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FOR AERONAUTICS
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TECHNICAIJ
LIFT
AND P17TCHINGMOMEN’T
CYLIND131CAL
ASPECT
NOTE 3795
INTERFERENCE
BODY AND TRIANGULAR
RATIOS
By Jack N. Nielsenj
AT MAC,H NUMBERS
Elliott
— —-.
D. Katzen,
Ames Aeronautical
Moffett Field,
A POINTED
WINGS OF VARIOUS
OF 1.50 AND 2.02
and Kenneth K. Tang
Laboratory
Calif.
I
I
I
Washington
December
.
I
1956
... . . ..
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...
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.,
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... ..._. . .... . . -..
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-.
.-
TECH LIBRARYKAFB,NM
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Ilunllmllnlllilllill
llClbLL34
TECHNICALNOTE3795
.
LIFT AND PITCEUNG-MOMENT ~NCE
I
BETWEEN A PO13WlXD
CYUNDRICAL BODY AND TRIYdlGUIARWINGS OF VARIOUS
ASPECT RATICS AT MACH NUMBERS OF I.yl and 2.021
By Jack N. Nielsen, Elliott D. Katzen, and Kenneth K. Tang
‘
sUMmRY
In. order to investigate the effects of interference on wing-body
combinations, tests were conducted at Mach nuaibersof 1.50 and 2.02 of
a pointed, cylindrical body, of six triangular wings having asyect ratios
from 0.67 to 4.00, and of the whgs and the body in combination. The
body had a fineness ratio of 7.33, a conical nose with a semiapex angle
of 15°, and an ogival trsmsition section to a cylindrical afterbody. The
wings had 8-percent-thick double-wedge sections with the maximum thickness at the midchord, and the wing-body combinations were made by inserting the wings at zero incidence into the cylindrical pait of the body.
Experimental Uft and pitching-moment results were obtained for a nominal
angle-of-attack range of *5.5° and a constant Reynolds number, based on
the body length, of 5.5 million. Theoretical characteristics of the
body and wings alone and in combination, as well as the interference,
were calculated from the available theories and compa~d with the
experimentzilresults.
The theory described by AUen ahd Perkins in N/WA Rep. 1048, 1951,
produced results in good agreement with the measured values of lift and
pitching moment for the body. The agreement was better at a Wch number
of 1.50 than at 2.02. For the wing-body combinations hatig low-aspectratio wings, the theoretical.predictions of Spreiter in NACA Rep. 962,
1950, were in good agreement with the experimental values of lift and
moment. For the wing-body combinations having higher-aspect-ratio wings,
a modification of the theory of NACA Rep. 962 produced predictions in
good agreement with experiment. Comparison of the wing-alone data with
the results of Love in NACA Rep. 1238, 1955, indicated a marked effect
of the position of maximum thichess on the lift-curve slope. The liftcurve slopes for the wings tested were considerably greater than for
wings with the msximwn’thickness at 18-percent chord in the upper range
of wing aspect ratios.
%upersedes recently declassified NACA RMA50F06 by Jack ~. Nielsen,
Elliott D. Katzen, and Kenneth K. Tsu, 1950.
~
“
——-. .—.— —
.-
.. —-
——
. . . .—.——
The results for the components alone and in combination W&
used to
determine the total interference, Wch
iS *f tied = the S~ of the ~te~
ference effects of the body on the wing forces smd of the wings on the body
forces. The interference effects were important for the wing-body combinations havfng small wings relative to the bcdy. Both the restits of the
theory of NACA Rep. 962 and of the modified theory were in good sgreement
with the expe~ntally
measured interference results.
.
‘
INTRODUCTION
The forces on a conibinationof a w&
snd a body can be considered to
consist of the sum of the forces on the wing alone, the body slone, and
the interference forces of the wing on the body and of the body on the
wing . Several investigators have presented theoretical methods of pretivestigated
dicting interference forces. Spreiter, in reference 1, W
the effect of interference
on the Wt-curve
slope and center-of-pressure
position of slender wing-body combinations. This theory assumes that the
body is slender and the leading edges of the wings are swept well behind
the Mach cone. I?errari,in reference 2, has investigated the problem of
interference between a rectanguhr wing and a body. ~ this paper the
effect of the wing on the body forces, -s*t
fie flow field due
to the wing is unchanged by the presence of the body, W
the effect of
the body on the wing forces, assuming that the body flow field iS ~cmed
by the presence of the wing, were determined. Brown, Friedman, and Hodes,
in reference 3, have investigated the conical-flow problem of interference
between a triangular wing and a conical body, the apex of which coincides
with the wing apex.
The present experiments were designed to measure the total lift and
pitching-mrnnentinterference of triangular wing-bmly combinations at supersonic speeds and to compare the data with the theory and a modification of
the theory of reference 1. The experiments also afforded an opportunity
for comparison of the Mt
force and pitching mcment of the body and wings
alone with values predicted by the available theories. The total interference, which is defined as the sum of the interference effects of the
body on the wing forces and of the wing on the body forces, was determined
by subtracting
sum of the lift, or pitching moment, of the wings and
body alone fran
lift, or pitching mment, of the corresponding
Combinations.
.
NOTATION
A
wing aspect ratio
Ap
plan-form area of body (2~: adx),
a
loti body radius, in.
—-—
————
S~
in.
_——
,
NACA TN 3795
3
o
2
aerodynamic chord - cr , h.
me~
cd’
cross-flow section drag coefficient of a circular cylinder
CL
lift coefficient based on total wing plan-fore area for wings
and combinations and on base area for body
%
%
increment in lift coefficient due to stream angle
pitching-moment coefficient about wing.centroid for wings
and cmribinationsand about body nose for body, based on
total wing plan-from area and mean axmodynsmic chord for
wings and combinations, and on base area and body len@h
for body
increment in moment coefficient due to stream angle
Cr
wing apex chord, in.
E
complete elJiptic integral of second kind
L
l&t
2
body length, in.
force, lb
total lift-interference
M
pitching moment, in.-lb
%
free-stream Mach number
total.manent-interference ratio, moments about body nose
*MC
,P %+%
‘r%-l
)
loading coefficient, ratio of difference between lower- and
upper-surface static pressures and free-stream dynsxnic
pressure
s
local wing Semispsn, in.
s
tOtal Wing pl&l-fOrm area as *ended
Sq in.
v
volw
-—. —,. . . . .. . . —.-.
in figure 1 (S =
CrSm)
,
of body, cu in.
_
.—.
-----——
.————
..—
free-stream velocity, in./see
longitudinal coordinate, measured along body axis from body
nose for body alone and combination, or measured along wing
apex chord from wing apex for wings, positive downstream, in.
lateral coordinate, normal to vertical plane of symmetry, in.
angle of attack in radians umless otherwise specified
stresm angle, radians
wing semiapex
amgle, deg
modification factor to account for finite wing aspect ratios
correction for three-dimensional effects on body
sweep angle of wing leading edge, deg
sweep angle of wing midchord line, deg
velocity potential
Subscripts
B
bcdy alone
w
wing alone
c
~-body
WB
effect of wing onlody
BW
effect of body on wing
\
L+
O
combination
liqdting value of quantity as lift approaches zero
b
value at body base
2
value at intersection of wing leading edge and body
m
msximum value
s
value due to stream angle
t
value at the wing trsllinn edge
—
———.——
—.—
.
