An experimental investigation at a Mach number of 2.01 of the effects of body cross-section shape on the aerodynamic cha...

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Title:
An experimental investigation at a Mach number of 2.01 of the effects of body cross-section shape on the aerodynamic characteristics of bodies and wing-body combinations
Series Title:
NACA RM
Physical Description:
29 p. : ill. ; 28 cm.
Language:
English
Creator:
Carlson, Harry W
Gapcynski, John P
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
NACA
Place of Publication:
Washington, D.C
Publication Date:

Subjects

Subjects / Keywords:
Airplanes -- Wings, Swept-back   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
Abstract: An experimental investigation has been performed to determine the effect of changes in body cross-section shape on the aerodynamic characteristics of bodies and wing-body combinations. A series of 13 bodies having a given length and given longitudinal distribution of cross-sectional area but various cross-section shapes were tested at a Mach number of 2.01. The bodies were tested alone and in combination with a 47° sweptback wing having a 6-percent-think hexagonal section.
Bibliography:
Includes bibliographic references (p. 9).
Additional Physical Form:
Also available in electronic format.
Statement of Responsibility:
by Harry W. Carlson and John P. Gapcynski.
General Note:
"Report date April 29, 1955."
General Note:
"Declassified May 16, 1958"

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003853000
oclc - 153985920
System ID:
AA00009211:00001


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NACA RM L55E25

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


RESEARCH MEMORANDUM


AN EXPERIMENTAL INVESTIGATION AT A MACH

NUMBER OF 2.01 OF THE EFFECTS OF BODY CROSS-SECTION

SHAPE ON THE AERODYNAMIC CHARACTERISTICS OF BODIES

AND WING-BODY COMBINATIONS

By Harry W. Carlson and John P. Gapcynski


SUMMARY


An experimental investigation has been performed in the Langley 4- by
4-foot supersonic pressure tunnel to determine the effect of changes in
body cross-section shape on the aerodynamic characteristics of bodies and
wing-body combinations. A series of 15 bodies having a given length and
volume but various cross-section shapes were tested at a Mach number of
2.01. Each of the bodies had the same longitudinal area distribution as
the ogive-cylinder body of revolution of fineness ratio 10.5. The bodies
were tested alone and in combination with a 470 sweptback wing having a
6-percent-thick hexagonal section.

The results showed that changes in drag at zero lift due to changes
in body cross-section shape from the basic circular shape are small and
of the same order as the test accuracy. Significant changes occur in
body lift, pitching moment, and drag due to lift as the body cross section
is changed. A set of empirical correlations applicable to the present
tests was found relating the lift produced by a body at angle of attack
to certain geometric body cross-section-shape parameters.


INTRODUCTION


In supersonic aircraft and missiles the fuselage often comprises a
large part of the total plan-form area. Therefore, the fuselage as well
as the wing should be considered as a lift-producing medium. Furthermore,
mutual interference effects are important and need to be evaluated.
Although data are available for bodies of revolution alone and for the
interference effects when these bodies are used in combination with wings,
little data is available for bodies having the arbitrary noncircular cross
sections which are coming into use.





2 NACA RM L55E23


The present investigation has been undertaken to determine the
effect of changes in body cross-section shape on the aerodynamic charac-
teristics of bodies and wing-body combinations. A series of 13 bodies
having a given length and volume but various cross-section shapes were
tested at a Mach number of 2.01. Each of the bodies had the same longi-
tudinal area distribution as the fineness ratio 10.5 ogive-cylinder body
of revolution. The bodies were tested alone and in combination with a
wing having 47 sweepback, an aspect ratio of 5.5, a taper ratio of 0.2,
and a 6-percent-thick hexagonal section.


