Title: Hydrodynamic modeling of nets and trawls
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 Material Information
Title: Hydrodynamic modeling of nets and trawls
Physical Description: xviii, 223 leaves : ill. ; 28cm.
Language: English
Creator: Krishnamurthy, Muthusamy, 1945-
Copyright Date: 1975
 Subjects
Subject: Fishing nets -- Design and construction   ( lcsh )
Trawls and trawling -- Design and construction   ( lcsh )
Civil Engineering thesis Ph. D
Dissertations, Academic -- Civil Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by M. Krishnamurthy.
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 220-222.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00098314
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000162565
oclc - 02710681
notis - AAS8913

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HYDRODYNAMIC MODELING OF NETS AND TRAWLS


By

M. KRISHNAMURTHY











A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY











UNIVERSITY OF FLORIDA

1975















ACKNOWLEDGEMENTS


The author wishes to express his sincere gratitude

to Dr. B. A. Christensen, under whose guidance this work was

carried out, for his advice and invaluable suggestions

throughout the study. This work would not have been

accomplished but for his patient guidance.

The author would like to thank Dr. Pop-Stojavanic

for his discussions during the course of the study. Thanks

are also due to Dr. Huber for serving on the supervisory

committee of the author.

Appreciation is extended to all of his friends in

the hydraulics laboratory, especially to Fred Morris and

Tracy Lenocker for their help during the period of experi-

ments. Assistance from the Marine Extension Center of the

University of Georgia is acknowledged. Mr. W. H. Burbank of

Fernandina Beach has provided invaluable suggestions and

assistance in the net designs.

The author appreciates the financial support received

from the National and Oceanic and Atmospheric Administration

Office of Sea Grant.

The typing of this dissertation has been ably per-

formed by Mrs. Carolyn Lyons.















TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS ................. ........... ......... ii

LIST OF TABLES ................ ........................ vi

LIST OF FIGURES ...................................... vii

LIST OF SYMBOLS ........ ............................. xi

ABSTRACT .............................................. xvii

Chapter

1 INTRODUCTION .................................. 1

1.1 Statement of Problem ................... 1
1.2 Objectives ............................. 7

2 COMPONENTS OF A GEAR .......................... 9

2.1 Net .............. .. .................. 9
2.2 Ropes ............. .... ............... 28
2.3 Sweeplines ............................. 32
2.4 Doors ........... ... .................. 33
2.5 Towing Warp ................. ........... 36

3 LITERATURE REVIEW .............. .... .......... 41

3.1 Mathematical Modeling of Fish Nets ..... 41
3.2 Physical Modeling of Nets and Trawls ... 44
3.3 Prototype Experiments .................. 70
3.4 Pitfalls in Existing Physical
Model Laws ........................... 71

4 DEVELOPMENT OF MODEL LAWS ..................... 74

4.1 Froude Modeling ........................ 74
4.2 Mesh-Twine Distortion .................. 74
4.3 Elongation of Twine .................. 80
4.4 Modeling of Ropes ............ ........ 84
4.5 Modeling of Floats and Sinkers ......... 86
4.6 Modeling of Doors ........................ 88








TABLE OF CONTENTS-Continued


Chapter Page

5 PROTOTYPE FIELD TESTS .............. .......... 89

5.1 Parameters Measured ..................... 89
5.2 Net and Towing Site ..................... 90
5.3 Instrumentation ........................ 91
5.4 Test Procedure ......................... 107
5.5 Test Results ........................... 109

6 MODEL EXPERIMENTS ............................. 113

6.1 Selection of Scale Ratios .............. 113
6.2 Instrumentation of Model Net ........... 123
6.3 Description of Experimental
Apparatus .......................... 131
6.4 Test Procedure ......................... 140

7 DISCUSSION OF RESULTS .............. .......... 160

7.1 Validity of Model Laws ................. 160
7.2 Effect of the Movable Belts ............ 164
7.3 Comparison Between Physical and
Mathematical Models .................. 166

8 APPLICATION OF MODEL APPROACH IN
DESIGNING A BEAM TRAWL ..................... 171

8.1 Introduction ........................... 171
8.2 Description of the Beam Trawl .......... 172
8.3 Design of the Beam Trawl ............... 175
8.4 Model and Field Experiments ............ 181
8.5 Discussion and Results ................. 185

9 CONCLUSIONS AND RECOMMENDATIONS ............... 191

Appendix

A BIBLIOGRAPHY ON CHARACTERISTICS OF FISHING
TWINES AND THEIR TESTING ................... 195

B BIBILOGRAPHY ON MODEL LAW ..................... 198

C BIBLIOGRAPHY ON MODEL EXPERIMENTS ............. 201

D BIBLIOGRAPHY ON PROTOTYPE EXPERIMENTS ........ 209

E CALCULATION OF FISHING NET DRAG BY THE
NUMERICAL METHOD DEVELOPED BY
KOWALSKI AND GIANNOTTI (1974) ............ 214

iv









TABLE OF CONTENTS-Continued


Page

REFERENCES .............................. ............. 220

BIOGRAPHICAL SKETCH .................................... 223















LIST OF TABLES


Table Page

2.1 VALUES OF COEFFICIENT OF FRICTION ............ 32

3.1 BASIC AND DERIVED MODEL SCALES FOR
HYDRAULIC MODELS ........................... 54

5.1 SPECIFICATIONS OF BURBANK FLAT NET ........... 91

5.2 RESULTS OF FIELD TESTS ....................... 110

6.1 SUMMARY OF SCALE RATIO ....................... 127

6.2 MODEL RESULTS WITH MOVABLE BEDS .............. 157

6.3 MODEL RESULTS WITHOUT MOVABLE BEDS ........... 159

7.1 PROJECTED FIELD DATA FROM THE RESULTS
OF MODEL EXPERIMENTS WITH MOVABLE
BEDS ........................ .............. 162

7.2 PROJECTED FIELD DATA FROM THE RESULTS
OF MODEL EXPERIMENTS WITHOUT
MOVABLE BEDS ............................... 165

7.3 COMPARISON BETWEEN PREDICTED VALUE OF
NET DRAG BY NUMERICAL METHOD AND
MEASURED VALUE IN THE FIELD TEST ........... 170

