ASE fiLE RM L53K17

RESEARCH MEMORANDU M

TRANSONIC DRAG MEASUREMENTS OF EIGHT BODY -NOSE SHAPES

By William E. Stoney, Jr.

Langley Aeronautical Laboratory

Langley Fie ld, Va.

NATIONAL ADVISORY COMMITTEE

FOR AERONAUTICS
WASHINGTON
,i
February 5, 1954
Declassified October 14, 1957
lV
NACA RM L53Kl7

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

RESEARCH MEMORANDUM

TRANSONIC DRAG MEASUREMENTS OF EIGHT BODY - NOSE SHAPES

By William E . Stoney, Jr.

SUMMARY

Zero-lift drag data were obtained on a series of eight fin-stabili zed

bodies having fineness-ratio-3 noses and differing only in nose shape.
The models we re launched from the Langley helium gun (at the testing
station at Wallops Island, Va.) and data were obtained for Mach numbers
from 0.8 to 1.25 with corresponding Reynolds numbers (based on body
length) of 8 x 10 6 to 15 x 10 6 .

The results were compared with theoretical calculations and with

wind-tunnel measurements. Lowest transonic drag values were obtained
with nose shapes defined by the Von Karman optimum and by a parabola
with its vertex at the nose tip.

INTRODUCTION

At supersonic speeds the pressure drag of the nose of a body may

be an apprec iable part of the total drag . This is especially true for
noses whose fineness ratio is low (less than 5 ) which may be necessary
for various design conditions . Be cause of the importance of nose shape
on the drag of noses, tests were conducted on a series of fineness-
ratio-3 nose shapes for Mach numbers from 1.24 to 3.67 at the Ames
Aeronautical Laboratory and results were presented in reference 1. The
results showed good agreement with second- order theory (ref. 2) above a
Mach number of 1 . 4. Since theoretical calculations, in general, either
gave poor results or could not be made at all at lower Mach numbers,
the present tests were initiated to determine experimentally the nose
pressure drags in the transonic and low supersonic speed range. The
nose shapes selected for testing were chosen because they were the results
of various "optimum calculations," had shown low drag in the tests at
the Ames Laboratory, or were in general use.

The fineness ratio of 3 was chosen so that the resulting drag dif-
ferences would be large enough to measure and to allow direct comparison
2 NACA RM L53Kl7

with the data of reference 1. This fineness ratio is definitely not

recommended for low-drag supersonic bodies.

Data were obtained for a Mach number range from 0.8 to 1.25 and a
Reynolds number range from 8 x 10 6 to 15 x 10 6 based on body length.

The data are presented herein with only brief analysis in order to
expedite their publication.

SYMBOLS

r Radius
Maximum radius

x Distance from nose

Total nose length

length

d maximum diameter

Drag
Q x Maximum frontal area

Friction drag
C~ Q X Maximum frontal area

Friction drag of eQuivalent flat plate

Q x Wetted area

Local pressure - Free - stream static pressure

p
Q

Q dynamic pressure

MODELS AND TESTS

The test configurations are shown in figure 1) and photographs of

all the models are presented in figure 2. The basic configuration
(fig . l(a)) behind the nose section was the same for all models. The
nose section was followed by a cylindrical section of lid = 4 to
which was attached a conical afterbody of lid = 5 . The models were
made of wood and the fins were aluminum.
NACA RM L53Kl7 3

The nose shapes tested were all of fineness ratio 3 and may con-
veniently be divided into three groups (fig. l(b)).

Power Series

These nose shapes are defined by the equation

r (0 < x ~ 1)

The three noses of the power series had values of n = 1, 3/4, and 1/2.
Note that for n = 1/2 the equation describes a parabola with the
vertex at x = o.

Parabolic Series

These meridians are defined by the equation

r = 2x - Kx2 (0 < x ~ 1)
2 K

Three noses of the parabolic series having the following values of K

were tested . The cone may also be considered a member of thi s family
with K = 0

Parabolic
K 1
~P
4
K 0·75
~P
2
K 0·5
4 NACA RM L53Kl7

Haack Series

The meridians of the Haack series are defined as follows

r ! sin 2¢ + C sin 3¢
2

where

cos- l (1 - 2x) (0 ;S x ;S 1)

Two noses having the following values of C were t ested :

Von Karman
C =0
L-V Haack
C = 1/3
The Von Karman
nose is also called the L- D Haack nose in reference 1.
The letters L-D and L-V refer to the boundary conditions for which the
drag was minimized. The former signifies given length and diameter and
the latter given length and volume ..

The models were fired from the Langley helium gun (at the testing
station at Wallops Island, Va.) which is described in reference 3 and
the data were reduced in the manner described in reference 4. Data
were obtained over a range of Mach numbers from 0.8 to 1.25 and for
Reynolds numbers (based on body length) between 8 x 106 and 15 x 10 6 .

The accuracy of the data as estimated from experience with previous

models is of the order of ±0.008 in total CD and ±0.005 in M.