NACA TN 3795
5
m
theoretical value for infinite aspect ratio
bc
centroid of body plan-form area
Cp
center of pressure of wing-body canbination
~
CONSDEMTIONS
Apysratus and Procedure
.
The tests were performed in the Ames 1- by 3-foot supersonic wind
tunnel No. 1. This closed-circuit continuous-operationwind tunnel is
equipped with a flexible-plate nozzle that cam be adjusted to give testsection Mach nuuibersfrom 1.2 to 2.4. Reynolds number variation is
accomplished by changing the absolute pressure b the tunnel fran onefifth of an atmosphere to approximately three atmospheres depending on
the Mach number and ambient temperature. The tunnel is equi~ed with a
strain-gage balance for measuring the aerodynamic forces on stingsupported models (ref. 4). ~ the ~t
descfibed ~ refer=ce 4,
the pitching moment was obtained fran the reactions on the main balance
springs and was not sufficiently accurate. Therefore, the pitching mament
in the present investigation was more accurately determined fra straingsge measurements of the bending mcment in the sting support (ref. 5).
‘
The modem were tested through a nominal angle-of-attack range of
5.5° at Mach nunbers of 1.50 ti-2.@.
A const&rb Reynolds nmiber of
0.5 million per inch was maintained and, in order to make the effects of
condensation negligible, the humidi~ was held to less than 0.0003 pound
of water vapor per pound of dry &&.
Models ti
@pOrtS
The body (fig. 1) had a fineness ratio of 7.33, a conical nose with
a semiapex angle of 15°, and an ogival transition section fairing into a
cylindrical sfterbody. The length of the body was limited by the condition that the nose wave reflected from the tunnel side wslls should fall
behind the body base.
The geometrical properties and designations of the six wing models
used in the investigation are summmxized in table I. A photo~aph of
the wing fsally is presented in figure 2. The wings had symmetrical
double-wedge airfoil sections in the stresmwise direction with a msximum
thickness of 8 percent at the midchord. All the wings were made of
hardened tool steel and were f~shed
by grinding. They were all equipped
with small supports which were designed to reduce the effect of the
supports on the aerodynamic forces of the wing alone to a ne~gi.ble
quanti~.
. .. . .—.
—- —
—-—
—
.——
———
———
6
NACA TN 3795
.
For all the wing:bcdy combinations the wings were located along the
cylindrical part of the body. The meth~ of =sembling the combinations
is shown in figure 3.
All the models were mounted on the same st~.
However, as shown in
figure 4, difYerent shrouds were used for the wing tests than for the body
sad combination tests.
Corrections to E&perimental Results
The experimental Et
and mmnent data have been corrected for the
nonuniform flow conditions in the tunnel test section. The measured
values of the stresm sagle and pressure coefficient in the vertical plane
of symmetry of the empty tunnel were used, together with the theoretical
results of the appenti, in estimating the corrections. It was found,
in general, that the correction to ldft and mcnnentwere small but not
entirely negUgible. The maximum correction to Mft-curve slope for all
configurations at both Mach numbers was 10 percent of the measured liftcurve slope. The corrections to the mcment data, at both l@ch numbers,
shifted the center of pressure of the body 4 percent of the body length;
the center of pressure of the wings, a maximum of 3 percent of the wing
mean aerodynamic chord; and the center of pressure of the wing-body
caibinations, a maximum of 3 percent of the body length.
Precision
The precision of the experimental data has been evsluated by the
method outlined in Appendix A of reference 5. This includes an estimate
of the precision of each measurement and the resulting uncertainty in
the measurement. There is a further uncertainty involved in the accuracy
of the corrections applied to the experimental data of the present tests.
The latter inaccuracy is estimated to cawe an uncertainty of *O.007 in
the lift coefficients for body, wings, and wing-body combinations; an
uncertainty of 30.006 in the moment coefficients for the body and an
uncertainty of 30.@
in the moment coefficients for the wings and the
wing-body ccmibinations
. The total uncertainty in the results is taken
as the square root of the swn of the squares of the individual
uncertainties.
The following table lists the total uncertain@ for all configurations
at both Mach nuoibers:
—
—
—.
——_ . .
.
——
.
NACA TN 3795
7
Quantity
Uncertain~ for
body
Uncertainty for wings and
wing-body combinations
*().
@
Mo
H.(X2
CL
f.oog
*.ocg
%
+*W
*o@
a(deg)
+.10
*010
THEORETICAL
CONSIDERATIONS
Body
.
Tsien (ref. 6) showed that the lift force and pitching moment on
slender bcdies of revolution at low angles of attack are the same at supersonic speeds as at subsonic speeds, and that the results are the ssme =
those predicted byllunkts airship theory (ref. 7). Thus, the Mft-curve
slope of a baly with a finite base is 2 for all Mach nmibers if the base
is used as the reference area. Experiments have shown that, while this
is a good approximation at low angles of attack, at higher angles of attack
the lift-curve slope increases and the slender-body theory is no longer
adequate. Slender-body %heory neglects the effects of tiscosity and considers only the potential flow about the body. A large effect of viscosity
can be included by considering the flow of a real fluid about an infinite
cylinder inclined to the stresm. h reference 8, Jones has shown that the
forces on sm inclined infinite cylinder are determined by the cross flow,
that is, the ccmponent of the flow perpemltcular to the cylinder. Since
the flow of a real fluid normal to a cylinder usually separates, a drag
of cross flow occurs and appears as a normal force on the inclined cylinder. AUen (ref. 9) has estimated the effects of cross-fluw separation
on the aerodyasmic coefficients.of slender bodies of revolution. The lift
coefficient, by the method of tiference 9, is
(1)
CL =
The first term represents the contribution of slender-body theory. The
second term accounts for the added lift due to the cross-flow separation.
In the second term c%
is the drag coefficient experienced byan infinitely long circular cylinder at the Reynolds number and Mach number based
upon the diameter of the body and the cross component of the velocity.
The factor q allows for the effect of the finite length of the circular
cylinder with the assumption that the reduction in drag coefficient for
fineness ratio is the same for each element of the cylinder. It is also
. . . _ ..—-,—
,.
———
—
NACA TN 3795
8
.
assumed that the reduction in drag is the ssme for a body (of varying
cross section) and a cylinder of equal fineness ratios. For a cylinder
with the same fineness ratio as the present body, reference 9 gives
~ =0.65. This value, together with c% = 1.2, has been used with equation (1) in determining the theoretical lift curve for the body.
-
If the moments are taken about the nose and the body length is used
as the reference length, the pitching-mment coefficient is given by
(2)
wings
The lift-curve slopes for the wings were determined from the results
of the linearized supersonic wing theory (refs. 10 or Il.). When the parameter ~ tan e is less than unity (subsonic leading edge), the lift-curve
slope is given by
dCL
—=
da
231tanE
E(jl-@%m2e)
(3)
J
For the triangular wings for which p tsm e is greater than unity (supersonic leaiMng edge), the lift-curve slope is given by (ref. 12)
(4)
Linear theory gives the result that the pitching-mcment coefficient
with the ~oment taken about the centroid of the wing plsm-fom area is
zero for alJ triangular wings having symmetrical sections.