8.1 MODEL TEST RESULTS OF BEAM TRAWL ............. 183

8.2 RESULTS OF FIELD EXPERIMENTS ................. 185















LIST OF FIGURES


Figure Page

1.1 Components of a gear research program ......... 2

1.2 Physical elements of a fishing operation ...... 3

1.3 Iterative procedure in trawl and trawler
design and selection ........................ 4

2.1 Components of a gear .......................... 10

2.2 A netting twine ............................... 11

2.3 Load elongation curves ........................ 13

2.4 Load elongation curves for polyamide
netting twine ............................... 15

2.5 Logarithmic linearization of load-strain
curve for polyamide ........................ 16

2.6 The mesh ........................ ........... 17

2.7 Net panels ..................... ........... 20

2.8 Net diagram of Burbank flat net ............... 21

2.9 Drag coefficient for nets as a function
of Reynolds number ........................ 25

2.10 Hanging the net on the headrope ............... 29

2.11 Equilibrium condition of door ................. 34

2.12 Forces acting on a towing warp ................ 38

3.1 Force polygon of a fluid flow ................. 46

3.2 Force polygon in the model and full-
scale net ................................... 59









LIST OF FIGURES-Continued


Figure Page

4.1 Idealized mesh and twine in prototype
and model ....... ............. .......... 76

4.2 Typical stress-strain curve for polyamide
tw ine .................................... 81

4.3 Evaluation of average stress in a twine ...... 83

4.4 Headrope ............................. ........ 85

4.5 Attachments in a rope ........................ 86

5.1 Net diagram of Burbank flat net .............. 92

5.2 Dimensions of door ................ .. ......... 93

5.3 Site of prototype field study ................ 94

5.4 Instrumentation of prototype net ............. 95

5.5 Attachment of bolt to the cable .............. 97

5.6 Bolt load cell, its attachments and the
recorder ......................... ......... 99

5.7 Underwater load cell ................ ........ 100

5.8 Attachment of underwater load cell to
the footrope and headrope .................. 101

5.9 Attachment of underwater load cell to
the door .................. ................ 102

5.10 Twine load cell .............. ........... 103

5.11 Twine load cells in the net .................. 105

5.12 Channel selector switch and strain
indicator for the twine load
cells ............. ........ .......... 106

5.13 Relationship between warp tension and
trawler speed .................. .......... 112

6.1 Tension testing of twines .................... 115


viii









LIST OF FIGURES-Continued


Figure Page

6.2 Grip for testing of twines ................... 116

6.3 Elastic characteristics of twines ............ 117

6.4 Model net diagram ................. ........ 119

6.5 Elastic characteristics of ropes ............. 122

6.6 Dimensions of model door ..................... 124

6.7 Model doors ..................... .......... 125

6.8 Model net .......... .......... ........... 126

6.9 Load cell to measure warp tensile force ...... 128

6.10 Load cell to measure the tensile force in
the rope between door and net .............. 129

6.11 Load cell to measure tensile force of the
midsection of headrope ..................... 130

6.12 Gate, main and return flumes ................. 132

6.13 Storage tank, pump and bypass pipe ........... 133

6.14 Relationship between weir head and
flume discharge .......................... 134

6.15 Electric point gauges for measurement
of the head on the weir .................... 135

6.16 Weir and flow straighteners .................. 136

6.17 Sand filter for the flume .................... 138

6.18 Mounting of motor and regulator for
the movable belt ......................... 139

6.19 Movable bed ...................... .......... 141

6.20 Velocity distribution at center
section of right belt .................... 142

6.21 Isovel for run 1 .... ........... ........ 144









LIST OF FIGURES-Continued


Figure Page

6.22 Isovel for run 2 ............................. 145

6.23 Isovel for run 3 .................. .......... 146

6.24 Isovel for run 4 ............................. 147

6.25 Isovel for run 5 .................. .......... 148

6.26 Isovel for run 6 ......... ................... 149

6.27 Point gauge and Ott current propeller ........ 150

6.28 Net profile during testing ................... 151

6.29 Plan view of net during testing .............. 152

6.30 Side view of net during testing .............. 153

6.31 Front view of net during testing ............. 154

6.32 Side view of door during testing ............. 156

7.1 Prediction of warp tensile force from
model results ............................ 167

7.2 Prediction of drag force acting on a
net ............. ............. ... ......... 168

8.1 Beam trawl ................... .............. . 173

8.2 Trawl head .......... ......... .......... 174

8.3 Continuous beam .................. ........... 176

8.4 Prototype net for beam trawl ................. 180

8.5 Model net diagram for beam trawl ............. 182

8.6 Ocean testing of beam trawl .................. 184

8.7 Relationship between net spread and
trawler speed for otter door trawler ....... 186

8.8 Relationship between warp tensile force
and trawler speed for otter door trawler ... 187

8.9 Relationship between warp tensile force
and trawler speed for beam trawler ......... 188
















LIST OF SYMBOLS


a

4
a

A

b

B


B

B.M.


c

C
a

CD

Cf


C1,C2,C3
Cq,C5,Cg

d

D

D.

D
O

D
w


- Half of wing spread

- Acceleration


- Elastic constant, area

- Half of headline height

- Elastic constant of twine


- Buoyant force

- Bending moment

- Length of net


- Cauchy number

- Drag coefficient


- Friction coefficient of flow

- Constants



- Subscript denoting door

- Twine diameter

- Inside diameter

- Outside diameter

- Depth of water










LIST OF SYMBOLS-Continued


E Float diameter

E' Modulus of elasticity

E Euler number
U

f Coefficient of friction, subscript denoting float

F Force

F Froude number
r

g Acceleration due to gravity

H Horizontal dimension

H Rope diameter

I Moment of inertia


kl,k2 Float constants

K Bulk modulus of elasticity

1 Length

L Characteristic length

L Length of towing cable

m Subscript denoting model

m' Number of meshes (depth wise)

m" Mass

M Bar length, moment

M Mach number
a










LIST OF SYMBOLS-Continued


n Number of floats or sinkers per unit length of rope

n Frequency of vortices

n' Number of meshes (lengthwise)

ni A factor considering the rate of filling of fish

N Number of meshes

N Total number of floats or sinkers

Nbd Reaction of ocean bottom to door
bd

0 Surface tension

p Subscript denoting prototype

p' A factor denoting twine porosity

p" Pressure

P Power

r Resistant force, subscript denoting rope

R Tensile force in towing cable at door

R Reynolds number
e

s Cable length, subscript denoting solid

S Solidity

S' Circumference

S Strouhal number
n

t Time


xiii









LIST OF SYMBOLS-Continued


T Characteristic time

TI Cable tension

T Tensile force

v Velocity of flow

v Velocity at depth y

V Trawler velocity, subscript denoting vertical
dimension

w Weight per unit length or area or volume,
subscript denoting water

W Total apparent weight

W Weber number
n

x Longitudinal axis (along the width of net)

X Total force in the x direction

y Vertical axis

Y Total force in the y direction

z Transverse axis (flow axis)

Z Total force in the z direction

Z Sectional modulus
m

Greek Symbols

a Angle of incidence

w Unit weight of water









LIST OF SYMBOLS-Continued


ys Unit weight of twine

y' Unit weight of float or sinker


Yr Unit weight of rope

e Strain

n Mesh number scale

K Force scale

A Length scale

AD Twine diameter scale

AE Float or sinker size ratio

AH Rope size ratio

A Mesh size ratio

24 Total angle between two adjacent bars

p Dynamic viscosity of water

v Kinematic viscosity of water

p Density

o Stress

- Time scale

S- Frequency










LIST OF SYMBOLS-Continued


Abbreviations

cfs Cubic feet per second

F Fahrenheit

fps Feet per second

ft Feet

gf Gram force

hp Horsepower

in Inch

lb Pounds

OD Outside diameter

rpm Revolutions per minute









Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of
Doctor of Philosophy


HYDRODYNAMIC MODELING OF NETS AND TRAWLS


By

M. Krishnamurthy


December, 1975


Chairman: B. A. Christensen
Major Department: Civil Engineering


Design of efficient fish nets by means of small-scale

hydrodynamic models is of relatively recent origin in the

United States. While investigators have developed basic

equations for modeling flow around fish nets by considering

the intertia and gravity forces as primary forces, they assume

that the elongation of twines and ropes in the net is negli-

gible. However, the shape of the fish net and, therefore,

the forces acting on it are affected by the stretching of

twines and ropes under load. In order to permit the correct

numerical transfer of model observations to the prototype, it

is necessary to establish special hydrodynamic model laws

which take the stress-strain characteristics of the model and

prototype materials into consideration. Such model laws were

developed in this study.

These developed model laws were verified by full-scale

ocean tests and by laboratory experiments. A movable bed was


xvii









constructed in the laboratory flume in order to obtain uniform

velocity profiles similar to the uniform velocity profiles in

the prototype. Experiments conducted in the flume yielded

results comparable to those of the field tests, thereby,

confirming the validity of the developed model laws.

Using the model approach, a beam trawl was designed

to harvest deep-water shrimp. The results of laboratory

tests and field trials indicated that a substantial decrease

in the overall drag force was achieved with the designed beam

trawl in comparison to a conventional otter door trawl. The

major benefit of the reduction in the drag force would be a

decrease in the fuel consumption of the trawler.


xviii














CHAPTER 1

INTRODUCTION


1.1 Statement of Problem

The manufacture of nets and trawls is an art which

has been handed down from father to son through generations.

Fishing gears of the past were designed by trial and error.

Nowadays an attempt is being made to supplement this empiri-

cal approach with analytical theory and with physical tests

in the laboratory and in the oceans.

The optimum performance of a fish-trawling operation

depends on the efficiency of the gear and the behavior of

fish. Therefore, any research program of gear design should

include the biological study of fish reaction. The compo-

nents of one such program are shown in Figure 1.1.

The major physical elements of a fishing operation

are the net, the otter doors, the sweep-lines, the towing

warps, and the ship or the trawler as indicated schematically

in Figure 1.2. The design of these elements is an iterative

process, an outline of which is given by Dickson (1971) and

is shown in Figure 1.3.

From Figures 1.1 and 1.3, it can be seen that fish

biology should also be considered in the iterative design









I Iprc-vemr. of isting Fish Trcl in


I. taoia __S___uof

Engineering Stud. of ; .. .. -- c c' |


y .Ic _
Ana iy v ical Mo2 e i I S.mc *s Ele c tri o I
Reserch -i !'I

S____ __ ___j

Results 'X :.

SC r_____-____C_ a -_-Q


Field Tests Field Tesis


G -- -- c r---- --

Generalztiion of -eas bn Ce ne-rli:tion of
Gear Design Co c ia ; F ish Eehavior



N ___. _
tiew DK;".g n aind ?ocedL're oa Fishinig


Figure 1.1. Components of a gear research program.


















A




0::
w
-j


Cu








a





C




0









c




a
L





















-



CO
c
*a-










Trawler available
Estimate wind conditions
Estimate current conditions
Estimate weather conditions
Determine towing speed

Calculate propeller thrust
Calculate permissible trawl drag

Estimate trawl size
-* Choose mesh sizes
Choose material -
- Choose twine sizes

Determine trawl drag
Consider bottom conditions

Determine rigging to suit bottom conditions
Consider fish species
Consider fish sizes
Consider catch size

Determine any special rigging to handle catch
Determine handling system for trawl and trawler
Consider most vitial environmental conditions,
particularly light and temperature
Consider stage in fish life cycle during the
fishery
Estimate proximity of fish to bottom and
vertical distribution
Consider any special ecological conditions
Decide on trawl shape
Decide on rigging requirements to achieve
shape
Determine trawl size






Figure 1.3. Iterative procedure in trawl and trawler
design and selection.


Source: Dickson, 1971.






5


of a trawl and a trawler. However, these aspects are beyond

the scope of the present investigation. Also, the inter-

action of the propulsive system of the trawler with the

performance of the trawl is itself a major study. Therefore,

the current research focuses attention on the engineering

behavior of the gear. This behavior of the gear can be

studied (1) by analytical approaches, (2) by physical tests

in the ocean and (3) by model experiments in the laboratory.

