Effect of bilge keels and a bulbous bow on bilge vortices

EFFECT OF BILGE KEELS

AND A BULBOUS BOW

ON BILGE VORTICES

by

Jean-Claude Tatinclaux

This Research Was Carried Out Under The Naval Ship Systems Command General Hydrornechanics

Research Program Administered by the Naval Ship Research and Development Center.

Prepared Under the Office of Naval Research

Contract Nonr-1611 (05)

DATUMI

Bibliotheok van de

Afdeng Scekcw- *

Stheevartkunde

-

hWTcche c'O

De4#

uHR Report No. 107

Iowa Institute of Hydraulic Research

The University of Iowa

Iowa City, Iowa

February 1968

This document has been approved for public release and sale; its distribution is unlimited.

ABSTRACT

Wind-tunnel experiments were performed in order to investigate the influence of bilge-keels and of a bulbous bow on the drag induced by vortices generated at the bilges of an ogive. It was found that as the ratio of the height of the keels to the maximum width of the ogive is

increased from O to 0.08, the vortical drag increases from 2 to 11

per-cent of the surface drag. The presence of a bulbous bow does not appear

to affect the vortical drag of a model with a fine entrance, such as the one studied here other investigators claith -the contrary when the

NOMENCLATURE

a radius of a circular vortex core

b half the distance between two parallel vortices half the distance between two conjugate points

DE drag induced by a system of n pairs of vortices

D reference drag, frictional resistance of body

E total energy per unit length of a system of n vortices

E0 energy per unit length of the region exterior to the vortex cores

Ec internal energy per unit length of a vortex core

H local total head

H0 total head of the uniform stream

h maximum width of the ogive

hk height of a bilge keel

I moment of inertia

k vortex strength

L length of the ogive

R radius of a circle enclosing the system of vortices

R radius of curvature at bilge

R Reynolds number UL r,6 polar coordinates U mean-flow velocity W complex potential Z complex variable r circulation

V kinematic viscosity of the fluid

potential function stream function

p fluid density

Previous reports [1,21* have described investigations of the formation of vortices at the bilges of a sharp-edged ogive and the drag

that they induce. Ir1 addition, the influence of the bilge

radius-of-cur-vature on the generation of the vortices and on their induced drag was

studied. The drag was found to decrease rapidly from 1)4 to 2 percent of

the surface drag when the ratio of the radius of curvature to the maxi-mum width of the ogive was increased from O to 0.12.

In order to make this experimental study more complete and com-prehensive, it was decided to consider the effect of bilge keels and of

a bulbous bow. This report presents the results of these complementary

investigations.

Effect of Bilge Keels

The presence of keels along the bilges of actual ships has the primary purpose of diminishing the roll amplitudes. They are in general located along a mean flow line determined by testing a ship-model in a

towing-tank. In the present case, the tested model was a simple ogive,

and hence the only possible location of the bilge keels was along the four edges, as is shown in Fig. 1. Each keel was made of a thin sheet of brass which was glued in a groove cut at _{)45° along each bilge of the}

dou-ble model. The model's ratio of radius-of-curvature R to model width

c

h is R ¡h = 0.12.

C

The measurements of the total head and of the velocity

compo-nent in the transverse plane at the stern were obtained using the

five-hole probe described in [1]. This previous work had shown that it gave

results in agreement with those obtained with a hot-wire aneinonieter, and

its use is simpler. The results obtained when no bilge keels were present

[2] are repeated here in Figs. 2 and 3 for comparison.

