Investigation of the hydrodynamic loading on ribbon towcable

DINSRDC/SPD 1030-01

IGATION OF THE HYDRODYNAMIC LOADING ON RIBBON TOWCABLE

dD ' SSeS on LA mer oma!

DAVID W. TAYLOR NAVAL SHIP
RESEARCH AND DEVELOPMENT CENTER

Bethesda, Maryland 20084

INVESTIGATION OF THE HYDRODYNAMIC LOADING
ON RIBBON TOWCABLE

WHOI

Reece Folb DOCUMENT
John Nelligan COLLECTION

APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED

SHIP PERFORMANCE DEPARTMENT
DEPARTMENTAL REPORT

January 1982 DINSRDC/SPD 1030-01

MAJOR DTNSRDC ORGANIZATIONAL COMPONENTS

DTNSRDC
COMMANDER
TECHNICAL DIRECTOR:

OFFICER-IN-CHARGE
CARDEROCK

OFFICER-IN-CHARGE
ANNAPOLIS

SYSTEMS
DEVELOPMENT
DEPARTMENT

AVIATION AND
SURFACE EFFECTS
DEPARTMENT

SHIP PERFORMANCE
DEPARTMENT

15

COMPUTATION,
MATHEMATICS AND
LOGISTICS DEPARTMENT

STRUCTURES
DEPARTMENT

SHIP ACOUSTICS PROPULSION AND
DEPARTMENT =a AUXILIARY SYSTEMS
DEPARTMENT

SHIP MATERIALS CENTRAL

ENGINEERING ! ; INSTRUMENTATION
DEPARTMENT OB DEPARTMENT

TL

0 0301 0037113 4

MBL/WHO!

I

Geiguinaclons NDW-DTNSRDC 5602/21 (:

UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)
REPORT DOCUMENTATION PAGE BERS CoE eo eid
1. REPORT NUMBER 2. GOVT ACCESSION NO./ 3. RECIPIENT’S CATALOG NUMBER
DINSRDC/SPD 1030-01

4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED

INVESTIGATION OF THE HYDRODYNAMIC LOADING ' DEPARTMENTAL

ON RIBBON TOWCABLE =
6. PERFORMING ORG. REPORT NUMBER

DINSRDC/SPD 1030-01
7. AUTHOR(2) 8. CONTRACT OR GRANT NUMBER(a)

Reece Folb and John Nelligan

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK
AREA & WORK UNIT NUMBERS

David Taylor Naval Ship R&D Center Element 62543N
Ship Performance Department SF 43-400-001
Bethesda, MD 20084 DINSRDC WU 1507-101

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE
Naval Sea Systems Command January 1982
2

4. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of thie report)

UNCLASSIFIED

1Sa. DECLASSIFICATION/ DOWNGRADING
SCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED

17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, If different from Report)

18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse aide if necessary and identify by block number)

Ribboned Towcables

Ribbon Fairing

Loading Functions

Towcable Performance Improvement

20. ABSTRACT (Continue on reverse side if necessary and identify by block number)
Hydrodynamic loading functions and drag coefficients have been developed for
a ribbon towcable. These functions represent a mathematical fit to data
measured on a towcable at sea. The functions should be used with caution in
predicting the towing configuration of other types of ribbon cable design or
other cable diameters because of the difficulty in scaling ribbon character-
istics such as material stiffness.

DD ans; 1473 EDITION OF 1 Nov 65 Is OBSOLETE UNCLASSIFIED

S/N 0102- LF- 014-6601 SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

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SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered)

TABLE OF CONTENTS

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APPENDIX A -— A COMPARISON OF THE HYDRODYNAMIC LOADING FUNCTIONS WITH

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A. 2-
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SOME CRITICAL ANGLE TOWING DATA. ..........
LIST OF FIGURES

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Danes soynys; ONE IHMC WapymAsceies 5.6 6560000056 560606

Depressor Performance as a Function of Speed... ° 0 0
3(a)-Cable Angle at the Depressor; 3(b)-Cable Tension ae the
Depressor

Ratpoem Weal, o 6 6000000500000 000 5000 6
Schematic Diagram of the Towing Arrangement. .... .

