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::?a~='~O<:: fit: A/&T..S ~~ cy' ~ /f'G .:s / /_o/ . ? / .f1 / /A? T 1 / /-~ c;-.s,-/// i' iHPlfJ!HfTIJ II
/~ .se=C- 2.s-~- Gs · Departrr.ent of the Navy
Naval Ordnance. T.est.Station Contract Nl2.3s·57251
HYDRODYNAMIC COEFFICIENTS OF THE
Report No. E-40 August 28, 195 2
MK 13-2 TORPEDO
By R. L. Waid
Hydrodynamics Labotatory California Institute of Technology
Pasadena, California
, , J. T. lv;. cGraw Project Supervi-sor
' . Copy No. 19
I
i Uf£ lbbh lll!L
HYDRODYNAMIC COEFFICIENTS OF THE
MK 13-2 TORPEDO
ABSTRACT
GANFIRSNTB Ie
Force measurement runs were made on a model MK 13-2 Torpedo
to correct previously reported results for the discrepancies which were
attributable to the interaction of pitching moment on the force me"!-suring
apparatus. The plain body, the body with fins, and the body with a
shroud ring tail were tested at yaw angles of -10 degrees to +1 0 degrees.
Drag-force co\!fficients, cross-force coefficients, and yawing moment
coefficients were calculated and are presented in this report.
INTRODUCTION
The results from experimental force measurements made in the
High Speed Water Tunnel in the past have shown considerable variation
when the model was supported at different points along its length.
The Experimental Towing Tank of the Stevens Institute of Technology
has recently compiled the results of force tests on the l\IJK 13-2.1
The Stevens report contains results from the David Taylor Model
Basin, the Wind Tunnel of the Naval Torpedo Station at Newport, and
the Experimental Towing Tank. Discrepancies arr.ong the various
sources are very obvious as well as the discrepancies in the results
presented by this laboratory. The interaction of pitching moment on
the force measu-ring apparatus has been shown to be the cause of the
discrepancies in our data. 2
An internal pitching moment balance has
been fabricated to allow determination of the pitching moment so that
the other forces can be properly corrected. The laboratory's 2-inch
diameter models of the lVlK 13 have been tested by this technique to
correct the previously published data.
are given in this report·
The results of these tests
i8HI £££14 illiY
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Fig. 1 - Two-inch diameter models of the MK 13-2 Torpedo
MODELS
Three models of the MK 13-2 were tested, Fig. 1.
follows:
1. A plain body without fins, (upper).
2. A body with fins only, (center).
They were as
3. A body with fins and a shroud ring, (lower).
The models were 14. 37 inches long, and they were supported at
42. 45% of the model length aft of the hose. The center of gravity used
for the calculations (0. 44 L aft of the nose) was based on data published 3
by the Bureau of Ordnance.
66242 2££24 £££'!.
-3- 66141 lb£14 I ill£ •
PROCEDURE
The tnodels were tested at yaw angles from +10° to -10° at a
velocity of 30 fps. Drag forces, cross forces, and yawing moments
were obtained. Fitching moment readings were taken to obtain correc
tions which were applied to the other forces.
The model with the shroud ring tail was tested above, at 20, 30,
and 40 fps to observe the effect of velocity upon the force coefficients.
Drag forces were measured at zero degrees yaw for velocities
from 10 to 70 fps.
A duplicate run was made for each test incorporating a dummy
image shield to provide the support interference corrections.
RESULTS
Figures 2, 3, and 4 show the effect of velocity on the force
coefficient~ of the MK 13 with a shroud ring tail. The drag coefficient
curves, Fig. 2, vary as expected at small angles of yaw. Beyond 8°
yaw the curves seem to approach a common curve. The cross-force
coefficients, Fig. 3, show a small increase over the velocities tested.
The moment coefficient curves, Fig. 4, show no definite velocity
trends. Based on a study of these graphs, the remainder of the tests
were conducted at a velocity of 30 fps.
Figures 5 through 7 show the curves of force coefficients for each
individual model.
pari son.
Previously reported data is also included for com-
Drag coefficients at zero angle of yaw are presented in Fig. 8
as a function of Reynolds number. The difference that occurs between
the new and the old data can be entirely accounted for by the pitching
moment.