Effect of Bilge Keels and a Bulbous Bow on

Bilge Vortices

Introduction

-2-Two heights, h1, of bilge keel were tested: hK/h = 0.O1 and

0.08. The results of the measurements are presented in Figs. 1 and 6 _as lines of constant total head and in Figs. 5 and

7,

in which the component of the velocity vector in the transverse plane at the stern has been

drawn at numerous points. It can be readily seen from these figures that

the vortex increases in size as well as in strength when the keel height

is increased. It can be noted also that the vortex has a tendency to

de-part farther from the ogive, and therefore there is an increase in the

para-meter b, the distance of the center of the vortex to the XZ-olane of

slrrn-metry of the model. A very interesting point to note in Fig. 7 is the

presence of a second smaller vortex in addition to the larger one which was observed in the previous experiments. This second vortex appears to be much weaker than the primary one. However, comparison of Figs. 6 and

7 shows that this vortex corresponds to the outside zone of low total head,

which was observed in the previous study and for which no satisfactory

explanation could be given. Therefore it is reasonable to believe that,

although this second vortex was strong enough to produce a noticeable reduction in pressure, it was too weak to be revealed in the earlier study by measuring the velocitr of the induced secondary flow. Measure-ment of the circulation around each vortex shows that for the primary and

stronger vortex = 0.022, and for the smaller one F2/UL = -0.0055

if the circulation is measured around a path enclosing both vortices, the value of the circulation, which should be equal to (r1 + r2)/UL = 0.0187,

is /TJL = 0.0l8L. This provides a very good check on the measurements.

Tagori [3], in a recent paper, presented the results of flow visualization of bilge vortices, using a tuft grid and pairs of tufts. He

found that a set of conical vortices is generated at the forebottom of the model as well as another set of large conical vortices at the afterbody. These results confirm those presented in this report. It seems that the bow vortices mentioned by Tagori are the weaker ones discussed above, while the stern vortices he observed correspond to the stronger ones.

Because of the presence of a second vortex, the formula previous ly derived [i] for the drag induced by bilge vortices is not valid, since it treated the case of a single vortex at each bilge. Accordingly the

-3-of various strengths and sizes and is presented in the Appendix. The

re-suits of the drag computations (Eq. of the Appendix) are given in Table 1, together with the experimental data for a. , the radius of the ith vortex b. , the distance from the center of the ith vortex to the

XZ-i

plane of symmetry of the ogive d., the half-distance between two pairs of ith vortices (see Fig. li); and r., the circulation around the ith vortex, with i = 1,2 in the present case. The drag used as a reference is the estimated surface drag of the ogive for the Reynolds number at which the experiments were performed, = 106.

Table 1. Variation of vortical drag with height of bilge keel

It is concluded from the foregoing results that the introduction of bilge keels is responsible for an increase in the strength and size of the bilge vortices, indicated by an increase in r and 'a", respectively. It

also causes the vortices to depart farther from the ogive, as is indicated by the increase in the value of the parameter "b". The most important effect is a large increase in the vortical drag. A secondary, but still important effect of the bilge keels is that they strengthen the bow vortices enough that they can be detected and visualized. This also explains the presence of the outer region of low pressure which had been observed in the previous

series of experiments.

Effect of a Bulbous Bow

The bulbous bow, introduced by Inui in 1962 [] to reduce the wave-making drag of a ship, has been the subject of numerous investigations, especi1ly by Japanese researchers [5, 6,

1].

Even at very low Froude

nuin-bers, when there is practically no wave-making drag, it has been found that the presence of a bulbous bow reduces the total drag. _{Consequently,}

bk/h al

:.

r2/UL _DE/D 0 0.08 0.0125 0.0625 0.0625 0.0375 0.1125 0.1625 0.158 0.l13 0.155 -0.0125 -0.338 -0.205 0.0113 0.0180 0.02)42 --0.0055 0.021 0.060 0.11)4

-4-.

it has been believed that the drag reduction was due to a diminution in

the vorticFil drag. Recent studies by Takahei [5] on flow around the

en-trance of full-huJl forms showed that, after introducing a bulbous bow,

the trailing vortices become hardly noticeable, though their presence was readily detectable when the bow was without a bulb.

The present study was therefore continued by attaching a bulb, made of plasticene, at the bow of the ogive with bilge keels of height

hk/h = 0.08. This bulb was made according to the shape shown in Inui's

paper [)4]. see Fig. 8. The usual measurements of the total head and of

the velocity component in the transverse plane at the stern were performed and the results are presented in Figs. 9 and lO. From these figures, which are essentially identical to Figs. 6 and , it can only be concluded that

the bulbous bow did not affect the generation of bilge vortices on this

model. T'ne results of the computations of the circulation around the

vortices obtained with the ogive with bulbous bow are given in Table 2 together with the values of the parameters a., b., and d., (i = 1,2).