Cable Tension at the Ship as a Function of Cable Scope...
Depressor Depth as a Function of Cable Scope .......

Hydrodynamic Loading Functions ....... Bh ce op POL ros he
8(a)-Normal Hydrodynamic Loading Function vs Cable Angle;
8(b)-Tangential Hydrodynamic Loading Function vs Cable Angle

Drag Coefficient Cc, as a Function of Reynolds Number...
Towcable Tension per Unit Length versus Towspeed for
\Weneslors MERCEINIERG 6 0°50 6 6 0060 000000060 50-0 0 0
Towing Angles versus Towspeed for Various Towcables. ....
Tangential Hydrodynamic Loading vs Cable Angle .....

iii

LIST OF TABLES
1 - Cable and Ribbon Geometry. ........
2 - Measurement Sensors. . .« »« « « « « « « « »
A.1— Ribbon Configurations. | 6. 3 6 5 6 6 w.
A.2- Derived Normal Drag Coefficients .....
A.3- Tangential Hydrodynamic Loading Values. .

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NOTATION

Dimensionless coefficients

Normal drag coefficient based on cable diameter

Diameter

Normal component of hydrodynamic force per unit length
Normal hydrodynamic loading function ;

Tangential hydrodynamic loading function

Tangential component of hydrodynamic force per unit length
Tangential component of force per unit length

Normal component of force per unit length

Cable drag per unit length when the axis is 90° to the flow
Reynolds number

Cable scope

Cable tension

Velocity

Cable weight per unit length in seawater

Density of seawater

Towcable angle relative to horizontal

Towcable critical angle

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ABSTRACT

Hydrodynamic loading functions and drag coefficients have been
developed for a ribbon towcable. These functions represent a mathe-
matical fit to data measured on a towcable at sea. The functions
should be used with caution in predicting the towing configurations
of other types of ribbon cable design or other cable diameters because
of the difficulty in scaling ribbon characteristics such as material
stiffness.

ADMINISTRATIVE INFORMATION

The work described in this report was performed in support of a number of
projects sponsored by the Naval Sea Systems Command, the Naval Ship Engineering
Center and the Naval Air Systems Command. The effort was carried out jointly by
David Taylor Naval Ship Research and Development Center under Program Element
Number 62543N, Task Area Number SF 43-400-001, Work Unit Number 1507-101 and MAR
Associates, Inc. under DINSRDC Contract Number N00600-79-D-2507. J. Nelligan is
with MAR Associates, Inc. of Rockville, Maryland.

INTRODUCTION

Various devices can be attached to round towcables to improve hydrodynamic
performance. A streamlined fairing reduces the normal component of drag allowing
the towline to span a greater depth per unit of scope, at the same time reducing
cable strumming. Fairing, however, is expensive and can be difficult to store
and stream reliably, especially in certain applications, e.g., submarine towed
systems.

Ribbon towcable does not have the hydrodynamic efficiency of streamlined
fairing, but it is much more easily stored and handled, in addition to being less
costly. Ribbon is used primarily to reduce cable strumming which can be a source
of noise or cause early fatigue. In so doing it appears also to reduce the
normal component of drag below that of the fully strumming bare round cable. The
mechanism by which strumming is suppressed is not fully understood but is thought
to involve the disruption of spanwise coherence in vortex shedding and drag
damping. A negative in the use of ribbon as with all cable-attached devices is

the increase in the tangential component of drag (tension) relative to bare cable.

As ribbon towcable has found important applications in fleet systems,
particularly in submarine towed communications buoys and various airborne mine
countermeasure systems, the need for accurate towing configuration prediction
has increased. Knowing the hydrodynamic loading on the ribbon cable is required
for configuration prediction.

Typically one of two methods is used by the David Taylor Naval Ship Research
and Development Center (DINSRDC) to develop the hydrodynamic loading functions.
The first involves direct measurement of the hydrodynamic loading on a two-dimen-
sional (rigid) model in the towing basin.” In the second technique an at-sea
experiment is performed in which certain parameters describing the towing con-
figuration are measured and the hydrodynamic loading functions are deduced by a
regression analysis process until a match of computed and measured configurations
is attained.

