General design criteria for cable-towed body systems using faired and unfaired cable

COPY. NUMBER_Z=

GENERAL DESIGN CRITERIA
FOR
CABLE-TOWED BODY SYSTEMS
USING

FAIRED AND UNFAIRED CABLE

Prepared under Contract Nonr 3201(00)
Sponsored by the
Office of Naval Research

or

SYSTEMS ENGINEERING DIVISION
PNEUMODYNAMICS CORPORATION
BETHESDA, MARYLAND

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GENERAL DESIGN CRITERIA
FOR
CABLE-TOWED BODY SYSTEMS
USING
FAIRED AND UNFAIRED CABLE

Prepared under Contract Nonr 3201(00)
Sponsored by the
Office of Naval Research

October 1960

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

LL Wi) Ellawor FR

W. M. Ellsworth, Manager
Maxine Sys Department

Prepared by:

Approved by: :
. K. Richards, Division Manager

TABLE OF CONTENTS

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Technical PUSCUSSLON oie; ceseral eiavele ere erence ee ele clerahevetevera atone

System Contiguratonis eis icicieeveleielelelotelelatelereieicrc ele

Calculations for Unfaired Cable........c.ccecces

Calculations for Faired Cable.......ccceccecscs

Illustrative Examples

Unfaired Cab OG Sercrevere oc 6.6. 616 © 6 6 6-8 0 on ares eters

Faired CADW Ais a tcrstace Wis ereve cl siisreworals enc veleheuchene

ROLEOTOCNCES ais cia cvsnelaie ie) svete e166) site) e086, 6 elere | eueiete: ¢cvelereyersijee

Appendix I -

Appendix II-

Appendix II-

Appendix IvV-

Tabulation of Calculations for
Unfaired Cab Grave 5 acts overs ese ence) bre ore aueaane
Design Curves for Unfaired Cable.....

Tabulation of Calculations for

Faired Cable tcen hehe nee eben ens

Design Curves for Faired Cable........

33

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A method for rapid selection of design parameters to

satisfy requirements for cable-towed instrument systems is
1)

described. The method is applied to both faired and un-

faired cable systems. Curves are presented which facilicacem
the determination of cable diameter, cable length, and re-

quired down force without the need for performing laborious

cable calculations previously required.

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INTRODUCTION

In the design of cable-towed systems, the problem is
complicated by the large number of independent variables
which must be considered and the necessity for performing
laborious calculations using tables of cable functions such
as those in Reference 1*, There is a need, therefore, to
provide the designer with a more simplified and rapid method
for determining the feasibility of meeting system requirements
and selecting system parameters which are in a range of prac-
tical interest. This need for a more practical approach to
cable-body system design was encountered in the course of
studying requirements for a towed instrument array to be used
in measuring physical characteristics of the ocean. Asa
result of this study, sponsored by the Office of Naval Research,
a design technique was devised to permit selection of a practi-
cal configuration to meet requirements for attaining a particu-
lar depth at a given speed using armor ed electrical cables
both with and without cable fairing. Since this method is
felt to be generally applicable to a variety of such design
problems, it is described in this report as a separate part
of the study.

* References listed on page 32,

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SYSTEM CONFIGURATION

The general cable-system configuration to be considered
in this discussion is shown in Pigure 1. We will restrict
our consideration to the case of a body towed from the water
surface with the cable lying in a vertical plane and curved
concave downward. This configuration is designated as the

"Quadrant I Case", in Reference l.

The forces acting on an element of the cable are shown

in Figure 2. These are defined as:

F, the hydrodynamic force per unit length acting
normal to the element,

G, the hydrodynamic force per unit length acting
tangential to the element,

W, the weight of the element per unit length, and

T, the tension in the cable.

The principal distinction between calculations for bare
cable and those for faired cable lies in the description of
hydrodynamic forces F and G. This distinction will be dis-
cussed in detail in a later section, however, in either case,

the hydrodynamic force is generally described in terms of the

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FIG. 4

CABLE CONFIGURATION

FIG 2 | |
*.. FORCES ACTING ON AN ELEMENT... 2 a

| OF THE TOWING LINK | ee ee ee
f oF Se < ‘ty es)
ae

drag of the cable per unit length when the cable is normal

to the stream. The drag is given by:

R= cy & av? (1)

where:

cp is an empirical drag coefficient,
p is the mass density of the fluid,
qd is the diameter of the cable, and

V is the stream velocity.

To reduce the problem to a case of practical interest
several assumptions will be made. These and assumptions

already made are listed as follows:

les The cable is assumed to be completely flexible

and thus cannot sustain a bending moment.

as The cable is assumed to lie in a vertical plane

parallel to the direction of motion.

3. It will be assumed that the cable to be used is
American Steel and Wire Type H. This cable is of
the double-armor type which is available in various
diameters with a variety of electrical cores.

Table I lists a number of sizes and types presently

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Cocper Weight

3 | (Lbs. /1000 ft. )

TH .CCE
A&C Copper

Th C08
A&C Copper
TR .012

Tinred
Copver
fe? OL]
Tinned
Copper
Te .020

Tinned
Copper

5/64"6x7
Co; per
Sash Cord
5 /64"6x7
Copper
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24 Solid

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Tinned
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9,09

4.11

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933

18 .66

Cable Weight in Air

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302

C 332

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24. 1500
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5.24 7200
3.26 9200
4. 2 11000
le 2 16000
24 2700
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1l.1 7200
ay)
25,7) 6300
15.4 9200
15.4 11000
Lik 16000
“11.1 18000
2he6 7200
11.1 16000

2.60

3300

4200

None

a60

None

2760

3300

4 00

8000

2169

6000

Diameter

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292"
2322"
375"
2425"

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322"

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10

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in use. For these cables the weight in water per
unit length and the breaking strength are propor=
tional to the square of the diameter. These

relations are:
w= 210 ae a? (2)

ibs
£t?

'

Taax * L-15 x 107 ao (3)

The cable tension at the water surface, T, ,
will be assumed to be limited to 1/3 of the

rated breaking strength. Thus:

lbs
£t?

T, (design) = 3.84 x 10° a? (4)

This safety factor of 3 is employed to take ac-
count of inertial loads due to motion of the tow
point, and the reduction of cable strength due
to corrosion and fatigue. Actually, in a conser-
vative design, this factor ahoata probably be as

much as 4 or 5.