The results obtained for the ogive without bulbous bow are repeated in this table for comparison.

Table 2. Effect of bulbous bow on vortical drag

It should be noted that the present experiments were carried out on an ogive which had a bow with a fine entrance, while the experiments conducted by Takahei [5], which showed a decrease in the strength of the

bilge vortices, dealt with a blunt-bowed oil-tanker model.

a 1 ft. b 1 ft. d 1 ft. a 2 ft. b 2 ft. d 2 ft. r1/uL r2/TJL _DE/D Plain Bow 0.0625 0.1625 0.155 0.0125 0.338 0.205 0.0242 -0.0055 0.111 Bul-bous Bow 0.0625 0.1625 0.155 0.0125 0.338 0.205 0.0238 -0.0050 0.110

-5-ACKNOWLMENTS

The investigation described in this reDort was conducted at the Iowa Institute of Hydraulic Research under the sponsorship of the Bureau of Ships Fundamental Hydromechanics Program, Project Nonr 1611(05), tech-nically a±ninistered by the Naval Ship Research and Development Center.

The guidance, and helpful advice of Dr. L. Landweber, the prin-cipal investigator, are gratefully acknowledged.

-6--REFERENCES

J. C. Tatinclaux, "Experimental and Analytical Determination of the Induced Drag Due to Bilge Vortices," I.I.H.R. Progress Report to

D.T.M.B. November

_1966.

J. C. Tatinclaux, "Influence of the Radius of Curvature on the Drag Induced by Bilge Vortices" I.I,H.R. Report No.

102,

Iowa Institute

of Hydraulic Research, The University of Iowa, Iowa City, Iowa.

February

_1961.

T. Tagori, 'lnvestigations on Vortices Generated at the Bilge," 11th International Towing Tank Conference,

1961.

[)4] T. Inui, "Wave-Making Resistance of Ships," Transactions of the Soci-ety of Naval Architects and Marine Engineers Volume

70, 1962.

T. Takahei, "Investigations on the Flow around the Entrances of Full Hull Form," 11th International Towing Tank Conference, Tokyo,

1967.

H. Maruo and M. Ikehata, "Observation of the Flow Pattern around Ship Models," 11th International Towing Tank Conference, Tokyo,

1961.

H. Sasajiina and I. Tanaka, "On Flow Field near Stern of Full Ship

iO.

z-z.

r e il jl iO.

Z-Z.

=r. e j2 j2 -T-APPENDIX

Drag Induced by a System of n Bilge Vortices

The drag induced by a system of n pairs of vortices is equal

to the kinetic energy, E, per unit length of filament of these n pairs

of vortices. If the vortices are assumed to be Pankine longitudinal

vor-tices, their kinetic energy E is equal to the sum of the energy

Ec

associated with the rotational vortex cores and of the kinetic energy

E0 of the irrotational region exterior to the rotational cores.

In the case of vortices generated at the bilges of a ship,

as-suming that the free surface acts like a rigid wall, or in the case of a double model studied in a wind-tunnel, such as the one investigated in this report, the energy E0 _{is equal to half the kinetic energy of the}

system of 1n _{vortices formed by the n pairs generated at the bilges}

and of their image system with respect to the free surface, or in the case

of the double model, formed by n vortices generated at each of the four

bilges. Such a system of 1n vortices is shown in Fig. 12, where n

has been taken equal to 2 for the sake of clarity.

The expression for the energy E0 will now be derived using

potential theory. If it is assumed that the complex potential _{w(P) of}

the irrotational region is identical to that due to n systems of 4

point-vortices located at

C.

with i = 1,14 and

j

= l,n., then

n (z-z. )(z-z.

w(P) = -i k. log

_{T.2)(z-zT -}

(P) + i (P)

where k. is the strength of a vortex of the jth group, z is the complex

coordinate of the point P,

z.

