 
62 


BRL 


tail 


hex. 




1.6J3 


12.61 


2.80 


60° 


.253 


.625 


.294 


m 


-« H 


1.72 


I.2W10'' 


.625 


1.25 


9.125 


15.00 




hex. 




2.89 


6.69 


1.87 


.268 


.625 


.265 


BRL 


tail 


hex. 




1.68 


12.61 


2. Bo 


50° 


.253 


.625 


.294 


lk2 


-MBI^^ 


1.72 


.8>10* 


.625 


1.25 


9.125 


15.00 


wing 


hex. 




1.9? 


7.43 


4.00 


43° 


.250 


.625 


.198 


63 

38 


BRL 
CAL 4 OFT 






_ . - 


l.ffi 


12.61 


2. So 


50° 


■ 253 


.625 


.294 


11.3 


-4-* 


M 


1.9CX10*' 


2.00 


8.38 


36.46 


61*.itl 


wing ■ 


*d.w. 


1 ,029 


7.51. 


23.24 


2.03 


60° 





2.00 


.216 


tail 


d.«. 




030 


ii)2 


57.53 


..i.49 
2.59 


45° 





2.00 


.254 


HI. 


-^^ 


1.50 


1.2x10^ 


.5^ 


2.26 


9.62 


19.90 


wine 


d.«. 




02q 


2.26 


7.70 


60° 





.54 


.216 


64 


OAL 


tail 


d.w. 




DID 


1.21 


17.40 


4.1.7 


450 





.54 


.230 


US 


^ ^ 


1.99 


.81x10* 


.563 


10.5 


5.25 


10.5 




d.w. 




08 


l.-Xl 


3.75 


6.88 


45" 





.563 


.200 




Ames 
1x3 ft 


'^ % 


tail 


d.w. 




08 


.835 


9.16 


6.88 
' 1.87 


45" 





.563 


.310 


11.6 


.m ■ 


1.90 


1.51x10" 


1.8 


11.31 


29.11* 


57.31 




d.w. 




03 


11.31 


22.28 


0° 


1 


1.80 


.216 


65 


Ames 
&<6 ft 


1 ' 


tall 


plate 




02 


10.91. 


46.37 


.782 


0° 


1 


1.60 


.405 




NACA RM A53G08 




65 



TABLE III.- SUMMARY OF GEOMETRIC AND AERODYNAMIC CHARACTERISTICS 
AND TEST CONDITIONS FOR BODY-WING -TAIL COMBINATIONS - Concluded 
(d) Aerodynamic Characteristics 



No. 


5l 


% 


KW(B) 


Kb(w) 


Kt(b) 


H(T) 


Theoretical 


Experimental 


'Lift 


Center of pressure 


^Llft c.p. 


"^S, 


'^^ 


Kl^ 


'''^ 


"^ 


'b 


•«(B) 


■b(h) 


't(b) 


'b(t) 


"ic 


'C 


m 


iiX 


""^ 


"^-OO 


(U 


■120 


0.221 


^0.067) 


1.11 


0.12 


1.19 


0.069 


3.65 


3.60 


0.23 


5.73 


5.W 


(0.317) 


5.67 


6.29 


8.35 


8.47 


5.97 


5.78 





602 


0.661 


0.23 


5.36 


0.673 


121 


1.00 


(.'•77) 


1.30 


.53 


1.30 


.53 


3.62 


3.62 


1.51 


11.. 97 


9.78 


(l.W) 


3.51 


4.05 


8.23 


8.58 


5.48 


4.01 




609 


.446 


(1.72) 


9.09 


">.486 


122 


1.00 


(.1.77) 


1.30 


.53 


1.30 


.53 


3.62 


3.62 


1.51 


11.. 97 


9.78 


(1.1.6) 


5.11 


5.55 


8.23 


8.58 


6.18 


5.08 




686 


.564 


(1.72) 


9.94 


.570 


123 


1.00 


(.'•77) 


1.30 


.39 


1.30 


.53 


3.62 


3.62 


1.51 


11..53 


10.73 


(l.W) 


3.87 


4.15 


8.23 


8.58 


5.65 


4.70 




628 


.522 


(1.72) 


10.02 


.515 


12k 


1.00 


(.'•77) 


1.30 


.39 


1.30 


.53 


3.62 


3.62 


1.51 


1'..53 


10.73 


(1.1.6) 


5.37 


5.65 


8.23 


8.58 


6.23 


5.59 




696 


.621 


(1.72) 


9.82 


.615 


125 


1.00 


(■■.77) 


1.30 


.39 


l.» 


.20 


3.62 


3.62 


1.51 


13.29 


9.U9 


(1.1.6) 


3.87 


4.15 


8.59 


8.58 


5.52 


4.43 




613 


.492 


(1.72) 


9.00 


.486 


126 


1.00 


(.'.77) 


1.30 


.39 


1.30 


.20 


3.62 


3.62 


1.51 


13.29 


9.1.9 


(1.1.6) 


5.37 


5.65 


8.59 


8.58 


6.21 


5.40 




690 


.600 


(1.72) 


9.00 


.580 


'*127 


1.00 


(.310) 


1.30 


.39 


1.30 


.53 


2.79 


2.79 


.76 


11.02 


6.79 


(l.W) 


3.63 


4.15 


8.34 


8.57 


5.74 


4.11 




638 


.457 


(.87) 


6.99 


10 


■^128 


1.00 


( . 310) 


1.30 


.39 


1.30 


.53 


2.79 


2.79 


.76 


11.02 


6.79 


(1.46) 


5.13 


5.65 


8.34 


8.57 


6.43 


5.23 




714 


.581 


(.87) 


7.05 


.588 


■^129 


.667 


(.263) 


1.30 


.53 


1.30 


.53 


2.19 


2.76 


.50 


7.96 


I..67 


(l.W) 


3.30 


3.70 


8.34 


8.57 


5.44 


3.34 




604 


.371 


(.58) 


4.55 


.392 


"■130 


.667 


(.263) 


1.30 


.53 


1.30 


.53 


2.19 


2.76 


.50 


7.96 


1..67 


(1.1.6) 


4.80 


5.20 


8.34 


8.57 


6.20 


4.63 




689 


.514 


(.58) 


4.48 


10 


131 


5.61. 


(.727) 


1.28 


.'« 


1.23 


.3'. 


2.81 


2.08 


.33 


1..I.1 


3.61 


(2.13) 


2.3a 


3.19 


13.89 


13.93 


11.65 


LI. 15 




611 


.585 


(■36) 


3.38 


.559 


132 


.35 


(.129) 


1.22 


.38 


1.33 


.1.1 


2.13 


1.79 


.22 


U.76 


3.71 


C..!!) 


8.94 


9.70 


14.00 


14.11 


9.96 


8.82 




664 


.588 


(.28) 


3.26 


.535 


133 


.35 


(.154) 


1.22 


.35 


1.33 


.1.1 


1.79 


1.79 


.22 


1..12 


3.21 


('..17) 


9.08 


9.31 


14.00 


14.11 


10.09 


9.04 




672 


.602 


(.28) 


3.25 


".575 


13'! 


.70 


(.259) 


1.29 


.51 


1.33 


.1.1 


2.13 


1.79 


.10. 


6.55 


3.98 


(1..17) 


9.00 


9.69 


14.00 


14.11 


10.38 


3.05 




692 


.537 


(.56) 


3.74 


.545 


135 


.70 


(.306) 


1.29 


.'.6 


1.33 


.1.1 


1.82 


1.79 


.10. 


5.95 


3.62 


(4.17) 


9.08 


9.40 


14.00 


14.11 


10.50 


0.27 




700 


.551 


(.56) 


3.64 


.575 


136 


.513 


(.131) 


1.18 


.21. 


1.25 


.23 


3.61 


3.68 


.39 


8.18 


6.1.9 


3.17 


9.26 


9.56 


14.06 


14.17 


10.46 


9.56 




696 


.637 


.47 


"6.10 


»'.620 


^37 


.500 
.500 


(.123) 


1.12 


.12 


1.25 


■ 23 


3.73 


3.68 


.38 


7.86 


7.37 


3.17 


9.24 


10.10 


14.06 


14.17 


10.64 


10.44 




710 


.696 


.46 


"r.26 


».691 


(.150) 


1.22 


.37 


1.25 


.23 


3.06 


..3B 


8.10 


5.61 


3.17 


9.22 


9.93 


14.06 


14.17 


10.66 


9.16 




710 


.611 


.46 


"5.30 


".M 


139 


.500 


(.1'.9) 


1.22 


.38 


1.25 


.23 


3.08 


3.68 


.38 


8.18 


5.1.5 


3.17 


9.17 


10.27 


14.06 


14.17 


10.66 


8.96 




710 


.597 


.46 


"5.72 


"■^1 


Ho 


.500 


(.157) 


1.22 


.38 


1.25 


.23 


2.93 


3.68 


.38 


7.9k 


5.05 


3.17 


9.16 


10.23 


14.06 


14.17 


10.69 


8.79 




713 


.586 


.46 


"5.50 


^.608 


lUl 
11*2 


.500 
.500 


(.157) 


1.22 


.30 


1.25 


.23 


2.91. 


