Department of the Navy

Bureau of Ordnance Contract NOrd-16200

Task 1

STATIC FORCE COEFFICIENTS OF

THE BASIC FINNER MISSILE

IN FULLY WETTED FLOW

R. W. Kermeen

Hydrodynamics laboratory CALIFORNIA INSTITUTE OF TECHNOLOGY

Pasadena. California

Report No. E-73.2 September 1957

Department of the Navy Bureau of Ordnance

Contract NOrd-16200 Task I

STATIC FORCE

T H E B A S I C

IN FULLY

COEFFICIENTS

FINNER MISSILE

VlETTED FLOW

R. W. Kermeen

OF

Reproduction in whole or in part is permitted for any purpose of the United States Government

Hydrodynamics Laboratory California Institute of Technology

Pasadena, California

Report No. E-73.2 September 1957

ABSTRACT

The results of force tests of models of the Basic Finner missile

configuration in fully wetted flow in the High Speed Tiater Tunnel are

presented. The static lift, pitching moment and drag were measured for

angles of attack up to 14 degrees and for Reynolds numbers from 0.7 to

8.5 x 106. The results of these tests performed on the static force

balance are in good agreement with coefficients determined from free

flight drag studies in the Controlled Atmosphere Launching Tank and at

the U. s. Naval Ordnance Test Station, Pasadena.

INTRODUCTION

The tests described in this report are one phase of an extensive

program in the Hydrodynamics Laboratory to investigate the hydrody11a.mic

coefficients and free flight characteristics of underwater ballistic

missiles. Other phases of this program are the measurement of the dy­

namic force and moment coefficients of the Basic Finner missile in the

High Speed Water Tunnel on the angular oscillating and linear oscillating

dynamic balances and free flight studies2 in the Controlled Atmosphere

Launching Tank.

The Basic Finner configuration has been tested in the Bureau of

Standards Hind Tunnel and is being used in experimental and ·i:;heoretical

underwater force coefficients and trajectory investigations at the Experi­

mental Towing Tank, Stevens Institute of Technology, the Naval Prov:!.ng

Ground, Dahlgren, Maryland, and the Naval Ordnance Test Station3, Pasadena.

The principal dimensions of the Basic Finner missile configuration

are shown in the sketch, Fig. 1. Models of 1 and 2-inch diameters were used

in these tests. The larger model was fabricated to accommodate the inter­

nal force and moment balances necessary when making dynamic tests and in

order to minimize the effects of strut and shield interference. Because of

the extreme length of the 2-inch diameter model, (20 inches), the l-inch

diameter model was tested in order to minimize the wall effects at high

angles of attack.

EXPERIMENTAL SET-UP AND TEST PROCEDURE

The models were mounted on the three component static force balance4

in the 14-in. diameter closed jet test section of the High Speed Water

Tunne15• The models were supported on a single strut, or spindle, at­

tached near the midpoint of the body. Two types of support configurations

were used. For most of the tests the model support spindle was shielded

from the flow leaving only a small clearance gap between the model and the

spindle shield. This set-up is shown in the lower photograph of Fig. 2.

In order to calibrate the effect of the shield interference on the forces

a second, image, shield was mounted on the opposite side but not touching

the model (upper photograph, Fig. 2), and the tests repeated. The dif­

ference between the runs made 'vith and without image gave the effect of

the addition of the second shield, and, assuming that the shield inter­

ference effects were additive, this correction was subtracted from the

first single shield run.

Because of the large chord of the spindle shield compared to the model

diameter for the l-inch model some of the tests were made with the models

mounted on a partially unshielded spindle in order to reduce strut inter­

ference at large attack angles. The bare portion of the spindle consisted

of a 1/2-in. diameter circular section tapering in one inch to a straight

cylindrical section 0.290 in. in diameter. The total length of the un­

shielded portion of the spindle was 2-in. for the l-in. diameter model and

1-1/2 in. for the two-inch model. With this set-up the· forces and moments

~ere measured on both the model and the unshielded portion of the spindle.

This set-up requires two additional tests in order to calibrate the forces

on the bare spindle and the interference effects. After testing the model

on a single spindle the test was repeated with the model mounted on a simile~

spindle from the opposite tunnel wall, and a second spindle attached to the

force balance with small clearance gap at the model. In this manner the

forces were calibrated for the unshielded portion of the spindle. The inter­

ference effects of the spindle were calibrated in a third test by using an

image spindle as was done with the shielded strut.

