Department of the Navy

Bureau of Ordnance Contract NOrd -9612

DYNAMIC COEFFICIEtNTS OF THE MK-13 ·TORPEDO

Taras Kiceniuk

Hydrodynamics laboratory CALIFORNIA INSTITUTE OF TECHNOLOGY

Pasadena, Co lifornia

_Report No. E-12. 20 ,

April 1957

Approved by Haskell Shapiro

Department of the Navy Bureau of Ordnance Contract NOrd-9612.

DYNAMIC COEFFICIENTS OF THE MK-13 TORPEDO

Taras Kiceniuk

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-12..2.0 April 1957

Introduction

The forces and moments which act on a submerged body undergoing

unsteady motion can be described in terms of selected dimensionless con-

stant hydrodynamic coefficients if the instantaneous angles of attack are

kept small. To determine the values of these coefficients a model of the

body can be supported from the spindle of a dynamic balance ( 1) in the

flowing stream of a water tunnel working section. This procedure was

carried out for certain coefficients on a 2 -inch diameter model of the Mk-13

torpedo (Fig. 1) using the Angular Dynamic Balance in conjunction with the

High Speed Water Tunnel at the California Institute of Technology, Hydro-

dynamics Laboratory.

Experimental Method and Analysis of Dat<l;_

The method which was used to obtain the dynamic measurements was

the following: Angular motion of small known amplitude and controllable

frequency was imparted to a driving platform by means of a motor-d:.-iven

car.:1. This platform is coupled to a model support spindle throug:• a cali-

brated torsion spring. By allowing the spindle (and model) to rotate very

freely in a bearing-seal assembly, it is possible to determine the dynar.:1ic

moment reactions acting on the model. This requires knowledge of the

amplitude ratio and phase angle of the ensuing motions, quantities which

were determined through the aid o.f optical levers and a pulsing light

source. The reader is directed to Reference 1 for a complete description

of the equipment and experimental method employed in this study.

The dimensionless dynamic coefficients investigated in this pro-

g ram were N ·' N ' - N ·' N 1 which are described in Reference 2, and r • r v • v '

/ r---- ~

14.3

7

------

z 0

--

-o

--

-

j ----

-----c-

5.7

41

6.3

88

7.0

45

Fig

. l

-T

wo

-in

ch

dia

mete

r m

od

el

of

the M

k-1

3 t

orp

ed

o s

ho

win

g

the t

hre

e a

ltern

ati

ve s

up

po

rt p

oin

ts u

sed

in

th

is i

nv

esti

­g

ati

on

. A

ll d

imen

sio

ns

are

in

in

ch

es.

-p

r--

-~

LJ

N

3

which are defined on page 9 of this report. It is to be noted that N 1 - N. 1

r v

is presented in a combined form rather than completely separated, as is

desired. A complete analysis requires that N • 1 be measured in a separate v

program using a balance which imparts a translatory motion to the model

and which measures the moment reaction by means of a supplementary

internal strain gage balance.

Data reduction curves for obtaining the coefficients are presented in

Figures 2. and 3. Figure 2. shows the in-phase component of moment re-

action and Figure 3 shows the quadrature component. The in-phase compo-

nent comprises the spring-like and inertia -like components, whereas the

damping (or velocity dependent) reactions comprise the quadrature compo-

nent. If these reactions are plotted as functions of frequency, certain

hydrodynamic coefficients can be identified with the slopes and intercepts

of the resulting curves. For example, N is found from the y-intercept v

of the in-phase component, while N • is directly related to the slope. From r

the slope of the damping component plot (Fig 3), the linear combination of

coefficients N 1 - N · 1 can be determined. The method of changing sup-r v

port points permits determination in principle at least, of the lateral

forces arising from the angular displacements, velocities and acceler-

ations, but the attainable accuracy is very limited. Instead, use of an

internal strain gage type balance measuring lateral reactions is to be

recommended. Appropriate instrumentation had not been developed at the

time these data were taken, so that the method of changing support point

was used to obtain the original data. This feature has not been exploited

for the reason given above, but the original data have been presented to

permit a more thorough investigation by interested persons.