_{is the complex coordinate of the point}

C.., (P) is the potential function at point P, and i(P) is the

stream function at point P.

The following notation is introduced:

and iO.

z-z.

=r. e J3 j3 j3 iO.

z-z.

r e 324 324

-8-where _r.k (k = l,2,3,)-i) is the distance between the point P and the

point _C.k and (k = l,2,3,) is the angle between an horizontal

axis and the radius vector

0jk (See Fig. II). The potential and stream

functions can then be expressed as

n n + ) = _k

_[(e

- e

₎

+ (e

- es)] =.

j=l

ji j2

j

n r. r. n

=- k.[log+log]=

( + J r

j=l

jl

j2 r.

The potential functions . = k.(. - O ) and = -k. log are

ji j ji j2

ji

j

associated with the first pair

(OjOj)

of the jth group of four vortices,

and the functions . = k.(O. - O. ) and . = -k. log

j3

are

as-j2 j j3 j)4 j2 j r.

sociated with the second pair (O3O)) where represents the

closed streamline which encloses the core of the ith vortex of the jth grour, i.e. it is the streamline which forms the boundary between the ro-tational region of the core and the outer irroro-tational zone. Therefore the stream function i4 is constant along each In the case of a

simple system of two vortices these streamlines have a circular shape, but in the present case, because of the interaction between the various vortices of different strength and sizes, they have an unknown oval shape.

From Green's first identity it is well known that the kinetic

energy 2E0 of the region exterior to the vortex cores can be expressed as

2E0 = 11m d (1)

with the restriction that the region enclosed by the path of integration c be a simply connected domain in which the functions and are

regular and single valued. To meet these requirements the contour of

inte-gration has been chosen as shown in Fig. 12, where the ovals

U.

have been represented by circles as an approximation to the unknown

shapes of the vortex cores.

Because of symmetry the total strength of the system of vortices is equal to zero, and therefore the induced velocity vanishe when R

goes to infinity, fast enough for the integral of d t around the circle

of radius R to go to zero when R approaches infinity. Thus

um

d O

R

-Furthermore, since the closed curves O.. are streamlines, i.e. ii is

constant and di = O along them, then

i=l,

°ij

j =

l,n

The expression for the kinetic energy 2E0 of the irrotational region is then reduced to the simple form

t I 2E0 = A.1 d + AI + d +

At3

d

and because of' the symmetry of the system of 1n vortices the drag induced

by the formation of n vortices at each bilge of a ship is given by

A. At. n

rr2

L)

d+

dJ

(2)

j1

A.1 A'12 or -9-,

Expanding this expression in terms of the various components of the potential and stream functions, we get

A. .12 E0 = .

{ J

q.i

l

+ d ml + m2 +

m1

il A'

jl

n n J ( + _{2)d[ (} +

_m2]

rnl ml A'12 q=1

with and A n n n

r

.12

E0=

[J

( + )d( +

j=l q1 ml

al q2 imi m2 A'

JAT21 +

2)d( +

_m2]

il

=k(S

-e

ql q ql q2

=k(e

-e

q2 q q3 q1 -lo-and rml j

=-k Log

ml m r m2 r m3 i

=-k Log

in2 m r rs

For any value of q the potential function

q2 takes the

same value at any point along A11Al2 as at the same point along A'2A'1

since the quantity (0q3 - is not affected b.T the rotation around

O. and therefore (O - e ) = (e - e Furthermore, since

31 q3

q1-11

q3

the paths A.1A.2 and A'12A'.1 are described in opposite senses, and

the functions J and P take identical values along the two paths

ml m2 of integration, we have A A'

JAq2 d(ml

+ m2 =

-J,3q

d(mi +

m2 Al2

A'1

n n n

[J

1d(+

)+

I d( + )] rs2 A' ql ml in2

ql rnl

ji

It can be shown that for similar reasons, when q j we also have

A A' j2 il

f

d( + m2 = -

J,q1 d(

ml + rn2 JA ql ml il

-11--Finally the only terras which contribute to the expression of the kinetic

energy E0 are those for which q = j. The exoression to be evaluated

is then: A. A'. ji E =

_I

JA d( + + JA d( + )1 ml in2 0 2

i

ml

ra2j

j=i m=l

L

j2

Along the path A.1A.2 the value of the potential function is = _k

r

and along tiae path

A'.2A'.1,

= +k rr.