The cable angle at the bottom, 9, is assumed to
be 90 degrees. This means that the drag, Dy, of

any body attached to the cable is assumed to be

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very small compared to the down force, Lo: This
assumption considerably reduces the effort in
making cable calculations since the tables of
functions, such as Reference 1, are usually set up
with 9 = 90° as a reference point. Furthermore,
it is usually feasible to achieve a value of at
least 9 or 10 for = using either weight or a

o)

combination of weight and a depressing wing to

produce the down force,

In carrying out calculations of the cable configuration,
the cable characteristics, defined in Figure l1, are generally

expressed in non-dimensional form in the following manner:
1
= eS (6)

oF Sag (7)

Rs ‘
o = To (8)

We will now consider the use of these functions, which
have been tabulated for a range of variables, in calculating

the configuration of a system using bare cable,

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As a result of a considerable number of experiments it
can be assumed that the drag coefficient, Cy > of a circular
cable is about 1.2 over the range of interest. The validity
of this assumption is subject to question depending upon the
roughness of the surface, vibration, free-stream turbulence,
and the Reynolds Number. The Reynolds Number is defined by
Re = be » where v is the kinematic viscosity of the fluid.
Figure 3 shows the variation of Cp with R, for a smooth
cylinder normal to the stream, and it can be seen that Cp
falls considerably below 1.2 at the so-called transition
point. The value of Rg at which transition occurs, as well
as the values o£ Cp, are highly dependent on the cable rough-
ness, the free-stream turbulence level, and the vibration of
the cable. Nevertheless, it is believed that a value of 1.2

is a good compromise for use in these calculations. With

this value for Cp we can therefore write

R= 1.2 PSE aye (9)

We must now consider the manner in which the hydrodynamic

loading on the bare cable depends on the angle g. It has been

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determined by a number of experiments that the normal force,

F, per unit length of cable is given by:
2
F = Rsin 9 (10)

For the tangential force, G, we will make the same assump-
tion as that made in Reference 1, namely that G is inde~
Pendent of angle and © for a reasonably smooth cable is
approximately equal to .02. This is obviously not a completely
valid assumption but, for a wide range of values of go it has
been found to be of sufficient accuracy for engineering calcu-
lations. Actually, the value of G is, in general, quite small
compared to F for the case of a circular element, and does

not have much influence on the calculations for values of o
greater than about 25 degrees. For smaller angles the value
of G is of importance in determining the tension, however,

and this should be borne in mind in assessing the accuracy of

these calculations.

To further facilitate the calculation of cable configur-
ations it is conventional to define another parameter known
as the "critical angle" of the cable. If a completely flexi-
ble cable is towed in a fluid and there is no force applied
to the unsupported end, then the cable will lie in a perfectly
straight line inclined at some angle, 9,, to the stream.

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==

For the case of an unfaired cable, as a result of equation
(10), 9, is a function only of the ratio y. The functional

relationship for a cable having positive weight in water is:

———<—— ——=

W +
con 9, * - oR + y (oz) +1 (23)

It can be seen that if 95 = 9c then the cable will remain
in a straight line regardless of the value of the tension,
T,, applied at the bottom. If 99 < 9, then the cable will
be curved concave upward. If 99 > 9, then the configuration
will be concave downward. It may be further noted that the
angle, 9,, at the bottom end of the cable is determined only
by the ratio of down force, L,, to the drag, D, . Thus:
Qo = arctan Lo (12)
Do
As previously noted, this discussion will be restricted

to the cases where 95 2 9, -

As a result of equations (2) and (9) we can now specify
W
the value of R and, hence, the critical angle in terms of

stream velocity and the diameter of the cable. Thus:

ma us

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. (£1) a ASIII * ED
ry . oS
a bedulialwe® eG, 4iiv noteevcet picd _ Kan tenes Ul sami veny PR
oe ‘ av aka sito Ka Wee, , : ;
i ee
: tebceqe wom map mw. (C) bam. te) aied seupe 30 ated
to anved p aiies [oni ep em Spaart abn pt pmipuany om
,.

a "aes mid Se. wotminat» ohh on agape Pie |

‘ '
(En) The ee.

‘ ox

If we now consider that the tension at the top, T, ,
is limited, as specified in equation (4), we can calculate

the limiting case of the maximum amount of cable, 5,, that

can be towed at the critical angle with nothing on the bottom

end , by simple geometry. These values and the corresponding
values of x, and y, are given as follows:
c lbs
S, (Wsing, + 0.02 R) = 3.84 x 10° — a? (14a)
Substituting from equations (2) and (9)

3.84 x 10° £t2 (Se

5s. = (14b)
"(10 £t) ain 9, (=) + 0.024 sec

Ym = Sq 5in 9 | (15)
Xn = 8, COS Pe (16)

The results of these calculations are given in Table II,

TABLE IL
d
Pe v= Sry Yn Xn
dege Beg" /ft as ee a ae, = ft.
5 0.435 x 10 * 6,740. 586 6,700
10 L74. x 107% 22,000 3,830 21,700
15 4.00 x 107* 33,700 8,730 32,500
20 7.15 x 10~* 36, 400 12,400 34,200
25 Lia) a 2e* 35,100 14,800 31,800
30 16:6 “* 167* 32,200 16,100 27,900
35 23.0 x 167° 29, 400 16,900 24,100
40 30.9 »x 107% 26,800 17,200 20,500
45 40.5 x 107¢ 24,800 17,500 17,500
50 51.5. * 197* 23,200 17,800 14,900
55 68.5 x 107° 21,800 17,900 12,500
60 88.5 x 107% 20,800 18,000 10, 400
65 114 x 10°* 19,900 18,100 8,440
70 149 x

17

im

bs ye ay 2iaing ao: rivet samme api
gah ee MS ‘pndstiron ed bee taoasas tae

nt Nese ae 0.8 gy a

(2) kan 6) iors pated via r

¥ (xy) ard *, 0.8 - ae
ee Ee Yee i aay Dr N40 A en emcee reer ti ‘ais pal
"San O29. o + a’, any, i ia (on Oh