Analytical gear design requires a knowledge of the

hydrodynamic resistance of the net, bottom friction of the

otter doors and the behavior of the rigging under different

towing conditions. The literature on mathematical modeling

indicates that this design procedure involves long and

tedious numerical computations. Further analytical approaches

to these problems are to be made before this approach may be

considered practical.

Ocean tests of fishing gear are expensive and time

consuming. Determination of the shape of the net under

various conditions is cumbersome because underwater observa-

tions of the net depends upon the clearness of water. The

outcome of field tests also depends on such factors as

weather conditions, shark problems, etc.

Another method of designing the fish net is by small-

scale model experimentation in the laboratory. Hydraulic

models and laws governing their use have been applied suc-

cessfully to the problems of dams, spillways, energy









dissipators and ships. The hydraulic model has proved to be

a powerful research tool even in the study of fluvial phe-

nomena (Graf 1971), where the interaction between water and

sediment is considerably more complex than the case of nets

and trawls. Therefore, the fishing industry may reap sub-

stantial benefits through improved net structure and improved

performance derived from the hydraulic model concept in net

and trawl research.

Physical model tests in the laboratory offer various

advantages over ocean tests. Costs: Whereas field testing

for one net may require $5,000,laboratory costs may be only

$500, with fewer logistic problems such as weather and ship-

time (Hillier 1974). Visual observation: It is possible to

detect easily the deficiencies in net design and to implement

modifications immediately. Time factors: A model test

requires by far less hours than a field test. At least a

week is needed to conduct a particular aspect of a gear test

in the ocean whereas the laboratory tests covering the same

modifications can be done in a day. However, model test

results should be extrapolated with caution because of scale

effects of the models. Therefore, an ideal gear design

would be a method which combines the analytical approach

with model and full-scale experiments.

Summarizing, a simple method is necessary to design

and to test efficient fishing gear. Though not satisfactory,

existing mathematical analyses can be applied to the initial









and preliminary gear design. At the present time, however,

physical scale modeling in the laboratory seems to be the

only reliable alternative tool in the evaluation of gear

performance. Development of such a tool is the general

objective of the present investigation.


1.2 Objectives

The specific objectives of the research are a review

of literature on mathematical and physical models of fishing

gear and their deficiencies, the development of adequate

model laws and the verification of the developed laws and

procedures by field and model tests.

The presentation of the objectives is as follows.

The gear and the behavior of its elements under fluid motion

are introduced in Chapter 2. In Chapter 3, the literature

on mathematical analyses of fishing gear, physical modeling

in the laboratory and full-scale field experiments is

presented. The pitfalls in the existing analyses are

brought out. Development of adequate model laws is pre-

sented in Chapter 4. To verify the model laws, prototype

experiments were conducted in the Gulf of Mexico as explained

in Chapter 5. Chapter 6 illustrates the model experiments in

the hydraulic flume. The validity of model laws is given in

Chapter 7. Using the model approach, a special beam trawl

was designed for deep-water shrimping. The design and

testing of this trawl in the laboratory and in the field

are given in Chapter 8. Conclusions on the experimental






8


results in the laboratory and in the field are presented in

Chapter 9. Suggested future research is mentioned also in

the same chapter.















CHAPTER 2

COMPONENTS OF A GEAR


In Chapter 1 the main components of a gear were

briefly mentioned and shown in Figure 1.2. Their physical

structure and behavior, when towed through water, are

described below.


2.1 Net

A net consists of three sections, namely cod end,

belly and wings (Fig. 2.1). Each section may be of different

netting twine and may have different mesh dimension. The

net is usually treated by dipping it in a solution of tar

to give greater resistance to wear, tear and aging due to

storage in the sun.

2.1.1 Netting Twine

Netting twine may be of a natural fiber such as

cotton and coir, or of synthetic polymers like nylon

(polyamide) and polyethylene. Single yarns are'plied

together and twisted to make a netting twine (Fig. 2.2).

The voids in a twine depend on the amount of twist and the

diameter of plied yarns. Nylon is widely used in the United

States in making a net.









11







; z
o Z









I-U
0<




WI
O









/ a





ci
Z Q)

z




z






Z 0




W Z-



z < 0
9,>-









The cross-sectional shape of twine and plied yarns

may be approximated by a circle (Fig. 2.2). The solid area

of a twine consisting of three plied yarns may then be

found from the expression


Aolid = 0.508 D2 (2.1)


where

Asolid = Area of solid mass
solid

D = Diameter of the netting twine

Therefore, the ratio of solid area to the total twine area

and porosity in the twine are equal to 0.646 and 0.354,

respectively.

Properties of the twine that are specially important

in the fishing industry are density, tenacity, tensile

strength, knot strength, loop strength, elasticity, tough-

ness, stiffness, water absorption, resistance to heat,

sunlight, seawater and mildew. The definition and determi-

nation of these properties are described by von Brandt and

Carrothers (1964). Additional information on characteris-

tics of fishing twines and their testing may be found in

the bibliography which is given in Appendix A.

The elastic behavior of a netting twine under a load

is described by its stress-strain curve or load-strain curve.

Figure 2.3 shows the relationship between load and strain of

man-made fibers used in making nets. This relationship for































S0



H \)
D a
"Z o
z



SL 0

-L 0 0
S- 0 <
u- --H H- \ - o "

z <
w o \ \ \



0 0
_02 0 co
z < U 1
w 0 0G nc
>" -J w W w :I.c.
-J O U)) p
0s o r4
o: t 5 5 S f "--- -\ \ -

Mn W


oD- 0- a- rL C








S OVO- 'V3a iON d7VH
EL EL E L E
w 0
Zw 4: En


OVzl )4OU I0N>


3HiL A0 .LN3OHUd NI OVO9










polyamide netting twines of different linear density is

drawn in Figure 2.4. It can be seen from Figures 2.3 and

2.4 that the fibers do not obey the linear Hooke's law.

However, a nonlinear law is expressed by


o = AEB (2.2)

where

o = Stress

E = Strain

A and B are constants which may be derived from the log-log

plot shown in Figure 2.5. The value of stress is obtained

by dividing the load by the original solid area of the

twine. This definition of stress is used without exception

in this study.

2.1.2 Mesh

The basic structure of a net is the mesh. A mesh

is defined by Kawakami (1964) as a rhombic opening enclosed

by four bars of twine of equal length firmly knotted at the

four corners. Since one bar is common to two meshes and

one knot to four meshes, a mesh consists of two bars and a

knot. The area of a single mesh depends on the angle

between two adjacent bars (Fig. 2.6). This angle may be

changed by different hanging or mounting of the webbing to

the frame line. The surface area of a mesh can be calcu-

lated from the geometry of the mesh and is given by the

simple formula










































































J6bI NI OVO-l


-,4

.LJ





.--
0




o




0
z U 0
O















o M
S, 0
-1







z o
n-j 0
LZ 0

0 1










43
m -
0 0

-A -







4 c0

W p
0i 0
r-


s C
*T C~









































1 2 5 10 20 50
LOAD kgf


Figure 2.5.


Logarithmic linearization of
load-strain curve for polya-
mide.















































Figure 2.6. The mesh.









Amesh = 2M2 sin c cos ( (2.3)

where

A = Surface area of the mesh
mesh
M = Bar length

2I = Total angle between two adjacent bars

The weight of one dry mesh W, in air, is the sum of

the weight of its two bars and the knot.


W = 2([ 1 (M.py.) + [ [MkP ns) (2.4)


where

Ys = Unit dry weight of twine
1-p' = Porosity of the twine

Dk = Diameter of the knot

1-p' = Porosity of the knot

Mk = Length of twine included in one knot

Since the density of the fiber is unaltered by

tightening of the knots,

iD2 rD2
D- p' = P (2.5)

and

Dk = D[P (2.6)
k Pk

From Equations (2.3) to (2.6), the apparent weight,

w, of one mesh in water per unit area is obtained:











sin 2= KJy (2.7)

where

Y = Unit weight of water


2.1.3 Net Panel

A net panel is an array of meshes. It is either

straight or tapered (Fig. 2.7). A net consists of a combi-

nation of straight and tapered panels sewed together. The

combination and tapering of panels depends on the judgment

of the net maker who uses a net diagram to show this combi-

nation. For example, Figure 2.8 is the net diagram of a

"Burbank Flat Net" which is widely used by Florida and

Texas shrimpers.

The length and depth of a rectangular panel of n'

by m' meshes (m' meshes deep) can be computed from the

geometry and hanging of the net panel


LH = 2n'M cos i (2.8)

and

L = 2m'M sin p (2.9)

where

LH = Length of panel

Lv = Depth of panel

When a net panel is placed in a current with a uni-

form velocity, a hydrodynamic force acts on the panel in a







20






























I 4


z



c<)
Q)

to






n-




l--
C')


Al
YX7 v





































0 4J













I c o
c c
Cbo









^ O ^4-1

rC)









direction normal to the panel. The component of this force

to the current is the drag force. The magnitude of drag

force is calculated by


S= C 2 A + C V2 A (2.10)
Db 2 b Dk 2 k

where

F = Drag force

CDb = Drag coefficient of bar

CDk = Drag coefficient of knot

p = Density of water

V = Velocity

Ab = Projected area of bars onaplane normal
to current

Ak = Projected area of knots onaplane normal
to current

The first and second terms in Equation (2.10) represent the

drag to the bars and knots, respectively.