Wing-Body Combinations
The lift-curve slope for a slender wing-body combination consisting
of a low-aspect-ratio triangular wing mounted on the cylindrical part of
a pointed body is by the method of Spreiter (ref. 1)
21’r~2
dCL
—=—tanE+2fil——
sm2
du
22
%
()
Sm2
tan E
(5)
.
——.
.——. .—..—.— —.
Iw!A TN 3795
9
where the total wing plan-form sxea (including the part within the body)
has been used as the reference area. The first term in equation (7)
represents the contribution of the body nose to the lift, and the second
term represents the contribution of the winged part of the configuration.
The lift force on the cylindrical afterbody is considered to be zero for
the angles of attack of the present tests.
In order to extend the method of reference 1 for application to combinations consisting of trismgular wings of higher aspect ratio, the
second term in equation (5) must be modified. When the method of Spreiter
is applied to w3ngs alone, the results become identical to the low-aspectratio trianguhr-wing results of Jones (ref. 13). It iS hlOm that the
lift-curve slopes estimatedby this theory are too large when the parameter ~ tsm c is not small ccnnpsredto unity andnmstbe multiplied bya
factor A to bring them into agreement with the linearized theories applicable to triangular wings of higher aspect ratio. The factor X is
obtained by dividhg equations (3) and (4) by the low-aspect-ratio res-tits
(dC~da = 2YCtan e):
1
1’
E(~l-
.
ptane<l
f32tan2e)’
1
A=
(6)
2 e;
I-@tau
we assumption is now made that the wing factor X canbe applied to the
lift on the winged psrt of the combinations. TheoreticaXl_y,this assumption has been shown to be vslid for the conical flow case of a triangular
wing mounted on a conical body, the apex of which coincides with the wing
apex (ref. l.). By physical reasoning, this-asswption is a good approximation for SW
vslues of 13tan ~ (the range where the theory of ref. 1
should be applicable) since A is then nearly unity. It is also good
when the ldft on the tinged part of the combination is carried mostly by
the wing, which is the case if ~ tan c is large when the wing is large
relative to the body. By the application of the factor A to equation (5), there is obtained
CICL 2Yca#
—=—tszle+2fiAl——
sm2
da
22
()
%
sm2
-bane
(7)
This equation hss been used to detemine the modified theory values of
lift-curve slope forthe wing-body combinations.
By the use of the foregoing method, the value of dCm/dCL fOr
moments taken about the wing centroid with the mean aerodynamic chord as
reference length is given as follows:
- ..—.
. . ..—.—
-—-———
.—c—..—
—
–—
10
d%
dCL
—=
0 [ +—-~l+~(’-a’[(’-s+=
)=(-+a+l’l
~ ab’
23c~
(%-2)
v
lT~2Cr
ab=
—+
%2
ab2
xl-—
()
2
Sm’
(8)
The position of the center of pressure with respect to the nose of the
body iS given
by
Xcp
—=
z
S(’-+)+’6-32[?(’+32
-Z(’-9+39191
,,,
ab’
—+
sm2
RESULTS ti
%2 2
()
Al-—
Sm’
DISCUSSION
in order to isolate the total interference
characteristics of the body alone, the wings alone, and the combinations
must be measured. The results of-the tests to det&mine these character:
istics are discussed individually and are presented in the form of lift
and pitching-moment coefficients in figures 5 to 7 for the body, wings,
.ad combinations, respectively. The results are sumarized in table II.
From these data, the total interference was determined and the results
are presented b figure 8 in terms of the total lift-intetierence ratio
and in figure 9 in terms of the total mcment-intetierence ratio.
Lif-t.-At ~ = l.~0, the experimental curve (fig. 5) was in good
agrea~
with the curve predicted by the theory of reference 9. At
MO = 2.02, the experimen~ lift coefficients were greater inmsgnitude
than the theoretical values at any angle of attack, consequently the
experimental value of the lift-curve slope at zero angle of attack was
greater than the theoretical. Since cross-flow separation does not affect
(dC~da)L+ 0, the difference between the theoretical.and experimental
values of this quantity must be attributed to other effects of viscosity
or to the fact that the body was not sufficiently slender to warrant the
use of slender-bdy theory. With regard to other effects of viscosity,
it
is known that Reynolti-number can have a large effect on the value of
(d~@L+O
of a body of revolution (ref. 4), but it was found that for
,
WA
Ill
m 3795
the present body (dC~du)L+O
was independent of scale above a Reynolds
number of 3xl& (based on the body length) for ~ = l.~0. Since the
Reynolds number was ‘5.5x106for the data presented at both ~ = 1.50
and ~ = 2.02, it is believed that the scale effect was insignificant. ,
Pitching moment.- On the basis of slender-body theory, the center
of pressure of the present body is approximately 19 percent of the body
length behind the nose. According to the theory of reference 9, a force
due to cross-flow separation, proportional to the square of the angle of
attack, has been assumed to act at the centroid of the body plm-form mea.
As the angle of attack increases, the cross force due to separation causes
the center of pressure to move rearward, produc~
a stabilizing influence,
as the theoretical curve of figure 5’shows. A comparison at the two Mach
numbers of the experimental mmnent curve with the viscous theoretical curve
shows that the agreement was good and there was little change with Mach
number.
wings
Idft - The lift results for the wings alone are summarized in figure 100
‘The
wing lift-curve slopes are dividedby the two-dimensional
lift-curve slopes and are shown as a function of B tan e. The experimental results obtained by Love (ref. 14) for triangular wings with the
ssme thiclmess ratio as the present wings (8 percent), but with the maximum thickness at 18 percent of the chord instead of 50 percent of the
chord, are also shown in figure 10. The Reynolds numbers in the tests of
?eference 14 were not greatly different from those of the present tests.
Comparison of the present results with those of reference 14 shows that
the lift-curve slope was much less h the upper range of B tan e for the
wings which had steeper leading-edge wedge angles than those of the present
wings. Thus, airfoil-section shape has a decided effect on the lift of
triangular wings. When the flow perpendicular to the leading edge is considered, the bow wave should become attached to the wing leading edge at
lower values of p tan e for the present wings than for wings with maximum thickness at 18 percent of the chord. Better agreement with-the
linesr theory is thus to be expected in this range of f3tan e for the
present wings. According to the linear theory, the wing lift-curve slope
should fsll on one line when plotted aE shown in figure 10. The present
experimental results at l&ch nuuibersof 1.50 and 2.02 did not fall on one
line, thus additional effects of Mach number beyond those predictedby the
linear theory were indicated. Why these effects of Mach number shouldbe
important for the present wings and not for the wings with maximwn thickness at 18 percent of the chord is not clear.
●
Center of pressure.- The experimental.variation of center-of-pressure
position with B tan e is presented in figure Il. The data show that the
center-of-pressurepositions were 3 to 8 percent of the me~ aerodynamic
chord forward of the wing centroid of area for all the wings of the present
investigation except WI at ~ = 1.50 and 2.02 and W2 at ~ = 1.50.