~1o types of tests were made. The drag coefficient was determined as

a function of Reynolds number at zero attack angle for water velocities

from 4.0 to 65 fps. The maximum speed was limited by the strength of the

model spindle. The lift, drag, and pitching moment \7ere measured by run­

ning the tunnel at constant velocity and varying the angle of attack of

the model. l';iost of the tests v1ere made with the model pitched in a plane

normal to one set of fins; however, one series of runs was made with the

afterbody of the model indexed 45 degrees relative to the plane of pitch

angle. The results of these tests are shown separately. Details of the

force balance, read-out system, and data handling methods are described in

Refs. 4 and 6. The force and moment data were reduced to dimensionless coefficients

as follows:

Drag coefficient, CD = DRAG

p/2 v2 A

Lift coefficient, CL LIFT =

p/2 v2 A

Pitching moment coefficient, = MO~!ENT ABOUT MIDPOINT p/2 v2 AD

where:

v

p

A

D

::

= =

=

free stream velocity fps

density of water, slugs

cross sectional area of model, ft2

diameter of model, ft

3

The moments are given about the midpoint of the model, 5.00 diameters from

the nose tip. In addition to the shield and strut interference corrections

the drag coefficient was corrected for horizontal buoyancy. This spurious

drag is due to the static pressure gradient along the test section.

RESULTS AND DISCUSSION

The drag coefficient as a function of Reyno~ds number for the Basic

Finner is shown in ffig. 3. Lift, drag, and pitching moment coefficients

are shown as functions of angle of pitch for several Reynolds numbers in

Fig. 4 for the model pitched normal to the fins and in Fig. 5 for the fins indexed at 45 degrees.

4

Drag data from free flight tests at the Naval Ordnance Test Station,

Pasadena, and in the California Institute of Technology Controlled Atmos­

phere Launching Tank, are included in Fig. 3. The drag coefficients re­

ported by Stubstad and Waugh3 of NOTS are for Reynolds numbers from 8 x 104

to 9.6 x 105• The drag coefficients are shown in the figure only at the

upper limits of the Reynolds number ranges. Price2 reports a drag coeffi- .

cient of 0.493 at a Reynolds number of approximately 3.6 x 105 in the free flight test at CIT. The agreement between the water tunnel drag coeffi­

cients and those of NOTS i.s excellent. Though the CIT free flight tests

were made at smaller Reynolds numbers than the tunnel tests these results

are also in close agreement.

The drag coefficient showed a sharp peak at a Reynolds number of

2.7 x 106 for all tests of the 2-inch diameter model. In addition the drag

coefficient increases with increasing Reynolds numbers over the entire range.

This trend is also apparent in the curves of drag coefficient vs attack

angle, .:o"':tg. 4. Lift, drag, and pitching moment coefficients are shown for Reynolds

6 numbers of 1.7, 2.5, 3.4, and 5.1 x 10 for angles of attack up to 14 de-

grees in Fig. 4. The lift and moment show almost no variation with

Reynolds number over this range. I''or the test results shown in Fig. 4, the

model was pitched in a plane normal to one set of fins. In the tests of

lig. 5, the model afterbody· was rotated 45 degrees and the model pitchad

in a plane 45 degrees to all four fins. nith the model pitched 45 degrees

to the plane of the fins, the lift, drag and moment coefficients, as ex­

pected, are less than with the model pitched normal to one set of fins for

angles of attack greater than 5 degrees.

REFERENCES

1 Kiceniuk, Taras, 11An Experimental Determination of Dynamic Coeffi-cients For the Basic Finner Missile by Means of the Angular Dynamic Balance 11 , California Institute of Technology, Hydro­dynamics Laboratory Report No. E-?3.3, June 195?

2 Price, D. A. Jr., 11.r"'ree Body Modeling of the Dynamics of a Fin-Stabi­lized Ballistics Missile in Honspinning Vertical Trajectories", California Institute of Technology, Hydrodynamics Laboratory Report No. E - ?3.1, April 195?.

3 Stubstad, G. W ., .and Tiaugh, J. G., "Drag Coefficient of Fully W'"etted Basic Finner l'.iissile", u. S. Naval Ordnance Test Station, NAVord Report 5269, June 1956.

4 Hotz, G. M., and McGra'l7, J. T., 11The High Speed l7ater Tunnel Three­a omponent Force Balance", California Institute of Technology, Hydrodynamics Laboratory Report No. 4?-2, January 1955.

5

5 Knapp, R. T ., Levy, J ., O'Neill, J. P ., Brorm, F. B., 11The Hydrodynamics Laboratory of the CaJifornia Institute of Technology 11 , Trans. ASME, Vol. ?0, No. 5, pp 43? - 45?, July 1948

6 Kermeen, R. n., "Water Tunnel Tests of NACA 4412 and Walchner Profile ? Hydrofoils in Noncavi tating and Cavitating Flows 11 , California Institute of Technology, Hydrodynamics Laboratory Report No. 4?-5, ? ebruary 1956.

F'IGURE TITLES

Fig. 1 Sketch of the Basic Finner missile configuration.

Fig. 2 One inch diameter Basic Finner model mounted in the High Speed Dater Tunnel. Upper photograph - single shield; lower photograph, image set-up.

Fig. 3 Drag coefficient as a function of Reynolds number for the Basic Finner in fully wetted fiow.

Fig. 4 Lift, drag and pitching moment coefficients for the Basic Finner as a function of angle of attack.

Fig. 5 Lift, drag and pitching moment coefficients for the Basic Finner as a function of attack angle. Model pitched at 45 degrees to plane of fins.