3.68 


.38 


7.70 


1..89 


3.17 


9.20 


9.51 


14.06 


14.17 


10.64 


8.69 




710 


.580 


.46 


4.74 


.565 


.128 


1.16 


.22 


1.25 


.23 


3.59 


3.68 


.38 


8.18 


6.89 


3.17 


9.24 


9.76 


14.06 


14.17 


10.60 


9.97 




706 


.665 


.46 


7.26 


"'.691 


11.3 


.381 


.108 


1.18 


.31 


1.21 


.37 


2.22 


3.12 


.21. 


i.ho 


1..25 


11.6 


30.19 


28.79 


60.75 


60.04 


39.80 


33.33 




618 


.518 




3.75 


.509 


Ikk 


.192 


.100 


1.18 


.25 


1.19 


.16 


3.10 


1..0O 


.31 


7.37 


5.1.5 


3.13 


9.95 


10.03 


19.10 


19.10 


12.98 


10.78 




652 


.542 




5.57 


.553 


US 


.309 


.169 


1.16 


.23 


1.27 


.12 


1..00' 


U.OO 


.68 


7.99 


7.20 


1.62 


5.25 


5.86 


9.99 


9.99 


6.03 


5.62 




575 


.535 




7.74 


.550 


llt6 


.392 


.076 


1.18 


.31 


1.36 


.62 


2.93 


1.50 


.22 


5.71. 


5.19 


10.4 


27.26 


31.33 


49.51 


53.35 


32.02 


29.18 




559 


.508 




5.00 


.485 



R based on c of larger lifting surface 

- (Jenotea nonuniform or imknowr t/c, thl denes s -chord ratio 
A.v. IrdlcatCB double vedge 
*hex. Indicates hexagonal 
^b.c. Indicates biconvex 

Slight variation betveen Bubaonlc and supersonic model ving proportions, subsonic configuration test 
'^All lift curve slopes (per radian) referred to exposed area of larger lifting surface except BCr^ 
svalue by r.eglecting ulng-tall interference 

^[) indicates experimental value used in theory for combination 
^"Experimental Cl or Ca curve nonlinear near o ■■ 0. 
^^Alden-Schindel technique applied In estimating interference. 

^^Experimental lift or mcment curves v.s. ot do not pass through origin for symmetrical models. 
^ 5 based on exposed area 



;d with extended, 

■>■■ "'u^- 



:yllndrlcal tall boom coaxial with body. 



66 



NACA KM A53G08 




NACA RM A53G08 



67 



Tail afterbody- 




(a) Parts of a wing-body-tail combination. 









^ 


^^^ ^W(B) 




1 


^T(B) 


I 


1 - 


~l 






\ 


\ — 
\ 
> 




' 1 




L^ 


— if— 


> 


^B(T) 






"\ 


^,^W(Bl 






^--izT(BI 


1 



(b) Lifts without wing -tail interference. 



Wing vortex- 




> Lg(^) > 




(c) Lifts due to wing vortices 



Figure I -Parts and lift components of a wing-body-tail combination. 




68 



NACA RM A53G08 



2.0 



1.8 



1.6 



1.4 



1.2 



1.0 



.8 



.6 





















// 


















/ 


7 










K^(B) or KTiB)—y 


A 


/ 














/ 


/ 


/ 














/ 


/ 




/ 












y 


/ 




/ 


/ 










y 


/ 






/ 










y 


/ 






y 


/ 








y 


y 


Kb(W) or Kb(t)^/ 








y 


/^ 










/ 








^-^ 


-— 








/ 









y 






/ 


/ 




f^WfB) ^'^ ^T(B)^ 


/ 


















/ 




















/ 




y 














A 


















/ 


/ 


















A 


y — f^B(W) or kgfj-j 










A' 


y 
















^ 


//\ 


















^r 




















\naca^ 



.2 .4 .6 .8 1.0 

Radius - semispan ratio, (r/s)w or (r/s)j 

Figure 2. - Values of lift ratios based on slender-body theory. 




\ 




./ .2 .3 .4 

{r/sjyf or (r/f)^ radius 'Semispan ratio 

Figure 3. - Comparison of slender - body theory and theory of Lennertz 
for fraction of lift carried by body. 




70 



NACA RM A53G08 




r^;^ 



Region of influence 
of wing or tail on 
body 



U 




Mach lines — 



(a) Nonplanar model. 



(b) Planar model. 

TnacaT! 



Figure 4.- Equivalent planar model for determination of Kgf^^ and Kgfj^ 
for ttigh-aspect-ratio range at supersonic speeds. 




NACA RM A53G08 



71 




















' 






. ._ _- _ 










































' 














4> 




























\ 


\\ 




\m 


I 




A 










1 








1 i 






11 


1 






M 






J 




// 






n 


1 




/ 




// 






//I 




1 


w - 




/ 


1 1 


/ 1 


' i 




/ / 












// 


// 


1 


// 




/ / 












1 


7/ 


// 


n 


/ 




// 












// 


// 


// 


/ 


1 


/ i 












1 


// 


/- 


7 


/// 




// 


' 








/ 


1 


' 1 


/ / 


'/ 


// 


II 


// 










/ 


n 


1 


// 


/ 


' 


J 


/ 


' 






/ 


// 


7 


V 


/ J 


// 


' 1 


7 


// 


/ 




/ 


'a 


^/ 


/ 


// 


'A 


V/ 


[// 


// 


/ 


// 


y 


0. 


^/ 


// 


^ 


y/ 


V/. 


7/ 


/. 


/ 


(y 


// 


-'x 


^^ 


<x 


y:. 


/^ 


^A 


-v. 


y/ 


V 


/ 


/ 


^ ' 



^ 



>o 



•*^ 



CVl 



(I - /-)(/ + ^Y)Y''0S^/^^^)i 



M. 



JO (/-J-JO+^YA''''og/^'^}f 



^ 









00 




<\i 



00 



-5 

0) 






5 
■J. 

I 
t 



X5 



I 
I 

■§ 
■I 

I 

I 




72 




MCA RM A53G08 





























m^ 




























































z? 






























f^ 






























<\l 












V. 

_ c:_ 


















TJ 




























_. 00 








A 

1 
















' 


«vi 




















1 




-^ 


ody. 
uded. 


















/ 






















/ 






'terb 
"oncI 


















// 






















/ 


// 


/ 




§ 1 












N 










/ 


7/ 


// 




§ 










^•^ 










/ 


/^ 


v 


// 


_0g 






















A 


y 


// 


7 






















/, 


// 


'/ 


// 


/ 


















y 


{/ 







// 


/ / 
/ 












^ 






y. 




> 


V 


/ 


/ 


— ^ 










.^t* 


.■^ 




X 




y 


y 


/ 




/ 






i 


^"^8 
^ ^ 




^h 


<v 


1 




00 


<c 


'■ 


^ 




^ 






K 


< 


o 


1 


o 


(1- 




t 


^ 

>i'- 






f 


•**. 


Xi 





JO (/-^)(l-^^Y)Y^O^/*'^^>f 




NACA RM A53G08 



73 



Tail center 
of pressure 




Wing 

trailing 

vortex 




Figure 6- Vortex model used in determination of wing-tail interference. 




Ih 



NACA RM A53G08 




*^y 



Figure 7- Circulation distribution at wing trailing edge and 

equivalent horseshoe vortex. 




NACA RM A53G08 
1.0 



.8 



75 



























































X'l 

~ Xsl/P 










"^ 


^ 


-«^ 






































— ■ 












A-0 
































1 







































/.o 



I 






.8 



(a) No leading-edge sweep. 





1 






















































X'l ~ 












- X-l/2- 














— 









































" 




X- '' 


u 


— - 





































































(b) No midchord sweep. 