RESULTS AND DISCUSSION

Total-Configuration Drag

The drag coefficients for the test configurations are presented as

a function of Mach number in figure 3. Also shown are values of the
body-plus-fin- friction drag coefficients calculated by the method of
NACA RM L53K17 5

Van Driest (ref. 5) assuming completely turbulent boundary- layer flow.

The difference between these friction values and the subsonic (M ~ 0.8)
total-drag curves is about the same for all models (Cd ~ 0 . 025) except
for the conical nose body. This constant difference may be attributed
to base pressure drag and to body pressure drag caused by the cutoff
base. The drag difference noted indicates base pressure coefficients
of the order of P = -0 . 13 and thus close to the value of P = -0.125
obtained on the base of a cylindrical afterbody (ref . 6). This is rea-
sonable since the present afterbody is long and its slope is small
(1. 63 0 ). The higher subsonic drag of the conical model may be due to
additional pressure drag caused by the sharp angle (9 . 48 0 ) at the nose-
cylinder juncture. It is reasonable to assume from the above compari-
s ons that all the models had turbulent boundary- layer flow throughout
the test Mach number range .

Nose Pressure Drag

In order to present the test results i n a form more applicable to

general use and to allow compari son wi th the data of reference 1, it is
necessary to separate the nose pressure drags from the drags of the
total configurations . The nose pressure drags obtai ned are directly
applicable to the drag of such noses on any body shape at supersonic
speeds although their effect on t he f low f i eld over the afterbody must
be considered i n a tot al- drag e s timation . At t ransoni c and subsonic
speeds the isolated nose drags deri ved herein wil l be correct only for
bodies which approximate the test configuration.

In order to obtain these nose pressure drags the following assump-

tions were made. These per tain to the conditions at supersonic speeds.

(1) The different pressure f i elds of the vari ous nose shapes do not
appreciably affect the pressure drags of the afterbody, fins, or base.
This relative independence of the afterbody pressures appears reasonable
from the linear calculati ons of reference 7 since the nose is separated
from the afterbody and tai l by a fineness - ratio - 4 cylinder. The effect
on total drag of even large percentage changes in fin pressure drag
would be small since their isolated pressure drag i s of the order of
7 percent of the total supersonic drag .

(2) The sum of the afterbody, fin, and base drags, which has been
assumed the same for all models , may be obtained by subtracting a known
nose pressure drag from any of the models . The tare drag coefficient
so obtained does not vary appreci ably with Mach number in the supersonic
range.

The tare drag presented in figure 4 is equal to the sum of the

afterbody, fin, and base pressure drags . The value at M = 1.2 was
6 NACA RM L53Kl7

obtained by subtracting from the total drag the sum of the calculated
friction drag and the pressure drag for the cone obtained by the theo-
retical calculations of reference 8. The subsonic level was assumed to
be the constant value of 0.025 shown previously. The curve was com-
pleted by fairing the M = 1.2 value to peak-drag and drag-rise Mach
numbers estimated from the data obtained with a configuration having
the same fineness - ratio-5 afterbody as the present models but headed
by a fineness - ratio - 7.13 parabolic nose (ref. 4). The value of the
tare drag at M = 1.2 obtained in the above manner agreed well with
that obtained from this reference body.

The tare drag having been determined, the procedure was reversed
and the nose pressure drags were obtained for all the noses tested.
The resulting drags are shown in figure 5 attached to and compared with
the higher Mach number da ta of reference 1 and with the theoretical
values obtained by the method of reference 2. The lines connecting the
data from reference 1 have been faired a nd in some cases represent a
compromise between the two sets of data.

The agreement of the data obtained in the present tests with those
of reference 1 is within the combined accuracy of the two test tech-
niques for all models with the exception of the x l / 2 body. The agree-
ment of the parabo·l ic series with the second- order calculations of ref-
erence 2 appears to be quite good also.

The drag coefficients shown are based on the maximum frontal area .
To allow easy estimations of the relative effect of the various nose
shapes on the friction drag and on the drag per unit volume, the non-
dimensional factors obtained from the following equations are presented
in the subsequent table.

CDf
Cf
1 11
42/d = 0 r dx (1)

For bodies of normal fineness ratio the expression of equation (1)

gives substantially the same numbers as the more usual equation

CDf J;vetted area

Cf Frontal area
NACA RM L53Kl7 7

Equation (1) is, however, the correct one in that it sums only the drag
components of the friction force, whereas the other includes those com-
ponents normal to the axis of symmetry as well.