SYMBOLS


D drag, Ib

L lift, Ib

M pitching moment, ft-lb


free-stream dynamic pressure, lb/ft2

total wing plan-form area, 1.143 ft2

body maximum frontal area, 0.087 ft2

wing mean aerodynamic chord, 0.656 ft

body length, 3.50 ft

tunnel stagnation pressure, lb/sq in.

angle of attack, deg


body drag coefficient,


body lift coefficient,


body pitching-moment coefficient about body station


0.6971, (c/4 of d),


CL


M
qFl


body lift-curve slope per deg


wing-body drag coefficient, D
qS






NACA RM L55E25


CL' wing-body lift coefficient, L
qS

Cm' wing-body pitching-moment coefficient about (c/4 of a), M
qSc'
CL wing-body lift-curve slope


b body cross-section breadth, in.

h body cross-section height, in.

p body cross-section perimeter, in.

hi distance from body cross-section centroid to bottom of section

kl,k2 constants of proportionality

Subscripts:

B arbitrary body

CB circular body

W wing

0 refers to conditions at zero angle of attack


MODELS


The models tested are shown in figure 1. The basic circular body
had a fineness-ratio-5.5 ogive nose and a cylindrical afterbody, giving
an overall fineness ratio of 10.5. Each of the other bodies had the same
longitudinal area distribution as the circular body. The bodies were
tested alone and in combination with a wing having 470 sweepback, an
aspect ratio of 5.5, a taper ratio of 0,2 and a 6-percent-thick hexagonal
section. The wing-chord plane coincided with the horizontal center line
of the body sections and was located longitudinally with the quarter
chord of the wing mean aerodynamic chord at the 69.7-percent-body station.
Of the nine bodies shown, four were not symmetric about the wing plane and
these were also tested through the angle-of-attack range in the inverted
position. Lift, drag, and pitching moment were determined from measure-
ments made with a sting-supported internally mounted electrical strain-
gage balance. The bodies were constructed of Paraplex and Fiberglas
coated wood and the wing was made of steel. Further dimensional data on
the models are shown in table I.





NACA RM L55E25


TESTS


The tests were performed in the Langley 4- by 4-foot supersonic pres-
sure tunnel at a Mach number of 2.01. The body-alone tests were run at
stagnation pressures of 4.5 and 7.5 pounds per square inch corresponding
to Reynolds numbers of 5.9 x 106 and 6.5 x 106 based on body length, while
the wing-body combinations were tested at a stagnation pressure of
7.5 pounds per square inch. Tunnel surveys show that at the lower pres-
sure under some conditions (moist air) the Mach number may be as low as
1.98. This effect has been neglected. For the wing the angle-of-attack
range was from -2 to 100. For the bodies the angle-of-attack range was
from -20 to 100 at the low pressure and from -20 to 80 at the high pres-
sure where the pitching moment reached the balance limit. All of the
data presented are for a stagnation temperature of 1000 F.

Transition strips composed of No. 60 carborundum grains set in shel-
lac were used on all configurations to insure turbulent flow. The strips
were placed on the bodies 1/2 inch back from the nose but were not used
on the wing.

From an examination of the test repeatability and the static balance
calibration, the test accuracies are estimated to be as follows:


Body Wing-body

CD t0.01 CD' +0.001
CL 0.05 CL' 0.002

Cm 0.05 Cm' t0.002
a 0.10 a t0.1
CL 0.005 CL 0.0005

L/D +0.15 L/D 0.15



RESULTS AND DISCUSSION


The basic test data, which have been adjusted to the condition of
free-stream static pressure at the body base, are presented in figures 2
and 3. By the use of offset vertical scales, curves for all thirteen body
shapes are shown on one page. Care must be exercised in reading the fig-
ures to use the proper zero line for each of the curves. To aid in this
identification, the symbol for a given curve is shown in the margin oppo-
site the zero line for that curve.






NACA RM L55E25


Figure 2 gives the aerodynamic characteristics of the bodies when
tested alone. For each of the two stagnation pressures (P = 4.5 and
7.5 pounds per square inch) lift, drag, pitching moment, and lift-drag
ratio are presented as a function of angle of attack. The pitching
moment is taken about the 69.7-percent-body station which is the station
at which the quarter chord of the wing mean aerodynamic chord occurs for
the wing-body combination.