S eS | | ee ae

r (aij) | Et RO A gE

oft wi aut mi miVig ake anebtglyoles enact? ke ii Lcaseory eka

Fem Ret

aS ~ i —

ut” : a“ | ta * | i! Priel ? ; wv MX i A J
oto . — io me > Was i ‘seein CTA ve ae wl ie |

oot eS SBE O88, 84 TOPO

@ot is \ Pie, & POG, 25 a

Ooo .e2 ERD | 60d tk
a an O08, 3.5 00d, af

i OCR, Lt O00 bi 02, R6
ot BORE OOF as Ory he
GOL #5. O02 .e4 | ORD ee:
a OOS, Tk Oe. bh
oOe.SL O02 TL °° OOS LOR
OOH at . SOB SL OOK ee
OOe Ts COe, tL | ote Ee
Gir Ge | a
BHR OR RES AOR RE |

ten = ee a % =
= ©
P &

S: ia

The values for the general cable characteristics can
now also be expressed in terms of the diameter of the cable,
the free-stream velocity, and the non-dimensional cable

functions which have been tabulated in Reference 1. Thus;

2° “Boe 25E (17)
¥, = 3.20 x 10° ie eS (a=) (18)
x, = 3.20 x 10° — te (2) (19)

a
~
i]

3.20 x 10° i> = (2) | (20)

Values of these parameters have been calculated for a range
ef critical angles (hence a range of values of oe) and results
are given in Appendix I. Results have also been plotted and

the resulting curves are given in Appendix II.

18

ir =a
oe Sena —
(sige — de ‘at,

yi eos tf “ oe

yl An ¥ Of,6-¢

“gegen: mY RIS taste. en
i © ,
Bers Gee Ce 8s
Donat Seizila “se: Ofc oat SOTuawk s ARES eee NY wid

liners apt (tks ox wet tety Pe! iy des |

As pointed out previously, the principal difference
between the faired-cable case and the unfaired case lies in
specification of the hydrodynamic loading. This is, providing
the forces acting on the fairing are assumed to be transferred
into the cable at intervals along its length as will he the

case here,

It appears that the clip-type fairing, illustrated in
Figure 4, is a reasonable design upon which to base design
calculations. Experimental evidence indicates that a configu-
ration having a thickness-to-chord ratio of about 1/4 and a
ratio of fairing thickness to cable diameter of about 0.8 is
an optimum design. This configuration will have a drag coef-
ficient, Cp, of about 0.2 in which case the expression for

R becomes:

5 2
db sec" aye (21)

If it is assumed that the fairing, which is constructed of
xubber, is weightless in water, then the expression for W is

still that given in equation (2). Namely,
w= 210 428 g? (2)
ft

19

pO)

haw Ae ceomty nin Joel cae . ian

vit CAT RAIE L eM ASR: eternity eat Seite w seaiqe

items. ecu a2 rei: poe whee wytuaviedn'y rn rs ei

é |
: ay 3 ae mS oer hades = bis) (iia tad ae LaNeinairepae Jaesany

my 6 Bir D2 Sede te -esed: Gesu. ad won a oakent

: : : ws O.0 pce, et Ue an, aes ib pting bbe et a 0

‘a gy ee PAAN o WAN CL mebtas Ah Ay Bins waa

ae wa tend 2, AER MY AFR Myla 8 ab Dis oi sen

r fis} | : | hats th, we gas om

; : , se

i a : iy ek ee j
f ! fi
yraily aig v '-
‘ i

i ‘a

ee eee AL i ake eee south sabia * oh ua
‘ 7 q wh af “297 el erecta Be? tai ee ey 5 a ina nb) ty P cite hem ig ig eed 1 ;

Hy na IIR oes 9 ear a) bac Aare be) iM

Zi

Figure 4

SECTION A-A

We must now consider the question of how to express F
and G. Actually, there is presently a great need for experi-
mental data on the values of these loading functions for
faired shapes at angles to the stream. As a result, there
is still considerable disagreement as to the functional
relationship between F and G and the stream angle, 9. Eames,
in Reference 2, adopted a simplified approach to the problem

and made the following assumption:

Be si 22
ae (22)
S = cos 9 (23)
R :

This results from the assumption that the drag, R, is
always parallel to the stream which would appear reasonabie
if the total drag were due only to shear forces on the surface.
This would not be the case unless the faired cable approached
a flat plate of vanishingly small thickness. Eames contends,
however, that for reasonably high chord-to-thickness ratios,
this is a good approximation and the resulting Simplification
of the equations for the cable configuration justifies its
use. Whicker, in Reference 3, attempts to reconcile data on

faired struts and arrives at the following expressions which

21

= Ds

x neurite 6% wo ‘> ey, alia ete at tocs ae
Lent

os poune a beer “ane o ‘tae a 8 yet
its «ele avenged ant ands He cues oa tah ‘
Mes waahe . (vale iam suwata a sna hei

havi Jugenag age ad wae tpemep ven? > o scared id, ‘shite

4

aS ene

a (fees ri ‘a gue anche wat gas’ ® ine * reget tht Aa

fe micas, eat ag desoscee ‘= Ph ae oe 4 ine A ‘iv’ fi ou

» (he alregh et phy hAws ota ev Sap

-

’ ; wet oF ae oe al? nya’ ‘Wa.- ere ata
. ih Lions ¥

, i pk iv 3 nie oO wilh lie,

cn pig aatra tLe

ys ‘ Pp TS >i = me oo) ‘ ie Rey) st.

yhied S Mart add te wn :
ne Al hy & ] > ft “s sai patie }

- ie clvarsgar ei a4: ore

. oc nimi ebm sl Vapaahil? 4.2) ers Lee? oo %)
t i | x} | ! 4 | BE
oivet BeettislAs-O3~S9oto hy Lh GOOS , sabe ate |). Ta

oT , r a : lecwehs Py ne ri
: surreottiignyy puAssvee? mild, SA pies Foe" Pee bu y

eo en 3% +x ate cokve Stil ALO A OO gti oa
. . | a

} . y v # 1. ih a 9

; ‘ go estab elionese’ 27 BsqQnazey Ae) ee ee 4 adie,

i, > j | wt a “4
; be neoiede sane Balwelio® whe Je CNL ARE arta emis ® ves wm

Wu!

ve
®

i 7 it i : : ’ F a ¥
"7 ae ited ~ © pote yl “Mr Pe Pee

actually involve the thickness-to-chord ratio, (3) g

parla? S| sin 9 + © sin? 9 (24)

fs (0.386 - 0.303% eos “es (0.055 ~ 0.020 =) cos? @ (25)