1.0 



.8 



























































x=/ 

X=l/2 



















— 


■ — 







___ 




X-0 






































































































^^^itsb^ 



.4 
1 2 3 4 5 6 7 8 

Effective aspect ratio, /3A 

(c)No trailing -edge sweep. 

Figure 8. —Chart for determination of wing vortex lateral positions at subsonic 

speeds. 




76 



NACA RM A53G08 



1.0 



.8 - t^,>^~4 







r— -.i - 


i^ 


.^•^ 
















A=l 






cxfrapoianon 


^ 


^ 


' ' 


















—* -*- 


^^^T^ 


^ 


-^ 
















X=l/2 














^,^ 


-^ 












































X-0 







































(a) No leading -edge sweep. 



1.0 



•It 



■8 ^- =~-^ : 



.^ 



























X = l 
























^ 


-^ 


















^'— *' 


^ ~ 


"^ 


^ 

.. 






- — 












A=l/i^ 




























^^ 






, 












A= 














































































(b)No midchord sweep. 



1.0 



.8 



.6 



012345678 
Effective aspect ratio, /3A 

(c)No trailing-edge sweep. 

Figure 9.—Cttart for determination of wing vortex lateral positions at supersonic 

speeds. 

























_ 


/»-/ 






















^ 


.^ 












X-l/2 






■ 


-^ 




'^^ 


7^ 










-- 


. 




X=0 





































— - 


































































\ti^$5^ 




NACA RM A53G08 



77 






I 

••I: 



-*-X 



M = 2.0 
s^= 1.25 
r = 0.75 
Cr= 3.0 
X/Cr=l.8 



± 



■*~x 



h-^r-HT 



'tr 






. Theoretical lateral position from figure 9 

t 




/■irsr boay vortex^ i 

Tfieoretical asymptotic lateral-^ 
position 



Second body vortex 




f„/Cr 



4 8 12 16 20 

Angle of attack, a , deg 

(a) Lateral position of vortex at tail position. 



24 



1.5 



5 

I 






1.0 



Ttieory: 

Vortex path in free -stream direction 

— , ; Vortex path corrected for cross -flow 

and induced effects 




(b) Vertical position of vortex at tail position. 



Figure 10. - Comparison between theory and experiment for lateral and 
vertical positions at wing vortex at tail position of aspect ratio 2/3 
triangular wing and body combination. 




78 




NACA EM A53G08 



< 
O 

.§ 



?3 






M= 2.0 
sl= 2.25 
r = 0.75 
Cr = 3.0 
x/Cr = 1.8 




i 



4 



Theoretical lateral positi 

1.^1 1 


on fi 


'om figure 9 

1 







" T 


~ ~j 


V 


_ _ 


^ 


'^^ 


^"Z— 


-Tip 


vortex 


^. _ 


. —^ 


^Theoretical asymptotic 
lateral position 




-^ 










-Inboard vortex 
































5 


'ecoi 


Id b 


ody vortex-- 




::;-i 


-~^ 














First body vortex 

1 1 , 1 


k 



























fw/Cr 



4 8 12 16 20 

Angle of attack, a , deg 

(a) Lateral position of vortex at tail position. 



24 



1.5 



■Q \ 
Ci N 



1.0 



Theory: 

Vortex path in free -stream direction 

— ; • Vortex path corrected for cross -flow_ 

and induced effects 




(b) Vertical position of vortex at tail position. 

Figure II.- Comparison between theory and experiment for lateral and 
vertical positions of wing vortex at tail position of aspect ratio 2 
triangular wing and body combination. 




MCA RM A53G08 



19 



1.5 



•k 
o 



5) ^ 



5| 

>4 



,5 



1.5 



5 V 
"§^ 1.0 






.5 



''S 



2.0 



s^= 3.75 
r = 0.75 
Cf= 3.0 
x/Cr=t.8 




*-x 




Theoretical lateral position from figure 9 



^Theoretical a symp totic lateral p osition 



First body vortex_ 



Inboard vortex 



Second body vortex -j_ 



f^Cr 
fao/Cr 



4 



20 



8 12 16 

Angle of attack, a , deg 

(a) Lateral position of vortex at fail position. 



24 



Theory: 

Vortex path in free - stream direction 

- Vortex path corrected for cross -floffi^ 
and induced effects 




'Firstbody^ 
vortex 



Second body vortex 



(b) Vertical position of vortex at tail position. 

Figure 12."- Comparison between theory and experiment for lateral and 
vertical positions of wing vortex at tail position of aspect ratio 4 
triangular wing and body combination. 




80 



NACA RM A53G08 




.8 1.2 1.6 2.0 

(a) Xj-0, (r/s)j-0 



2.8 



< 20 
I 1.6 



1.2 



.8 



1 


, 

0.2 


1 




/ 


r 
















i 


/«-( 


^\ 


,/ 














— . 










/ 


-O.t/ 








/ 


/ 


—c 


)C^ 


^ 
















\ 


1 


/ 


/ 


T 




















/ 


/ 


/ 




'^'^^O 










*v^ 








/ 


A 


O 


-> 








~~-~ 


^s 




S 


S. 








7/ 


^ 


r 


•20 


5 








\ 






\ 






w 


/ 






\ 








\ 




\ 


L 


a\ 




/. 


^ 


t,, 


T^v. 




\ 






\ 








A 




^ 


<^ 


h^ 




\ 












\ 




O 4 .8 1.2 1.6 2.0 24 

Vortex lateral position, (f/s) 

(b) Xj=0, (r/s)j=0.2 

Figure 13. -Charts for determination of tail interference factor as determined 

by strip theory. 




NACA RM A53G08 

2.0 




81 






(cJ Aj.'0, (r/s)j.-0.4 



2.0 




■8 1.2 1.6 2.0 2.4 

Vortex lateral position, (f/s) 
(d) Xt'O, (r/s)j.-0.6 

Figure B^^CQntmiied. 



2.8 




82 



ZO 



l£ 



12 



.8 




^kCk RM A53G08 



^ 

<: 



I 







^1* 





/ 




> 


/ 




















J 


/ 


/ 


/ 




















i-C 


,J 


0.4j 


/ 















^ 




\^ 






■ 


-0£ 


^ 
















V 


\ 




1 


/ 


/-0.8^ 








^^ 














1 


/ 


/ 






— 






'\ 


\, 








I 


/ 




T 








"^ 


\ 




\ 


\ 




1 


7/ 


^ 


r 


-1.5 ^ 


"^, 






s 


\ 




\ 




1 


7/ 




z'' 


-2. 





s 


\- 


2.5 




\ 




\ 


1 


ill 


// 


/, 


/; 


^ 




^ 


n" 


3.0 
■CO 













(e) kT'l/2, (r/s)j=0 




4 



.8 1.2 1.6 2.0 2.4 

Vortex lateral position, (f/s) 

(f) Xr=l/2, (r/s)j'0.2 
Figure 13. -Continued. 



2.8 




NACA RM A53G08 

2.0 
1.6 
1.2 
.8 




83 



I 






.4 



^ih 


/ 






^ 


^ 


^ 














i-0.2\ 






/ 


y 






















-( 


o.y 
























/ 


. 




- /^ y^ 


. _^ 


^ 


^ 










^ 








/ 




A 


















\ 






/ 




A 






'^ 




V 












/ 






— . 


^->. 


\ 




^ 


s 









\ 


/ 


V 


r 

-15 






\ 


\ 




\ 






■--V 


A 


// 


'■A 


^-k^Z 


V 


^-23 

"7 (O 


\ 




> 


\ 






^ 


i 


// 


^ 




-^ -o.U 


\ 






\ 





(g) V/-?/ (r/s)j=0.4 



2.0 




.8 1.2 1.6 2.0 2.4 

Vortex lateral position, (f/s).^ 

(h) Aj.=l/2, (r/s)j.=0.6 
Figure 13. -Continued. 



2.8 




81+ 




NACA RM A53G08 






I 



e.u 


1 


/ 






/ 


/ 
















1.6 




1 


f 




/ 




















i^-aej 




/ 


r 


-*<• 


^ 


■^ 






^ 


-^ 


•k 










1.2 




/ 


7 


/ 


/ 


y 














\ 


\ 




/ 


/ 


-0.B 

/ 


/ 

'0.8, 









-- 


^ 








s 






.8 




' 


/ 


/ 


/I 


i 










X 


s. 










A 


// 


^ 








\ 


\, 




\ 


V 




ji 




// 


// 


/ 


,,^-] 


r^ 








\ 


s. 