Notice in figure 2 that the bodies having the greatest breadth pro-
duce the highest drag, lift, and pitching moment at angles of attack.
Also, those bodies produce higher lift-drag ratios and their (')

seems to occur at lower angles of attack. These changes are in the
direction one would expect, since the body approaches a wing shape as
its breadth is increased. However, it is obvious that breadth or plan-
form area is not the only factor, because the triangle, tent, and tear-
drop shapes do not produce the same results when inverted as when
upright.

Aerodynamic characteristics for the wing-body combinations at a
stagnation pressure of 7.5 pounds per square inch are shown in figure 3.
Lift, drag, lift-drag ratio, and pitching moment about the quarter chord
of the mean aerodynamic chord are plotted against angle of attack. Dif-
ferences between the various bodies here are in general accord with the
previously mentioned changes in body-alone coefficients.

The values of the drag coefficients at zero angle of attack for the
bodies and wing-body combinations, taken from the basic data, are repro-
duced in table II. The small changes in drag and the relatively large
experimental error prevent any conclusions being drawn from these drag
data, except that the changes in drag due to changes in body cross-section
shape from the basic circular shape are small and of the same order as the
test accuracy.


Body-Alone Lift Analysis

The following analysis has been developed from several emperical
relationships suggested by the experimental data, rather than from a
rigorous theoretical treatment. There exists little or no information
on the cross-flow characteristics of these arbitrary shapes and the
present investigation included no pressure distribution data necessary
for a detailed flow study.

It was found convenient for the purpose of analyzing these data to
divide the lift produced by the bodies of arbitrary cross section into
two parts. The first part is proportional to the angle of attack and is





NACA RM L55E25


determined from the body lift-curve slope at zero angle of attack. The
second part, which has been called the incremental lift, was found to
vary with the angle of attack cubed.

The incremental lift at a given angle of attack was found by first
adjusting the lift coefficient to the condition of zero lift at zero angle
of attack (a small tare correction for the balance and an adjustment for
the lift produced by the nonsymmetrical bodies at a = 00), then sub-
tracting the quantity (CL:)a. The cube root of this incremental lift
coefficient is plotted in figure 4 against angle of attack for each of the
bodies for both values of stagnation pressures. All the points can be
represented reasonably well with a straight line from the origin.

With this information, an empirical relation for the lift of a body
having an arbitrary cross-section shape can be written as follows:


CL = klac + k2m3 (1)

The constant kl is the lift-curve slope at zero angle of attack for
the body under consideration and k2 is the incremental lift constant
of proportionality. These constants can be determined from experimental
data as given in figures 2 and 4.

The form of this equation is similar to that given by Kelly in ref-
erence 1 and Allen in reference 2. In both these theories the first
term of the lift equation represents the potential lift which is propor-
tional to the angle of attack. The second term represents the contribu-
tion due to the viscous cross flow and is proportional to the angle of
attack squared in Allen's theory (ref. 2) and to the angle cubed in
Kelly's theory (ref. 1).

An inspection of the data indicated the possibility of obtaining a
correlation of the previously mentioned constants with certain geometric
shape parameters. Correlations were attempted on the basis of a large
number of parameters with those shown in figure 5 yielding the best over-
all agreement. These parameters do not necessarily have any theoretical
basis; therefore, their use should be limited to configurations within
the range of this report.

The body lift-curve slope at zero angle or ki is shown as a func-

tion of the primary lift section-shape parameter, b_ -P in figure 5.
h IF
This parameter consists of a term b/h which is the reciprocal of the
cross-flow fineness ratio, and a wetted area ratio term, p/F. The
incremental lift constant k2 is shown as a function of a second shape






NACA RM L55E23


parameter (-) --- involving the body breadth and a symmetry

2hl
term where hi is the distance from the bottom of the section to

the centroid of the area. The typical section shown in figure 5 will aid
in identifying the symbols.

In view of the reasonably good correlation obtained, it is expected
that the lift curve could be obtained at this Mach number for other bodies
having the same distribution of cross-sectional area. From the geometry
of the cross sections, the appropriate parameters can be determined, the
constants kl and k2 found from figure 5, and the lift obtained by use
of equation (1).

Since the determination of lift depends on two separate correlations,
a more direct comparison of the correlation method with the experimental
points is presented in figure 6. Here experimental lift is plotted
against angle of attack and compared with that calculated from the corre-
lations as outlined previously.