For a thickness-to-chord ratio of 1/4 these expressions

reduce to
EF = 0.75 sin 9 + 0.25 sin® 9 (24a)
g 2
R = 0.31 cos 9 - 0.05 cos* 9g. (25a)

Pocuaiiy there appelite to be only a small difference in the
two expressions for E and the simpler one used by Eames is
probably acceptable. There is, however, a serious difference
in the two expressions for a, Whicker's values being only
about 1/3 of those given by Eames. Since the relationship
given by Whicker is based on some actual data it is likely
that it is much closer to the actual case, and use of Eames'
expression would probably result in an overestimate of the
xesulting tension. Nevertheless, there is a compelling argu-
ment for using the relation suggested by Eames in that he has
tabulated the resulting evaluation of the integral functions
for the cable configuration. Tables computed with the re-

lation proposed by Whicker are not available, although it is

22

i i a » UD) uate Da a

; ay ae é - a | | i vee on
Ry “> (2 od See

a

ub a
ih af

:
i
iby
/

7 eh hae enn ONE is 1%, sta )

Co o. Paye te

pF ee f . 4 i 7 i ‘ 1 i ¥ yy } ie
BOF fd Poe td2 Mier BOO be. OC WERE Ort WED

4

me Bae) WS Sern, Pao Ee a mite nih * we wet

wdbdtgirse db alloys & Wevewell wt wane mr Gy aC:

NAP Riche Gu! os

iio os book MRR pM: parte panned s hap oiha

wail . 7 py gant LPP wang a0 Bavansyat ws raat yd

CY

.

mi

' “ese he we twa area: saa eae ined ve “wanke a sa ee a!

- “et? to acrasesepiiies man oo Yldeaowa Linen ‘ral
“ote Dillleqeas ee dianth mee) OOO oi tt enti

eet od Ja) al acm Yel betey yi iu diet ala wet wks he

ganitaan> Leste snk ory te, esrb abe ave
j mn colt glikw he dimpts ep tat

Si 32 Motes laA. (WIA LOV A A

Pes eee) | a ee yr

ay

understood that such a formulation has been programmed for
machine calculation by the Taylor Model Basin. Should tables
using Whicker's expressions for F and G become available,

the calculations made herein should be repeated but, for

the present purpose, we will make use of Eames' calculations.
In doing so, however, the caution must be made that computed
values of the tension are apt to be greater than might

reasonably be expected in actual fact.

If we adopt the relations expressed in equations (22)
and (23) for the loading functions, then the critical angle

(designated as y to avoid confusion) is given by:
ys arc tan # j (26)
R
which, upon substitution, becomes:

£t d
=z — 7
tan ¥ = 1050 qa (27)

As in the previous case for unfaixred cable, we can now
determine by simple geometry, the limiting case for the
maximum amount of faired cable which can be towed with
nothing on the bottom end. Thus, with the limitation imposed

on the maximum value of T, we obtain:

s,, = 1.83 x 10* (sin y) £t (28)
%m = 1.83 x 10* (sin y cos y) ft (29)
Ym = 1.83 x 10* (sin? y) ft (30)

23

}
¥.

‘vo a : enon ii fiom, oe tid fn

v

ei iim bimpvie ; ary. a cine soe ‘ona on kk of

alexi ave ond B bn ain read eee a saben
| wet. donner nd paubag whered’ ‘mbes hnorsoxentae |
cir idials te ‘eter 20 op’ oxen bile ww sacar calaiat é
ex Bi svgiaa Pa toa o0t ee idigis wit coi |
Mei risa xedowky ay | os fea wake 0 LI tt i ”

hans See uid rand aye wit aa

1 ov , \y a ry
it) sotgdene of Swaeteeee anoigaies #62) Jhohs Om BF, :

(we Lehto ree Onl aertt . ee ow yokes ants aoe vet)

*

i“ uty ip «th (api Buedow bicvae 02. 4 ae WOR

evn (ie ta yl te ks | eee Mo “Gn: au sia ett: ne oM

at? Jah SGa ce? ae " mite ee) aD stank Al
f Adiow iia tl cade 1 aay alas big ed ko 4 oY
teicrgiul OL I63 4! aye ay paige Se en (2 | is
4 a a 4 ; a ft
(asi | mn (endat Sore tele
fen) 3 79 - ; enna "OA oa at fe + a i bo

7?) ay “win POL! eu, : * iat

: ryan ne ee we iP vere) ee he " « add ’ we re we von ful

The values obtained from equations (27), (28), (29), and

(30) for a range of values of y are given in Table III.

ZABLE IIL
v = Sry Ym %m
deg. sec” /£t £t £t £t

5 8.33 x 1075 1,600 140 1,595
10 16.8 x 107% 3,180 560 3,130
15 25:5 x 1075 4,740 1,200 4,470
20 34079 30 Ler 6,260 2,140 5,880
25 44.4 x 1075 7,740 2270 7,010
30 55.0 x 107° 9,150 4,570 7,920
35 66.0 x 1075 10, 480 6,010 8,580
40 159 en 4 11,740 7,550 9,000
45 95h 2x Lone 12,930 9,140 9,140
50 Tees xome 13,950 10,700 8,960
55 136 x 1075 14,980 12,270 ~~ 8,600
60 165 xLOnS 15,850 13,710 7,910
65 204 x 107° 16,600 14, 400 7,030
70 262 x 1078 17,200 16,200 5,880

The general relations for the faired cable configuration
can now also be expressed in terms of the cable diameter, the
free-stream velocity, and the non-dimensional cable functions.

These relations are:

9 = 3.84% 10° Ibs (31)
2
d T) £t
s,= 19.2 x 10° ie es z) (F) (32)

24

2?
be

Eka

Bat

7 & 4) ©
EP
> ae on
‘ ie
= vi a
4 wr
os ov
o ces
t= Ea*
& cf
ee
a @& &
5 se
= soo
te ee Se =
nserte “2s =
a + s-
ao ee A
ee
ee

EzEs

005 .& ones Bt l CHP . wil a Ye | is
oj7,5 OL EL Ota, ei eee ne OM
by ie oto | OOS oF , a SOR RRR.
le GnRH 2 oe a BRE SE fi - haa

>f /.
—- mA
oe e lang ert OT tg ce eal a
as | =, |
aif

. ; (te hParteetd 206r> B.C be ¢ ee on 4
aot etek Sldwe mid > Bie me ti orc vga ‘wth oni wo
and Ltotied phdas LeAGA Mahe! solo GID) Daun rr. staal nsoitead

\* 2 rn re tae iw,

1 i? by ie, tlie’ ie
(fe) | > ae

& } yy are i, gs mr a, [
7 <t . f Ms { am } enn i "Sj GP’ Bh ih es
' ' , Tay ] \ 7 a ‘ PH H
ar ="

hf.