The values of drag coefficient for the bar and the

knot depend on the Reynolds number of the bar and knot,

respectively. The Reynolds number is defined as


R VL (2.11)
e v

where

v = Kinematic viscosity of water

L = Characteristic length

Kowalski and Giannotti (1974) consider the bar length as the

characteristic length. In the turbulent region where the









Reynolds number is greater than 20,000, a value of 2.02 for

CDb is given. Taking the diameter of the knot as the
characteristic length, a value of 0.47 for CDk is shown.

For a net panel placed normal to the current, the

drag on the panel is


F = C n pV A S (2.12)
D panel 2 surface

where

CD panel = Drag coefficient of the panel
D panel
A surface = Total projected area on a plane normal
to the current

S = Solidity, the projected solid area per
unit surface area of the panel.

The values of S and CD panel are


(2MD + D2]
S = (2.13)
M2 sin 2)

and


( k AkNk + CDbbAb) (2.14)
D panel AkNk + AbNb
kk k b b


where

Nk = Number of knots

Nb = Number of bars


Fridman (1973, p. 63) considers the diameter of the

bar as the characteristic length and defines the Reynolds

number as









R VD (2.15)
eD v

From the results of the laboratory experiments, he estab-

lishes a relation between ReD and CD panel (Fig. 2.9). The

values of CD panel were averaged from the drag coefficients
D
for net panels with M values ranging from 0.0024 to 0.1500.

Carrothers and Baines (1975) present an empirical

equation to compute the value of CD panel for ReD > 500.



CD panel = 16 for S < 0.1 (2.16)


If the axis of the net panel is inclined at an angle

a with the velocity vector, the corresponding drag coeffi-

cient of the net panel can be found experimentally.

Carrothers and Baines (1975) analyzed the experimental

results of various investigators and concluded:


C' = C sin2 a (2.17)
D panel D panel

where

CD = Drag coefficient for the panel
D panel for a = 90

CD = Drag coefficient when the panel is
D panel inclined at an angle a with the
velocity vector

For values of a approaching 900, Tauti (1934)

approximates the value of sin2 a and gives an expression

for the drag coefficient.


C' = C sin a
D panel D panel


(2.18)























'4-1




-d
a




0

3







U


-,
S,



















4-.
1o o


c Q)






U a




Q r-







U-, 0


MP-4
a
/ ~ ~ ~ .- a 0 i 0 "9 <
/ \ ? (
0 I









Miyake (1927), Revin (1959) and Kanamori (1960) verified this

approximation by laboratory experiments. Giannotti (1973)

has conducted wind tunnel tests on two different net frames

and given results which support this approximation.

However, at low values of a, the component of

resistance normal to the net becomes small. The predomi-

nant force will be the component parallel to the frame.

Carrothers and Baines (1975) have found that Equation (2.18)

predicts low values of drag coefficient for low values of a

and, therefore, cannot be applied to compute the drag force.

For this case, Kawakami and Nakasai (1968) determined the

magnitude of the force acting along the length of the panel

by

F = C"D panl 2 [. tan 4 cos a (2.19)
D panel 2 J M

where

C" = Drag coefficient for the net panel
D panel for a =


Equation (2.19) considers the resistance of the knots to the

flow to be small compared with the resistance of the bars.

2.1.4 The Cod End

The cod end is the tail of the net where the catch

is collected. It has a thicker twine and smaller mesh

compared with the other parts of the net. To protect the

cod end from wear and tear, soft strands of twines known

as chaff are attached to each knot.









During a tow, Kowalski and Giannotti (1974) consider

the cod end a hollow cylinder with its longitudinal axis

parallel to the flow. To compute the drag force acting on

the cod end, they suggest:



Fod = (0.82) 22 d od n, + C
= cod 1 2


x [Nb -MD + NknD2] 1 ni (2.20)


where

Fod = Drag

dcod = Diameter of the cylindrical cod end

Cf = Friction coefficient

n, = Factor which considers rate of fish filling
in cod end: ni = 0 for t = 0, and nl = 1
for t > 0

Equation (2.20) holds good for Reynolds number,

R =VM greater than 107 and with an aspect ratio greater
eM V
than 2. The aspect ratio is the ratio of the length to the

diameter of the cylindrical cod end.

2.1.5 Belly

The belly refers to the top and the bottom tapered

part of the net extending from wing to wing and from the

hanging lines to the cod end. The shape of the belly

during a tow is complicated. Kowalski and Giannotti (1974)

approximate the belly by a conical net with an elliptical

mouth, where the major axis of the ellipse is given by the









wingspread and the minor axis by the headline height. They

compute the resistance of the belly to the flow by Equation

(2.18).

2.1.6 Wings

The wings are the sides of the net, tapered along

the top seam and straight along the bottom seam. The wings

facilitate the required mouth opening of the net.

2.2 Ropes

2.2.1 Headrope

After the sections of the net are sewed, the top

portion of the net is hung on a headrope (Fig. 2.10). The

headrope is a combination rope of steel and manila. The

floats are attached to the headrope when a larger mouth

opening is required.

Fridman (1973, p. 73) analyzes the shape of the

headrope under towing conditions. He assumes a catenary

shape for the rope and presents a procedure to compute the

magnitude of the tension along the length of the rope.

The resistance of a rope lying at an angle a to the

flow is computed by


F rope = Crope sin3 a] ] H (2.21)
rope D rope 2 r r

where

H = Diameter of the rope

Zr = Length of the rope
r



























(J









O


O 0
zw
z U



-J
I I






oC
w



0-









C = Drag coefficient of the rope when it is
D rope lying perpendicular to the flow

The value of CD rope is given as 1.1 by Kowalski and

Giannotti (1974), whereas, Fridman (1973, p. 56) offers a

value ranging from 1.2 to 1.3. The resistance of the head-

rope can be computed by Equation (2.21).

2.2.2 Floats

To achieve a larger fishing height, floats are

attached on the headrope. They may be hollow cast aluminum

or plastic spheres or solid bodies made of plastic foams.

The drag acting on the floats is determined by


F = N C p A (2.22)
float f D float 2 f (2.22)

where

N = Number of floats

CD float = Drag coefficient for spherical float

A = Projected area of float to a plane
normal to flow

For a single spherical float, Fridman (1973, p. 51)

expresses a value of 0.475 for CD float when the float

Reynolds number is greater than (2.0)(105). The float

Reynolds number is defined as

VD
R (2.23)
ef v

where


D = Diameter of the spherical float









However, if the floats are grouped together, there is an

interaction of flow between the floats and, for this case,

Fridman gives a value of 0.93 for CD float

2.2.3 Ground or Footrope

The bottom portion of the net is hung on the foot-

rope. Sinkers are attached to the footrope to keep the net

in contact with the bottom. Spacing and weight of the

sinkers vary with the type of the net.

Kawakami and Suzuki (1959) and Suzuki and Kawakami

(1960) studied the shape of the footrope during a tow and

its load distribution. The resistance of the footrope to

the flow are the drag and friction forces. The magnitude

of the drag force may be computed from Equation (2.21) if

the angle between the rope and flow direction is known.

However, the magnitude of the friction force depends on the

bottom condition and the material of the rope. Fridman

(1973) estimates the friction force as


friction = f W (2.24)
friction

where

Ffriction = Friction force

W = Apparent weight of the rope

f = Coefficient of friction between the
soil and the rope

The values of f for two different bottom conditions

and for different materials are given in Table 2.1. The








coefficient of friction is dependent on the angle between the

flow direction and the rope. Fridman (1973) establishes a

graphical relation between a and f.


TABLE 2.1

VALUES OF COEFFICIENT OF FRICTION


Coefficient of Friction


Material


Gravel with
Sand


Fine Sand


Cast iron 0.47 0.61

Wood 0.51 0.73

Stone 0.54 0.70

Lead 0.44 0.53

Sand bags 0.63 0.76

Vegetable ropes 0.70 0.80
hempss)


Source: Fridman (1973, p. 38).


2.3 Sweeplines

To increase the wingspread, it is customary to insert

extra lengths of rope between the door and the wing. These

ropes are known as sweeplines. They may be the same material

as the footrope, the headrope or the towing warp. The length

of the sweeplines depend on the fishing conditions and the

towing speed.










2.4 Doors

The doors in a trawl provide the all-important fish-

ing spread of the net. The doors of the bottom trawls used

in Florida are rectangular in shape. They are wooden boards

reinforced with iron strips and no attempt on streamlining

is made. At the lower edge of the door, a heavy metal shoe

plate is fitted for stability and for protection of doors

against the hard bottom. The towing warp is connected to

the doors by a chain and a shackle arrangement. If the

sweeplines are used in the net, they are connected to the

backstops of the door by shackles.

Figure 2.11 shows the equilibrium condition of the

door. The forces acting on the door are the tensile force

in the towing warp R1; the hydrodynamic force, R2; the

tensile force in the sweepline, R3; the apparent weight of

the door, W; and the friction of the door against the bottom,

F. The governing equations for the equilibrium conditions

are

EX = 0 EM = 0
x
EY = 0 EM = 0
y
ZZ = 0 EM = 0 (2.25)
z

where

ZX, EY and ZZ = Sum of components of all forces
of x, y and z directions,
respectively

















x

R3 \R2
R. z









y


n lxy


-- z
R3zy


WI


Figure 2,11. Equilibrium condition of door.