6

MOM

ENT

REFE

REN

CE

CENT

ER

~

J 0

0

-------------------.. ~~~~ 0

0

--.

0 g

• 0

. 0

..:

r<l

"""

-1 ~ I

5.0

00

D

_,

I' '-

-S

UP

PO

RT

SP

IND

LE

r---------~.9eo

.!

1 j

1-1

.00

0 0

r---------------------1

0.0

00

0 _

__

__

__

__

__

__

__

__

__

___j

I

Fig

. 1

. S

ketc

h o

f th

e B

asi

c F

inn

er

mis

sil

e c

on

fig

ura

tio

n.

Fig. 2. One-inch diameter Basic Finner model mounted in the High Speed Water Tunnel. Lower photo - single shield. Upper photo - image setup.

1.0 .8 ' '

.6 '

t­ z w.5

I u lJ

.. ~.4

0 u

~

(.!)

c:

r.3

Q:

0

p 0 u '

.2 I .I

~

"''

L

:---

----,...

..-~I

-C

AL

T z

C

IT

~ N

OT

S3

I

i

----

-1

-.2

.3

.4

.5

.6

.8

1.

0 2

.0

3.0

4.0

5.

0 6.

0 8

.0

RE

YN

OL

DS

N

UM

BE

R

x 1

0 6

Fig

. 3

. D

rag

co

eff

icie

nt

as a

fu

ncti

on

of

Rey

no

lds

nu

mb

er

for

the B

asi

c F

inn

er

in f

ull

y w

ett

ed

flo

w.

4. 8. ..... 1.5 ..... ..... z z z w w w u u u u.. iL u.. u.. u.. u.. UJ w 3. 6. w 0 0

0 u u u

~ 1.0 ..... ..... u.. z a:: :::::; w

0 ~ ~ .:. 2. 4 . 0

0 Re= 2.5xl0 6 u ~

u ~

Re=3.4x 106 ::E

5.1 xl0 6 u

.5

I . 2.

Ol--------~----------+---------~~---------5~--------_.o------~ -I 0 -5 I

a, ATTACK ANGLE

Ll FT

+MOMENT

Fig. 4 . Lift, drag and pitching moment coefficients for the Basic Finner as a function of angle of attack.

o~---------~o-----------~5~--------~----------~5-----------~~o------~

a, ATTACK ANGLE

-I. - 2. ----t------t--------1

-2. -4 . ----1------+----~

BASIC FINNER

-3. -6.

~------~----------+-~----- -4 . -8 .

FIN POSITION- 45°

Fig. 5. Lift, drag and pitching moment coefficients for the Basic Finner as a function of attack angle. Mode l pitched at 45 degrees to plane of fins.

Copy No.

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DISTRIBUTION LIST

Chief, Bureau of Ordnance, Navy Dept., Washington 25, D. C. Attn: Code Re0-3

Chief, Bureau of Ordnance, Navy Dept., Washington 25, D. C. Attn: Code Re U

Chief, Bureau of Ordnance, Navy Dept., Washington 25, D. C. Attn: Code Ad3

Chief, Bureau of Aeronautics, Navy Dept., Washington 25, D. C.

Chief, Bureau of Ships, Navy Dept., Washington 25, D. C.

Chief, Office of Naval Research, Navy Dept., Washington 25, D. C. Attn: Code 438

Commanding Officer, Cffice of Naval Research Branch Office, 1030 East Green Street, Pasadena 1, California

Commanding Officer and Director, David Taylor Model Basin, Washington 7, D. C.

Commanding Officer, U. S. Naval Underwater Ordnance Station, Newport, Rhode Island

Commander, U. S. Naval Ordnance Laboratory, White Oak, Silver Spring, Maryland

Commander, U. S. Naval Ordnance Test Station, Pasadena, California

Commander, U. S. Naval Ordnance Test Station, China Lake, California

Director, Experimental Towing Tank, Stevens Institute of Technology, via: Bureau of Aeronautics Representative c/o Bendix Aviation Corp. , Eclipse -Pioneer Division, Teterboro, New Jersey

Director, Ordnance Research Laboratory, Pennsylvania State University, University Park, Pennsylvania

Alden Hydraulic Laboratory, Worcester Polytechnic Institute, Worcester, .Mass., via: Inspector of Naval Material, 495 Summer Street, Boston 10, Mass.

Librarian, U. S. Naval Postgraduate School, Monterey, Calif.

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DISTRIBUTION LIST (cont'd)

British Joint Services Mission, Navy Staff, via: Chief, Bureau of Ordnance, Navy Dept., Washington 2.5, D. C., Attn: Code AdS

Commander, U. S. Naval Proving Ground, Dahlgren, Virginia

National Advisory Committee for Aeronautics, Langley Memorial Aeronautical Laboratory, Langley Field, Virginia

National Advisory Committee for Aeronautics, Lewis Flight Propulsion Lab., Cleveland Airport, Cleveland, Ohio

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