Using the relation CD CD = CL sin a, the lift correlation was

used to calculate drag due to lift, which is compared with experimental
points in figure 7. There is reasonable agreement at po = 4.5, but at
Po = 7.5 it is somewhat erratic.

In summary, as was noted previously, the bodies having the greatest
breadth produce the highest lift, drag, pitching moment, and lift-drag
ratio, and their ax seems to occur at lower angles of attack. How-

ever, from the foregoing discussion it is apparent that breadth is not
the only factor involved.


Wing-Body Lift Analysis

It might be expected that changes in body lift would be evidenced
to some degree in the lift of the corresponding wing-body combination.
In figure 8 the ratio of the lift-curve slope at a = 00 of the wing-
arbitrary body to that of the wing-circular body is plotted against the
primary lift section-shape parameter. The solid line shows the value
calculated from the primary body lift correlation neglecting mutual
interference. The equation used is:






NACA RM L55E25


CL (W + B) kl klc

CL (W + CB) CL (W + CB)



where kI is now based on the wing area. Within the limits of the experi-
mental accuracy and the assumptions made in the analysis, any difference
between the values given by this line and the experimental points repre-
sents the relative interference effects compared to the wing-circular-
body combination. It can be seen that the circular body and square body
produce the most favorable interference in the presence of the wing. How-
ever, the absolute amount of the interference is not known since no wing-
alone data are available. It is a necessary condition of the correlation
that the line pass through the point for the circular body. It may be seen
from figure 8 that the horizontal ellipse, which has the greatest lift-
curve slope, must have a relatively large unfavorable interference. A
similar attempt for correlation of wing-body lift-drag ratio failed to
show any trend. Although no correlation was shown, it should not neces-
sarily be assumed that none exists, since the experimental accuracy was
nearly as large as the scatter of the data.


CONCLUSIONS


From an experimental investigation at a Mach number of 2.01 of the
aerodynamic characteristics of a series of bodies of arbitrary cross
section tested alone and in combination with a swept wing the following
conclusions are shown:

1. Changes in drag due to changes in body cross-section shape from
the basic circular shape are small and of the same order as the test
accuracy.

2. Significant changes occur in body lift, pitching moment, and drag
due to lift as the body cross-section shape is changed. In general, the
bodies having the greatest breadth or plan-form area had the highest lift,
pitching moment, and drag due to lift.






NACA IM L55E25


3. A set of empirical correlations applicable to the present tests
was found relating the lift produced by a body at angle of attack to
certain geometric body cross-section parameters.


Langley Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., April 29, 1955.


REFERENCES


1. Kelly, Howard R.: The Estimation of Normal-Force, Drag, and Pitching-
Monent Coefficients for Blunt-Based Bodies of Revolution at Large
Angles of Attack. Jour. Aero. Sci.,vol. 21, no. 8, Aug., 1954,
PP. 549-555, 565.

2. Allen, H. Julian, and Perkins, Edward W.: A Study of Effects of Vis-
cosity on Flow Over Slender Inclined Bodies of Revolution. NACA
Rep. 1048, 1951. (Supersedes NACA TN 2044.)





NACA RM L55E23


TABLE I


MODEL DIMENSIONS


length, ft . .
cross-sectional area, sq ft
mean aerodynamic chord, ft
plan-form area, sq ft .


5.5
0.087
0.656
1.145


Body
Body
Wing
Wing


Section geometric constants, in.
Body cross-section shape
b h hI p

Horizontal ellipse 4.90 3.27 1.635 12.94
Diamond 4.46 4.46 2.25 13.12
Triangle 4.50 4.10 1.635 13.74
Inverted triangle 4.50 4.10 2.465 13.74
Tent 3.60 4.17 1.85 13.14
Inverted tent 3.60 4.17 2.32 15.14
Circle 4.00 4.00 2.00 12.58
Square 3.62 5.62 1.81 13.12
900 teardrop 3.89 4.37 2.015 12.73
Inverted 900 teardrop 3.89 4.57 2.355 12.73
45 teardrop 3.49 5.02 2.16 13.60
Inverted 450 teardrop 3.49 5.02 2.86 13.60
Vertical ellipse 3.27 4.90 2.45 12.94



















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NACA RM L55E25


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Typical wing section

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Basic Layout
Circular body shown


Horizontal ellipse


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Body cross section shapes
All radii .8 in unless otherwise noted

Figure i.- Dimensions of the basic wing-circular-body configuration and
the cross sections of the body series. Wing chord plane coincides
with section horizontal center line. All dimensions are in inches.