This latter technique was used to determine the hydrodynamic loading func-
tions for a particular ribbon cable. This report describes the at-sea experiment
including towcable model, instrumentation, and experimental procedures; presents
the results of the sea-trial and loading function analysis; and presents conclu-
sions. Comparison of the loading functions with an independent data base is

performed in Appendix A.

BASIC CONSIDERATIONS
The differential equations describing the steady-state two-dimensional
towing configuration and forces in a cable-body system are well defined based on
certain simplifying eae eOMe.” Solutions can be obtained by numerical inte-

Swe: Ae :
gration requiring as inputs:

dhe Tension and angle at some point on the cable, usually an end condition
specified at the towed body termination,
2. The form of the hydrodynamic loading functions, and

Bo The characteristic drag coefficient for the towline.

The body forces defining the cable end conditon typically are measured

quite accurately in towing basins or wind tunnels.

Tn complete list of references is given on page 21.

Thus the problem of predicting the steady-state towing configuration becomes
one of expressing the hydrodynamic force on the towcable. As noted previously,
DINSRDC has developed a method for directly measuring the hydrodynamic loading
functions in (two-dimensional) towing basin experiments. These measured loading
functions must ultimately be verified by at-sea measurements since there are some
artificialities introduced with the two-dimensional model. In time, as this
verification process proceeds on different designs, confidence in the two-dimen-
sional measurements as a basis for loading functions will grow and the need for
at-sea verification diminish.

The second method is based on an at-sea experiment in which measurements are
made of cable tension, body depth, and cable angle, all as functions of cable
scope and speed. The computer model is then exercised assuming different values
of hydrodynamic loading until an acceptable match of predicted-to-measured con-
figurations obtains. This regression analysis method is used here to develop
ribbon cable loading functions.

A towcable configuration can be defined mathematically by specifying an end
condition (tension and angle) and by knowledge of the loading along its span in

terms of the normal, Q, and tangential, P, force components expressed as follows:

Q

F - w sino

(1)

ae)
i]

G - w cosd

where is the normal component of hydrodynamic force per unit length,

F
G is the tangential component of hydrodynamic force per unit length,
w is the cable weight in water per unit length, and

0)

is the cable angle relative to horizontal.

The effort of this report is to evaluate these expressions of P and Q for the

ribbon towcable. Since the weight of cable is readily measured the task becomes
one of determining by regression analysis the normal and tangential hydrodynamic
force components which produce a fit of computed-to-measured data and which can

be expressed as:

£ (o)°R

£.(o)"R o

(ep)
i}

where £ Co) is the normal hydrodynamic loading function,
£.(o) is the tangential hydrodynamic loading function,
R is the cable drag per unit length when the axis is 90° to the
flow (R = 450 ,Vd) ,
p is the density of seawater,
CR is the normal drag coefficient based on cable diameter,
V is velocity, and

d is cable diameter.

As seen in Equation (2), F and G are expressed as the products of two terms.
Essentially the process of determining the hydrodynamic loading functions is one
of assuming various forms of £ Cd) and £.() until, through the regression analysis,
a value of Cy (as a function only of Reynolds number) is obtained for which the
computed configurations match those measured. Since the fitting process is based
on the products £ Co) °R and £ Co) °R, it appears that there could be a family of
solutions rather than a unique solution. However a constraint on the range of
solutions is that the CR values be plausible. Nonetheless it must be recognized
that the derived value of CR may be different from that which would be obtained
by physical measurement and, therefore, it is not valid to imply that this CR is
a characteristic of the cable independent of the hydrodynamic loading functions.

The above caveats notwithstanding, there is confidence in this technique for
developing the hydrodynamic loading functions and in applying these functions to

the configuration predictions of ribbon towcable provided:

1. the ribbon towcable design is similar,

cable diameter is not greatly different from that measured, and

3. the Reynolds number is within the range from 5.2 x 10° to 1.28 x 10.

In conformance with established marnodalloasy.." ff) and £.(¢) are represented

in this analysis by selected terms from the following trigonometric series:

f(¢) = A, + A, cosd + A, sind + A, cos2>o + A, sin2o.