Therefore, since the 's are single valued,

A. ji k r

1d(

₊

j=l

ra=i A

ml

m2 o r and

j2

n n

E0

= rp

k{1(A1)

-

ç(A2)

₊

_{m2(Aji) -}

_m2(Aj2)]

j=i m=i

Furthermore since the system of vortices is symmetric with respect to the

vertical Z-axis then:

mlji =

mlj2

m2jl =

m2j2

so that n n

E0=2rrp

k[P

(A

)+

(A )]

ji m=i

j

ml

ji

m2

j2

(3)

Now let us assume that the streamlines bounding the vortices are

E0 = -lTp

kk

j=l înl

r,

_i

with k. where i =

-12-and 3 -12-and , as shown in Fig. II. We then get

r(A1)

k _(a

_1m

a )2 + [(b

mm

_-C )

-

(b.-aj]2 4J _(A. ) = -k Log ml ji n

-Log

(a d )2 + [(t -c ) + (t -ai]2 .1 m

mm

j j r (A.2) k (a +d )2 + [(t -c ) + (t.-aj]2 m3 j m

jm

mm

j j = -k Log m (A )

= -Log

(a +a

)2 _{+ [(t -c} ) - (t -a m)4

ji

j

m

m m

j j with _{Cm = bm}

_/b2

- a2 therefore Log (dj+dm)2 + [/t a

+-a1)]2

i (d.+d )2 + [/t 2-a 2 - (b -a )]2 j m

mm

j j J (d.-d )2 + [/t -a -j m m m j _j Log (d.-d )2 + [¡b -a + (t.-aj]2 j m

vn m

j j

is the Circulation around the ith vortex. +

We have to add to this expression the kinetic energy of the vor-tex cores to obtain the total kinetic energy of the entire system. Assuming that the oval shaped cores of the vortices can be approximated by circles,

and that the vorticity is constant within the cores for each type of

vortex, then each element of a core has a constant angular velocity w./2.

Hence each core is rotating as a solid body with angular velocity

and has a kinetic energy per unit length E. = 1/2 I.(W./2)2 where I. is the moment of inertia

a. I. = j 2 a. 2 E . = lrP 16

r

i

-13-If r = îra2W is the circulation of each vortex then

J J J

pl 2

cj -

i6n

and the total energy of the system is then

E = E0

2E1

or n r.2 n n (a -d

)2

+ [1b 2-a

2_

_(bai]2

V J F F [Log m / in m 2 " (d -d

)2

+ [/

2-a 2 + (b -a )]2

j=i m1

_jm

Vm

in

jj

(d.+a )2 + [/ 2-a 2 + (b.-a )]2

j in

im

m

j

Log

(d +d )2 + [/b2_ani2

_jm

_{- (b._a)]2 )}

+

The formula just derived can be checked against the _{one derived in a} pre-vious report [i] by taking n eauai to unity. For n = 1, equation (14)

gives

E PF2

ti

b-a +

Ç2

(-b+a + /b2-a2)2 +

2x

J-+Log

+Log

[ -b+a +

2a2

2

(b-a + 2a22 + 14d2

which is precisely the formula obtained in the aforementioned report.

It is to be noted that, in the present derivation _{of the vortical}

drag, two assumptions were made: _{(i) The potential outside the}

vortex-cores was identical to the potential of a system of point vortices, (2) The cores of the vortices could be reoresented by circles _{containing a}

constant vorticity distribution. _{These two assumptions are obviously}

in-compatible and the final expression for the vortical drag, _{is, therefore,}

only an approximation. _{It was then attempted to determine the vorticity}

dis-tribution inside the cores which would be compatible with the first as-sumption; unfortunately this attempt was unsuccessful, yielding unwieldy equations that we were unable to solve.