It should be mentioned that one by-product of this type of

40 1-----+ SOLID SYMBOLS INDICATE --f------1---+----=-"'+--=,.......:qi---____,,..-~::.__--!------l

IMAGE STRUT SHIELD 30

.------,, 0 .06~---r--~---+---+-~~~~~~----=~~----11------=--~-=~~20 ""'-"' I 0

I

~/_,; ~D4r---~,.......:~~~~-~-c~-j---~,.......:~=-~~~~~----1---+----+--~

30 40 50 60 70 100 110

.12

VELOCITY I~ FPS

SOLID SYMBOLS INDICATE ---__. _lso .10

IMAGE STRUT SHIELD ----- ~ =----+ ----- ~ -- ----:-. l----140---- - ---.08

.------, -- - ~ ~I~ I --- ~ v-:- ~30 . - ----~

~

~ !--'"" -v v-: ~ f-" ~

~20--- ~ --~10 ~~_,; .06

L.....:.._j

~ --- ~ ~ I-- ---~ ~ ~ ,_...-

----_-o--!--'"" __.-o---~ ~ ~

.04

o---<J" ..-o--~ ~ ~ ....

~ ~ ::---...-CrTER SUTORT

~~ ~0 FPS ~

.02

0 0 10 20 30 40 50 60 70 80 90 100

JELOCITY I~ FPS .08

~ ;

30 v

110

.06 SOLID SYMBOLS INDICATE -----= ~ _.., 20 _

IMAGE STRUT SHIELD ---== ~ i,....--

~ ~ 10

_.-~ ~ ~ ~---!---" ....-~ ~ ~ ~ ~ ~

~ ~ ~ ~ ,......

~

~ ~ -::::-~ \_ .1 FPS AFT SUTORT -""":;....o'

~

.02

0 0 10 20 30 40 50 60 70 80 90 100

(CYCLES )

2

SQUARE OF FREQUENCY IN SECOND

Fig. 2 -Spring-inertia (in phase) component of moment reaction on a 2 -in. diameter model of the Mk-13 torpedo.

110

4

.12

. 10

.OB

,-----,

CD' "' 06 a-"' · L______j

,----,

CD/ "' 3 ..x;

L____l

r---1

CD/ "' 3 ..x;

L____l

.0 4

.02

0 0

.10

.OB

.06

.04

.02

0 0

.06

.04

.02

0 0

~

~

/ / v

Y~s FOR WARD SU PPORT .,o

I I :p ~ SOLID SYMBOLS INDICATE -.~,«:

IMAGE STRU T SHIELD / 7 / / v ~

/ / v .............. __y:-

/ (""'/ ~ ----I-'"

~ ____.

// y""' ---- ---./ ..............

~~ ~ 'r' ~

y--- 10 -

~ ~ ~ y-o--

~ 0 1- 1-- f-·

2 3 4 5 6 7 8 9 10

~ I~ .,o

~ € ~ .-.!.

CENTER SUPPORT _....../ ~ I I / v--

-------SOLID SY MBOLS INDICATE .......... .,_,o

IMAGE STRUT SHI ELD / ~ v ---~ /. ~ __. ~ 2S-----' --~ ~_..-( ~ ~ ~ ~ 10

~ ~ ~ y--

~ r- 0 ·- -- -- --2 3 4 5 6 7 B 9 10

I AFT SU PPORT

I I SOLID SYMBOLS INDICATE

IMAGE STRUT SHIELD

--~ ~ ;.---·

2 3

lori'S-~ 'J~ --- .--<

v--- ~ --- -~ r---~ ~~------

·- - 0 1-4 5 6 7 B 9 10

(CYCLES)

FREQUENCY, SECOND

II

--

I I

I I

Fig. 3 - Damping {quadrature) component of moment reaction in a 2-in. diameter model of the Mk-13 torpedo.

5

6

investigation is the familiar · static -moment coefficient which is directly

related to N 1 and which can be found from the data reduction curves. v

This serves as a check on the measurements and computations leading to

the final results, since it can be obtained from experiments conducted else-

where with different types of equipment.

Results and Conclusions

The desired coefficients are presented in dimensionless form in

Figures 4, 5, and 6 where they have been plotted against velocity. The

sensitivity of N ' to model support configuration should be noted, as should v

the dependence on velocity. Values obtained by conventional static force

measurements which can be related to N 1 show similar behavior. The v

three curves represent £aired values derived from the processed data

points and corrected for the estimated effect of the spindle shield. This

correction was made by assuming that the image spindle shield contrib-

uted as much influence as did the support spindle shield.

Figure 5 shows the computed value of N ' and, excepting for the bad r

points exhibited by the center -support runs, also shows the independence of

fluid velocity predicted by perfect fluid theory on selected body shapes. Th-e

combined coefficient N '- N.' is the linear combination of two separate r v coefficients which can be analyzed completely by employing the method

outlined above but which has considerable utility in the present combined

form.

> :z -.4

w > ~ > cr w 0

1--.3

:z w :::i' 0 :::i'

2 1- -.2.