1 2 3 4

DESCRIPTION OF EXPERIMENTAL EQUIPMENT

The experimental equipment consisted of a towed depressor body and the
experimental ribbon towcable. The towed body is shown in Figure 1; its dimen-
sions are given in Figure 2. This depressor weighs 1609 pounds (7204 N) in water
and has a variable incidence mid-wing. For this experiment, the wing incidence
angle was set at 57 (leading edge down). The hydrodynamic performance of the
body as measured in the towing basin is shown in Figure 3.

The ribbon towcable consisted of a 1450-ft (442-m) length of 0.78-inch
(1.98 cm) diameter, double-armored, electrical-mechanical cable with ribbons
attached, as shown in Figure 4. The cable consisted of two layers, reverse lay,
of galvanized steel armor strands surrounding a 10-conductor electrical core.
The cable weighed 0.688 pounds per foot (1.02 kg/m) in sea water and had a
breaking strength of approximately 50,000 pounds (223,880 N). The ribbons were
polyurethane strips threaded under the outer layers of armor. Ribbon geometry

is given in Table l.

TABLE 1 - CABLE AND RIBBON GEOMETRY

Cable diameter 0.78 in. (1.98 cm)
Cable length 1450 ft. (442 m)
Ribbon loop length 9.36 in. (23.77 cm)

Ribbon length-to-cable-
diameter ratio 6

Ribbon width 0.78 in. (1.98 em)
Material thickness 0.015 in. (.038 cm)

Spacing (centers) 0.78 in. (1.98 cm)

Ribbon coverage 100%

The towcable was marked at 100-ft (30.5-m) intervals to permit estimation

of cable scope in the water to about + 5 ft (+ 1.5m).

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Figure 1 - DINSRDC Depressor

5.6x7 = 2.18’

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DEPRESSOR WEIGHT IN WATER = 1609 POUNDS
DIMENSIONS IN FEET

Figure 2 - Dimensions of DTNSRDC Depressor

SPEED (m/s)

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0 4 8 12 16
SPEED (knots)
Figure 3a - Cable Angle at the Depressor
SPEED (m/s)
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SPEED (knots)

Figure 3b - Cable Tension at the Depressor

Figure 3 - Depressor Performance as a Function
of Speed for a Wing Angle of -50

CABLE TENSION (N x 107°)

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Figure 4 - Typical Ribbon Towcables

DESCRIPTION OF INSTRUMENTATION

The experimental system was instrumented to measure the following parameters:

ike body depth below the water surface,
Zs cable tension at the ship, and

3ic towing speed.

A watertight instrument housing in the depressor body contained electronics for
amplification and remote electrical calibration of the body depth sensor. The
housing also contained a voltage-controlled oscillator-type telemetry assembly
to transmit the depth signal through the towcable to the graphic and digital
recorders aboard ship. The cable tension at the ship sensor was direct wired to
a control unit within the ship laboratory which contained the tension sensor
amplifier and electrical calibration circuit. Ship speed was measured by the

DITNSRDC knotmeter. The sensors and their accuracies are listed in Table 2.

TABLE 2 —- MEASUREMENT SENSORS

Sensor
Measured Measurement

Cable tension Dyna-Line 0-10,000 + 200 1b

at the ship tensiometer 1b

Body depth Diaphragm OSS) ie ap Do wie
pressure gage

Ship speed DINSRDC knotmeter 0-25 kts ae Wo (Ohl Ise

The design of the electrical calibration circuits in this measurement system
virtually eliminate the effect of long-term zero drift and sensitivity error
within the amplifier and recording electronics external to the sensors. As a
result the total readout error is limited to that of each individual sensor.
These calibration principles are discussed in detail in Reference 5. The ship-
board readout electronics consisted of a 6-channel strip chart recorder providing
a time history of cable tension at the ship, depth of the body, and ship speed;
an integrating digital voltmeter, and two preset electronic counters provided
digital displays of the cable tension, body depth, and ship speed, respectively.
A digital recorder was used in conjunction with the digital display units to

obtain a printed record of the data.

iS} 2

EXPERIMENTAL ARRANGEMENT AND PROCEDURES

The experiment was conducted at sea from the R/V PATRICK KILEY in the New
Providence Channel off the Bahamas during July 1970. The operational area was
selected for minimum sea state conditions to obtain, as nearly as practicable,
steady-state towing.