The nondimensional factors determined by the above equations are:

Nose shapes

Cone 0·500 0·333

x 3/ 4 ·571 .400
xl / 2 .667 ·500
Parabolic .667 ·534
q . 600 . 445
4
~ . 556 · 393
2
L-V Haack · 700 · 562
Von Karman . 653 · 500

CONCLUDING REMARKS

The present results together with the results . of NACA RM A52H28

indicate that the Von Karman
and the x l / 2 noses have the lowest drag
over most of the Mach number range eM = 0 . 8 to 2). While the x l / 2 nose
apparently had a low initial drag rise, its drag continues to rise slowly
over most of the Mach number range shown. This appears to be a result
of its extremely blunt apex. The drag of the Von Karman nose however
peaks at about M = 1.4, after which Mach number it decreases with
increasing M. This characteristic of decreasing drag coefficient at
high supersonic Mach numbers is also shown by the x 3/ 4 nose. In fact
this nose (x3/~ approximates closely that derived for minimum hypersonic
drag for given length and diameter (see NACA RM A52H28) and it is inter-
esting to note that in the limit as x ~ 0 the equation for the
Von Karman nose approaches r = x 3 / 4 (where r is the ratio of radius
to maximum radius and x is the ratio of the distance from the nose to
total nose length) . The Von Karman
nose has the further advantage of
fairing smoothly into the body behind it which apparently is a factor
in obtaining low subsonic drag and high drag-rise Mach numbers. It
also seems reasonable to assume that this factor would also tend to
8 NACA RM L5~Kl7

reduce the interference drag of the nose on an afterbody in comparison

with noses having finite slopes at the nose-afterbody juncture.

These tests of noses of fineness ratio 3 are not intended to imply

that this fineness ratio is considered a good one from the point of
view of low supersonic drag. The effect of fineness ratio on the com-
parative results of these noses is not known; however, it appears rea-
sonable to assume that, for the low fineness ratios where the pressure
drag will pe fairly high (fineness ratio of approximately 5 or 6), the
comparisons measured here at a fineness ratio of 3 will be essentially
correct; above fineness ratios of 5 or 6, the pressure drag becomes
less important and so probably does nose shape.

Langley Aeronautical Laboratory,

National Advisory Committee for Aeronautics,
Langley Field, Va., November 3, 1953.
2V
NACA RM L53Kl7 9

REFERENCES

1. Perkins, Edward W., and Jorgensen, Leland H.: Investigation of the

Drag of Various Axially Symmetric Nose Shapes of Fineness Ratio 3
for Mach Numbers From 1.24 to 3.67. NACA RM A52H2B, 1952.

2. Van Dyke, Milton Denaan: Practical Calculation of Second-Order Super-

sonic Flow Past Nonlifting Bodi€3 of Revolution. NACA TN 2744,
1952 .

3. Hall, James Rudyard: Comparison of Free-Flight Measurements of the

Zero -Lift Drag Rise of Six Airplane Configurations and Their
Equivalent Bodies of Revolution at Transonic Speeds. NACA
RM L53J21a, 1953.

4. Stoney, William E., Jr.: Same Experimental Effects of Afterbody

Shape on the Zero-Lift Drag of Bodies for Mach Numbers Between o.B
to 1.3. NACA RM L53I01, 1953.

5. Van Driest, E. R.: Turbulent Boundary Layer in Compressible Fluids.

Jour. Aero. Sci., vol. lB, no. 3, Mar. 1951, pp. 145-160, 216.

6. Katz, Ellis R., and Stoney, William E., Jr.: Base Pressures Measured
on Several Parabolic-Arc Bodies of Revolution in Free Flight at
Mach Numbers from o.B to 1.4 and at Large Reynolds Numbers. NACA
RM L5lF29, 1951.

7. Fr aenke 1 , L. E. : The Theoretical Wave Drag of Some Bodies of Revolu-

tion. Rep. No. Aero. 2420, British R.A.E., May 1951.

B. Staff of the Computing Section, Center of Analysis (Under Direction

of Zdeneck Kopal) : Tables of Supersonic Flow Around Cones. Tech.
Rep. Nc. 1, M.l .T., 1947.
10 NACA RM L53Kl7

1-?oI~~-<
- 2/d ' 4 --~~ E::-----
IooEI 2/d 5---~
:<

~--------------18" ------------------------~

(a) Basic configuration.

__
-
----
---- ----- ~
_-- - --
II
I
- I
I
_ ----.l

Payabolo.
3/4 P
1/2

L-V HaacK ~ _-
Von Kc{rman _-- - - - - - - -
----- I
I
I
I
I
I
-----l

(b) Nose shapes.

Figure 1.- Test configurations.

NACA RM L53Kl7 11

~P !p
4 2

Cone L-V Haack Von K8.rmB.n Parabola L-79889

Figure 2.- Photographs of models.
12 NACA RM L53K17

CD
.2

.1
Friction dTag
r!-lm

0.7 .8 .9 1.0 1.1 1.2 1.3

M
(a) Power series .

.4 H+H I

1Al:t1
1/2P
.3 3/4P
Parabola.
CD
.2

.1
f,.kti.on drag
l-tttl

0.7 .8 .9 1.0 1.1 1.2 1.3

M
(b) Parabolic series.

Figure 3.- Total-configuration drag coefficients.

3V
NACA RM L53Kl7 13

.3
CD L-V HaacK
.2 Von Karman
Friction draB

.1

°.7 .8 .9 1.0 1.1 1.2 1.3

M
(c) Haack series.

Figure 3.- Concluded •

•1

CD

~7 .8 .9 1.0 1.1 1.2 1.3

M
Figure 4 .- Tare drag .