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3/48

HULL FORM

RESEARCH

WITH A FLEXIBLE

MODEL

by

P.C.

Pien,

Ph.D.

November 1959

_ _

.x-wrrruranrnrrrnmnrq-

~r~*~l~~~ CrrU*l1*LC-~------~--

I----

Report

1344


4/48

TABLE

OF CONTENTS

Page

A

BSTR

A C T

.......................................................................

IN

TR O D U C

T ION ...................................................................

DESIGN

CONSIDERATIONS

OF

A FLEXIBLE MODEL....................................................

2

THE

CONSTRUCTION

OF A FLEXIBLE

MODEL,

MODEL

4634 ..................................

2

THE

INITIAL TEST

PROGRAM

..........................................................................................

4

DISCUSSION

OF

TEST

RESULTS

........................................................................................

6

C

O NC

L U SIO

NS .........................................................................................................................

7

ACKNOWLEDGMENTS

...........................................................................................................

8

R

E

FE

R E N CE

S

..........................................................................................................................

8

LIST

OF

FIGURES

Page

Figure

1

- Metal

Portion

of

the

Midship

Section

of

Model

4634.....................................

9

Figure

2

-Details

of the

Bilge

Piece

...............................................................................

9

Figure

3

-

Inside

View

of Model

4634

...............................................................................

10

Figure

4

- Outside

View

of Model

4634........................................................................

11

Figure

5 -

Plot

of

the

Test

Spots

of

a

Typical

Resistance

Test

.................................

12

Figure

6 -

Typical

Wave

Profiles

of

the

Flexible

Model

under

Towed

Conditions

..........................................................................

....

13

Figure

7Ta -

Sectional

Area Curve

and

O

versus

() Curves,

M

ode

l 4634-1

.......................................................................................................

14

Figure

7b

- Rr/A

versus

V//Ii

Curves,

Model

4634-1

.....................................................

15

Figure

8a -

Sectional

Area

Curve

and

0

versus

( Curves,

M

ode

l 4634-2

......................................................

............................................

16

Figure

8b -

Rr/A

versus

V/

Curves,

Model

4634-2

.....................................................

17

U

II I I I I IIII II

I-

III I II


5/48

Page

Figure 9a

-

Sectional

Area

Curve

and

©

versus

®

Curves,

M

odel

4634-3

......................................................................................................

18

Figure

9b

- Rr/A versus

V/

1

/ Curves,

Model

4634-3...................................................

19

Figure

10a -

Sectional

Area

Curve

and

@()

ersus

Curves,

M

odel

4634-4

......................................................................................................

20

Figure

10b - Rr/A versus

V/v/-

Curves,

Model

4634-4

.................................................

21

Figure

11a

- Sectional

Area

Curve

and () versus

()

Curves,

Model

4634-5

..................................................

................................................

22

Figure

11b

- Rr/A

versus V/

1

/E

Curves, Model

4634-5 ....................................

............ 23

Figure

12a

- Sectional

Area Curve

and ( versus

(

Curves,

Model

4684-6..................................................................................

24

Figure 12b -

Rr /A

versus

V/VL

-

Curves,

Model

4634-6.................................................

25

Figure

13a - Sectional

Area Curve and © versus

(

Curves,

Model 4634-7

..................................................................................................

..

26

Figure 13b - Rr/A

versus

V/l

Curves,

Model

4634-7 ..................

.................

27

Figure 14a

-

Sectional

Area Curve

and

()

versus () Curves,

M

odel 4634-8

.................................................................................................

28

Figure

14b - Rr/A

versus V/vfL

Curves,

Model 4634-8

...............................................

29

Figure

15a

-

Sectional Area Curve and

(

versus ()

Curves,

M

odel

4634-9

..............................................................0

Figure

15b -

RFr/A

versus V/l-Curves,

Model

4634-9...............................................

31

Figure

16 -

Composite

Plot

of Rr/A

versus

V// Curves

of

Group

I M

odels

..........................................................................................

32

Figure

17

- Composite Plot of

Rr/A versus

V L

Curves

of

Group

II M

odels

.......................................................................................

33

Figure 18 -

Composite Plot of Rr/A

versus

V L Curves

of

Models

4634-4

and

4634-5

......................................................................

34

Figure

19

-

Composite

Plot of

Rr/A

versus V L Curves

of Group

III Models

......................................................................................

35

Figure

20 - Composite Plot of the

Experimental and

Theoretical

Values of Rr/A

versus

V T

of

Group

III

Models..................................

36

rrl~lrru-~s ~+~rarr

----


6/48


7/48

ABSTRACT

A project of

finding the effect of

the change in

sectional area curve of

a

ship

model upon

resistance has

been

initiated

at

the

David

Taylor

Model Basin

by using a

flexible model

technique.