The general towing arrangement is shown in Figure 5. A cable dominated
system was chosen assuring curvature over a significant portion of the towline.
Use of the AN/SQA-13(XN-1) winch and handling system accommodated the large size
towcable and simplified system deployment and retrieval.

The system was towed in a calm sea at nominal speeds of 6, 8, 10, 12 and
14 knots (3.1, 4.1, 5.1, 6.2, and 7.2 m/s). At each speed, measurements were
taken at nominal wetted cable scopes of 200, 400, 600, 800 and 1000 ft (61, 122,
183, 244 and 305 m).

Prior to recording data for each new speed and scope, body depth was
monitored to assure that the system had established a new equilibrium configura-
tion and was no longer influenced by speed change transients. Four separate sets

of measurements were taken for each data run.

RESULTS AND DISCUSSION
The averaged measured values of cable tension at the ship and depressor are
shown in Figures 6 and 7. Also shown in the figures are computer model predic-—
tions (solid lines) based on a regression-analysis determination of the hydro-
dynamic loading functions fo and f. and the drag coefficient Ce: These functions
represent the best fit to the data and were obtained through a trial and error

process. The values of the functions are:

fs = 0.4986 - 0.2499 cosd + 0.2527 sing - 0.2487 cos29 (4)
f. = -0.2255 + 0.3417 cosd + 0.2255 sind - 0.0811 sin2¢ (5)
Coyne 5.7467 - 0.93 log,, R, (6)

These functions are shown graphically in Figures 8 and 9 and apply to the
Reynolds number range from 5.2 x 10 to 1.28 x 1028 In assessing the goodness of
fit of computed-to-measured data it is seen that tension predictions are generally
within 10% of measured values with the body force zeroed out (within 5% with body

force included). Body depth predictions are within 5% of measured values except

14

y, | ae au les ss

Son a =

WATER SURFACE

TOWING SHIP

RIBBON TOWCABLE

_ CABLE ANGLE

DIRECTION OF TOW

|__==z
TOWED BODY

Figure 5 — Schematic Diagram of the Towing Arrangement

15

CABLE TENSION (1b)

0 61
7000

CABLE SCOPE (m)
122 183

Speed in Knots (m/s)

O 6.06 (3.1

6000 O 8.09 (4.
Ool17 (Ss2
A 12.09 (6.2
(we

)
2)
)
)
A 14.03 )

5000

4000

3000

1000

0 200

400 600
CABLE SCOPE (ft)

244

800

1000

Figure 6 - Cable Tension at the Ship as a Function of Cable Scope

16

CABLE TENTION (N X 1072)

DEPRESSOR DEPTH (ft

CABLE SCOPE (m)

61 122 183 244 305
600

Speed in Knots (m/s)
O 6.06
500 O 8.09 (4. 152
© 10.17
A 12.09
AAS

400 |

300

200

100

0 200 400 600 800 1000

CABLE SCOPE (ft)

Figure 7 - Depressor Depth as a Function of Cable Scope

17

DEPRESSOR DEPTH (m)

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19

for scopes of 400 and 200 feet where the average differences are about 6% and
8.7% respectively.

The relationships between £0) > £ (>) and CR have been discussed previously.
With respect to the problem of fitting predicted-to-measured configurations
another factor should be considered. In this methodology the term CR accounts for
the effect of Reynolds number on both the normal and tangential components of
hydrodynamic force. However, it should not be expected that the Reynolds number
effects are physically the same for the normal component at steep cable angles
where pressure drag predominates and for the tangential component at shallow angles
where frictional drag predominates. The final curve fits shown in Figures 6 and
7, therefore, reflect a compromise in the expression of Cc, with Reynolds number.

Ribbon represents a type of "fairing" unlike streamlined rigid fairing in
that the geometry changes with speed and with cable angle inclination. It has
been observed that at an angle of the cable 90° to the flow, the ribbons stream
out normal to the cable axis. At shallow angles, the ribbons have been observed
to lay down along the trailing edge of the cable. In addition to cable angle,
intuitively such factors as ribbon material stiffness, percent cable coverage,
and method of attachment are judged to influence the detailed geometry of the
ribbons and therefore the hydrodynamic loading. Some insight into this is given
in Appendix A. However, primarily because of a lack of knowledge of how to scale
the material stiffness factor, caution must be exercised in applying these loading
functions to a cable of significantly different diameter. Scaling should not be

attempted outside of the Reynolds number range covered in these tests.