Source: Fridman, 1973.









EM EM and EM = Moment of forces about x, y and
x y z z axis, respectively


The equilibrium condition of the doors is detailed by Crewe

(1964) and by Fridman (1973).

The resistance of the door to the flow arises from

the drag of the door and the component of the friction force.

The hydrodynamic drag of the doors is


F C 2V2 A (2.26)
door D door A (2.26)

where


Fdoor = Drag force acting on doors

CD door = Drag coefficient for door
A = Area of door


The drag coefficient for the door depends on the

door Reynolds number which is defined as

Vad
R = -d (2.27)
ed v

where


zd = Length of door


It also depends on the angle of incidence of the flow, the

shape of the door and the ratio of the length to height of

the door. For Red > (0.8) (106), Fridman (1973, p. 276)

presents the values of the drag coefficient for oval and

rectangular doors with angles of incidence ranging from 20









to 40. The CD door values vary from 0.5 to 1.0 for a

rectangular door. This range agrees with the trials of

Crewe (1964) and Scharfe (1959).

The friction force of the door against the bottom

depends on the apparent weight of the doors and the soil

condition. Literature on the evaluation of this friction

force is scarce. As a first-order approximation, the magni-

tude of the friction force may be evaluated from Equation

(2.24) and by using Table 2.1


2.5 Towing Warp

Towing warps are steel wire ropes, the diameter of

which depends on the towing power of the trawler and the

type of trawl. Length of the warps is determined by fishing

conditions, trawl type and drum capacity.

Drag force acting on a towing warp is a function of

its (warp) shape which, in turn, is determined by the system

of forces acting on it. The hydrodynamic drag F of a

straight circular cable inclined at angle a to the flow is

F = CD wr [V2l sin2 a] H( ri) (2.28)
D warp [2 rr

where

CD warp = Drag coefficient for warp
D warp

For steel cables, the value of CD warp is 1.1

(Fridman 1973, p. 57). However, if the frequency of the

vortices forming behind the cable is equal to the natural









frequency of the cable system, the value of C warp will be

greater than 1.1. Literature on the evaluation of this

value is not presently available and research is wanting.

Figure 2.12 shows the forces acting on a towing cable

system. The tangent at any point to the cable makes an

angle a to the incident flow. Therefore, the towing

velocity can be resolved into V sin a and V cos a as the

normal and tangential velocity components, respectively.

Let F be the drag force per unit length of the cable when

the cable lies normal to the flow and F be the drag force

when the cable is tangential to the flow. For the flow

system represented in Figure 2.12, the force acting normal

to the cable is F sin2 a. Similarly, the force tangential
n
to the cable is F cos2 a. But Streeter (1961) approximates
t
the value of F cos2 a to F cos a to fit the experimental

data. The forces acting on an element of length ds are

given in the free body diagram of Figure 2.12. By resolving

these forces in the tangential and normal direction, the

equilibrium condition of the cable system is obtained.


dT
dT + F cos a w sin a = 0
ds t

da
T da F sin2 a + w cos a = 0
f ds n

=d cos a; = sin a (2.29)
S ds


where







38












LO <
o u
+ 0 LL Q_

IL~ 4











0














S>
>-
LU M

> r














i


0
4U
Cfb











C
\ 3


\ u > \













c-
to

to
\42
\> s V ^C(

\ ^*c





\^ ^ > )
\ s _i *-I
\'" ^ C-i^







1^ -i
!> ,..



I-\










w = Weight of cable per unit length

Tf = Tensile force per unit length


The solution of Equation (2.29), for the values of

z, y, a and Tf as a function of the length of the cable,

yields (Streeter 1961)


T = To Ftz + wy


al
T T w sin a F cos a
=n da
To F sin2 a + w cos a
"0 n



al
f Tf cos a
z = ---------da
F sin2 a + w cos a
a0 n





y = fsin a da (2.30)
F sin2 a + w cos a
a0 n


The magnitude of the tension To in the warp at the

point of attachment to the door can be computed by assuming

that the warp lies in the vertical plane z y (Fig. 2.12).



TO = n + door] + F2 (2.31)


where

Fnet = Drag of the net
net









F = Drag of the door

F = Vertical component of tension in cable
v which is given as


F = W + F N (2.32)
v v door bd

where


W = Apparent weight of door

F = Vertical component of hydrodynamic
v door resistance

Nbd = Reaction of the bottom to door


From Figure 2.12, it is seen that the hydrodynamic

drag of the warps is computed by the following expression:


F = TI cos aI To cos ao (2.33)
warp

The power required to pull one cable is, therefore,

given as


P = T1V cos a (2.34)


where

P = Power

V = Towing velocity

TI = Cable tension















CHAPTER 3

LITERATURE REVIEW


3.1 Mathematical Modeling of Fish Nets

The computation of drag force of a fish net by

analytical approach is known as mathematical modeling of

nets. An estimate of the magnitude of drag at a given speed

determines the capability of a trawler to tow the net at

that speed. Also, if the net is to be physically modeled

and tested, an estimate of drag is necessary to design the

force measuring instruments. However, published research

papers dealing with the calculation of drag on fish net by

mathematical models are scarce. The main features of one

approach found in the literature are described below.

Giannotti (1973) assumes the total resistance of a

fish net to a current to be equal to the sum of the indi-

vidual resistances of the components of the net. This

assumption neglects the effect of the interference between

components. The fish net is divided into two major sections,

namely, cod end and belly. The minor components include

foot- and headropes and floats. The shape of cod end is

assumed to be cylindrical and the drag acting on the cod

end is computed by Equation (2.20).









Giannotti approximates the belly by a conical net

with an elliptical mouth where the major axis of the ellipse

is given by the wingspread 2a, and the minor axis by the

headline height 2b. To compute the drag force acting on

net panels, he conducted wind tunnel experiments on two net

panels and presented an empirical formula on the form

F = CD p l sin a + 0.005] ( ] (Asurfe
CD panel surface

(3.1)

Applying Equation (3.1) to an elementary surface area of the

elliptical cone and integrating it over the entire surface,

the drag force acting on the belly is obtained.


Belly= (S) (CD panel rab) + 0.005w


x c2ab + a2b2] (3.2)


where

Fbelly = Drag force
belly
c = Length of net

The second term in the radical of Equation (3.2) is

very small compared to the first term. Therefore, this

equation shows that the length of the net does not have any

major effect on the drag force. Giannotti (1973, p. 56)

also infers that "the flow essentially sees only a projected

area as it passes through the cone, and the aspect ratio of

the cone has no effect on the drag force." If the drag on









the belly is independent of the net length and depends only

on the projected area of the net to a plane normal to the

flow, it is to say then, that the shape of the net does not

affect the drag force which is not true. Therefore, the

basic equation (3.1) should not be applied to computing the

drag force on the belly.

The angle of incidence of the flow in the belly

varies from tan-I (a/c) to tan-I (b/c). For practical cases,

the value lies in the range from 2 to 300. As discussed in

section 2.1.3 for this range, Equation (3.2) will predict

low values of drag force because of the low prediction of

projected solid areas. When a net panel is inclined at a

small angle, a, Equation (3.1) estimates the projected solid

area to be in the order of (SAsurface sin a). But the

actual value of the projected solid area is in the order of

(SAsurfac ) since the projected area of an inclined cylindri-

cal bar is in the same order of area of the cylindrical bars.

Therefore, Equation (3.1) is not the proper form of equation

in evaluating the magnitude of the drag force.

The resistance of minor components, footrope, headrope

and floats has been calculated by equations given in section

2.2. The total resistance of the net is, therefore, the sum

of the resistances of the cod end, belly, footrope, headrope

and floats.

As Giannotti predicts very low values of drag force,

his approach is not adequate. Hence, an adequate method of






44


finding the forces on and of testing fish nets is necessary.

At present, physical model testing seems to be the only

alternative and appropriate method of testing fish nets.


3.2 Physical Modeling of Nets and Trawls

Laws relating to the construction of hydraulic models

and the interpretation of the results of model tests are

described below.

3.2.1 Forces in a Fluid Flow

The forces acting on an element of fluid in a flow

can be classified under active and reactive forces. Active

forces include inertia, gravity, viscous, elastic, surface

tension forces and, in rare cases, compressive forces.

Reactive forces are the pressure forces.

Inertia force arises from the acceleration and

deceleration of fluid mass. By Newton's second law of

motion,


F = m" a (3.3)
inertia

where

m" = Mass
4
a = Acceleration

The gravity force if calculated by


F = mr" (3.4)


gravity









where


g = Acceleration due to gravity


Viscous resistance to shear is the property of the

fluid which varies directly with the velocity gradient

normal to the direction of flow. Viscous forces, thus,

depend on the motions in a system at an instant of time

and feedback to modify the motions at succeeding instants

of time.

Surface tension force exists at interfaces between

fluids, whether liquid and liquid,or liquid and gas. The

value of surface tension is the energy required to increase

the surface area one unit.