However, if one computes the kinetic enerr of the vortex-cores

alone, given by

E =

F2

o j

for the case hk/h = 0.08 (see Table I), one finds that this energy Ec

represents only 13% of the total vortical drag which itself is about

11% of the surface drag. Therefore, even an error of i00% in the

evalua-tion of the kinetic energy of the vortex-cores would yield an error of the order of 1 to 2% of the surface drag, which lies well within the range of

a

bilge

keels

Fig, 1.

Sketch of the Double Model Equipped with Bilge Keels

h

vieW

-i6-o

oV

Fig. 2. Lines of Constant Total Head. in a Transverse Plane

9

0.1'

Fig. 3.

Secondary Flow in a Transverse Plane at the Stern (hk/h = 0.0)

-.

--V

-.

-90

H H

90

85

0

011 I I

-i8-Fig, 1. Lines of Constant Total Head in a Transverse Plane

at the Stern (hk/h = O.O-t)

0

0.11 I I

-4

/ / /

I \\N\

,

/

/

i \

\

\

.

/

/

I I

\

\

\

Fig. 5.

(hk/h = 0.08)

Fig.

6.

Lines of Öonstant Total Head in a Transverse Plane at the Stern

o

-4

-a

4-o

oi

$

4- #-_

.-7

/

/

T I

r

i

Fig. 7.

Secondary Flow in a Transverse Plane at the Stern (hk/h

o

o.,'

7

Fig. 9.

Lines of Constant Total Head in a Transverse Plane at the Stern

-

N

O

01'

t-Fig. 10.

Secondary Flow in a Transverse Plane at the Stern

Model EquiDped with a Bulbous Bow (hk/h= 0.08)

2d

-26-2b1

2b2

Fig. 12. Path of Integration in the Case of Two Systems

Unclassified

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f i 'arpr.a)a' ,,rati,ur)

Iowa Institute of Hydraulic Research

ft C) f C Li If CL.A '.a C aL I ON

Unclassified

2h, CR0UI'

''I '(rat L_f

Effect of Bilge Keels and a Bulbous Bow on Bilge Vortices

4 vLsÇftlP I )Vf' NOTES (7)';aa' a! 'a'port ,r,a1 ir,c/aa.',p,',' datIert)

Technical Re'port

'a Aid THOR(S) (/rrta) raranra'. tirO/dir' atijtr,,!, fartI raarna')

Tatinclaux, Jean-Claude t) Porti (AT)

February 1968

70. TOTAL NO. OF PAGES 26

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Nonr-1611(05)

h. PatOJvciNo

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₁₀₇

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I'

Wind-tunnel experiments were performed in order to investigate the influence of bilge-keels and of a bulbous bow on the drag induced by vortices

generated. at the bilges

of an ogive.

It was found that as the ratio of the

height of the keels to the maximum width of the ogive is increased from O to 0.08, the vortical drag increases from 2 to 11 percent of the surface drag. The presence of a bulbous bow does not appear to affect the vortical drag of

a model with a fine entrance, such as the one studied here; other investigators

claim the contrary when the form is that of a blunt oil tanker.

D

1473

(PA,L 1)

Uncias si fi ed.

Unclassified

S,UttÎv ClHssiIiIation

D fl

FORM 1473

_{NOV 6 I} (BACK)

Unclassified

KEY WORDS LINK A LINK B LINK C

ROLE WI SOLE WI SOLE WI

Experiment and Analysis Bilge Vortices Vortical Drag Bilge Keels Bulbous Bow I Security Classification _{31 409}

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Naval Ship Research and Development

Center, Attn: Code 0141 ₍₃₉₎

Department of the Navy

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Attn: Library

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Naval Ship Systems Command Department of the Navy

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219 S. Dearborn Street Chicago, Illinois 606014