\ 




.f 




/ 


// 


/ 




5 

^ 
^ 


\^ -? 


/^ 






\ 




^ 









'/i 




l\ 


Y^ 


V"\ 






\ 









(nXj=l, (r/sJr'O 




.8 1.2 1.6 2.0 2.4 2.8 

Vortex lateral position, (f/s) '^^^^^^S^ 

(J)h=l, (r/s)j.''0.2 
Figure 13.- Continued. 




NACA RM A53G08 

2.0 




85 



I 



(k)Ay.=l, (r/s)j=0.4 




8 1.2 1.6 20 2.4 2.8 

Vortex lateral position, (f/s) '^naca; 

(t)Xj.'t, (r/s)j.=0.6 
Figum^^gg^ggj^ded 




86 



NACA RM A53G08 




*J04ODJ 90U9JajJS^Uf l!0± 







NACA RM A53G08 




87 



Qo <<i M: (\| 

(S/lf) *UOI4ISOd ID0IJJ9A XSfJOA 




«0 



I 

"v. 
C: « 

§^ 
Is 

t 

Ss. 

5 



I 



I 




NACA RM A53G08 






vs- 






0) 

J 



to 






























>f >f 






























^.^ 






























4.0 


X 


= 0; A^£ or 

1 


At.e.'0^ 


^ ^ 




























/ 














3.6 


X - 0; A 


M.C.' - 




--/. 


/^ 


^^ 


^^ 





















/ 


7. 




^ 












3.2 










I 


I 
























/ 


'/, 


> 


k ' 


h 


i 1 


r.£. 


-0 


2.8 








/ 


y 
























It 


/ 


r 




1 


>A 


U.C. °' ^ 


T.E. = 


9 A. 






// 


/ 






















C.*r 






// 


/ 






















2.0 






L 


/ 


























1 
























1.6 




// 




























// 


1 
























1.2 
































A/ 


























.8 


















Linear theory 


i 


















L.Ai 










a. 


/ 




























rr 


/ 































/ 






















\nl^ca/ 



12 3 4 5 6 

Effective wing aspect ratio, /3A 



Figure 16. - L ift-curve slopes of supersonic wings as determined by 

linear theory. 




NACA RM A53G08 




89 



'$'' 



5 

o 
«> 

o 



O 
.6 

.4 



3 4 5 

Effective aspect ratio, /9A 

(c) No trailing-edge sweep. 



— 


— Extrapolation 
























































































^'• 


















X^I.O 










'"^ 


















1/2 










/ 


























































































(a) No ieading-edge sweep- 






















































































x=o 










































/ 


> 




















1/2 
























W 






































/ 
































(b) No midchord sweep. 









































»™»^^ 














A'O 






































, 










^ 










1/2 










,^-' 


■^^ 
































*«• 


^^- 


















1.0 




































/ 


f^ 






























1 

1 ■ 



































8 



Figure 17. -C ft arts for determination of wing -alone center of pressure at 
subsonic speeds as determined by lifting -line theory. 




90 




NACA RM A53G08 



.4 



O 
£ 






5 

5 -2 



1^ 



Extrapolation 


























^=1. 






























/ 


4 


^^' 


.-' 












































—r- 
/ 
f / 






























/ 
/> 


— /*- 
/ 






























-f/ 

r 

































(a) No leading -edge sweep. 







































[^ *^^ 


^^"^ 




























y 




























i/ 


/ 

f 






























' / 

1/ 
































f 

1 

































(b) No midchord sweep. 



^ 



































X'O 










• 
























' z^ 




-- 


_ .^ d 


"" 






















i/ 


^' 


^ 


^^ 



























/ 


/ 


/ 






























/ 
/ 

f 






























/ 
// 
































/ 



































O 12 3 4 5 6 7 8 

Effective aspect ratio^ fiA 

(c) No trailing-edge sweep. 

Figure 18.— Ctiarts for determination of wing- alone center of pressure at 
supersonic speeds as determined by linear theory. 




NACA RM A53G08 




91 



2.0 



1.6 



1.2 



"7^ 8 



'd 



0- 



^ 






•^k*- 



v. 
o 



(a) With afterbody. 

























m/3 


= 00 

1— 


/ 










1 1 1 1 1 — 




'■'M 










if^ 


1 1 1 1 . 


^^^ 


^ 


^^ 




















^ 


s^ 


















^ 


^ 


^ 
















' — -^f 


^ 


^ 






















^ 


^ 








































































































^ .8 1.2 1.6 2.0 24 2.8 

Effective body -diameter, root-chord ratio, /9d/Cr 
(b) Without afterbody. 

Figure 19. -Charts for determination of ff) or f/j at supersonic 



speeds. 




92 



NACA RM A53G08 



2.0 



1.0 



Theory of 

fig fti(0) 


nr 










1 






— 


linear theory 
Extrapolation 








.4 












1 

■ 2 




































(a) No leading-edge sweep, X^O. 



2.0 



E/.6 



1.2 



o 
-? .8 

I 

^ 0^ 













} 


/ 1 

r/S' 


.6 












^ 










> 


/ 












^ 












/ 


/ 










^ 
















/ 
/ 






^ 


<i 


















/ 

/ 




y 


.^ 












___^ 




— 




t 

/ 

/ 


' 










o 
















/ 

1 


/ 
/ 


r^' 


.-' 


"^ 




-£^ 














/ 


/ 
/ 


/ 











































/ 

// 




.^^ 


























y 



























(b) No leading- edge sweep, X=l/2. 




2 3 4 5 6 7 

Effective aspect ratio, /9A 

(c) No leading- edge sweep, X=l. 

Figure 20. - Charts for determination of (^) or (-^) at supersonic 

^r B(W) ^r B(W) 

speeds for winas and tail s with afterbodies. 



^mm 



NACA RM A53G08 
1.4 



1.0 



93 



^ ^ 











/^5-.'^ 






^ 


-- 












A 


/ 




^ 




"^ 














/ 

f 

/ 


^^ 




^^.5 















— 


/. 


.^ 


-''^ 




2 


















.<; 


^-' 











































1^- 



























s" 



(d) No midchord sweep, X-0. 



!il 1.6 



i 
I 









/ 
/ 


/ 1 1 

r/s = .6 




^ 


^ 














/' 










-^ 


















/ 
/ 
f 




^ 


^4 
















^ 




/ 

/ 
/ 


/ 


.-' 










--- 


-^ 










/ 


> 

/ 




^--"' 


-^ 


^.2 




















'> 


^' 


— 









































1^ 


<-- 























































(e) No midchord sweep, X '1/2. 



2.0 



1.6 



1.2 



.8 











/ 










y 


/ 














/ 


S».( 






/ 


y 


















i r/ 


b 


y 


y 


















/ 




y 


y 
















^ 




/ 




y 
y 

-' 


y _, 


i 








^ 












/ 


/■ 






^ 


-^ 


' 














i 

1 


> 

/ 


y'' 
^ 


^ 


- * 


^ 
















1 

I i 




^^ 
























— 






















h 


'/ 


/ 






7 


















I'i' 


/ 




















1 


NACA 


y 



12 3 4 5 

Effective aspect ratio, /9A 

(f) No midc/iord sweep, X-i. 

Figure 




9k 



MCA RM A53G08 



I 



I 
I 

a 



l.o 














/ 














^ 


12 










yr/s=.6 








^ 












/ 






^ 
















.8 




/ 


^^ 




-^4 















— ■ 


/ 


/ 


^ 


^-^ 




'\2 


















^ 


^- — ■ 








1 
















/t 






























(g) No trailing-edge sweep, X = 0. 



1.4 



1.0 







/ 


r/s=.6 






^ 
















f 








-^ 














^- 


— ' 




/ 


' ^^ 


^ 


A 






^^ 




-^ 










t 

/ 

1 


y 
/ 


^.^ 


^ 


.2 




















i/' 





















































1^'-' 





























(h) No trailing-edge sweep, X - 1/2. 




12 3 4 5 

Effective aspect ratio, /9A 

(i) No trailing-edge sweep, X = I. 

Figure 20. - Concluded 




NACA RM A53G08 



Quarter- chord 
line 




95 



(a) Plan view. 



Circulation 
distribution 



Image quarter-chord line 




Quarter-chord 
line 



Trailing 
vortices 



(b) Vortex system 



Figure 2 1. -Vortex model for determining center of pressure of body in presence of 

wing or tail at subsonic speeds. 