20

CONCLUSIONS
As a result of this experiment and the data analysis here and in the Appendix

the following is concluded;

ibe The derived hydrodynamic loading functions and drag coefficients
will support a good estimate of towing configurations for this
design of ribbon towcable and for the range of variables covered

by the experiment.

Dap The functions and coefficients should be applied to other cable
diameters and/or ribbon designs with caution since ribbon material
thickness appears to be an influential parameter and methods for

scaling material stiffness have not been developed.

REFERENCES

bs Folb, R., "Experimental Determination of Hydrodynamic Loading for Ten Cable
Fairing Models," DINSRDC Report 4610, November 1975.

De, Pode, L., "Tables for Computing the Equilibrium Configuration of a Flexible
Cable in a Uniform Stream," David Taylor Model Basin Report 687, March 1951.

Bye Cuthill, E.H., "A FORTRAN IV Program for the Calculation of the Equilibrium
Configuration of a Flexible Cable in a Uniform Stream," Naval Ship Research and
Development Center Report 2531, February 1968.

4, Springston, G., "Generalized Hydrodynamic Loading Functions for Bare and
Faired Cable in Two-Dimensional Steady-State Cable Configurations," Naval Ship

Research and Development Center Report 2424, June 1967.

5h Singleton, R.J., "BIAS Buoy Measurement and Depth Control Instrumentation,"
David Taylor Naval Ship Research and Development Center Report 4451, November 1975.

Zl

APPENDIX A

A COMPARISON OF THE HYDRODYNAMIC LOADING FUNCTIONS
WITH SOME CRITICAL ANGLE TOWING DATA

Figures Al and A2 show hydrodynamic data on ribbon towcables obtained in
critical angle towing tests by DINSRDC. In these experiments long lengths of
cable were towed at the critical angle while cable tension at the towpoint, cable
angle and speed were measured. From these data a few points can be extracted for
comparison with the hydrodynamic loading functions and drag coefficients developed
earlier in the body of this report.

Two ribbon towcable models were evaluated, the models differing primarily in
the thickness of the ribbon material. Models A and B each had a 0.84-in. (21.3-mm)
diameter, double-armored electrical cable weighing 1.02 1b/ft (1.51 kg/m) in

sea water. Ribbon configurations were as shown in Table A.1.

TABLE A.1 - RIBBON CONFIGURATIONS

RIBBON RIBBON MATERIAL % CABLE
MODEL LENGTH WIDTH THICKNESS COVERAGE

A 6D 2D 15 mil (0.38 mm)
B 6D 2D 30 mil (0.76 mm)

The ribbon material was polyurethane and the ribbon density (or percent cable

-coverage) was 50% compared to 100% for the model described in the body of the
present report. Note, however, that the latter model and Model A have the same
material thickness, namely 15 mil (0.38 mm) which is one-half the material thick-
ness for Model B.

In reviewing Figures Al and A2, which are the reduced hydrodynamic measure-
ments of towcable tension per unit length and towing angle, it can be seen that
the Model B cable tows at a more shallow angle and develops a much higher tension
than the Model A cable. (In the graphs showing 30-mil (0.76-mm) thick ribbon
cable data Model B refers to the curve marked R/S = 50/00. The other curves result
from parts of the test in which increasing percentages of the ribbon were clipped

off.)

22

dT/dS (lb/ft) (N/m)

TOWING ANGLE (deg)

cu

RIBBON-FAIRED TOWCABLE RIBBON/STUB-FAIRED TOWCABLES

50% RIBBONS, 15-MIL THICK 30-MIL THICK
TRIAL 4H8 ye TRIAL 4H8
=
=
cc R/S% a f=
as ae ai
i sO a pees
S 25/25
as) 13/37 a
00/5007
0 6(3.1) 12(6.2) 0 6(3.1) “12(6.2)

TOWSPEED (knots) (m/s) TOWSPEED (knots) (m/s)

Figure A.1l -— Towcable Tension per Unit Length
versus Towspeed for Various Towcables