Elastic forces in a fluid occur by virtue of change

in volume. Reactive forces result from the active forces.

The equilibrium condition is, therefore (Fig. 3.1),

-4- -* -4- --4
F +F + F + F + F
gravity viscous surface elastic pressure
tension

+F. = o (3.5)
+ Finertia


3.2.2 Similitude

To model a hydrodynamic flow system, the prototype

and the model should satisfy the following three types of

similarity.

Geometric similarity-Two objects are said to be

geometrically similar if the ratios of all homologous



































Inertia



Felastic

Surface tension


Figure 3.1. Force polygon of a fluid flow.


Gravity






Fviscous









dimensions are equal. Thus, geometric similarity involves

only similarity in form.

Kinematic similarity--Two flow motions are kine-

matically similar if the patterns or paths of motion are

geometrically similar, and if the ratios of the velocities

of the various homologous flow particles are equal.

Dynamic similarity-This is the similarity of forces.

Therefore, the force polygon in the model must be geometri-

cally similar to the force polygon in the prototype. This

requires that the force scale must be the same for all

forces.

3.2.3 Model Scales

The term model scale refers to a quantity in the

prototype divided by the corresponding quantity in the model.

Greek letters are used for the model scales while the sub-

scripts p and m refer to the prototype and model, respec-

tively.

The fundamental model scales are:

L
Length scale A = L (3.6)
m

T
Time scale T = Tp (3.7)


F
Force scale K = (3.8)
m

in which L, T and F stand for a characteristic length time










and force. All other model scales may be derived from the

fundamental scales.


Velocity scale:


L /T
LmTm


(3.9)


Pressure scale:


F /L 2
F P/L
F /L 2
m m


K
X2


(3.10)


Mass scale:


m" F F

m" L /T 2 L /T 2
p force scale:

Inertia force scale:


K inertia
inertia


p L3 L /T2
P p p p
p L3 L /T
mm m m


Gravity force scale:


K = p ___-
gravity 3 p
m mgm m

Viscous force scale:



pITL L p2
Kp TR J p
viscous L
m 1 L2
ST L m
mm


KT2
A


P p A
2
P_ T


(3.11)


(3.12)


(3.13)


= p 2


(3.14)










Surface tension scale:

0 L 0
K = f P (3.15)
surface 0 L 0
m m m
tension

Elastic force scale:

K
Pi K A (3.16)
elastic K
m

where

u = Dynamic viscosity of fluid

0 = Surface tension

K = Bulk modulus of elasticity


Dynamic similarity condition requires that


K= =K K K
inertia gravity viscous surface elastic
tension

(3.17)


From Equations (3.12) to (3.17),


p 4 p p 2 k

Pm T2 m m m


The length scale, A, can be selected at will but all

other unknown scales are to be solved as a function of A.

Equation (3.18) is actually three equations. They cannot

be simultaneously solved for the unknown time scale, T,

unless a suitable fluid satisfying these equations is found










by chance. Therefore, the usual procedure is to neglect

minor forces in the flow under consideration.

3.2.4 Model Laws

The ratio of the gravity force per unit mass to the

inertia force per unit mass is Lg/V2. The inverse of this

ratio is called the Froude number. Therefore,


F = V = Inertia force .
r /- [Gravity forceJ (3.19)


The Froude number is an important parameter whenever gravity

is a factor which influences fluid motion. In such a case,

the Froude number in the model and prototype must be the

same.

The inverse of the ratio,


Viscous force/mass V/pL2 _(
Inertia force/mass V2/L pVL (3.20)

is the Reynolds number. It is important when viscous forces

influence fluid motion. To model such fluid motion, the

Reynolds number should be kept the same in the model and

prototype.

The relationship between the inertia and pressure

force defines Euler number E
u

Inertia force pL3 L/T2 pV2
Pressure force L2pt pr

Therefore,


E V2
u P'


(3.21)









If the predominant forces are inertia and surface

tension, the Weber number should be kept constant both in

the model and the prototype. The Weber number W is defined

as:


W Inertia force V2/L
n Capillary force 0/pL2

W p2L (3.22)


If similitude with respect to elastic force is to be

insured, the Cauchy number or Mach number should be kept the

same in the prototype and model. This is defined as:


Inertia force pL3 L/T2 (L/T)2
Elastic force L2E' r L/L E'/p

2
C 2 pV (3.23)
a a EF

where

C = Cauchy number

M = Mach number
a
E' = Modulus of elasticity

In short, the predominant force scale ratios and the model

laws are:










K K. = = K =K K
inertia gravity viscous surface elastic
tension (3.24)


Froude Model-


-- Reynolds Model


--Weber Model


-Cauchy Model



3.2.5 Derived Model Scales

In all the cases mentioned above, if the length

scale, A, is chosen, depending on Lhe predominant forces,

the time scale can be found from the model law. Then, the

model scale ratio for any derived quantity can be solved.

For example, in the case of Froude's model law

which considers the gravity and inertia forces as predomi-

nant forces, the inertia and gravity force scale ratio

should be equal. From Equations (3.12) and (3.13), the tii,

scale, T, is:


T = / (3.25)

When g = g the corresponding velocity scale is:


V
P = (3.26)
V T
m


Similarly, the force scale ratio is obtained as:










K = _3 L (3.27)
P T P

and so on.

Scales for derived quantities for different model laws

can be obtained in a similar fashion. Table 3.1 summarizes

the basic and derived scales for the model laws considered

above (Christensen 1975a).

3.2.6 Limitations

In model studies, the following limitations are

usually encountered.

Reproduction limit-As the size of the model decreases,

the magnitude of the predominant forces in the model decreases

significantly, such as,by the cube of the length scale in the

case of Froude modeling. If the model is small, a surface

tension force may become large enough to be of the same

order of magnitude as that of the active forces since sur-

face tension force is proportional to the first power of the

length scale. In this case, extrapolation of model results'

to prototype conditions, where surface tension forces are not

predominant, will be incorrect. However, this difficulty can

be overcome by using the Weber model law in deriving the

model scales, in which case,the Froude model law,of course,

will be violated.

Cavitation limit-When atmospheric pressure is not

reproduced in the model, cavitation phenomena in the proto-

type are not reproduced correctly in the model.

















Lo
C

C
0


l-
> L


r=


4-1








cu
C N


0) 0|
C cU
C) C') t'f Q. 0- '

a 42 0



'la
> 0 -7




4J

01 4-' NM __
C) C)


3 C. NN -
0 I 0 -< I o'
p! U M m << --- *
>^ I- r< r-<
& >ElS .D*01a6


43


Ic
0)


-K


: 6 :


r-
0
o a-

a) N C)
Q *il4-' 4L.l 4-' C) .fl
g U/) | 4-4 '4- '4-4 c) -
H p~



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a0
n].-I 'a

a< 4 < ^ ^ -" V
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CO
o *H

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WO
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43

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t 4

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ol 0 37oJ 3'
s 2j 0440 0MK 'I7' 04j1 s
u

V] i CN I- i- l
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13 O C- >^ CM
i- C^ .alM ------ >--,-, <
o o - o j
C e jS ?1? :S Q

oiSec "t ~ a v e &)la e e &1E


43
'3

O
44
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Ili r
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rob
04 ^
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43 U) Nr'-
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00 1 0

'34



M O PO O Or
33 04









Wave limit-If waves are to be reproduced correctly

in the model, wave velocities in the model should be greater

than 0.755 ft/sec corresponding to the minimum capillary

wave velocity.

Laminar-turbulent limit-The model should not be so

small that the flow in the model becomes laminar while the

corresponding prototype flow is turbulent. By obeying

Reynolds' model law, this limit can be avoided.

Subcritical and supercritical limit-Sometimes it

is necessary to use a different scale for the vertical

dimension than for that of the horizontal dimension. This

is known as vertical distortion. Where subcritical and

supercritical flows of the prototype are to be reproduced

properly, the Froude model law should be used.

Sediment transport limit-If a sediment transport

phenomenon is to be modeled, the sediments cannot usually

be scaled down to the length or depth scale. E.g., if

normal sand is the prototype bed material and if it is to

be scaled down to a realistic scale, say, x = 50, then clay

or silt should be used in the model. But clay and silt

behave differently than sand due to their cohesive proper-

ties. Therefore, special model laws are usually needed for

these types of models (Christensen 1975b).

Roughness limit-Small wall and bed roughness in the

prototype cannot be reproduced correctly in a small model.

Christensen and Snyder (1975) present a procedure to model

the roughness elements by distortion.









3.2.7 Model Laws Applied to Fish Net

Tauti (1934) has applied the hydraulic model laws to

fishing nets by assuming: (1) that the elongation of the

netting twine is negligible, (2) that the netting twines are

flexible, (3) that Newton's law of hydrodynamic resist-

ance is valid for every portion of the net irrespective of

its Reynolds number and (4) that any change in the form of

the net occurs so slowly that the external forces acting on

each element of the net can be considered to be in quasi-

equilibrium. Considering an element of the net with area, A,

and circumference,S'(Fig. 3.2), he examines the forces acting

on it under equilibrium conditions. From assumptions (1)

and (4), the forces are gravity, drag and webbing tensile

forces.