In

this

technique

a flexible model was

built.

The

sectional

area area

curve of this

model

can

be

readily

changed from

one

form

to

another.

Thus

the necessity

of

building a

large number

of models

in

the above mentioned

project

has

been

eliminated.

The

design considerations

and the

details of construction

of

a

flexible

model,

Model

4634, are given.

The

mechanical

properties

of

this

model

have been found

to

be

satisfactory. The

results of

a

short

experimental program

of nine different

forms

are given.

INTRODUCTION

The basic question

of

what makes

a

ship's

hull good,

resistance wise, is

still largely

unanswered,

at

least

quantitatively.

Despite

the long history

of

shipbuilding

and the

large

amount of research work

which has been done in

the

field

of naval architecture,

ship hull

de-

sign,

to a

large degree, remains

an art rather

than

a

science.

The objective of

putting the

complicated ship hull

design

work onto

a

more

scientific basis

has been

pursued

both

theoret-

ically

and experimentally.

Because of

the complexity of

the

phenomena, the theoretical

ap-

proach

is very

difficult.

A

great amount of

effort has been contributed

in this direction

by

many

mathematicians

and

naval architects. Some

advancements have been

achieved;

however,

for the most

part, no

reliable

quantitative

result

of ship resistance

can

be

predicted

by

theory

alone. On the other hand,

the

experimental

approach,

especially

the

systematic series,

has

yielded valuable design

information.

However,

the scope of the experimental work so

far com-

pleted

is

very limited.

For

example, in

this

country both

Taylor's

Standard

Series

and

Series

60

have

explored only the

effect

of

fineness

and proportion upon

resistance.

Aside

from

the

gross

effect upon

resistance,

due to

the shifting

of LCB location as in

Series 60, very little

systematic information is available on the design

of ship hulls

for a

given set

of

proportions.

It is very desirable to enlarge the scope of experimental

work so that

reliable criteria

may be

obtained

for

deriving

a good

set of ship

lines under

a

given design condition. The

experimen-

tal work in

this

field is expensive,

mainly

because of

the

tremendously

large number

of

models

required in any

extensive

testing

program.

It was considered that if model

construction

could

be

minimized,

an extensive

testing

program

could

be accomplished

within a

much

shorter time

and with much

less expense. For this purpose,

a

flexible

model was designed and

built

at the

David

Taylor

Model

Basin.

This report covers the

details of the

construction

of

this flexible

model, and some

of the preliminary testing results obtained from

this model.

_ -II

I

I-

I II~


8/48

DESIGN

CONSIDERATIONS

OF

A FLEXIBLE

MODEL

From

both theoretical

considerations

and experimental

evidence,

it can

be

shown

that

for a

given

type of

section

form

there

is

a

corresponding

optimum

sectional

area

curve.

The

optimum

longitudinal

displacement

distribution

of a

ship

hull

is

related

to the

vertical

distri-

bution.

The problem

of obtaining

a

favorable

sectional

area curve

depends, to some

extent,

upon

the section

form

selected.

For

each

of

the so-called

U-,

V-, extreme

U-,

and

extreme

V-

section

forms,

if

some design

criteria

can be

obtained so

as

to

obtain

the

most

favorable

sec-

tional

area curve,

a

great uncertainty

of

the practical

ship

hull

designer

will

be

removed.

To

begin

with,

an extreme

U-section

was

chosen

to

be

explored

because

of the

inherent

simplicity

of

construction.

If

tests

on

this

section

form

should

yield

useful

results,

it

was

intended

to

extend

the

program

to

other section

forms.

An ideal

model

for

the exploration

of

the effect

of

change

in

the

sectional

area

curve

upon

the

resistance

would

be

one

in which

the

area

curve

of

the

model

could

be changed

at

will.

For

the wall-sided

model

(extreme

U-sections)

the

two-dimensional

side

walls

can

be

bent to

conform

with

any predetermined

curve.

The

flat

bottom

can be

made of

a rubber

sheet,

properly backed

by a

flat

plate,

so that

the

bottom of

the

model

will

conform

with the varying

shape

of the

side

walls.

This

gives a

picture

of a

model

with

rectangular

sections,

of

which

the

area

curve

can be

readily

changed.

This

would

serve

the purpose

at hand.

However,

a

large

amount

of

eddying

would

be

induced

along

the lower

corners

of

the

rectangular

sections.

The

model

results

obtained

would be

extremely difficult

to analyze.

To avoid

this

difficulty,

the

bilge

portion

of

the model

should

be

curved.

This

would

introduce

a

three-dimensional

surface

to

the

model,

thus

destroying

the

flexibility

of

the model.