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NACA RM L55E23


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9 0


-4 -2 0 2 4 6 8 10

Angle of attack, a deg

(af) Drag; Po = 4.5 pounds per square

Figure 2.- Aerodynamic characteristics of the body
of angle of attack.


o Horizontal ellipse


o Diamond

a Triangle

v Inverted triangle

Tent


o Inverted tent

o Circle


o Square

o 90 teardrop


o Inverted 900 teardrop

O 450 teardrop


O Inverted 450 teardrop

0 Vertical ellipse
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14 NACA RM L55E23




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o 0 0 o Horizontal ellipse


o O o Diamond

a0 a Triangle

v 0 v Inverted triangle

o 0 =a Tent


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o O

o O o Circle

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0 o.4 90* teardrop

o 0 .5 o Inverted 900 teardrop

6 0 .2 6 45 teardrop

O 0 .II i Inverted 45" teardrop

0 0 o 0 Vertical ellipse
-4 -2 O 2 4 6 8 10 12
Angle of attack, a, deg

(b) Drag; Po = 7-5 pounds per square inch.

Figure 2.- Continued.






NACA RM L55E25


o 0 o Horizontal ellipse

o 0 -.4 o Diamond

A a Triangle

SO v Inverted triangle

S0 Tent


S O o Inverted tent

0 0 o Circle

[ 0 ]a Square

o 0 o 900 teardrop

o 0 1.2 0 Inverted 90* teardrop

SO0 .8 8 450 teardrop

9 0 .4 9 Inverted 450 teardrop

0 0 0 0 Vertical ellipse

-.4
-4 -2 0 2 4 6 8 10 12
Angle of attack, a, deg

(c) Lift; po = 4.5 pounds per square inch.

Figure 2.- Continued.






NACA RM L55E25


1.2


.8


.4


S0 0 O Horizontal ellipse


o 0 -.4 o Diamond


a 0 ". n a Triangle


v 0 Inverted triangle

S0. 6 Tent
-j

0- 9 O o Inverted tent

47-
So 0 o Circle


.0 a Square


o 0 "o 90* teardrop


SO 1.2 o Inverted 900 teardrop


6 0 .8 6 450 teardrop


9 0 .4 O Inverted 450 teardrop

0 0 0 0 Vertical ellipse


-.4
-4 -2 0 2 4 6 8 10 12
Angle of attack,a,deg

(d) Lift; p = 7-.5 pounds per square inch.


Figure 2.- Continued.





NACA RM L55E23


o 0


o 0



v 0


o 0


o 0

o 0


a 0


o 0


o 0


0 0


9 0

0 0


-4 -2 0 2 4 6 8

Angle of attack, a, deg

(e) Pitching moment; po = 4.5 pounds

Figure 2.- Continued.


10 12


per square inch.


o Horizontal ellipse


o Diamond

a Triangle


v Inverted triangle


o Tent


o Inverted tent


o Circle


o Square


o 90 teardrop


o Inverted 90* teardrop

0 45" teardrop


O Inverted 45" teardrop

0 Vertical ellipse


.4


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NACA RM L55E25


0o O o Horizontal ellipse

o 0 -.I o Diamond

aO A Triangle

v 0 v Inverted triangle

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r- 0 Inverted tent

o 0 o Circle


a 0 ]o Square


o O .4 o 900 teardrop

o 0 .3 o Inverted 900 teardrop

6 O .2 1N6 45" teardrop

O0 I Inverted 450 teardrop

0 0 0 0 Vertical ellipse

-. I
-4 -2 0 2 4 6 8 10 12
Angle of attack, a, deg

(f) Pitching moment; Po = 7.5 pounds per square inch.