96 



NACA RM A53G08 



Extrapolation 



























r/s=0 












^-' 


■i**^ 


— -*' 


"" 














.2 








• 


< 


¥^ 


X"'- 


■ ^^^ 


r_-- 


__ ^— ™ 












4 
















.6 






y 








"^ 
























r 




























r 

































-J 



s 



^^^ No leading-edge sweep, X^O. 



IVc 



I 
I 



























r/s=0 












y^ 


^^ 


^___^^ 


— -^- 












^1 


.2 
















L 






^^ 




> 


— y 


?^^ 




■^ 
















.6 










r 




























i 


'y 






























r 

































/7>/ /Vo leading-edge sweep, X - 1/2. 



.2 



























1 
r/s=0,.2,4,.6 










^ 


■-— 
























J 


y 




























































/ 


\ 






























1 





























2 3 4 5 6 

Effective aspect ratio, /3A 
(c) No leading-edge sweep, X=l. 



8 



Figure 22. - Charts for determination of (zr-) or fjr-) at subsonic speeds 

I Cr ^B(W) * ^r ^B(T} 




Q 



NACA RM A53G08 




97 



























r/s 


'.6 














•^x 


.---- 


t_~- 


— — _ 






















\ 








-•^ 


-Cr^ 




""" 


















4^ 


.^ 








































































































































































(d) No midchord sweep, X=0- 



yo- 












ST 
I 



./ 



























































r/s 


'.6 














■z,-^ 


zz- 


- -^' 


: — = 




























4-^ 


.2 








> 






■ -- 


-"" 

























:-> 






























f" 

































































































(e) No midchord sweep, A=//2. 



.2 



.1 



























r/s '0^.2,. 4,. 6 















-"*' 






















>i 


^ 






























/ 






























/ 
































1 
































■^NACA^ 



2 3 4 5 

Effective aspect ratio, /ffA 
(f) No midchord sweep, X- t. 



Figure 22. - Continued. 



8 





NACA RM A53G08 



.5 ^ =~. "I llj ;_ J 



.2 











































-— — - 


.^».. 


_^ 













r/s=.6 






















^ 


O" 


"" 





— 


— 


— 


1 — 












.4 
























\ 


K 




— — 


- — 

















.2 












\ 




































^ 


^^ 




































--. 




■*■—.- 

















































N,s 



^. 



y 



9fc 

0- 



(g) No trailing-edge sweep, X=0. 



■a? 



4 






"^ ^-^ 


^--^ 


]!,_-— 


'~- — 















r/s 


-.6 








~" — 





























4^ 


.2 








/^^ 


f" 














3 


^ ^ 






























2 


































































.1 
































































n 



































(h) No trailing-edge sweep, X=l/2. 



.1 



^ 
























r/s = 0,. 2, A 


S.6 








^ 






— - 


""* 




















y 


X 






























A 






























/ 
































/ 


























"v^CA,^'^ 



2 3 4 5 6 

Effective aspect ratio, /3A 
(i) No trailing-edge sweep, k=i 

Figure 22.-Concluded. 



8 




NACA RM A53G08 



99 




1^ 



I 

I 

















































' 


— - 














































































































































































































^^-^^,HA<iA^ 



10 20 30 40 

Nose half-angle^ degrees 



50 



60 



Figure 23. -Center of pressure of ogival nose as determined from 

slender-body theory. 




100 



NACA RM A53G08 




Estimated lift-curve slope, /9(4^) 



da ^C 



Figure 24. - Correlation between experimental and estimated lift-curve 
slopes for subsonic wing -body combinations. 




NACA RM A53G08 
10 



101 



.1 ' 



Ci 21- 


10 

8 

6 

4 





Experiment o 






























Theory 


















































































c 


^ 


































T^ 


H 


r^ 


























-T 






m^ 


' 














































































































«^^^^. 


































— i 




V 





































(a) Wing-body combination I. 






s 

r 






I 

s 

J 




10 

8 

6 

4 























































































































































































i 


1 
































( 


r^ 


M 


— 








^ 










































"*^ 


<%-. 














































.'^^^ft 


































1 




1 


■ 






























1 





(b) Wing-body combination 2. 









1 






1 
































Theory using 
experimental -~^ 
body lift i 

— 1 — 1 — 1 — \ — \ — 






( 


> 






















< 


L' 


^^ 
























i-' 


^ 










^ 












































■^ 


^ 






























































































































1 1 



































^ . 


























'%,J^ACA,x^ 




r 


> 


.^ 


\ 


i 


) 


.i 


? 


/.( 


3 


/i 


9 


1* 


9 


/( 


s; 


/i 


R 


9/ 



:j 2 



Moc/i number. Mo 
(c) Wing-body combination 3. 

Figure 25. -Variation with Mach number of lift-curve slope of wing-body 

combinations. 




102 



NACA RM A53G08 



u 

I 






in 

o 

I 



^ 







I" 

s 

I 

it 

-J 



10 



8 



Zi 2 


10 



J 2 


10 





Exoeriment c 


> 




























Theory 


























































r/teory using 
































experimental 


"\ 








[} 


v^ 


^i( 




















Doay iirr ^ 

1 1-^3 




r-i 


>___ 






^^ 




n 




•a. 












































' 
















































^ 


i^ 








































;■ 





































(d) Wing-body combination 4. 



o — ^:^^«^ 

''^ '--^^i 

1 



le) Wing-body combination 7. 















































































































































K 




































( 


\/ 


V 


^ 




























< 


) 




^ 






' 


^^^ 


^ 


i-^ 











































^ 


' — 














































^ 




































^ 


'^ 




























'>^^^aca; 


y 



.2 



.6 .8 1.0 1.2 14 
Mach number, Mo 

(f) Wing -body combination 8 



Figure 25. - Continued. 



1.6 



1.8 2.0 




NACA RM A53G08 






or 
J 






2 

^1 



C5' 



I 



10 
8 
6 
4 



103 



10 

8 

6 

4 

2 

O 
10 

8 





i 


Experiment 































Theory 




















































































r 


^ 


































^■^ 


y 




< 


h 


s 
























H 


1— -< 


r <^ 








N 


k 












— 






























n 


^ 


-^ 










































\— 


_^^^^ 











































































(g) Wing-body combination 9- 



Q / \ . 

^^^ ^ 



(h) Wing-body combination 10. 



























































































































































































































t 


^^A 


























n 






c 


> __ 


t 


\ i 


y 








■"- 




o^ 






















■*— T^— _^ 






.^ 


^ 


































,-^H^B 






































"^ 


1 


























>^ 


5^ 


-^' 



S .8 1.0 1.2 14 1.6 1.8 2.0 

Mach number. Mo 
(i) Wing-body combination II. 



Figure 25 - Continued. 




lOij- 



NACA RM A53G08 



10 



.^ 8 



I 

o 

I 



I 



o 

I 






I 

s 

o 

I 



6 

4 

2 


10 

8 

6 

4 

2 


10 

8 





FxDeriment o 






























Theory 












































< 


/ 


\ 




































\ 


/ 




\ 


k 


























] 


) 




M 






iv 


^ 
























— 
















i 


*^ 


^. 










































^ 


»-. 






jj 






































































'I 


\ 

1 — 



































(j) Wing -body combination 12. 















































































, 




































































































f 


■> i 




































1.^. 




l/ 




-^ 


^^ 


^^ 


2 




















-< 


' " 


































— "O 


-"^ 








































^_^ 


































1 


1 





































(k) Wing-body combination 13. 



































































































































































































































































( 


) 


^ 


.^ 


■ — ■ 












-^ 


— . 











"""■ 










— < 


J 




























t 




^ 


±i 


. 




































■^ 


w 




























^Ssti^SA^ 





.6 .8 1.0 1.2 1.4 

Mact) number. Mo 
(I) Wing- body combination /4. 



Figure 25.- 




lluded. 



1.6 1.8 2.0 



NACA RM A53G08 



105 



12 



10 






« 



«r a 

t 

i 6 
I 



5 

I' 























/ 
y 
y 


A 




















^ y 
/ / 

y / 


/ 














•4 


/ 

/ 


/ 
/ 


/ / 

y / 








1 1 

Line of perfect 






v. 


y 


□ 
















^ / 


y- 
y 
y 








ayrwmcnf 

f 1 




/ 

/ 


/. 