The gravity force is the apparent weight of the

elemental area of the net and is expressed as:

w = f() ,(, ,j D + c, 2 (3.28)


where


fl() = T = Function depending on degree of
2 sin slackness of netting


Mk
cl = /p'-p' = Constant which depends on type
k of knot and its tightness


w = Apparent weight of net per unit
surface area















/


PROTOTYPE


Cir
/ \
\ / Circ
2"


MODEL


Figure 3.2.


Force polygon in the model and
full-scale net.









The resistance r acting on a unit area of the webbing

is expressed by


r = f2( ) + C2 V2 (3.29)


where


f2W() = Function which depends on incident angle
of the current and half of the angle
between two adjacent bars

Geometric similarity requires that a an ( should be

the same in the model and the prototype and dynamic simi-

larity yields:

T S'
wA rA f p F
P P P P P -P (3 30)
w A r A TS' F.
mm mm fm m


where

Tf = Tension per unit length

F = Total force acting on net

Tauti sets the twine diameter scale to be equal to

the bar length scale.


D M
D- > A P (3.31)
m m

He gives the scales of the area and the circumference to be

equal to the square of the length scale and the length

scale, respectively. From Equations (3.28) to (3.31),

Tauti gets:










Ps Tf F
SD -pE p2 =- (3.32)
2A{ o23 =V FA
s w m f m
m m m

Equating the first and second terms in Equation

(3.32), the scale ratio for velocity is obtained as:



V Ps Pw
P AD (3.33)
V p -p D
m s s
m
m m

From Equation (3.33), it is seen that the velocity scale

depends on the mesh scale AD' rather than the length scale

ratio A.

From the third and second terms, the scale for the

tension per unit length is:


Sf V 2
T = X P2 (3.34)
f m


and, the second and fourth terms give:


F V
P = 2 RP (3.35)
m m

Summary points of Tauti's model laws for fishing

nets: The linear length scale A is chosen arbitrarily; the

mesh length scale is distorted and chosen arbitrarily; the

velocity scale depends on the mesh scale rather than the

linear scale and the force scale is given by Equation (3.35)

which is in agreement with Froude's law.









Using the dynamic similarity concept, Dickson (1959)

argues that the velocity scale ratio should be dependent on

the linear scale A instead of the mesh length ratio. Neg-

lecting the small density difference between the prototype

and the model fluid, he presents:


V
P = T (3.36)
V
m

Fridman (1973) considers the diameter of the bar as

the characteristic linear dimension and reasons that the

drag coefficient for the net is independent of the linear

length of the net. Therefore, he supports the model laws

developed by Tauti.

Kawakami (1959) extends the results of Tauti to

model ropes, floats and sinkers. He considers two cases of

modeling of ropes. In the first case, the rope is used as

the main part of the net, the reduction ratio is equal to

that of the main body of the net, i.e.,


r
= (3.37)
m

In the second case, the rope length is independent of the

size of the main body of the net, as in the case of the

towing warp of a trawl.

In both cases, Kawakami (1959) considers the three

forces acting on a rope: The hydrodynamic force, the

apparent weight of the rope, and the tension in the rope.









He also assumes the elongation of the rope to be negligible.

He expresses the hydrodynamic resistance rr acting per unit

length of the rope as:


r = r sin2 a H V2 (3.38)
r r 0 r

where

r = A constant
r 0
H = Diameter of rope

a = Angle between rope and current

The apparent weight of the rope per unit length wr is given

by

nH2
Wr = r ( Yw) (3.39)

in which


Yr = Specific weight of rope

The force ratios must be equal in order to satisfy

the dynamic similarity. From Equation (3.35),


w 'r T 2
r r r r r V
P P= P = T = X2 k (3.40)
zw i r T V
r r r r r m
mm m m m

where


r = Length of rope

T = Tension in rope










For the first case, where the rope is used as a main

body of the net,


r
9.


Substitution of Equations (3.38) and (3.39) in (3.40),

yields:


H
r
P=
H
r


Yr Y
P P
Yr wY
m m


(V /V) 2


(3.41)


For the second case where the rope length is independent of

the size of the net,


r
9. r
r
m

Kawakami gives:




p A
H
r r
m


(3.42)









Tr i w V 2
-P p- = P r (3.43)
L 2
Yr -w V x
m m

Therefore, the diameter and density of the rope in

the model should be chosen to satisfy Equations (3.41) or

Equations (3.43).

To model floats and sinkers, Kawakami (1959) analyzes

the forces acting on them which are the apparent weight and

the hydrodynamic resistance. Denoting the number of floats

or sinkers per unit length of rope by n, the apparent weight

w, per unit length, is calculated by


w = k, E3 [' y] n (3.44)


where


kI = A constant depending on the shape of float
or sinker

E = Diameter

y' = Specific weight of material
S

The hydrodynamic resistance is expressed in the form,


r = k2 E2 V2 n (3.45)


where

r = Hydrodynamic resistance per unit length
a of rope

k2 = A constant










From the dynamic similarity condition and from

Equations (3.35), (3.44) and (3.45),


s w V n
p p = Vp p P IP 1
Y' y V n A
s w m m
m m

and


E = n ,
P = A (3.46)
m p

Therefore, the floats and sinkers of the model should satisfy

Equation (3.46). In cases where Equation (3.46) cannot be

satisfied, an approximation should be made in considering

the forces acting on floats or sinkers. Neglecting the

hydrodynamic resistance force compared to the apparent

weight, the similarity condition yields:



E 3 ^s- w V 2 n
{E] -{Y--RJ= [j2 A n^ (3.47)
E v Y V n P
Im s w m p
m m

A bibliography on development of model laws is given

in Appendix B.

3.2.8 Dimensional Analysis

The variables that can influence the profile of a

net characterized by a linear dimension S'are: (1) series

of linear dimensions defining the boundaries L, M, D

(2) kinematic and dynamic quantities such as mean velocity

V and force F and (3) the physical properties of the fluid









and of the net such as density p, viscosity j, specific

weight of twine ys and elastic properties. These variables

and the functional relation can be expressed in the form:


S'= f[p, L, V, p, t, M, D, F, e, e, ui, u2, Y (3.48)


Using Buckingham's 7 theorem, Fridman (1973) derives

the following dimensional numbers:


S'_ r fD M Vt pV2 pVL F
L L' L' L w L pV, 1, ul, u2, 2 (3.49)

where

5 = Elastic displacement

ul = Hanging coefficients
u2

E = Unit elongation of the twine

Therefore, for the complete similarity condition, the follow-

ing terms should be the same for the model and for the

prototype:

1. M/L and

2. D/L or these terms can be grouped into single

one term, D/M

3. Vt/L which is the Strouhal number

4. V a modified Froude number
y*gL'

5. VL/v, the Reynolds number

6.

7. 5, ul, u2, E (geometry of the net)









Fridman (1973) analyzes each term in detail and

determines whether it is possible to keep the term constant

both in model and prototype. He derives the model laws and

scales considering only the major forces acting on the net,

which vary from case to case.

3.2.9 Model Experiments

Model experiments are conducted in hydraulic flumes

generally by two different methods. In the first method,

the water is at rest and the net is towed by a carriage

moving on rails. In this case, the length of the flume

must be sufficient to allow enough time to conduct the tests

while not accelerating or decelerating. If the behavior of

the net is to be visually observed and photographed, the

sides of the flume should be transparent. Few such tanks

are available in the U.S.A. for testing of nets.

In the second method, the net is stationary and the

water flows through it. This facilitates visual observa-

tion of a conveniently stationary net. In this case, the

water velocity varies from zero, at the bottom of the flume,

to a particular value at the top of the water surface. The

mean velocity of water in the flume is found by the Froude

model law. However, the variation of velocity with depth

follows a logarithmic law (Nikuradse 1933):


S= 8.48 + 2.5 In ] (3.50)
Vf









where


V = Friction velocity

y = Depth from bottom

k = Equivalent sand roughness

v = Velocity at distance y from the bed

Literature on model experiments (Appendix C) indicates that

most of the tests on fixed nets are conducted in flume where

the velocity distribution of water follows Equation (3.50).

But in the prototype, the net is pulled through stagnant

water which means that the profile of water velocity with

respect to the trawl is uniform. Therefore, the relative

velocity has the same value at all distances from the bed.

To satisfy similarity conditions, the same velocity distri-

bution should be obtained also in the model. The uniform

velocity distribution can be achieved by constructing a

movable bed which can be moved at a velocity probably equal

to the spatial mean velocity.

The Chamber of Commerce at Boulogne-sur-Mer, France,

owns and operates a flume in which such a movable bed is

constructed. The details of the flumeare reported by World

Fishing (1972). However, this flume was used as a simple

observation tank rather than a testing tank. Therefore, in

the literature, quantitative test results of model experi-

ments of fish net, using a uniform velocity distribution

from the bed to water level, are not found, so far.









3.3 Prototype Experiments

Any model law should, of course, be verified both by

model and field (prototype) experiments. Reports on field

tests of fishing gear detail the parameters measured and the

instrumentation used in the tests. A substantial list of

such reports is found in Appendix D. The parameters measured

in the field tests can be grouped under the following head-

ings: (1) Linear dimensions, such as net spread and height;

(2) Angles, such as angle or attack, tilt, etc.; (3) Forces,

warp tensile force and (4) Velocity, such as towing speed

and current velocity.