Figure 2.- Continued.






NACA RM L55E25


4


3


2





0 o Horizontal ellipse


I o Diaomond


a Triangle


v Inverted triangle

Tent


o Inverted tent


o Circle


3 Square


4 o 90* teardrop


3 o Inverted 90* teardrop


2 6 450 teardrop


O Inverted 450 teardrop


0 0 Vertical ellipse


-I
-4 -2 0 2 4 6 8 10 12
Angle of attack, a deg

(g) Lift-drag ratio; po = 4.5 pounds per square inch.

Figure 2.- Continued.


o 0


o 0


S0


v 0


0 0


n 0


o 0


a 0





o 0





0 0

0 0





NACA RM L55E25


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S0 0 o Horizontal ellipse

o 0 -I o Diamond

^a 0 a Triangle


v 0 v Inverted triangle

S0 a Tent

-Jl0o 0 o Inverted tent
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o 0 o Circle

.I 0 = Square


0 0 4 o 900 teardrop

o 0 3 0 Inverted 90* teardrop

6 O 2 0o 450 teardrop

9 O I O Inverted 45" teardrop

0 0 0 0 Vertical ellipse

-1
-4 -2 0 2 4 6 8 10 12
Angle of attack, a, deg

(h) Lift-drag ratio; po = 7.5 pounds per square inch.

Figure 2.- Concluded.






NACA RM L55E23


.12


.10


.08


.06


.04


.02


S0 0


o 0


S0


v 0


v0


S0


0 0


o 0


o 0
00



o 0
6 0




0 0


o Horizontal ellipse


o Diamond


a Triangle


v Inverted triangle


a Tent


o Inverted tent


o Circle


o Square


o 90 teardrop


o Inverted 90 teardrop


o 45 teardrop


0 Inverted 450 teardrop

0 Vertical ellipse


-4 -2 0 2 4 6 8 10 12

Angle of attack, a,deg


(a) Drag.

Figure 5.- Aerodynamic characteristics of the wing-body combination as a
function of angle of attack. p, = 7.5 pounds per square inch.


.12


.10


08


.06


.04


.02


0






22 NACA RM L55E25


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.4


.3


.2




o0 0 o Horizontal ellipse


o 0 -. I o Diamond


S0 a Triangle


v 0 v Inverted triangle


-, 0 0 Tent

o 0 o Inverted tent


SoO 1 o Circle


S0 .5 sf Square

o 0 .4 o 90' teardrop


o 0 .3 o Inverted 900 teardrop


0 0 .2 0 45" teardrop


0 0 .I O Inverted 450 teardrop

0 0 0 0 Vertical ellipse



-4 -2 0 2 4 6 8 10 12

Angle of attack, a ,deg

(b) Lift.

Figure 5.- Continued.





NACA RM L55E23


.04

oO 0


o 0 -.04


S0 -.08


v 0


0 0




0 0


o 0


S0




0 0
o O




0 0
-O 08


-.04


-.08
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o Horizontal ellipse


o Diamond

A Triangle

v Inverted triangle

o Tent


o Inverted tent

o Circle


o Square


o 900 teardrop


o Inverted 90 teardrop

6 450 teardrop


O Inverted 450 teardrop

o Vertical ellipse


O 2 4 6 8 10 12
Angle of attack,a,deg

(c) Pitching moment.

Figure 5.- Continued.





NACA RM L55E23


5







2




o0 0 o Horizontal ellipse

0 0 0 Diamond

a a Triangle


0v O v Inverted triangle

0O ,o Tent

SO i Inverted tent

o 0 6 o Circle

0 5 t3a Square

0O0 4 o. 90* teardrop

0 0 3 o Inverted 900 teardrop

6 0 2 0 450 teardrop


9 O I 9 Inverted 45* teardrop

0 0 0 0 Vertical ellipse
-4 -2 0 2 4. 6 8 10 12
Angle of attack, a, deg

(d) Lift-drag ratio.

Figure 3.- Concluded.








NACA RM L55E25


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