//-lOX 


















^ 7 
/ / 


3 


















4 


P: 


n 


a 


















^ 


k^ 






















3 


o 


Hf// 


^ winA 


i~tm'i inhtrfmritttr'm 




/ 


^ 
/ 






a 


M? wing-tail interference 

1 1 1 1 


} 






















"^^^^-^NACA^,,^^ 



8 



10 



12 



Estimated lift-curve slope, JSf^) 



Figure 26r-Correlatlon between experimental and estimated lift-curve 
slopes for subsonic wing -body-tail combinations at a^O. 




io6 



NACA RM A53G08 



16 



14 



W^ 



* 10 



I 



s 



I 





























/ 


r 
/ 


/ 


























^ 


/ 
/ 


/ 


/ 






















/ 

-hlOX/ 


/ 












1 1 
Line of perfect _ 








/ 
/ 


^ 


/ 


/ 














,# 1 






/ 


A 


' y^ 






1 1 1 




/ 


/ 


/ 






















/ 
r1 . 


r 




1 






















* 

/ 


^ 


y-iO% 


Fl 




















/ 


^ 


r 






U 


3 




















z 


/ 










D 
















/ 


^ 


f 






u 
p 




















/ 


^ 


r 


























/ 


ED 


¥ 




s 






















/ 


^ 


Q 
























> 


0i 


f 









fill 

With wing- tail inter fereno 
Ato wing- tail interference 

1 1 1 1 1 


t> 








/ 


/ 








□ 








/ 
































^"^->!i^5^^ 



2 4 6 8 10 12 14 16 

dc 
Estimated lift- curve slope, /9(-r^) 



da ^c 



Figure 27. - Correlation between experimental and estimated lift-curve 
slopes for supersonic wing -body-tail combinations at a=0. 




NACA RM A53G08 
7 



107 



1 I ^ 1 1 1 1 T" 

Theory, no wing-tail 

interference 

Theory, wing-tail inter- 
ference included 




4 8 12 l€ 
(a) Combination IQi 



§ 



t.t 




















1.2 






















Mo- 0.1 8 










1.0 








! 
[ 
















1 




/ 




.6 












i 


/ / 














/; 






_,^. 


_^_ 


- 1^ 


__ 


, 


/ 


/_ 










/V 












// 


' 






4 


1 — j'' 






/^ 












'/^ 










.2 




/ 


A 


J 






■J 1 






.^ 


\ 








^^^^^^^^ 




A 


} 










T 


' 



I 

I 

a 



5Z 



.N 



O 
14 



2 4 6 8 

(b) Combination 102. 




2 4 6 8 

Angle of attack, a, deg 

(a) Combination 103. 



2 4 6 8 

Angle of attack, a, deg 

(d) Combination 104. 



Figure 28.- Lift and center-of-pressure characteristics of subsonic 

wing -body-tail combinations. 




108 



NACA RM A53G08 



1.4 
L2 
I.O 

.8 

■J 
> 

.6 
4 



— ^ — I — \ — I — I — I — I — I — 
Theory, no wing-tail 

interference 

Theory, wing-tail inter- 
ference included 




•5 



2 4 6 8 

(e) Combination 105 (a). 



^ 



l.t 




















1.2 






















Mo- 0.83 










LO 






































.8 


— 


__- 


— 


— 






















1 
.6 


1 






























/ 






4 










/, 


^ 
</ 














/a 


P 










2 






i^ 


V6 

■ 














/ 


r^ 






-4 


^_ 


^ 






^ 










-^ 


^ 


^ 


* 



72^ 

68\ 

\ 
64^ 

I 



2 4 6 8 

Angle of attack, a deg 

(g) Combination 107 (a). 




^ 4 6^ a 
(f) Combination 106 (a). 



1.^ 




















1.2 






















Mo' 0.80 










IV 






































.8 




















— 


— 


— 


— 


— 


— 


-- 


.< 


k 
/ 


.^/} 


u_ 


\ 


1 


i 


i 


I 


' x 


V 


I— 


CJ*.© 












S 
/ 








.4 










/ 


y 


r 












/> 


"/ 










.2 








y 














/ 


i" 






^ 






Z 


'' 








^ 




^ 


m 



% 



.58\ 
.505 



^ 



.i^i 



2 4 6 8 

Angle of attack, a, deg 

(h) Combination 108 (a). 



Figure 28.- Continued. 




NACA EM A53G08 



109 



2B 

2.0 
1.6 



"I r 



-I — I — r 



Theory, no wing-taH 
interference 

Theory, wing-tail inter- 
ference included 




I 

I 
\ 



^s 



4 8 12 16 

Angle of attack, a , deg 

(i) Combination 109(a). 



14 



1.2 



1.0 



.8 






.6 



4 



.2 



> 


















































_. 


Mo =0.20 








































/ 














// 


r 












y 












~y3 


F- 










-- 


, . 


^ 


A 


\ 








A 


y 




A 












a 




A 
















/ 












• 




z 










-, ,-, 1 



I 

i 

58% 
54% 



m^ 



2 4 6 8 

Angle of attack, a , deg 

(J) Combination 110 (a). 



Figure 28.- Concluded. 



110 



NACA RM A53G08 



— I — I — I — \ — I — I I r 
Theory, no wing-tail 

interference 




4 8 12 16 

(a) Combination /// 



4 8 12 16 

(b) Combination 112. 




4 8 12 16 

Angle of attack, a, deg 

(c) Combination 113- 



4 8 12 16 

Angle of attack, a, deg 

(d) Combination 121 



Figure 29- Lift and center-of- pressure characteristics of supersonic 

wing-body-fail combinations. 



MCA RM A53G08 



111 



2.9\ 



24 
2.0 



— I \ 1 1 1 \ 1 r- 

Theory, no wing-tai7 
interference 

Theory, w!ng~tail inter- 
ference included 




O 
2.8 






4 8 12 16 

(e) Combination 123 



£.0 




















24 






































20 




















— 


— 


— 


— 


-//- 











^,.6 










// 


■ a 


. 


- 








^ 


w 


% 


a 


D 


n 




1.2 




/ 


/ 


,f 













y 


/ 


°/ 


'/- 












8 


— ( 


Q 
1 


// 






Mo=l.62 


f 
/^ 


/° 














4 


1 


















//< 


) 














^ 




/ 












■* 




^ 






€4% 



60% 

\ 
52^ 



O 
1.4. 



4 8 12 16 

(f ) Combination 125. 




4 8 12 16 

Angle of attack, a, deg 

(g) Combination 127. 



4 8 12 16 

Angle of attack, a, deg 

(h) Combination 129. 



Figure 29.- Continued. 




NACA RM A53G08 




l.t 




















t o 












Mo =1.72 


IJi 







— 


— 


— 


— 


- 






in 












/ 








I.U 










/ 










o 










/ 


/ 








■O 






y 


\4 


L/ 


f 












w 


r 


/ 


f 












^ 




/ 


7 












^ 






',.' 


/ 
















/ 


/ 














o 




^^ 
















.£ 


J 


V 












A 


■ 




L 










•^ 


^ 


■< 


■ 
■ 



72 
68% 

I 
56^ 



■s 



4 8 12 16 

Angle of attack, a, deg 

(k) Combination 139. 




4 8 12 16 

Angle of attack, a, deg 

(I) Combination 140. 



Figure 29.r Concluded. 




NACA RM A53G08 




113 









Experiment o 






















1 — 1 — 
■ 


1 


Theory 






















"^^F^" 


*• 8 




^ 


























































u 


< 






















55 




i 




— i 


»___ 


i 


y^ 


























?^ 










































1 





































^.^ 









































































































































(a) Wing -body -tail combination 


105. 









f 


































T 


T 




1 




































1 I 1 


^ 




















































































«0 






















■>xi- 




















14 












-1 




3 


Si- 


^ 


■V. 


«^ 


—0 




~o- 












? 








































§^ 








































^ *- 


































































































b) 


Vin, 


9-i 


ioa 


'y-l 


'aii 


COl 


mbt 


nai 


ion 


to 


€. 










.2 



4 



.6 8 kO f.2 1.4 
Mach number, M^ 
(c) Wing-body- tail combination 107. 



1.6 1.8 2.0 



Figure 30. -Variation with Mach number of lift-curve slope or lift coefficient 

of wing- body-tail comiiiutions. 




114 



K) 
58 






K) 

si* 

t* 







NACA RM A53G08 





i 


Pyn/>rim0>nt 


n 




















1 — 1 


1 — 
■ 


A 


Theorv 
























r 








































































































< 


b 


^O c 






























s^- 






" 


— 


— 




, 


— 1 


t>-^ 






















































































— 




















































































(d) 


Wing -body - 


tail combination 108. 