The instruments to measure these parameters can be

grouped under two divisions: (1) Decktype instruments and

(2) Underwater instruments. Decktype instruments that are

used on the ship deck include warp tensile load cells, warp

declination and divergence meters, and ship's speed log.

Underwater instruments are generally batterypowered and

self-recording. Some of the underwater instruments are

load cells that measure door spread, tensile force on head-

and footropes, net height, etc.

de Boer (1959) used a differential manometer to

measure the net opening. Motte et al. (1973) describes an

accoustical transducer to measure the linear dimension of

door spread and net height.

The forces in the footrope and headrope can be

measured by a self-recording load cell. One such load cell









is described by Nicholls (1964). He also gives a method of

finding the loads acting on netting twines. The principle

of this method is the same as the Brinnell Hardness test, a

hardened steel used to give an indentation in a relatively

soft metal plate.

The angles measured in a full-scale field test are

the angle of attack, the pitch, and the heel of the doors.

If a rod is attached to a door and suspended to move in

horizontal and vertical directions, the free end sliding

over the ground will adopt the towing direction of the door.

This is the principle underlying the angle of attack meter

used by de Boer (1959) and Nicholls (1964). The warp

divergence and dip angles can be measured by a protractor

and indicator arrangement as described by Motte et al.

(1973).

The towing speeds of the trawler, with respect to

the water and with respect to the bottom, can be obtained

by a conventional ship's taffrail log and navigational

instrumentation.


3.4 Pitfalls in Existing Physical Model Laws

The existing model laws described in section 3.2.7

do not consider the effect of elongation of the netting

twine under load. If the geometric similitude is to be

satisfied, the strain of the twine in the model and in the

prototype should be the same. However, if the same netting









twine material is used, both in the model and in the proto-

type, strain cannot be the same because of the high change

in the order of magnitude of forces in the two cases. There-

fore, the geometric similarity will not be satisfied in this

case and predictions of prototype linear dimension from the

model results will be erroneous. Thus, adequate model laws

that take the elongation of twine into consideration should

be developed.

These model laws should be verified both by field

and model data. While conducting the model experiments, it

is emphasized that the velocity of water should have the

same distribution from top to bottom as in the field experi-

ments, i.e., in most cases,be constant. It will not be

adequate to set the mean velocity of water in the flume as

the desired velocity. Because the mean velocity occurs at

a point whose distance is 0.368 times the depth of flow from

the bed if a logarithmic velocity distribution is assumed.

This means that the water velocity below that point will be

less than the required velocity. This distance is crucial

for model tests of bottom trawl since the major portion of

the model lies in that region. Therefore, the model drag

forces will probably be less than the actual forces.

Consequently, the projection of model test results to

prototype conditions may not be correct.

In short, the model laws which take the elongation

of netting twine into consideration should be verified by






73


tests in the flume where the velocity distribution is uniform

from top to bottom as in the case of field experiments.

Such tests are conducted and will be explained in subsequent

chapters.














CHAPTER 4

DEVELOPMENT OF MODEL LAWS


4.1 Froude Modeling

To model a flow through and around a trawl, the

predominant forces acting on it must be considered. The

predominant forces are due to gravity, inertia and the

viscosity of the water. The viscous forces will have the

least influence on the model if its twine is not thin.

Therefore, it is assumed that this type of force has

negligible effect on the trawl and that the predominant

forces are due only to gravity and inertia. As discussed

in section 3.2.4 to model such a flow field, the Froude

model law is required.

Equating the inertia and gravity force scales, the

time scale ratio is obtained as given by Equation (3.25).

The model scale ratios for other derived quantities can

then be expressed in terms of the fundamental model scales

(Table 3.1).


4.2 Mesh-Twine Distortion

While the principal dimensions of the prototype

trawl (length and width of the net) are reduced by the









length scale X, it is not advisable to reduce the twine size

by the same length scale. Such a reduction will, in most

cases, result in such low values of the model Reynolds

number, which is based on twine diameter, that viscous

forces may predominate in the model but not in the proto-

type. This may happen in spite of the fact that the length

scale used in net and trawl models is usually approximately

one order of magnitude smaller than the length scales

usually used in models of rigid hydraulic structures. The

problem may be overcome by using a larger twine size and

compensating for the twine distortion by also distorting

the mesh size in such a way that the hydrodynamic drag

forces acting on any section of the prototype trawl and the

corresponding section of the model have the correct force

scale.

Figure 4.1 shows a prototype section of a net and

its corresponding model section. The drag force acting on

a section due to the flow velocity V, relative to the

trawl, is computed by calculating the drag force acting on

the bars and on the knots. The drag force acting on a

twine may be written:

F = C pV2 MD (4.1)
bar Db b

Similarly, the drag force acting on a knot is given by

PV2 k4
F knot k =C I-7 (4.2)
knot DkZ

















PROTOTYPE


FORCE Fp 7 FORCE


Y vm




Lm










Fm


Idealized mesh and
and model.


twine in prototype


Figure 4.1.









where

Dk = Diameter of knot

It is assumed that the diameter of the knot is proportional

to the diameter of the twine. The total solid areas of the

bars and the knots on which the drag force is acting may be

written:


Ab = (]LD) (4.3)

and

Ak =[ L2 D] (4.4)


From Equations (4.1) to (4.4), the total drag force

F, acting on the prototype section, is computed from

fL V L 2
S c LD p V2 + c2 D2 V2 (4.5)
P P P P P M ppp

where

cl and c2 = Constants of twine and knot,
respectively

If the Reynolds number based on the twine diameter is not

small, both in the model and in the prototype, then the

drag coefficients will have the same value in the model

and in the prototype. Therefore, the constants cl and c2

also remain the same for the model. The drag force in the

model is expressed as:

L 1 2 L 2
F = c LD p V2 + C2 D2 V2 (4.6)
m 1 M m m m mM m
m m









Therefore, the drag force scale ratio is:


clL2D D2
P + c L2 Pp 2
F M 2 p M2 p
P p p (4.7)
F D D2 p
m 2m c2 mD m
m m


But, the drag force and gravity force scales must be equal

to satisfy the dynamic similarity condition. Therefore,

from Equations (3.26), (3.27) and (4.7),


D --c + p
M M
P P
=1 (4.8)
D D
M c + Dm
m m

where


c = cl/c2 = A constant


The mesh scale, AX, and twine scale, AD, are defined

as:

M
m= p (4.9)
M M
m

and

D
AD (4.10)


Substitution of Equations (4.9) and (4.10) into (4.8), yields:











D

SD c D p
P P
1M c + M- c + M
P P



The solution of is:
AM


D
M


AD

hM


(4.11)


(4.12)


(4.13)


D
P_
M
P
D
P +p
D
P


Equation (4.13) gives a negative value for which is not
AM
possible. Therefore, the only solution of Equation (4.11)

is given by Equation (4.12), i.e.,


AD = xM


(4.14)


which is independent of the constant c.

Tauti (1934) has applied Equation (4.14) in deriving

the model laws, but he has chosen the result as an arbitrary

value instead of a necessary condition. Equation (4.14) is

also consistent with the findings of Fridman (1973) who

derives the condition from dimensional analysis. A special









case of Equation (4.14) occurs where both scales are equal to

one indicating that the same twine and mesh size may be used

in both model and prototype. However, the model twine size

is determined from the elastic properties of the prototype

twine material.


4.3 Elongation of Twine

As discussed in section 2.2.1, the stress-strain

relationship of netting twines is expressed in the form:


o = AcB (4.15)


in which


a = Stress corresponding to the strain E

A and B = Constants which are properties of the considered
twine

The stress-scale is, therefore, obtained:


B
o A P
= -P _-- (4.16)
o A B
m m m
E
m

Geometric similarity requires that the strain in the model,

Em, is equal to the corresponding strain in the prototype,

C '

Equation (4.15) is valid within the strain ranges

normally encountered in nets and trawls, and the dimension-

less exponent B is nearly the same in most net and trawl

materials (Fig. 4.2). A representative value is B = 0.9.




























90/



0-9
- =99000 &


I I I I I I I _LLO
0.01 0.1 1.0
STRAIN


Figure 4.2.


Typical stress-strain curve for
polyamide twine.


105







(I)
c3
104
a
di


10"


T


bg









The dimensional constant A varies substantially from material

to material. Therefore, Equation (4.16) reduces to:


o A
-= P (4.17)
o A
m m

The average stress on a twine oriented in the

direction of flow may be evaluated by considering the number

of twines existing in a prototype length L (Fig. 4.3). The

total area on which the total drag force F acts is calcu-

lated to be M c3D2, where c3 is a constant. Therefore, the

average stress is obtained as:


S= F (4.18)
Sc3D2


and, hence, the stress scale is:


F
_
F
o m
-P =- (4.19)
m L D P
L M c3 D
m p 3 m
M m


Because of the requirement of geometric similitude c3 and
m
c3 must have the same value. Therefore, Equation (4.19)
P
becomes:

F
P
o F
= m (4.20)
0 2

AM
NX




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