RIBBON-FAIRED TOWCABLE RIBBON/STUB-FAIRED TOWCABLES
50% RIBBONS, 15-MIL THICK 30-MIL THICK

TRIAL 4H8 TRIAL 4h8

TOWING ANGLE (deg)

0 6(3.1) 12(6.2) 0 6(3.1) 12(6.2)
TOWSPEED (knots) (m/s) TOWSPEED (Knots) (m/s)

Figure A.2 - Towing Angles versus Towspeed for Various Towcables

23)

Since these cables are trailing at a constant angle for each speed, each
experimental data point yields a set of hydrodynamic loading data points which
can be compared with the functions (or coefficients) developed earlier. Con-
sidering the normal components of force first, in a critical angle tow the
normal component of hydrodynamic force balances the cable weight component normal

to the cable axis. Thus
Ge), OR & wecosd (1A)

from which

wecoso
C 8 Sea (2A)
2,
Gy Gare)

where o- is the critical angle.

Applying the normal hydrodynamic loading function presented in equation (4),
C.'s were computed for the two models from the data shown in Figure A.2 and are
presented in Table A.2.

TABLE A.2 —- DERIVED NORMAL DRAG COEFFICIENTS

Reynolds Model A Model B
fo)

5)o 8) x 10°

8.86 x 10°

IG ALI/ o5 lop

1.477 x LO?

Also shown in Table A.2 is a column designated Cm These values of Ca were
computed by equation (6) for the corresponding Reynolds number in Table A.2. It
is seen that cn and Cc. for Model A agree rather well. It is concluded that the
representation of the normal hydrodynamic force developed in the body of the report
is also a good representation for Model A. This is in spite of the fact that
Model A has only 50% of the ribbon cable coverage. The reason may be that the data

base is comprised largely of shallow angle data. It has been observed that at

24

shallow angles ribbons tend to lie flat along the trailing edge of the cable. This
may reduce the effect of percent cable coverage on the normal component of hydro-
dynamic force.

In the case of Model B the ie eS drag coefficients Cc. are approximately
double the values for Model A (and Cc. ) a trend which could be inferred from the
data in Figure A.2.

It may be that the thicker (stiffer) ribbon material results in a higher
projected frontal area to the flow and this accounts for the higher drag co-
efficients when based on cable diameter. Or it may be that material stiffness
alters the wake to the extent that a different loading function applies or some
combination of the two. Regardless, it is clear that the normal hydrodynamic
loading function and Ce derived from a 15 mil (0.38 mm) ribbon data base is a
poor representation for a towcable with 30 mil (0.76 mm) ribbon.

In analyzing the tangential hydrodynamic force components, estimates of
tangential hydrodynamic loading function values can be made from the data in
Figure A.1 and the following relation:

(AT/AS - w sing)

Cas snl once alae ta . (3A)

Computed values of (Ey are shown in Table A.3.
c

TABLE A.3 — TANGENTIAL HYDRODYNAMIC LOADING VALUES

25

The computed values of £ (>) are also plotted in Figure A.3. Considering the
values of £.(o) as derived from the three data bases, neglecting for the moment
the CR values by which they were derived and how the CR values ultimately scale
the tangential hydrodynamic force, there is a consistency to the £() values.
First, Models A and B both representing 50% ribbon coverage have £($) values
which closely approximate a single trend line (Figure A.3). Second, these values
are approximately one-half those pertaining to the 100% ribbon coverage cable.

So it appears that wetted surface (percent cable coverage) is a key parameter
controlling tangential drag as would be expected.

However to compute the tangential force CR must be applied. If only the
15 mil (0.38 mm) thick ribbon models are considered, the consistency is maintained
and so is the concept of surface area as a key parameter. When the 30 mil (0.76 mm)
case is considered with its large CR values the tangential force scales up to
where the 30 mil (0.76 mm) ribbon tangential force is twice that of the 15 mil
(0.38 mm) ribbon although both have the same wetted surface. Now the concept of
wetted surface area having a linear effect on tangential force does not hold.

It must be concluded that the characteristics of the ribbon especially
material stiffness and possibly method of attachment are influencing hydrodynamic
forces both normal and tangential in important ways that are not understood. For
this reason scaling this data to ribbon cables of significantly different size

must be done with caution.

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