NACA TN 3795
12”
The results were not greatly different for the two Mach numibers. In
general, the center-of-pressurepositions for the wings of the present
tests were slightly forward of those for the wings of reference 14. The
deviation of the center of pressure from the theoretical position at the
wing centroid and the deviation between wings of different section must
be due to higher-order compressibility and viscous effects. A complete
explanation of the deviation must await a careful study of the boundarylayer behavior on the wings, together with experimen~ determinations-of
the wing-pressure distributions.
Wing-Bdy
Combinations
Lift.- The lift-curve slopes of the wing-body combinations are shown
in figure 12 as a function of the wing parameter ~ tan e. The figure
shows that the experimental results were in good sgreement with the theoretical results of reference 1 in the low range of values of ~ tan ~ for
which the theory was intended. The agreement between the experimental
results and the modified theoretical results was good throughout the test
range. It thus appears that the modified theory should be applicable to
wing-body combinations similar to those of the present tests - that is,
to those configurations for which the lift of the wings is large cmpared
to that of the body in the upper range of ~ tan e. The method would thus
be applicable to a triangular-wing airplane. However, for the case of a
small surface of lsrge j3tan e such that the lift of the surface is small
compared to that on the body, it cannot be assumed that the present method
would give valid results.
.
Center of pressure.- The center-of-pressurepositims at zero lift,
as fractions of the body length behind the nose, have been plotted against
~ tsn e for both Mach numbers in figure 13. The figure includes the theoretical center-of-pressurepositions calculated by the method of reference 1
for the combinations with the low-aspect-ratio wings, and by the method of
the modified theory for all the combinations. The figure shows a rapid
rearward movement of the center of pressure as p tsn E increased, smdat
high values of p tan e the center of pressure approached a constant position at x/z = 0.60. Since the moment was due prhnarily to the wings
as ~ tan .s becsme large, the center of pressure for the combinations
should a~roach asymptotically the limiting rearward position of the centroid for the wing fsmil.y. ‘l?his
corresponds to 0.636 z behind the nose.
The agreement between theory and experiment was good. The experimental
values for & = 2.@ and large values of 13tan e were slightly greater
than the theoretical values, but never by more than 2 percent of the body
length.
~
.
13
NACA TN 3795
Interference Effects
.
.
The Hft
of a wing-bdy
combination may be defined by
(lo)
k=h+%l+%l+%l
where the wtng alone is defined as the total wing, including the part
blaaketed by the body. The term ~W
is defined as the difference
between the lift force on the wing in the presence of the body and the
lift force on the W@
alone. ThuE ~W
is the effect of the body on
the wing Et
force. Similarlyj IWR is the effect of the wing on the
body lift force. The total Mt-fiZerference ratio is
%B+LBW
%2
LB+Lw ‘~&-l
(U)
and, correspondingly, the total pitching-moment interference ratio is
.
(12)
.
with all mcnnentdtaken about the body nose. Thus the total interference
ratios may be obtained from the characteristics of wings alone, body alone,
and combinations.
ratio was
Lift.-’Figure 8 reveals that the total ~-interference
negat=(i.e.,
unfavorable) throughout the test range. It must be
remembered, however, that the sign of this ratio depends to a large extent
on the wing definition. In the present paper, the wing alone included the
psrt inside the body. If the wing had been defined as the exposed halfwings joined together, the total lift interference would have been favorable, but of the same order of magnitude. The figure also shows that the
interference ratio was largest inmagdtude for the combinations having
the lowest ratio of the wing semispan to body radius. The interference
ratio decreased rapidly as the wing semispan was increased relative to the
body radius. For large values of #ah,
the interference ratio approached
zero.
-.
.
Even though the results of reference 1 were not derived for wing-body
combinations having wings of high aspect ratio, there is little difference
between the res”ultscalculatedly this methd and those calculated by the
modified theory when they are plotted in the form shown. The experimental
values of the interference ratio were smaller in mqgnitude than the
theoretical values, but the @geement between theory and experiment is
. —...———.
—-
.——
.—.— _—._—.
——
NACATN
14
3795
considered good. Better agreement is to be expected for a body of higher
fineness ratio and thinner wings than those used in the present
investigation.
Pitching moment. - F@ure 9 shows that, in general, the total momentinterference ratio was negative (i.e., ~ < ~+~)
and d&creased in msgnigreater than
tude rapidly as sm/ab was increased. For values of ~/ab
about 3~0 the inte%e~nce ratio was negligible. The e~–ertiental.values
of the interference ratio were less in magnitude than the theoretical
values, but the sgreement between experiment smd theory was considered
good. Figure 9 also shows that there was little difference in the momentinterference results for the two Mach numbers.
CONCLUSIONS
In order to evaluate interference, the lift and pitching moment of
a pointed cylindrical body, of six tri&gular wings having aspect ratios
of 0.67 to 4.00 and of the wings and body in combination were investigated
expetientally at Mach nunibersof 1.50 and 2.02. The experimental results
for the body, wings, and canbinations, as welJ as the interference results,
were compared with values predicted by available theories. The results
support the following conclusions:
1. The lift and pitching-moment curves of the body as predicted by
the method of NACA Rep. l@8, 1951, were in god agreement with the experimental curves.
2. Comparison of the results of the present investigation with those
in NACA Rep. 1238, 1955, indicated that the position of the maximum thickness had a marked effect on the lift of triangular wings having doublewedge sections with a maximum thickness ratio of 8 percent. For the
present wings of high aspect ratio and maximum thichess at 50-percent
chord, the H&t-curve slopes were conside-bl.y greater than those for wings
with maximum thicbess at 18-percent chord.
3. For the wing-body coribinationshaving low-aspect-ratio wings, the
theoretical predictions of NACA Rep. 962, 1~0, were in good agreement with
the experimental Mft and pitching-mament results.
4. For the wing-body cmnbinations having higher-aspect-ratiowings,
the theoretical.results of NACA Rep. 962 were modified and found to be in
god agreement with the experimental results. This modified theory should
be applicable to wing-body combinations similar to those of the present
tests - that is, to those configurations for which the lift of the wings
is large canpared to that of the bcdy.
.
NACA TN 3795
15
5= The interference effects were important for the wing-body combinations having small wings relative to the body. Both the theoretical
results of NACA Rep. 962-and the modified theoretical restits were in
good agreement with the measured values.
.-
Ames Aeronautical Laboratory
National Advisory Committee for Aeronautics
Moffett Fieldj Calif., June 6, 1950
.
—
●
I?ACATr? 3795
16
✎
APPENDIX A
DERIVATION (I?CORRECTIONS FCIRSTREAM IWNUNIFORMIT13ZS
The aercilynamiccoefficients of the present investigation have been
corrected for nonuniform flow conditions at the tunnel position where the
mcdels were tested. Corrections were applied to account for vertical and
horizontal pressure gradients and for stream angle. Although the corrections were not negligible, they were not sufficiently large to warrant
more refined methds in their calculation.