Lt}

y, = 19.2 x 10° St, @ (=) (33)

sec

x, = 19.2 x 10° St°. (Sr) (a. (34)
sec Ti) AVE
The values of these parameters have been calculated for
a range of critical angles using thetabulated cable functions
(for the “heavy fine" case) given in Reference 2. Results

are tabulated in Appendix III and plotted in Appendix Iv.

For the faired-cable case an interesting result is
obtained as a consequence of the particular chosen expressions
for the loading functions. In this case it can be seen, by
examination of the curves in Appendix IV, that there is a
maximum value of y, for a particular value of aa Cross-
plots of these maximum attainable depths and the correspond-—
ing values of (9).(%) » S,and x, are shown in Figures 5,

6 and 7. These curves provide a means for determining the

greatest depth which can be obtained for a particular value
of =] and the corresponding down force which ays be applied
at the bottom end of the cable within the limitation of 1/3

the breaking strength of the cable.

25

4

»

vz wed Covsmigghs Hb hes

Pon CRO SRR TOSS PiAGICs Shvioig

r

al eat. Seal os

, > hgneepdi race” vis terk’ catty
a. nt

= ows Weed sie sire

- ; mit pa hiadicns yea i), Wr ik
oulav “Ahly iineaas @ 3
} 7 7 Ms. GSA fc sealhicaa ch
o BX\L Oh ao ide Pd f wie, ages
-
| ef

Mids beet Ng ptt

BH.)

2 PS OR IR AMCLED MEME: wont Pie a, ae dh

u ne

oe et ae seipaitns a Mprehely fh) ‘ise 2 scat fe

adoe

ee en Se ee ee anny’ scene ‘ay or,
Bb YiPeOe del Katy i MRD MAS et

A BBO Gy ae mena nee we a a te wis “iy

it /sead> -)

a

exe athe wel es): fui te ‘resin

ani fe

bg" angi i

iw a ae

ci saree) ene wea mele

SUSAN, mee peat.

p,, ina Rong wn wil &
wie ine” fut ate ne

OA he eer podeeunt

Py:
» 2
f

Rees FO spuesnoyy ut TA

Sie L 9 S
mm as es Ty 321 a ee on oy 7 oa a a F
eS ue coer arte See ecrcate dee taet ae na ateaat:
wal is 4 i f LH
pop ee Heiter apn
‘mms jos om a! +
a SBE ; 8 it
a ea A ja om +
iat eee
sees ro i

oe
SOS RSASNaSP od

oh +t
aaa
in ire
ogee oa!
uaceeae t+

caus pesue seuss aeec-st a =
saga es t sme ms ph + =f
tt 2 1G Ba as path t emer

ge geesceses ry ‘es

HH
t
tet
+Ht 3 i c
a sae - : . t +i
a the { i i
ee Seed ee Hee eee eee .
5 Li vase ois i Lt Mt a
aw +
20 bi
Bueb aasoE
Saag AMMA MME rT
pis sb: eupe suas
6 ob a SO bart i
See ee mae

~ aes

ne nee
caeene

a ere
rt as ees

C

ea

Sutacieae

ert

+ :

t
i
punen I+ else
et
ro fe
BES emai Be aacena Ret
oh sees sgneane eae
Leta: (ERA seam ee Be
Bpad HALE RERSSY PARSE Bae E

a Oa Be
PRS Sa

eee

fhe
ae

uNwTUTu

fr
p

mths a

hoor
Soe
1 Ro

£

+44

pagan ewe:
ttt
pt

Han

+H
a

Giiine aifaet
Eatin
stati

ul
ae

oe

t
Hoa
a

44

eaee aeeee

+

A

ne

4
+
4

Hieeauetrntis
naa

ae

He tft Bing
es

+ 1)

Ssdaaaaiit

iss

ai

ee

oeeo
cae!

He

ped
Hy +

q
ol
2
ess!
rt

a
Hf
rH

mm)
10}
oO

U4

Wa
te)
a

OO
S
fc
v2
3
Q
te
rs)

Y, din

: ge
-ruft?

Haat

isaat

feet

£

1@}

nousands

}
i

Pn st

4

qeex FO spuesnoywq u

Wrath og ant

y
: i

| ees ary
Lik

Zllustrative Example

To illustrate the use of these results in selecting a
cable configuration to meet given requirements,consider the
case where it is desired to attain a depth of 5,000 feet at

a towing speed of 10 ft/sec.
Unfaired Cable

From the curves in Appendix II we can determine the
£
values of qe and S, corresponding to a value of y, = 5000 ft

for each value of Ty These values are given in Table IV.

T Iv
gd x 105 d a 8 To Om 1
ve a= 2
sec* /it £t in. ft lbs/£t? lbs
225 .0225 .270 22,500 (8) 9)
40.0 .0400 . 480 13,900 2.06 3,300
Ale 5 .0715 .857 9,300 2.54 13,000
114 sigs 137 7,000 2.64 34,300
166 . 166 1.99 6,000 2.70 74,500

These results may be cross plotted and a particular

configuration selected on the basis of a compromise between

the length of cable required, the down force required, and

the size of electrical core desired.