DISTRIBUTION LIST FOR REPORTS PREPARED URDER TF

GENERAL HYDROCHANICS RESEARCH PROGRAM

Office of Naval Research Resident Representative

207 West 2)4th Street

New York, New York 10011

Commanding Officer

Office of Naval Research Branch Office

1030 East Green Street Pasadena, California 91101

Commanding Officer

Office of Naval Research Branch Office

1016 Mission Street

San Francisco, California 914103

3 Crmnanding Officer

Office of Naval Research Branch Office

Box 39, FF0, New York 09510

Dr. F. H. Todd

Office of Naval Research Branch Office

Box 39, FF0, New York 09510

3 Commander

Naval Ship Engineering Center Department of the Navy

Washington, D.C. 20360

Attn:

Code 6120

Code 6136

Code 61140

Special Projects Office Department of the Navy Washington, D.C. 20360

Attn: Dr. John Craven

Code NSP-OO1

i Commanding Officer (Tech. Lib.) U. S. Naval Air Development Center Johnsviiie, Warminster, Pa. 189114

Commanding Officer and Director Naval Applied Science Laboratory

Flushing & Washington Avenues Brooklyn, New York 11251

Director

Naval Research Laboratory

Washington, D.C. 20390

Attn: Code 2027

Commanding Office

Navy Underwater Weapons Research and Engineering Station

Newport, Rhode Island O284O

Commander

Boston Naval Shipyard

Boston, Massachusetts 02129

Attn: Technical Library

Commander

Charleston Naval Shipyard Naval Base

Charleston, South Carolina 29408

Attn: Code 245b4 Technical Library

Commander

Long Beach Naval Shipyard Long Beach, California 90802

Attn: Technical Library

Commander

Norfolk Naval Shipyard Portsmouth, Virginia 23709

Attn: Technical Library

Commander

Pearl Harbor Naval Shipyard

Box )400, Fleet Post Office

San Francisco, California 96610 Commander

Philadelphia Naval Shipyard

Philadelphia, Pennsylvania 19112

Attn: Code 2)40

Commander

Portsmouth Naval Shipyard

Portsmouth, New Hampshire 03801

Attn: Technical Library

-2-Commander

Puget Sound Naval Shipyard Bremerton, Washington 9831)4

Attn: Engineering Library Code 2)45.6

NASA Scientific and Technical Information Facility

P.O. Box 33

College Park, Maryland 207)40

1 Library of Congress

Science and Technology Division Washington, D.C. 205)40

U. S. Coast Guard 1300 E Street N. W. Washington, D.C. 20591

Attn: Division of Merchant Marine

University of Bridgeport

Bridgeport, Connecticut 06602

Attn: Prof. Earl Uram

Mechanical Engr. Department

)4 Naval Architecture Department College of Engineering University of California Berkeley, California 9)4720 Attn: Librarian Prof. J. R. Paulling Prof. J. V. Wehausen Dr. H. A. Schade

2 California Institute of Technology Pasadena, California 91109

Attn: Dr. A. J. Acosta (i)

Dr. T. Y. Wu (i)

Cornell University

Graduate School of Aerospace Engr. Ithaca, New York 1)4850

Attn: Prof. W. R. Sears

1 The University of Iowa Iowa City, Iowa 522)40

Attn: Dr. Hunter Rouse

2 The State University of Iowa

Iowa Institute of Hydraulic Research Iowa City, Iowa 522)40

Attn: Dr. L. Landweber (i)

)4 Massachusetts Institute of Technology

Department of Naval Architecture and Marine Engineering

Cambridge, Massachusetts 02139

Attn: Dr. A. H. Keil, Room 5-226 (1)

Prof. P. Mandel, Room 5-325 (i) Prof. J. R. Kerwin, Room 5-23 (i)

Prof. M. Abkowitz (i)

U. S. Merchant Marine Academy Kings Point, L.I., N. Y. 11O24

Attn: Capt. L. S. McCready, Head

Department of Engineering

3 University of Michigan

Department of Naval Architecture and Marine Engineering

Ann Arbor, Michigan )48i0)4

Attn: Dr. R. F. Ogilvie Dr. F. Michelsen Prof. H. Benford 2 U. S. Naval Academy Annapolis, Maryland Attn: Library

Prof. Bruce Johnson i U. S. Naval Postgraduate School

Monterey, California 939)40

Attn: Library (1)

New York University University Heights Bronx, New York 10)453

Attn: Prof. W. J. Pierson, Jr.