In reference 1, the velocity potential Q for the steady~tate flow
around an infinite cylinder having flat=plate wings was derived and used
to determine the lift and pitching moment of slender wing~cxiy combina–
tions. It was sham that the theory is appliable to triangular wingbcdy conibinationsat supersonic speeds, Providei the bcdy is slender and
has a pointed nose and the wing is swept well behind the ~ch cone. The
loading coefficient for a wing~aiy ccmibinationin a uniform stream was
given in reference 1 as
(Al)
The lift cm a spe.nwisestrip of width
dx
was given as
(A’)
In a nonunifcmm stream, the leading on models is affected by both
the streaqle
magnitude amd the str~
e gadient. The magnitude
of the stream angle can be accounted for by substituting equation (Al)
in equation (A2) and integrating. This stistitution was nade in reference 1 for various configurations and the results are directly applicable
to the present corrections if ~
is .wibstitutedfor a in finding the
lift on a spanwise strip of width b
due to the strcam-angle magnitude
at the strip. An additional Wading term to account for a streawangle
gTadient in the x direction is
(A3)
The lift on a spanwise element of the configuration due to the gradient
of stream angle in the x direction can be found by substituting equation (A3) in equation (A2) and integrating. The total increment in lift
:x
ma
17
m 3795
due to stream angle can then be foti by adding the spanwise incremental
lift due to strcam-angle gadient and streawangle Mgnitude ana integrating the result in the x direction.
Body Corrections
The lift and.pitching+mment coefficients of the lxxiyhave been cor–
rected for stream angle, vertical pressure gradients, and for cross—flow
separation due to stream angle in planes
perpendicular to the bdly axis.
For purposes of making these corrections, the fluw about the bmiy has
been viewed in planes perpendicular to the bcdy axis as shown in figure 14.
Consider point P in such a plane with the tunnel empty. There will be a
certain pressure coefficient at point P due to conditions in its forecone. With the bcdy in place, the pressure coefficient at point P is
the sum of the pressure coefficient in the empty tunnel mcdified by the
shielding effect of the bcxiyplus the pressure disturbance due to flow
arounilthe body. The shielding effect will be a complicated.function of
how pressure disturbances arising in the shadow of the body from P pass
around the bdy to P. It is believed that the shielding effect is smll
if P is some distance from the body. Therefore, superimposed on the
pressure coefficient at P in the empty tunnel is the increment due to
the flow around the baiy. In slender~cdy theory, the flow in a plane
perpendicular to the baiy depends only on the component of the freestream velocity in this plane together with the strearuwisegradient of
this component. If it ‘isassumed that h the empty tunnel these qumtities are sensibly uniform in any vertical plane in the neigliborhocdof
the region to be occupied by the bcdy, the flow as viewed in the plane
will depend only on
a+as
and
d(a+as)
~
(where as
is the local stream
angle) for the given bciiycross section in the plane. The stream angle
will then cause an increment in the pressure coefficient at P which,
to the order of the accuracy of the forego~
assumptions, is additive
to the pressure coefficient for the empty tunnel. If the point P now
moves to the baly and the shield=
effect is still neglected, the pres—
sure coefficients as measured in the empty tunnel and those due to stream
angle both act on the bcdy and prcduce corrections to the aerodynamic
coefficients.
Vertical pressure [email protected].– The increments in lift and pitching–
moment coefficients due to the vertical pressure gradients of the empty
tunnel, LC~
respectively, nay readily be calculated. The
and &?m,
increment fi”lift coefficient with the base area as reference area is
(A4)
.—. . . . ..—
——
— ———
———
—.—
18
IIACATN 3795
where Apr/q is the ratio of the difference between the static pressure
at the positim of the body surface in the empty tunnel and the referencewall static pressure to the free-stream dynamic pressure, snd 19 is the
m=positi~
of the body meridian measured from the lower intersection
of the vertical plane of symmetry with the body. The increment in mcment
coefficient, taking the mment about the body nose and using the body
length as the reference length, is
(A5)
The fact that vertical pressure grailientsmay have a large effect on the
aerodynamic coefficients of a slender body is associated tith the inherent
inefficiency of a slender bdy as a Mfti&
device.
- For the body alone, the velocity potential given in
reference 1 wtth the velocity potential for unifom flow normal to the
horizontal plane of symmetry subtracted out) reduces to
-“
(A6)
When equation (A6) is substituted in equation (A3), the loading coefficient due to the stremn-angle gradient becomes
(A7)
Equation (Al’)can be substituted in equation (A2) to give the lift due to
stream-angle ~adient on a spsnwise strip of width &
as
(A8)
The incremental spsnwise lift due to the msgnitude of the stresm angle
can be found, by substituting equation (Al) in equation (A2), to be
(A9)
The adtition of equation (A8) and equation (A9) yields the kotalincremental spanwise lift due to stream angle as
.
NACA TN 3795
.
19
When equation (AIO) is integrated over the body length and converted to
coefficient form, the increment in lift coefficient due to stream angle
becomes
(All)
or
(AM)
Equation (AM) expresses the interesting result that the increment in
lift coefficient due to stream angle for a pointed body of revolution
depends only on the value of the stream angle at its base.
The increment in pitching-moment coefficient due to stream angle is
Cross-flow separation due to stresm angle.- The experhental data
can be corrected for the effect of cross-flow separation due to stream
angle by the methd of reference 9. When a is replacedby a+as,
reference 9 gives the force per unit length due to cross-flow separation
as
fv = 2qac~q
sin2(a+~)
(A14)
For small angles of attack, the cross force is nearly all lift and the
net cross force can be determined approximately by integrating fv over
the body length. By conversion to coefficient form, there is obtained
For small angles of attack, the part of
C~
due to stresm angle is
(A15)
The correction AC~
increases with @e
of attack, ~
is usually small compared to
second integral can be neglected.
-. - . .
..——
—.
..—
—.—
of attack. At large angles
a
so that in this case the
NACA TN 3795
20
The increment in pitching-mcment coefficient due to the effect of
stream angle on cross-flow separation is
Xb
q=-~npp~
fiab2z .
I
J=-%--*
0
where moments are taken about the nose and the body length is the reference length.
Experimental verification.- Body-alone corrections obtained by the
foregoing method have been compsred with experimental pressure clistributions obtained on a parabolic-arc body of revolution set at zero angle of
attack in the 1- by 3-foot supersonic wind tunnel No. 2. The contour of
the body is shown in figure 15. Stream angle and pressure surveys were
made in the vertical plane of symnetry with the wtnd tunnel empty. The
model was equipped with pressure orifices at a number of longitudinal
stations and pressue measurements were made by rotating the body one
revolution by increments of 30°. The increment in lift coefficient per
unit body length ~
(LCL) wasdetermined from thepressure meammements.
This distribution of &
(ML) includes the combined effects of vertical.
and the effects of stream angle on crosspressure gradient, stream @e,
flow separation and is representedby squares in figure 15. However, the
effect of cross-flow separation due to stream angle is negligible at zero
angle of attack, so that, if the pressure me&surements me corrected by
subtracting out the pressures in the empty tunnel, the resulting distribution of -& (A@)
should represent that duetostream
angle al.one.
This corrected distribution is representedby the circles of figure 15.
By the method already given, it is possible to predict the distribution
of ~
(ACLS) from the measured distribution of stream angle along the
body. The predicted distribution is shown in figure 15 and is in fair
agreement with the measured distribution corrected for vertical pressure
gradients. From the figure, it is apparent that the effect of vertical
pressure ~adients and stresm angle are of approximately equal magnitude.