29

ced iv?
Pty ee
aby

;

i ue @ntsooioe ‘al 1 esse a te wale oid ae

‘pita eubtabwn tape 2Ape% tev hy 2008 one ssid aha
s PS pa Sow OG0% ad dnd ry nner ay cde bal fy pee
=" rn bik tel 50) er eh

ou sia. dela

pit entrain a. o 2h a benya Al Rei RgE ote

> COVE Oy Ser ev thy a OS Pas baggun coy @ Beco ss 204

et olde? A; Vevio vas heuleV eeant whee wea ¥

ee Aer a

| wilt rey o Ree trio om eee wel ) Ad Ae of path
late ; Rahs, : ie

; ceewiet otic W) Te bh ee) Shuey ‘plat Lae pune a] pind OF

fie be cduped sowed gyeb 4? , be Le AS 2° HL QeeR

(Res. at.. & ci aa ea ote ou. a Bed

Faired Cable

In the case of faired cable we can refer directly to

Figures 5, 6 and 7 for the maximum value of y, attainable

toh

for a particular value of ve" In this case we obtain:

lbs
£t*

tk
ze = 1.14 x 10°

2
a MS) se qj SSeS

Zt
whence:
gd = 0,042 £t = 0.504 inches
T> = 2010 lbs
s, = 6200 ft
x, = 3500 ft.

There are other combinations of values, obtainable from
the curves in Appendix IV, which will satisfy these require-
ments. The above values, however, represent the minimum
cable diameter for the given depth within the >
limitation of a maximum tension equal to 1/3 the breaking

strength of the cable.

30

v

ee Yiter i @hkek, cam ae mde base ‘ne oe rage

o ithe Pee % % oy las nian nae sits was) ua ae

suet ane seen wed ik ce ‘hap ater hintsaba asd

a Dee sore

c
iS
¥

mec wierd Ape iv

w@ThODo’ oe ‘<n tw fy ine Na x kines rs wore

: ‘gle Det hrs wes Sey Orie 3 ww ¥\ .) one ist ‘en
: od tac sue. chee ret «4 wah xs’ ot imi 5
entheasd ete ENS G9 jae, wottidd gaya 2 bo ante me

mat rc ihyd

REFERENCES

L. Pode, "Tables for Computing the Equilibrium Con-
figuration of a Flexible Cable in a Uniform Stream"
Taylor Model Basin Report No. 687, March 1951,

M. CC. Eames, "The Configuration of a Cable Towing a
Heavy Submerged Body from a Surface Vessel", Naval
Research Establishment (Canada) Report PHx-103,
November 1956,

L. F. Whicker, “The Oscillatory Motion of Cable-Towed
Bodies“, Doctoral Dessertation, University of
California, 1957.

3

32

i: ante nid cea ails Weal
noha mace eet! @ nd efoing iy
‘oe Sala) ey: ee hh. te

eeobicigi
ei ‘ay

tawotine Lele +o WRALT UM Yekow aeaat wane her
« D scrote ah Se chewed Lksudioogy | pei
ERS, anim ed

4

ee APPENDIX I

a TABULATION OF CALCULATIONS FOR UNFAIRED CABLE

33

a hia is Pr

J i

SS SAS Cite ADL 078 WREST AD 6 vor rata

% = 5° os = 4.35 x 1075 ssc
T
—2 x 107°
oy Ti Oy Nh G4 a Yar xy 8,
Deg. lbs/ft* £t ft £t
5* == -- = -- ) 586 6700 6740
6 1.3517 16.0926 3.9144 15.0525 2.84 402 1550 1650
10 1.1554 6.7358 2.7191 5.7741 3333 327. 695 810
15 1.0981 4.0820 2.1639 3.1798 3.50 274 403 516
20° 20722 2159148" Jselg2 220654 3.58 235 268) 376
30 1.0462 1.7913 1.3561 1.0429 3,68 16i) “1898? S36
AGO 1.0322) Le21BA 1VoesTs 025717 3.72 139 77-164
50 1.0229 0.8520 0.7741 0.3115 3.75 105 42 116
60 1.0159 0.5833 0.5549 0.1568 3.76 76 21 80
70 1.0101 0.3663 0.3587 0.0647 3.80 49 9 50
80 1.0049 0.1769 0.1760 0.0155 3.82 24 2 24
2
= 10° G. = 17,4 x 1075 Sec)
Pe ve _ £t
T
—2 x 107°
Pi Ty Oi Nh 61 a Yi xy 6,
Deg. lbs/f£t* ft ft £t
io. | -— == == -- 0 3830 21700 22000
11 1.3126 10.1330 3.5891 9.0405 2.92 1940 3830 5450
15 1.1753 4.9662 2.4799 3.9952 3.24 1170 +1900 2350
20 1.1252 3.2404 1.9718 2.3464 3.41 976 1160 1600
305 1-090) 1.9857. 2.4173 1.1123 3.55 732 578, 970
40 1.0577 1.2574 1.0617 0.5953 3.635 560 313 662
50 1.0416 0.8699 0.7896 0.3201 3.79 4421 171 464
60 1.0290 0.5915 0.5624 0.1597 3.74 305 86 321
70 1.0185 0.3695 0.3617 0.0655 3.775 198 36°. ‘202
80° 1.0690 0.1776 0.1767 0.0156 3.81 98° #9 98

* Special case of cable towed at critical angle.

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coy Ty Oy Na Ey d? Y. Xa 8,
Deg. lbs /it? £t £t £t
15 =~ -- we ae ) 8730 32500 33700
16 1.4019 7.9397 3.5062 6.7658 2.74 4310 6170 7250
20 1.2457 4.1057 2.3590 3.1082 3.083 2420 3190 4220
25 1.1835 2.7569 1.8507 1.8594 3.24 2000 2010 2970
30 1.1481 2.0741 1.5378 1.2527 3.35 1710 1400 2310
40 1.1041 1.3296 1.1173 0.6394 3.475 1290 740 1540
50 1.0747 0.9020 0.8173 0.3356 3.57 974 400 1070
60 1.0520 0.6057 0.5756 0,1648 3.65 700 200 £736
70 1.0329 0.3749 0.3670 0.0667 37d: 454 83 465
80 1.0159 0.1788 0.1779 0.0157 3,78 224 20 225
% = 20° 4 = 71,5 x 1075 sec
Vv" ;
=. =—6
x 10
Pi T) Ox Na 61 Y xy 8,
Deg. lbs/ft* ft £t £t
20 -- -- -- -- ) 12400 34200 36400
21 1.5794 6.8861 3.5481 5.6003 2.43 5470 8130 10400
25 1.3580 3.6036 2.2968 2.5664 2.83 4040 4330 6350
30 1.2685 2.4378 1.7649 1.5294 3.03 3320 2760 4570
35 1.2166 1.8376 1.4444 1.0222 3,16 2840 1920 3600
40 1.1795 1.4496 1.2091 0.7139 3.26 2445 1390 2935
50 1.1262 .9523 .8605 0.3600 3.41 1825 730 2020
60 1.0867 .6273 .5955 0.1725 3.535 1310 364 1378
70 1.0543 .3829 .3747 0.0686 3.64 850 149 866
80 1.0260 .1806 .1797 0.0159 3.745 417 35 420