\ I \ 1 

^^^^^^^^ 



(e) Wing -body-tail combination 109. 

































1 

4 


1 


T- 1 


1 






































i 






















































































( 


> 
























-^ 


>^^ 














































-^ 


.,.^« 


























































































































1 



































4 .6 S 1.0 12 1.4 
Mach number^ Mq 
(f) Wing-body -tail combination HO. 

Figure 30, -Continued. 



1.6 13 2.0 




NACA RM A53G08 




115 



lO 



.8 






o 

2.0 



<«• 






Experiment < 


3 






















1 
■ 


1 


8 


Theory 




^ 


^OC'ZS' 










'^^^^ 






























^* 












r- 


{ 


6 




< 




■ — ' 








< 


\ 1 
5.2" 
























< 










'<^ 


^ 


\^ 




















q> 4 


1 


■"""*" 




r — ^ 






























z 



















^ 


3.1" 




















J 2 




< 


1 — 




— t 


















































^ 


' 1.0' 

1 

























i. 


\ 




— I 


J — 


-<y 
































(g) Wing -body-tail combination 105. 











































^^ 


















< 


1 


( 


> 










"^^^g' 














< 


) 


^ 


■ — 





:r~^ 






























-1 


















■Q n 


»• r 


?"- 
















< 


) < 


> 
















*' a -C 




































« 5" 


















J 


( 


) 


__l 


^ 












— 1 


4' 






































1 
















— ( 


M 


J 


~^ 


^~~ 












o < 


?• 
















































( 


h) 


Win, 


^-L 


"iOO 


y-i 


fail 


COI 


7?^/ 


nat 


ion 


10 


8. 










?^ 



•^ .8 1.0 12 1.4 1.6 1.8 2.0 
Mach number, Mq 
(i) Wing- body -tail combination 109. 

Figure 30. -Continued. 




116 




NACA RM A53G08 



1.0 



.8 



I 

'^ .4 
8 



^ 2 





FuDt^rintfint o 






















^- 


1 — 1 


1 1 




Theory 






















* 




W 












































































































5' 














* 
























T 






^ 




< 








































■~~- 


























a^ 


■2" 


















J 


























■ — 















































.2 4 .6 .8 1.0 1.2 1.4 1.6 

Mach number, Mo 
(j) Wing - body - taH combination HO. 




Figure 30.- Concluded. 




NACA RM A53G08 



117 



'~h 



I 



5 

I 




.2 4 .6 .8 1.0 

Theoretical center of pressure, (4-) 



Figure 31.- Correlation between experimental and estimated centers 
of pressure for subsonic wing-body combinations. 




118 



NACA RM A53G08 



.52 




Fxofirimen 


t 






























Theory — 


Uncorrected 


















48 


III" 





Corrected 

LJ 1 ' ' 



























( 


) 


( 


\ ^ 


) 






















44 


















































































40 




















































































A 


































.36 




1 


r 

1— - 



























































,^ 






















































/ 


^^ 


- 










'o 


- 


























/ 





































( 


\ 


























i 












































































































































































A 


1 








































"^ 


r 


































' 



'-u 



(b) Wing-body combination 2. 



(a) Wing-body combination I. 
.76 

.72 

.68 

.64 

.60 

.56 
.26 

.22 

.18 

.14 

JO 

.06 

O .2 4 .6 .8 1.0 1.2 1.4 1.6 1.8 20 

Mach number, l\4o 

(c) Wing-body combination 3- 

Figure 32. -Variation with Mach number of center-of -pressure positions for 

wing -body combinations. 


















































































































































( 


^ ^ 


) 


A 


1 


___ . 


- 


— 


— ■ 


1 — 


— 








































































































































































m. 






































— -* 


IP 




J 


j 
























"^^^^ 


L... 


J^ 




NACA RM A53G08 



119 



•-I 



l'>,|v 



.:yo 




Exoeriment 
































52 


Theory Uncorrected 




































1 1 






















48 
























































i 


i ) 


-^_ 


.-2. 


il 


L 







.___ 


1 


__ 




•v. 










G 






r 




^ 




















44 
















































40 














































^ 


4 




































.36 



































(d) Wing-body combination 4- 













































.68 


















































































aa 








































































^i*-^ 










.60 




~~ 






























"•»« 


•--• 


---_. 


-,-9 










































56 














































^ 








































L—^ 


w 


1 













































(e) Wing-body 


combination 


7 






















































.70 






































































































/ 


■ — 




i 


1 


2 


O 










.66 


_ — 


. 












. 


















( 


y 






















.62 












\ 


) 




^ 


/ 






























































.58 






^ 


































^^^^^ 






































^ 




























^VJljACA,,,^ 



.6 .8 1.0 1.2 1.4 

Mach number, Mg 
(f) Wing-body combination 8. 

Figure 32. -Continued. 



1.6 1.8 20 




120 




NACA RM A53G08 



.62 



58 



.54 



.50 





Experiment 


o 


Uncorrectec 
























i 


















Theory 













































































































^_ 










s 


p 


y 
































^ "l 


IT 1 




— 


— 


— 


■ — 


— 


• 




















\ 
































( 


. k I 


\ 




























A 










\\ 
























\ 


m 





































l-^l. 















(g) Wing-body combination 


9. 






















































.68 


















































































fiA 


































































/: 


^' 
















.60 


















f 


> 


/ 


^■^ 


r ■" 


































■\, 


/ 




























.56 


k 




I 


\ 


f' 


> 


\ 


/ 


























































V 




1^^ 

































•--I. 















(h) Wing-body 


combination 


/c 


?. 




















































.76 








































































































. 














1 






72 




i 


i> 





o_ 


1 






















j 






















.68 












< 


> . 


< 


U^ 


K 






























































.64 








^ 












































































^ 


























'^NACA,,^-^ 



.2 4 .6 .8 1.0 1.2 14 1.6 1.8 2.0 
Mach number, Mg 

(i) Wing- body combination II. 
Figure 32.— Continued. 




NACA RM A53G08 




121 









Experiment 


o 






























Theory 




Uncorrected 
Corrected 


















72 


.... 












































68 




















































































64 
























-J 


I 


< 


\ 




' Ui 






















c 


\ ]' 






■ -"" 




■ - 


— 




— 






60 


-^^ 




i 






/ 


















































1 


1 















































(j ) Wing-body combination 


12 






















































*>0 




















































































4/9 






































































. 






- — 


~ 


_j 




44 






















/ 










^7 
































/ 











l_ 








G 













.40 












L. 


— 


L_- 


.-i 


h 


1 








i 


^corrected 


^- 


^—tfteory using 


«A fii 








' ttieory using — 






^ 


1 


, J 














~i 


... 


) 








^AIJ 


^^rl 


wp) 

















(k) Wing-body 


combination 


13. 




















































to 










































0£ 










































48 










































































J 










44 



































^ 


— • 


-" 


c 


























/ 


/' 






' 










AC 














1 : 


L_ 


1 


) 


/ 


/ 




















A 
















^ 


/ 














1 














" 


























">^^ 



.6 .8 1.0 1.2 14 
Mach number, Mg 

(I) Wing-body combination 14. 
Figure 32. — Concluded. 



1.6 1.8 2.0 




122 




NACA RM A53G08 




Theoretical center of pressure, /-^J 



Figure 33. - Correlation between experimental and estimated centers 
of pressure for subsonic wing-body-tail combinations at a=0. 




NACA RM A53G08 




123 



1.0 



••s. 



1^ 



8 



5 

•v. 
5 






















> 


/ 








1 

Line of oerfsct 




^ 








agreement ^^ 


/ 


















r 














I 


M> 


m 


\ 












1 


# 




EO 












* 


/ 


V 




Lj 










-h.02t/^ 

7^' 


021 




> 










4 




/■ 


O With mng-tail interference 




^ 


f 




U ' 








r r VT vr 


»wv 



^ -? -^ .6 .8 1.0 

Ttieoretical center of pressure, (—) 

Figure 34.- Correlation between experimental and estimated centers 
of pressure for supersonic wing-body -tail combinations at a-O 




12U 



l^|. 