‘rrisagular
wing Corrections
The only corrections applied to the aerodynamic coefficients of the
to account for stresm
triangular wings were increments ACk cmdA~
single. For the wing alone, the velocity potential given in reference 1
reduces to
q)=“V&J’
(A17)
21
MACA‘m 3795
When equation (A.17)is substittied in equation (A3), the loading coeffi–
cient due to stram-angle gradient becomes
(Q8)
The lift ona
be
spnwise strip of width
dx
is found tiom equation (A2) to
(A19)
The incremental spanwise lift due to the magnitude of the stream angle can
be found by substituting equation (Al) in equation (A2). The result is
(A20)
The addition of equations (A19) and (A20) yields the total incremental
spanwise lift due to stream angle as
,.
(A21)
.
When equation (A21) is inte~ted
over the wing apex chord and converted to
coefficient form, the increment in lift coefficient due to stream an@e
becomes
Cr
Ac~8 = -=
Cr‘m
J
#-(cL@2)
&
(A22)
o
or
(A23)
Since equation (A23) is a result of slend.er-ing theory, the factor X
(described in the section THE-CAL
CONSIDERATIONS) iS used to extend
the results td hlgher~spec~tio
triangular wings. The resulting equa–
t-ion is
~Ls
= 2YcXusttan e’
The increment in pitching moment due to stream angle is
.- ——.
(A24)
22
–~ (%+%2%-J%
‘“s”5)
%3’ =
.
(A25)
with the moments taken about the wing apex. To transfer the moment increment to the centroid of the wing p~form
area, the following equ9tion
Is used:
%
Wing+oay
‘%5’ +%’
(A26)
Colillination Corrections
The only correctims applied to the wing40dy combinations were increments of lift and pitching+ment
coefficient to account fm stream angle.
The corrections have been determined ushg a theory analogous to that used
for the bcdy and the wings. The wing~dy
combinatims can be considered
to consist of three parts: (1) from the nose of the bcxlyto the intersec–
tion of the wing leading edge and the bdy
X2, (2) from X2 to the wing
trailing edge ~,
and (3) from xt to the bcdy base xb. Over the first
part of the combination the analysis is the same as that for the body alone,
but the limits of integration are changed. For this part the increment In
lift coefficient due to stream angle is given by
A12L’ =
-
(A27)
For wing~cdy combinations similar
to those of the present tests (in which
the exposed wing lies entirely along the cylindrical part of the body), the
velocity yotential due to the bdy, for the second Prt, is given by
(A28)
and
the velocity potential for the wing is given by
(A29)
When equations (A28) and (A29) ar,es~stittied in equation (A3), the loading coefficients due to the str~
e .gdient become
(A30)
-
23
NACA TN 3795
and
()
AP
Tw=
(A31)
‘~s~
The lift on a spanwise strip of width
dx
due to the gradient in stream
angle is found from equation (A2) to be
(A32)
The incremental spanwise Mft due to the msgnitude of the stream angle
can be found by substituting equation (Al) in equation (A2). The result
is
Zflg
[(
%s2
Thus the increment in lift coefficient
part is given by
AC%
_
~2
1-~+~
a4
)1
(A33)
~
due to stresm angle for the second
2YC
(A34)
.
For the third part, the analysis is again the same as that for
alone, with the li&ts of integration changed. When this psrt
body is cylindrical, as in the present case, the effect of the
of the stream amgle is zero, and the incremental spanwise lift
This is
stresm sngle is that due to gradient of stresm -le.
the body
of the
msgnitude
due to
given by
(A35)
The ticrement in HI%
is
coefficient due to stream angle for the third part
(A36)
The increment in lift coefficient for the combination is then found (by
integrating over the three parts of the configuration and applying the
factor A to the second part)’to be
..— — —.. .. —z
-
.—-——
.——
.——--
NACA TN 3795
24
AC%
%ab2
‘=%
23A
Z+%cr
[(
~m21_—
%2 +— %4
~m2
sm4
)
%-%%7
,1+
(A37)
The
corresponding
increment ii pitching-moment coefficient about the
body nose is
(A38)
The increment in moment coefficient transferred to the centroid of the
wing plan-form area is
(A39)
where <Jc is the distance frcm the body nose to the centroid of the wing
plan-fore srea.
REFERENm
1.
Spreiter, John R.: Aerodynamic Properties of Slender Wing-Body Combinations at Subsonic, Trsnsonic, and Supersonic Speeds. NACA
Rep. 962, 1950.
2.
Ferrari, Carlo: Interference Between Wing and Bdy at Supersonic
Speeds - Theory and Numerical Application. Jour. of Aero. Sci.,
vol. 15, no. 6, June lx,
pp. 317-336.
3.
Browne, S. H., Friedman, L., @
Hodes, I.: A W.ing-BO@ moblem m
NOV. 13, 1947.
Supersonic Conicsl F1ow. North Americsn Rept. -387,
4.
Van Dyke, Milton D.: Aerdynsmic Characteristics IncluUng Scale
Effect of Several Wings and Bodies Alone and in Connation at a
Mach Number of 1.53. NACA RMA61Q2, 1946.
25
NACA TN 3795
5.
Vincenti, Walter G., Nielsen, Jack N., and Matteson, Frederick H.:
Investigation of Wing Characteristics at a I@ch Number of 1.53.
I- Triangular Wings of Aspect Ratio 2. NACARMA7I1O, 1947.
6.
Tsien, Hsue-Shen: Supersonic Flow Over an Inclined Body of Revolution. Jour. Aero. Sci., vol. 5, no. W, Oct. 1938, pp. 48@@3.
7.
Munk, 14ax. M.: The Aerodynamic Forces on Airship Hulls.
Rep. 184, 1924.
8.
Jones, Robert T.: Effects of Sweepback on Boundary Layer and Separation. NACA Rep. 884, 1947.
9.
lCIIlen,
H. Julian, smd Perkins, Edward W.: Estimation of the Forces
and Mmnents Acting on Inclined Bodies of Revolution of High Fineness Ratio. NACA Rep. 1048, 1951.
10.
NACA
Clinton E.: Theoretical Ldft and Drag of Thin Triangulsx
Wings at Supersonic Speeds. NACA Rep. 839, 1946.
Brown,
1-1. Stewmt, H. J.: The Lift of a Delta Wing at Supersonic Speeds.
m.
of Applied Math., vol. IV, no. 3, Oct. 1946.
.—
12.
Puckett, Allen E.: Supersonic Wave Drag of Thin Airfoils.
Aero. Sci., vol. 13, no. 9, Sept. 1946, pp. 475-484.
Jour.
13.
Jones, Robert T.: Properties of Low-Aspect-Ratio Pointed Wings at
Speeds Below and Above the Speed of Sound. NACA Rep. 835, 1946.
14.
Love,
Eugene S.: Investigation at Supersonic Speeds of 22 Triangular Wings Representing Two Airfoil Sections for Each of 11.Apex
Angles. NACA Rep. w38, 1955.
.—..—
—
,*,.