35

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91 Ti Or Ta 61 Yi Ry 5,
Deg. lbs/£t* ft ft ~~ £€
25 -- — = -- 0 14800 31800 35100
26 1.8528 6.3531 3.6828 4.9197 2.07 7250 9700 12500
30 1.5126 3.2795 2.2684 2.1915 2.54 5470 5290 7900
35 1.3784 2.2044 1.6964 1.2816 2.79 4490 3400 5840
40 1.3011 1.6501 1.3607 0.8407 2.95 3820 2360 4620
50 1.2030 1.0282 29256 0.3375 yap be) 2850 1210 3120
60 1,1361 ~6581 6241 0.1837 3.38 2010 590 2220
70 «1.0838 3939 «§6..3844 0.0713 3.54 1800 240 1330
80 1.0395 - 1830 ~ 1821 0.0162 3.70 640 Sy7/ 642
Pe 166 x 10 €t
—2 x 107°
Pi. Ti Oy Ta Ga d* Ol xy dl
Deg. lbs/£t? £t £t £t
30 -— -- = == (9) 16100 27900 32200
31 2.2478 6.1162 3.8988 4.4917 Loy 9200 10600 14450
35° -Lovi2s 3.052. 2.22579 1.9047 2.24 7010 5900 9450
40 1.5116 2.0163 1.6326 1.0794 2.54 : 5740 3780 7060
45 1.3983 1.4872 1.2767 0.6881 2c¢5 4850 2620 5630
50 1.3187 1.1444 1,0247 0.4560 2.82 4130 1840 4610
60 1.2058 0.7018 0.6644 0.1997 3.19 2920 879 3100
70 1.1236 0.4089 0.3999 0.0748 3.41 1880 350 1930
80 1.0572 0.1862 0.1852 0.0166 3.64 930 83 935

36

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-= «107°
Px Ti Oy Na any d Yi xX 5,
Deg. lbs/ft? ft £t £t
35 — -- =< a ft) 16900 24100 29400
36 2.8043 6.0705 4.1902 4.2030 137, 11000 11050 15950
40 1.9617 2.8751 2.2513 1.6638 1.96 8450 6240 10780
45 1.6645 1.8482 1.5626 0.9025 2.31 6920 3990 8170
50 1.5024 1.3334 1.1844 0.5534 2.56 5800 2710 6540
GG) 153053 ..7G46 .7a22 “0.2232 2.94 4070 1250 4300
76 i.k776 4269. 2.4192, 6.0797 3,27 2620 498 2685
80 1.0795 .1902 .1892 0.0171 3.56 1290 117 1300
2
= 40° G_ = 309 x 1075 Sec-
Ve vz £€t
T
2 =-6
2 x 10
Pi Ti Oy Na Ga d Yi xy S,
Deg. lbs/£t? £t ft ft
40 -- -- -- -- 0 17200 20500 26800
41 3.5754 6.1516 4.5467 3.9821 1,07 12600 11000 17000
425 2.2567 2.7156 2.2331 1.4427 1.70 9790 6330 11900
50 1.8296 1.6819 1.4758 0.7395 2.10 . 7980 3990 9100
55 1.6044 1.1795 1.0770 0,4310 2.39 6640 2650 7250
60 1.4534 .8589 .8088 0.25912 2.64 5500 1760 5850
70 1.2495 .4562 .4456 0,0864 3.07 3530 684 3610
80 1.1087 .1953 .1942 0.0177 3,47 1735 158 1745

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Ye v2 £t

Pea) -6

Pi T1 Oj Na 6. So x Ya x1 5,

Deg. lbs/fit* £t £t £t
45 -- “— -=- —— 0 17500 17500 24800
46 4.6219 6.3013 4.9439 3.7710 83 13850 10600 17700
50 2.5954 2.5457 2.1843 1.2247 1.48 10900 6130 12700
55 1.9932 1.5034 1.3621 0.5847 1.93 8850 3800 9760
60 1.6913 1.0123 0,9491 0.3192 2.al 7280 2450 7756
65 1.4950 0.7084 0.6800 0.1782 2.97 5900 1550 6150
70 1.3512 0.4947 0.4827 0.0959 2.84 4630 920 4740
7> 1.2385 O.4332i 0.3279 0.0468 Sioa: 3430 490 3480
80 1.1460 0.2019 0.2008 0.0185 3505 2270 210 2280

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APPENDIX If

DESIGN CURVES FOR UNFAIRED CABLE

a a

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APPENDIX LIL

TABULATION OF CALCULATIONS FOR FAIRED CABLE

| Pena.
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: Li. Xi Gia
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Le

tie va, ee on y ; vo Puy J pitas biser aeie hy ok ae

=a5° 4. = 8,33 x 1075 Sec
. ve . £t

=-6
Pi Oj Ey Na IVA a a* 0 8, Xa Yi
Deg. lbs/£t® ft ft ft
5* <== oe -~ = ) 1600 1595 140

15 5.5413 4.4993 2.7138 .175 672 1552 1260 760
20 3.6169 2.6594 2.1655 .260 998 1504 1106 901
25 2.6397 1.7556 1.7953 .344 1332 1452 966 988
30 2.0413 1.2241 1.5206 .424 1.63 1385 830 1032
40 1.3303 0.6388 1.1186 .576 2322 1226 589 1031
50 0.9055 0.3370 0.8202 .710 2.73 1029 383 932
60 0.6081 0.1656 0.5777 .822 3.16 800 218 £760
70 0.3760 0.0670 0.3679 .910 3.49 547 98 536
80 0.1790 0.0157 0.1781 #£.970 1G Ie] 278 24 276
90 0 - 0 0 1,000 3.84 fe) 0 0
ey Gia -s sec”

vy = 10 ve 16.8 x 10 RE

2 -6

Pi Oy Ey Na 1/t, ane a Sr Ant

Deg. lbs /£t* ft €t £€
10* -- -- -- = ) 3180 3130 560
15 10.9142 9.4884 4.6189 .089 (6342. 3130 2720 1325
20 5.3292 4.1497 2.9580 .177 .680 3040 2370 1690
25 3.4485 2.4085 2.2487 7264 1.015 2930 2050 1910
30 2.4935 1.5600 1.8113 .348 1.335 2790 1750 2030
40 1.5087 0.7481 1.2561 .508 1.95 2470 1230 2060
50 0.9848 0.3754 0.8888 .653 2.51 2070 789 1870
60 0.6428 0.1780 0.6099 .778 2.99 1610 446 1530
70 0.3889 0.0701 0.3806 .880 3.38 1100 198 1080
80 0.1819 0.0161 0.1810 .954 3.66 558 49 556
90 0 ) 6) 1.00 3.84 fe) (0) )