I-,], 



.66 
.62 
.58 
54 
50 
.46 



'H^ 




MCA RM A53G08 



.66 




Exoeriment 


o 






























62 


Theory 






































































fiO 










































.Oo 










































54 


















































































.50 




\ 


i 




< 


\ 


\ 


c 
































■ 








t^^-'^J' 










^ M ■ 


.46 
















r 









9 


1 










f 


• 



(a) Wing- body -tail combination 105. 









































































































^ — \ 


1 



























O' 


_ 




-Tr 


^ 


"o 








"Tj 














































































































































































































^ 






































1., . 


i 





.76 










{bj Wing-body - 


taii combination 106. 


















































.72 


















































































.68 






















































a 






H 








t»— 


--xi>- 




-Xl_ 




—2. 





.64 
















°o 
































































SO 










































































^ 


1 


TAT 


































"^ 


1 


J 


" 



O 2 4 .6 .8 lO 1.2 14 l£ IB 2p 

Mach number. Mo \!i^5iv^ 

(c) Wing-body- tail combination 107. 

Figure 35.- Variation with Mach number of center -of -pressure location of wing- 
body -tail combinations. 




NACA RM A53G08 




125 



.66 
.62 
.58 
.54 
.50 
46 



oa 




Exoeriment 


n 




























.62 


Theory 
























0' 


























^ 


^ 




, — 1 


' 





'iR 






















/ 


V 


^ 


-^ 








w 
























, i 


1 ^ 


y t 


•^ 


















*!^ 
















1 ' 


• 






















O'r 










































50 












































































afi 






































^ 


1 



.66 










Id) Wing-body-tail combination 108. 


















































fiP 




















































































.58 




























































r^^ 




o 
















5' 


*i4 










o 




\ 


■) 


~^ 


P 




^^ 


^ 


> — 1 


r 




' 


L 




.slff 
































o 


< 


> 




0' 


50 










o 








< 


l\ 








^ 
















































^ 




A 


.46 
































T_ 



(e) Wing- body-tail combination 109. 





























































































































































































■^ 


= 


== 


= 


=^ 


i 


?«M 


i 


- 


































% 












































( 


H 


b — 1 


" 




































































- 


" 



































.6 .8 1.0 1.2 14 
Mach number, Mq 
(f) Wing-body-tail combination 110. 
Figure 35.— Concluded. 





126 






O 




^kZk RM A53G08 



F', 


mA ar 




,* r 


o d^ ~ 


0° 


kA 


- r> 


/o 






^ 


^ 


Ex^.,„u^.... y^ 8^=5" 


-J 




d 


p 


^ 


In 


u\jr J 












^A 


k 


:^ 


r 


















A 


^ 




J — 








[ 








^ 


J 


^ 


^ 










A 




L 


^ 


















▼ 


▼ 



(a) Lift. 



^2 



/ 


A 


n 


^ 


a 


Reference area = ^'jf 












-i 














- 


-- 


- 


y 






















- - 


— 






— 










"^ 




































J 


















t 




f 














^ 


-^ 


















( 


> 


■ — 



(b) Moment 



.4 

r 
I- 

v. 
o 



n 



2 4 6 8 10 

Angle of attack, a , deg 

(c) Center of pressure- 
Rgure 36- Comparison between estimated and experimental effects 
of wina incidence for CQ[Ot>inatiOn 10 1. 





NACA RM A53G08 



127 



I.O 


Experiment: 


O 


<V - 


O" 


/t/ 


?/9 49 


•/ 


n 


^^ 


IP 


la 
Theory: 




^^ 


^ 


















r 


1 ^ 










^ .8 














. ^ 


A ^ 


A^ 


^ 
















y 


-f- 


^ 












A 








w. 


J\ 


r 
















^ 


\. 


J 


Y 














a 


^ 


^ 


Y 














— 1 — 1 — 1 1 



r^; Z./Y/ 



.8 




r 


] — 


p 


r 


\ 
















I 


3 












t 


? — 


c 


1 


^ 




.^ 4 








^ •■* 


















~^ 


~-~ 


^^ 








/^ 






1) — 


i 




< 


) 


< 


) 


c 


» 


c 


!> 


-^ 


O 


















■ 


— ■ 


-- 




_^ 




-.4 































fbj Moment 




4 6 8 10 

Angle of attack, a , deg 

(c) Center of pressure. 



12 14 



Figure 37. - Comparison between estimated and experimental effects 
of wing incidence for combination 143 . 




128 



NACA RM A53G08 






I.O 


Experiment: \ 


oS 


w'O 





hi'i 


150 




^ 


A 




1.2 


ID S 
Th^orv- 


w'8- 




J 








, 4 












yti 


It 


^ 


X* 


7 




.8 












A 


1 




^ 


^ 
















A 


Y 


X •■ 


,^ 


^ 


J 












.4 

r 




a 


\/ 


y^^ 


^ 


J 


J 
















K 


^^ 


^ 


^ 


r 














.^ 




^ 







J" 
















1 


— 1 


1 


■^ 



/'a; Lift 



1.0 
I 


1 






■•^ 






















/^ 




T 


^ 


r^ 




*-_ 


















— < 




~--J 


L 


— ^ 


5^- 


r 


1 . 












-/ n 












I 


'^ 


-^ 


P 


( 


K 


N^ 


























1 


k. 


d 


\ 




-2.0 































^-^ 



L^ 



i 
I 



(b) Moment 



3 


V 




























\ 




























2 




\ 














"- - 














\ 


\, 




















i 
1 


1 




1 


\ 


s. 




























\ 


s 




















n 








t 


b \ 


X 


















\J 












I 


Y^ 


^^ 


r-. . 












1 




^ 


^^ 


_^ 


^ 






I 


J ■ 


I 


r- 


H 


} 














~~^ 






i>. 1 


-i 


^ 


■^ 

















2 4 6 8 10 12 14 

Angle of attack, a , deg ''^^:^^^p^ 
(c) Center of pressure. ^~'^-^^ 

Figure 38.— Comparison of estimated and experimentcri effects of 
wing i§atiMMa^taitpmbination 144 . 




NACA RM A53G08 
8 




129 



(a) Lift 



</ 



.1 




















Reference area = vs^ 







































CF^ 


5-- 




•>w, 




->^ 






















~ 1 








^ 




-^ 






\ 




























gM 




^ 


h> 


^. 


\^ 












- 2 























i^ 




-\ 


v^ 
























c 


r^ 




o^ 


i-^ 






-.3 


























— ^ 




^ 





I 

o 



8 

















(b) 


Moment 














04 


\ 


































\ 


N 





































^ 


^ 


_ 






















1 




T 1 








''^^ 




^ 




















04 






— 


a 




a 




r 


\ 




□ 


— 


— 




























— 










sP- 




^ 




08 




























' 



10 12 14 16 



Angle of attack^ a , deg 
(c) Center of pressure 

Figure 39.- Comparison between estimated and experimental effects 
of wing incidenq^ l^^^ggphinnHnn 145, 



ncid&^^J^^^nbin 



130 



1.0 




Exoeriment: 


1 


<v^ 


■0' 
'4' 


ML' 1.9 






.6 


in s^- 
Theorv ■ 






I 




















i ^ 


A 


.6 






















/ 




















y 




Vi 

^ 












^^ 




















}y 




Y 












.2 

i 




.^ 


Y 




Y 


y 














A 


X 


f^ 


/ 












^ 






fi 


^ 


^ 












4 




9 

1 1 


1 


1 



NACA RM A53G08 



/^>9 










(a) Lif\ 


r 














J 


^ 


^ 


3 




] 












.^ 
















>^ 


L 


J 


























1 


] 








C 


) 


^ 


) 


< 


\ 






"S 


X 




a ^^ 


















\ 






^N, 


-/Trf 
















■^ 




v,^ 






•l/nr 




















^ 


k 


"«v 


-/V? 




























(b) Moment 




4 6 8 to 12 

Angle of attack, a, deg 

(c) Center of pressure. 

Figure 40.- Comparison between estimated and experimental effects 

of wing incidence for combination 146. 




NACA RM A53G08 



V^ 




131 



em u 
for no afterbody. 



Figure 4 1.- Geometry and coordinate system used to obtain Kg^^^ and Kg(j.j 



~/o7 Jm 

( • »"~~~~~-W/>7^ vortices "{•-)-- 



Image 
vortices 



tail tip 




tail tip 



^V 



(a) Wing vortices in cross -flow plane of tail. 




^V 



(b) Tail plan form dimensions. 

Figure 42.- Model and dimensions for determination of tail interference 

factor by strip theory. 




132 



NACA RM A53G08 






-5 -s+c -a 







s-c 




Figure 43rGeometry of model used for determining tail interference fac- 
tor for rectangular tail by Alden-Sctiindel technique. 




NACA-Langley - 11-12-53 - 325