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0 . 16
0 . 12
0 . 08
0 .04
0 0
.
w ~~ h:'
___-!!!; --~
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2 4 6 8 10
YAW ANGLE-DEGREES
Fig. 2 - The effect of yaw on dr a g coefficient at several velocities for the Mk 13- 2 torpedo with shroud-ring tail
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0 .60
0 . 50
0 .40 / 20
30
VELOCITY (fps)
0 . 30
0 .20
0.10
40/~
~ ~
/ ~
v ~
0 0 2 4 6 8 10 12
YAW ANGLE-DEGREES
Fig. 3 - The effect of yaw on the cross-force coefficient at several velocities for the Mk 13 torpedo with shroud-ring tail
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0.08
0.07
0.06
t::J 0 0.05 (l)
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0.02
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0 0
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VELOCITY(fps)
---- 30
~ 20
l/ 40
v v
/
2 4 6 8 10 12
YAW ANGLE-DEGREES
Fig. 4 - The effect of yaw on the moment coefficient at several velocities for the Mk 13-2 torpedo with shroud-ring tail
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.06 (f) (f) 0. 30 0 cr u 0 z <!
.04 I 0.20 0 <! cr 0
--
v UNPUBLISHED DATA ( 1946) SUPPORT POINT 0.458 £ FR OM NOSE7
1/ Cc F
CCF /
~ <y/ . 0 2 0.10
0
:::;..- /
~ I
_ .....
~ ................... ---0
--- i 0
0 2 4 6 8 10
YAW ANGLE-DEGREES
Fig. 5 - Hydrodynamic coefficients v s yaw for the Mk 13-2 bare hull Reynold s number {based on length ) 3. 6 x 10 6
GGiiilliliUTT H.
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. 16 0.80
.14 0 .70
LL..
u u
. 12 00 _60 z <[
0 u
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. 10 20.50 w
...... u 2 w LL.
lL u w
0 LL. 0
0.40 LL. .08 w w 0 u u a::
0 ...... LL.
2 I
w .06 (f) cnO. 30
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. 04 <[
0.20 <..? <[ a:: 0
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UNPUBLISHED DATA (1946) SUPPORT POINT 0.458 _e FROM NOSE -~/
# CCF
/j ~
/; v ..-r7 :=::--.....
~ V// ~-Co
/ ~ cCG M
------.02 0.10 / /7
~ ~
#
. 0 0 0 2 4 6 8 10
YAW ANGLE-DEGREES
F ig . 6 - Hydrodynamic coeffic ients vs yaw for the M k 13 -2 with plain fins . Reynold s n umbe r (ba s ed on leng th) 3. 6 x 106
I 0 Ill' UU~ II I I& zts
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I ..... z w u
u. LL w 0 u ..... z w ~ 0 ~
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.12
.I 0
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.06
.04
.02
0
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(/) (J) 0. 3 0 0 a:: u . a z <t 1 0.20
(.!)
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0.10
~ 0 0
/ CCF
/ v
/ / ~
V CD
v ~ ~ L L------ CCG
~ M
/ ------v ........
2 4 6 8 10
YAW ANGLE-DEGREES
Fig. 7 - Hydrodynamic coefficients vs yaw for the Mk 13-2 torpedo with a shroud- ring tail
Reynolds number (based on length) 3. 6 x 106
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v- FI N LESS
~ v PL AI N FI N S
r-~~ v- SHROUD
~ v- PLAIN FINS-PUBLISHED DATA (REF.4)
~ ~-L SUPPORT POINT 0 .354.fL
~ FROM NOSE t-- r-- .
~ t--- -r---_ _,_ r-
2 3 4 6 8 10 7 2 3 4
REYNOLDS NUMBER
Fig. 8 - The effect of Reynolds number on the drag coefficient for all three configurations of the Mk 13-2 torpedo, yaw angle 0°
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BIBLIOGRAPHY
l. Jacobs, Winnifred R., "Correlation of Fluid Dynamic Experimental Data for MK ·· 13 Torpedo", Experimental Towing Tank, Stevens Institute of Technology, Report No. 424, January 1952. (Confidential)
2. Kermeen, R. W., "Pitching Moment Balance for the High Speed 'Hater Tunnel", Hydrodynamics Laboratory, California Institute of Technology, Mem.orandum Report, No. EM -12. 4, April 15, 1952. (Confidential)
3. "Torpedo, Mark 13 Type", Ordnance Pamphlet 950, November 30, 1944. (Restricted)
4. Knapp, R. T., "Water Tunnel Tests of the MK 13-1, MK 13-2, MK 13-2A Torpedoes'', Hydraulic Machinery Laboratory, California Institute of Technology, Report No. ND-15, November 9, 1943. (Restricted)
6 U24£ lb£141lf? I