—
TABLE I.– SUMMARY OF GEOMETRICAL HIOPERTIES OF WINGS
wing
Sketch
.i
i
A
i
A
A
A. (*g)
80.4
TL.6
63.2
56.0
50.3
45.0
A+ ( deg)
71.4
56.2
44.7
36.6
31.0
26.6
Sm (in. )
-25
1.75
2.25
2.76
3.24
3.74
2.97
2.73
2.60
2.49
=.
E
4.95
(in. )
L
+
(in. )
7.43
)
5.23
4.45
4.10
3.90
3.74
s
(in.a)
9.29
9.15
10.01
11.30
12.66
13.99
0.67
1.34
2.02
2.69
3.33
4.00
A
——
MACATIT 3795
27
TABLE II.- SUMMKRY OF RESUITS
c&flguration
Lift
‘
%da
Sydlol
-O
Mcmmnt
(per deg)
,()
Sketch
l&l.50
l&2.02
(l&
() dCL
l&l.50
Lao
“ l&2.02
B
~
0.0340
(.0349)
0.0460
( .0349)
-0.20
(–.190)
4.20
(–.lgo)
wl
e
.0208
(.0176)
.0186
(.0169)
–. 09
(o)
-.03
(o)
.0305 –
( .0323)
.02~\
(.0289)
(:)
.06
(o)
a
.0387
(.0442)
.0347
(.0374)
.03
(0)
.06
(o)
4
.0455
( .0533)
.0395
(.0398)
.03
(0)
.04
(0)
.0507
(.0602)
.0425
(.0398)
.06
(0)
.04
(o)
.0544
(.0624)
.0416
(.0398)
07
(o)
.08
(o)
w=
a
Wa
W*
W5
a
we
a
●
W.B
~
.0160
(.0137)
.0163
(.0134)
(::0)
.20
(.191)
‘,B
-
(“g::)
(“gg~
(“:7)
(::m)
W3B
.+[
,;:;;,
,;:3,
,::.,
.<%
+
.04~
( .0510)
.0415
(.0395)
.09
( .0941)
(:?!!)
+
.0526
(.0590)
.0451
( .0405)
(:%9)
.06
(.151)
.0460
, (.0410)
(::S8)
(::0)
w4B I
W5B
W6B
Note:
[
.0571 ‘
(.0622)
In each case the e~rimntal
value is given first and the
correspending theoretical value indicated in parenthesess
directly below.
- ———
-——.
—.—c.
. .
———
—
——
.——
—.
.——
—.
—.
Figure /.
- Plan-form
dimensions of body, wings, and wing-body combinations.
Figure 2
.- Wing series.
Figure 3,- Exploded view of body, wing, and s t i n g ,
( a ) Wing-body combination.
( b ) Wing alone.
Figure
4.- Wing and wing-body conibinat ion mounted i n tunnel.
jX
NAC!A!I?N3795
33
.4
.
.3
.2
C.S4
*. .I
$
*
,
I
I
4
:2
I
/
/
-. /
*Z 1
I
I
I
I
I
/
-6
I
I
<
1
K=
-8
I
:0
0
u
~. I
%“
4
1 ‘0””
m
#“
Y
:3
74
[
4
-2
Angle
0
of
2
attack,
d,
1.50
4
-6
4
Angle
of
attack,
4
d,
68
deg
.
Figure
5 .– L/I? and moment coefficients
-—_
:04
Pitching-moment
de9
OP
+
73
74
:08
68
,
-8
:2
for bo@Yat hW50
and 44=2.02
0
.04
coe ff[c[ent,
.08
Cm
34
r?AcAm 3795
.4
.3
—
——U78ar
theory
Angle
Angle
of
of
attack,
artack,
d,
>,
deg
Pitching-moment
de;
Pitching-moment
(0) U7ng 1.
Figure
6 .–
Lift andmomenf coefficients of wings at k%=150 and MQ.2W
—
—
coeff/c/ent,
coe fflclent,
Cm
Cm
~a
m 3795
35
.4
.3
.,?
Q“
# .I
~
.s
to
m
a
u
~ ~/
-.
4
:2
73
:4
-8
-6
-4
02
-Z
Angle
of
attack,
4
d,
68
deg
P/tching -moment
coe fffc[ent,
Cm
.4
.3
.2
.1
Qi
*.
to
$
<
a
o
u ;/
;
4:2
.
:3
Angle
of
attack,
d,
‘!08
:04
Pitching-moment
deg
0
.04
coefficient,
.08
‘
Cm
(b) Wing 2.
Figure
6.-
Continued.
-— ————._—
.—.
——
——
—
ma
36
m 3795
.
Angle
of
attack,
-2
Angle of
attack,
d,
deg
d,
4
deg
Pitching-moment
.4
.3
J?
& .1
~.
.$
*Qo
%
Q
Q
u :1
~
+
:2
,
:3
:4
-8
-6
4
02
68
(c) IWng 3.
Figure
6 .–
Continued.
we fficient,
Cm
NACA‘m 3795
.
37
.4
.4
.3
.3
.2
.2
04
*.
c
..Q
Q“
~. .1
c
.?
.$
~o
Q
Q
~ -et
..
4
.1
go
:
~ -./
..
-J
-.2
-.2
-.3
-3
-. 4
-8
-6
+
Angl;pof
o~ack,
2
d,
4
-.:08
68
:04
0
Pitching -moment
deg
.04
coe fficlent,
.08
Cm
.4
.3
.P
-I .1
u
*.
<
0
-Q
~
a
o
Q ~1
%
--+
:.2
73
-6
4
-2
An91e of
0.2468
attack,
d,
-4
:04
.:08
Pitching-moment
deg
0
.04
coefficient,
.08
Cm
(d) Wing 4.
Figure
6 .–
Continued.
.
—.
————
—
I’WA m 3795
38
.4
.3
.2
u<
.. .1
~
.Q
$0
Q
u
s
4
71
:.?
:3
+8
-6
4
-2
Angle of
6
02
attack,
8
c1, de:
Pitching-moment
(e) I$fng 5.
Figure
6 .–
Continued.
coeff/c/ent,
I&
—.-.
NACA
— .. . .
‘UN 5“(!D
39
“:08
Angle
.
of
attock,
d,
deg
:04
Pitching-moment
0
.04
coeff/c/ent,
.08
Cm
.
RfmRl
.P
d
~.
.1
-?0
.Q
:EB!!Ei3
:04
:08
Pitching-moment
(f)
.
Figure
6 .–
0
.@
coeff/c/ent,
.08
Cm
U7.ng 6.
Conchnfed.
.
——
—.———
.—
40
Pitching-moment
(a) Combinathm W, B.
Figure
7.-
Lift and moment coeffh”mts
of wing-body combinaths
at h&150
and 1%-2D2
coefficient,
C-
x
NACA ~
41
3795
,
Angle
of
ottock,
d,
Pitching -moment
deg
.4 -
.4
.3
.3
coe ffic/ent,
Gm
.2
c.? ‘
~.
$
~o
“~
m
W=B
:
u :1
z.4
:2
M.= 2.02
73
+8
-6
-4
-2
Angle
0
of
attack,
~
d,
H
4
deg
73
:4
708
68
:04
Pitching -moment
0
.04
.08
coe fffcient,
Gn
(b) Comblnaftbn W2B.