* Special case of cable towed at critical angle.
50

UN meme aha
(tem Yond peroneal 9h miami ;

SUESE ROW 4 0 gait Ne |

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per wR”; GAG, Beek Veta. eM
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Caos Offi = OVAR be.) 1) bins i ye"
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Oe . bs ¥ oe oh

ae -s sect
y= 20° 2 = 34.7 x 1075 S86

7 x 1O-*
Pi Oy G4 Th AGT a? od x) Vir
Deg. lbs/£t* ft £t £t
20 0 0 (¢} 0 i¢) 6260 5880 2140
25 9.7718 7.7999 5.4469 .093 0.357 6050 4820 3370
30 4.6864 3.2673 3.1439 - 185 0.710 5770 4030 3870
35 2.9742 1.8183 2.2324 e276 1.06 5460 3340 4100
40 2.1046 1.1265 1.7060 (2364 1.40 5110 2730 4140
50 1.2081 0.4863 1.0798 abysi3 2.04 4280 1720 3820
60 0.7310 0.2102 0.6915 684 2.63 3330 958 3150
70 O.4195 0.0774 0.4103 -816 3.14 2280 421 2230
80 0.1885 90.0168 0.1875 ~922 3.54 1160 YOs' 7 T5090
90 0 Q 0 1,00 3.84 19) (@] 10)
° d =5 sec“
y = 30 Vy = 55.0 x 10 rE
TS
o -6
—= x 10
Pa Oy 61 Ta Ir a? : Ss, xy Yi
Deg. lbs/ft* £t £t cc
30 (¢) 0 (9) 0 0 9150 7920 4570
35 8.1400 5.7341 5.5470 101 0.388 8670 6110 5910
40 3.8201 2.2827 2.9522 2201 0.772 8110 4850 6260
45 2.3659 1.2051 1.9761 299 dh aS) 7490 3810 6250
50 1.6276 0.7107 1.4338 395 1.48 ; 6780 2960 5970
60 0.8660 0.2612 0.8156 ASU 2.22 5280 1590 4970
. 70 0.4607 0.0874 0.4501 ~743 2.85 3620 685 3530
80 0.1963 0.0178 0.1952 .885 3.40 1830 166 1820
90 (0) (9) 0 1.00 3.84 0 0 (@)

52

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50 2.8356 1.3707 2.4318 .227 .872 9870 4770 8470
55 1.7035 0.6729 1.5334 .338 1.30 8840 3490 7950
60 1.1198 0.3606 1.0476 .447 1.72 7670 2470 7180
70 0.5239 0.1032 0.5110 #£.653 Zao: 5240 1035 5120
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60 1.8509 0.6651 1.7090 .271 1.04 10900 3910 10050
65 1.0496 0.2911 1.0007 .402 1.55 9170 2540 8750
70 0.6427 0.1340 0.6255 .534 2.05 7440 1550 7240
75 0.3937 0.0584 0.3882 .658 2.53. 5620 834 5550
80 0.2233 0.0211 0.2220 .776 2.98 3760 356 3740
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52

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APPENDIX IV

DESIGN CURVES FOR FAIRED CABLE

53

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DISTRIBUTION LIST

Reports Generated by Systems Engineering Division, PneumoDynamics
Corporation under Office of Naval Research Contract Nonr 3201(00)

SS eee

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Pennsylvania State University
University Station

State College, Pennsylvania

U.S. Navy Representative
SACLANT ASW Research Center
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Stanford Research Institute
Menlo Park, California

Department of Geodesy & Geophysics
Cambridge University
Cambridge, England

Lamont Geophysical Observatory
Bermuda Field Station
St. Georges, Bermuda

University of California, La Jolla
Marine Physical Laboratory

Scripps Institution of Oceanography
San Diego 52, California

Attn: Mrs. Christine Baldwin

General Motors Corporation

Defease Systems Division

General Motors Technical Center

Warren, Michigan

Attn: Mrs. Florence Armstrong,
Librarian

. Mr. L. L. Higgins

8433 Fallbrook Avenue
Canoga Park, California

Professor Basil W. Wilson
Texas A. & M. College
College Station, Texas

Mr. E.J. Okleshen

Section Chief

Advanced Development Engineering
The Magnavox Company

Fort Wayne 4, Indiana

The Perkin-Elmer Corporation
5670 East Washington Blvd
Los Angeles 22, California
Attn: Mr. George Artiano

Entwistle Manufacturing Company
1475 Elmwood Avenue

Providence 7, Rhode Island
Attn: Mr. O. Minardi

U.S.N. Underwater Sound Laboratory
New Longon, Connectivgut
Attn: Mr. Seymour Gross

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NORTRONICS,

Marine Equipment Department

77 “A" Street

Needham Heights 94, Mass.

ATTN: Mrs. MacWilliam
Technical Librarian

Lt. Cmdr. E.W. Sapp
U.S.S. Maloy

(DE 791A)

c/o FPO

New York, New York

Bureau of Ships
Department of the Navy
Washington 25, D.C.
Attn: Code 440 (Mr. Ferris)
Code 420 (Cdr. Aroner)
Code 447
Code 526
Code 632

Product Design Engineering
Department 4

General Electric Company

Building #1, Room 119

Farrell Road Plant

Court Street

Syracuse, New York

Attn: Mr. D.H. Harse

LCdr Thomas Sherman
Office of Naval Research
Department of the Navy
Washington 25, D.C.

American Steel & Wire Co.
1625 K Street, N.W,
Washington 6, D.C.

Attn: Mr. Phil Wright

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