~ (j)

u.. 0

1-:z w G :I

i:L u.. w 0 (.)

0

--- --- ----..... .......................

~---- ------ ---.

LEGEND

t::. -- FORWARD SUPPORT 0 -·- CENTER SUPPORT

'----- 0,-- AFT (UPPORT I

0 10 2.0

VELOCITY

4 ---- -

·- - -

NOTE

SOLID SYMBOLS INDICATE IMAGE RUNS .

I I I CURVES REPRESENT FAIRED VALUES

CORRErED FOR !STRUT SHIELD.

I 30 40 50

IN FT./SEC.

Fig. 4 - Coefficient of static moment derivative, N 1, as a function of

tunnel water velocity defined with respect to point of support .

. 07

2 .06

t­z w G tE .05 w 0 (.)

<( i=•04 a:: w z

~ .03 1-z w

~· -

LEGEND

t::. -- FORWARD SUPPORT :::i' 0.02. 2

- o --- CENTER SUPPORT

_j <( :::> tr .01

5

0 0

0 ---AFT SUPPORT

10

l

--' --- --- - ·- --c..::::..; ---·

NOTE

SOLID SYMBOLS INDICATE IMAGE RUNS.

2.0 30 40 50

VELOCITY IN FT./SEC.

Fig. 5 - Virtual moment of inertia coefficient, N . 1 , as a function of tunnel water velocity defined with respelt to point of support.

7

•> z

.... z f-z w 0 l:L lL w 0 0

0 w z co ~ 0 0

.4

.3

.2

.I

0 0

- --L..._ __

---- ---

LEGEND

6-- FORWARD SUPPORT 0 -·-CENTER SUPPORT 0--- AFT SUPPORT

10 20

VELOCITY

8

_!.

-f---- )--

NOTE

IMAGE SHIELD HAS NO PERCEPTIBLE EFFECT ON DATA .

30 40 50

IN FT./SEC.

Fig. 6 - Combined coefficient, N 1 - N · 1 , as a function of tunnel water

velocity defined with res:Pect to point of support.

9

List of Symbols and Abbreviations

The motion of the test body is restricted to the plane of yaw. The

symbols used to describe this motion and the associated hydrodynamic re-

actions on the body are in the greater part identical to those recommended

in the Technical and Research Bulletin N .1-5 of the Society of Naval Arc hi-

tects and Marine Engineers titled "Nomenclature for Treating the Motion

of a Submerged Body through a Fluid". These symbols are marked with

an asterisk(*) in the following list:

*

*

*

*

*

* *

*

*

*

A cross -sectional area of model in square feet.

B coefficient of velocity term in equation N = - IB - B~ - K~ which regards model-spindle assembly as single degree of freedom system undergoing forced oscillations.

I

K

K s

1.

N

N r

N. r

= =

coefficient of acceleration term in above equation due to inertia-like hydrodynamic quantities.

coefficient of displacement term in above equation due to spring-like hydrodynamic quantities.

spring constant of support spindle to which model is fastened.

length of body.

hydrodynamic moment acting on body.

Nr1 (l/2pAiu) coefficient of rotary moment derivative.

N. 1 (l/2pA.t3 ) virtual moment of inertia coefficient r (angular acceleration) .

Nv = Nv1 (l/2pA.lU) coefficient of static moment derivative.

N. = v N. I (l/2p AJ. 2 )

v virtual moment of inertia coefficient (tl•ansverse acceleration).

~ = angular displacement about yaw axis.

r =

' r = v

~ .. ~

=

angular velocity component about yaw axis.

angular acceleration component about yaw axis.

linear velocity component at right angles to longitudinal axis and in the horizontal plane.

List of Symbols and Abbreviations {cont'd)

*

*

v

u

linear acceleration component at right angles to longitudinal axis and in the horizontal plane.

velocity of origin of body relative to the fluid.

p mass density of fluid.

ill = 2.v f circular frequency.

References

1. Stallkamp, John A., "Measurement of Dynamic Coefficients of Ellipsoids", California Institute of Technology, Hydro­dynamics Laboratory Report No. E-35.4, Sept. 1956.

2.. The Society of Naval Architects and Marine Engineers, "Nomenclature for Treating the Motion of a Submerged Body through a Fluid", Research Bulletin N. 1-5.

10

Copy No.

1-4

5-8

9-10

11-13

14-18

19-21

22

23-24

25-26

27-28

29-30

31

32

33

34

35-36

DISTRIBUTION LIST

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

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Copy No.

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58-63

DISTRIBUTION LIST (cont'd)

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