2 The Pennsylvania State University Ordnance Research Laboratory

University Park, Pennsylvania i68Oi

Attn: Director (1)

Dr. G. Wislicenus (i)

2 Scripps Institution of Oceanography University of California

La Jolla, California 92038

Attn: J. Pollock

M. Silverman

3 Stevens Institute of Technology

Davidson Laboratory 711 Hudson Street

Hoboken, New Jersey 07030

Attn: Dr. J. Breslin (3)

-3.--University of Washington Applied Physics Laboratory

1013 N.E. I4Oth Street

Seattle, Washington 98105

Attn: Director

2 Webb Institute of Naval Architecture Crescent Beach Road

Glen Clove, L.I., New York 115)42

Attn: Prof. E. V. Lewis (i)

Prof. L. W. Ward (i)

Worcester Polytechnic Institute Alden Research Laboratories Worcester, Massachusetts 01609 Attn: Director Aerojet-General Corporation 1100 W. Holiyvale Street Azusa, California 91702 Attn: Mr. J. Levy Bldg. 160, Dept. 11223

Bethlehem Steel Corporation Central Technical Division Sparrows Point Yard

Sparrows Point, Maryland 21219

Attn: Mr. A. D. Haff

Technical Manager Bethlehem Steel Corporation 25 Broadway

New York, New York 1000)4

Attn: Mr. H. de Luce

Electric Boat Division

General Dynamics Corporation Groton, Connecticut 063)40

Attn: Mr. V. T. Boatwright, Jr.

Esso International 15 West 51st Street

New York, New York 10019

Attn: Mr. R. J. Taylor, Manager

R & D, Tanker Dept. Gibbs and Cox, Inc.

21 West Street

New York, New York 10006

Attn: Technical Information

Control Section

i Grumman Aircraft Engineering Corp. Bethpage, L.I., N. Y. 1171)4

Lockheed Missiles & Space Co.

P.O. Box 50)4

Sunnyvale, California 9)4088

Attn: Dr. J. W. Cuthbert, Facility 1

Dept. 57-01, Bldg. 150 Newport News Shipbulding and

Dry Dock Company 4l01 Washington Avenue

Newport News, Virginia 23601

Attn: Technical Library Dept.

Oceanics, Incorporated Technical Industrial Park Plainview, L.I., N. Y. 11803

Attn: Dr. Paul Kaplan

Robert Taggart, Inc. 3930 Walnut Street

Fairfax, Virginia 22030

Attn: Mr. R. Taggart

i Sperry Gyroscope Company

Great Neck, L.I., N. Y. 11020

Attn: Mr. D. Price G-2

i Sperry-Piedmont Company

Charlottesville, Virginia 22901

Attn: Mr. T. Noble

Society of Naval Architects and Marine Engineers

714 Trinity Place

New York, New York 10006

Sun Shipbuilding and Dry Dock Co. Chester, Pennsylvania 18013

Attn: Mr. F. L. Pavlik

Chief Naval Architect

i TRG/A Division of Control Data Corp.

535 Broad Hollow Road (Route

lia)

Melville, L.I., N. Y.

ii146

i Woods Hole Oceanographic Institute

Woods Hole, Massachusetts 025)43

Attn: Reference Room

2 Commander

San Francisco. Bay Naval Shipyard

Vallejo, California

Attn: Technical Library, Code l3OLI

Code 250

Commandant (E)

U. S. Coast Guard (Sta 5-2) 1300 E Street N.W.

Washington, D.C. 20591

2 Hydronautics, Incorporated Pindell School Road

Howard County

Laurel, Maryland 20810

Attn: Mr. P. Eisenberg