Figure
. .— ...—
7.-
Con f~nued.
—
—..
—
—
—
—-— ——
..
.——
MACATJ93795
42
.
.
‘:8
-6
4
-2
Angle
0
of
ottack,
z
d,
4
6
#
deg
M= 2.02
:3
:4
-8
-6
4
-2
Angle of
02
attack,
d,
4
dug
6
8
Pitching-moment
coefficient,
(c) CcmhhaiYm H$B.
Figure
—
7 .–
Continued.
—
—
Cm
NAcA m 3795
!,
43
.4
.4
.3
.3
.2
.2
Q<
+ .I
u<
.1
. a’
*
*
.$
$
>0
Q
u
$0
Q
b
$ :1
-J
~
+
:1
72
:2
73
73
:4
-8
-6
4
-.?
Angle
of
02
attack,
4
d,
68
deg
:4
:08
:04
Pitching-moment
0
.04
coefficient,
.o&7
Cm
1
Angle
af
aft ack,
d,
deg
Pitching-moment
(d) Combination
.
Figure
7. –
Continued.
——.. .-. ——z
coe ffic/en~,
Cm
44
NACAm 3795
.4
.3
.2
U4
~. -/
&
*
$0
Q
u
~ :/
4
:2
:3
:4
-8
-6
4
-2
Angle of
0
attack,
-2
d,
4
68
deg
.
.4
.3
.2
&
%’ - /
$j
*
$0
Q
o
2 -/
\-J
:2
:3
74
-8
-6
4
-2
Angle
4
02
of
attack,
ci,
68
deg
[e) Comhtnofkw ~B.
Figure
————
7 .–
Continued.
.4
.3
.2
04
~. .1
&
*
?O
m
o
Q
%- I
>.
-J
:2
:3
:4
:08
:04
Pitching-moment
.4
.4
.3
.3
.2
.2
C?
# .f
04
~. .1
&
&
.s
Q
Q
Q
~ ./
%“
-J
?0
@
Q
Q
; ~f
<
4
:2
T2
:3
:3
“$
o
-4
.:08
:04
Pitching-moment
:4
Angle
of
attack,
d,
deg
(f) Combl%atim
.
Figure
7 .–
Concluded.
Wg.
0
0
.m
.08
coefffcfent,
I&
.04
coefficient,
.08
Cm
IIAcA m 3795
46
.
,
,
% ‘m ModiYiedtheory
––+.&o
—- +=202
..
Yj$-.ql
~
~+
~
py$$l
I
w
_
o
Fgure 8.—
.4
Ilft -interference
Total
-Lo
.8
I
I I I
1.2
Figure 9.—
.4
Total
.8
24
2B
32
3.6
4~
.
I I I
‘+
I-2
moment -interference
—
20
of
roth at M.=L50 and M.=2.02.
-!~-~~
o
IJS
7zwy
Expedment
+ M.=L50
* A!$=2a?
(
20
M
A40d?fied thory
Tktzv
Experiment
-o- IUO=I.50
of
24
28
ratio ot AL=L50 ond Af.=2.02.
.-
3-2
3.6
40
h
a.
i“
IVACAm 3795
47
I
L?
I
Su&sonic
I
I
/eating
I
edge
LO
Linear
I
i
*
[
theory— >
/
f
/
~-.
---
@
/
->
_. -----
/
#-
-
~~enf
tests of wings
wifh maximum thickness ot 50% chord
4
.2
edge
/
/
/~ /
//
leading
— —
____---- ---- ---
/’
1 ,
/
/ /
.8
.6
1
Supersonh
/
Tests of wings with
moximum ti?ckne~
of 18 Z chord[refer-
./)
/;
It
-
~.=j 50
“
~
“
Me .~@
[
{{ ‘-___
IWe=L62
IIAx240
~..~2
L6
/..
ence ~)
OJ
o
.2
.4
.6
10
.8
L2
[4
20
Figure 10. — Lift- curve slopes for trlanguhm wings with maxt’mum thickness at 50-percenf
chord and at 18-percent chord.
IQ100
,
F
~ 80
$
2
b
~ 60
Q
5
2
t
Q
# ,
,
,
,
,
Subsonic leading edge _
&
40
4
y
,
,
,
leading
I
,
edge
Present fests of win~
*MO “130
with maximum thick—
ness at 50% chord
c
--- ---
__ --- ._
— .
_
_--- __
—
0
. .
—
L –Linear theory
o
0
Figure Il. —
2
4
A
—
.6
B
ID
L2
Center-of -pressure focotlons for triangular
at 50-percent
—_
chord and&
—G
~
{
—
18-percenf
14
~
—
Tests of wings with
moximum thickness
---—
ot 18% chwd (refer}{
ence /4)
$m
c
e
—------ ..—
,
w Supersonic
1.6
MO=202
—
——
M’RI.62
~**f92
IW240
18
2.0
wings with moximum thickness
chord.
—
..—.
—
48
MCA m 3795
./2
I
Theory
— ——~o.f.50
.10
—. —&=2.02
b
*
$ .08
fiperimenf
?
M’*=150
~
M.=2.02
7i3eory of
reference I
tj .06
1
R
I
1
~
<
.
$.04
<
/ ./ ~’
Aw
w
~
~ -y .02
[
<
I
L=&T-
111111
5-
.%
-1
00
leading edge t
Subsonic
.’
/
#
.2
.6
.8
p
i7@e 12.-
~
Supersonic leading edge
10
12
/.4
[6
~8
2.0
L8
20
ton 6
L/ft -curve slopes of wing-be@ combinations of M0=150 and M0=2.02.
.8
/{
Theory of
reference I
1
1
/J
1
//
m
..
b
,
/
.
“
-Modified theory-
Uv+
‘s--r
I
A.t
Theory
— --M.”i50
A
4
Experiment
0 IWO*I!O
E M.=2C?2
_-_~.2~~
.2 ~
S&onic
o
-o
Figure i3. —
.2
.4
i
Ieadi@
i
edge *
.6
.8
CWer-of-pn?ssure
1
t
Lo
A9fan 6
,
t
1
1
1
J
Supersonic kwding edge
L2
L4
is
postiiom of wing-body combinations at IU=iSO and ~e_202.
—-
——.
—
..—
——.._
K
49
IliuA ‘m 3795
.P
o
t kA
Section A-A
Figure
14.– 19ew of bo~ In fmet’, and cress-secffonul view mrmal to body UXLS
1
–—–distribution
Q measured
❑
.1
uncorrected
Q
~~
b
predict ed from
of*
distribution
of @&
corrected
for vertical
.0/
pressure
angles
gradients.
o
y
— — — — —
- .7 ~
c)
0
El
r1
-b
-D3
stream
dafo
a -.01
4
!& -.02
1
measured
c3
01234567&7
I
9
Distance
aft of body
10 II
f.
nose, x, inches
between measured Ih? distribution corrected for vert)cal pressure
f7gure 15. - Comparison
gradients and lift distribution predicted from measured streum angles on a parabolicarc body at zgro angie of attack.
NACA
- Langley
Fi6+d,
Va,
———c.——