This

difficulty

was

over-

come by

slotting

the

three-dimensional

surface

vertically

so

that

it

could

be bent

along

the

length.

This

idea

will

be more

clear

after

the construction

of

the

flexible

model

has been

described.

THE

CONSTRUCTION

OF

A

FLEXIBLE

MODEL

MODEL

4634

Figre

1

shows

the

metal portion

of

the midship

section

of

this

model.

The

main

strength

member

is

the

central

aluminum

I-beam.

On top

of this

beam,

there

are seventeen

adjustable

frame

assemblies.

Each

of

the assemblies

consists

of

an adjusting

hollow

rod

,

with two

nuts

, welded

to the

center

for

the purpose

of

turning

the rod.

At

each

end

of this

rod

is

a

nut

, one

end

with

a

right-hand

thread

and

the

other

one

with a

left-

hand

thread.

The

telescopic

piece

2

,

with

threads

along

its

length,

is

screwed

into the

hollow

adjusting

rod.

The

locking

nut

@is

used

to

lock these

two

pieces

tightly

together

after

the relative

position

between

them

has

been

properly

adjusted.

The

other

end

of the

telescopic

piece

is

a

fork

arrangement

which

is pin-jointed

to the matching

piece

The

piece

,

in turn,

is

attached

to the

side wall.

This

pin

joint

is

closely

fitted

and

is

in a perfectly

vertical

position

so

that

the

side

wall

is

free

to

turn

when

it

is pushed

out

or pulled

in.

Each

of the

adjustable

frame

assemblies

is free

to

slide longitudinally

on

top

I I I I I I


9/48

of

the beam

in

the process

of changing

the

model

form.

They

are

clamped

to

the

I-beam

after

the model

has

changed

to

the

desired

form.

The

bottom

plate,

which

is

made

of

a 1/4-in.

aluminum

plate,

is fastened

to

the

bottom

of

the

central

beam.

This

bottom

plate

is tapped

toward

the ends

so

that

there

is a

gap

between

this

plate

and

the

bilge

piece.

Figure

2

shows

the detail

construction

of the

bilge.

In

order

to make

the

curved

bilge

piece, a

wooden

pattern

with

the desired

form

was

built

first.

An

aluminum

plate

of I /8-in.

thickness

was

cut

to

the approximate

dimension

of

the

developed

surface

of

the

bilge

piece.

A

line

2

in.

from

the straight

edge

of

this

plate

was

drawn,

which

indicated

the

position

to

be

overlapped

with

the

side

wall.

On

the opposite

edge,

small

channels

about

1 ft

long

were

welded

to

the

plate,

as

shown

in

Figure

3.

The

whole

plate

with

the

channels

was

slotted

all

the way

up

to

the 2-in.

line mark

at intervals

of 1/4

in.

The

slotted

piece

was

then

bent

to

the

desired

form,

with

the

aid

of

the

wooden

pattern.

After

the

curved

bilge

piece

was

made,

it

was lap-jointed

to

the side

wall,

as

shown

in Figure

2.

Drill

rods

of

1/8-in.

diameter

were

pushed

through

the

small

channels.

There

was

a

very

small

clearance

in

the

vertical

direction

between

the

drill

rod

and

the channel,

so

that

the

slotted

edge

of

the

bilge

piece

was

held

in

line.

However,

the

horizontal

clearance

between

them

was

large

so

that

the

slotted

piece

could

be

bent

freely

in

the

longitudinal

direction.

After

the

curved

bilge

piece

had

been

lap-

jointed

to

the side

wall,

as

shown

in Figure

2, a

slightly

stretched

rubber

sheet

was

cemented

to

the

slotted

piece.

Then

the overall

rubber

bottom

sheet

was

stretched

and

cemented

on

to

finish

the

model.

Both

of

the

rubber

sheets

were

1/16

in. in

thickness

so

that a

flush

butt

joint

between

the

rubber

sheets

and

the

side

wall,

which

was

1/8

in. thick,

was

obtained.

From

the above

description,

it

is

clear

that

the

form

of

this

model

can

be readily

changed

from

one

form

to

another

by

adjusting

the

width

of

the various

adjustable

frames.

To obtain

any desired

form, the

sectional

area

curve of

this

particular

form

is

first laid

down

on

a drafting

board.

The width

of

the

model

at

various

frames

is measured

from

the

drawing.

A

set

of

spacer

bars is

made,

each

one

corresponding to the width

of one frame.

Starting

from

the midship

section,

each

frame

is

adjusted

to

the

measured

length,

with

the

aid

of these

bars.

In this

way,

the model

can

be

changed

to

the

desired

form

very

quickly.

Figures

3

and

4 show

the general

views

of

the inside

and outside

of

the model,

respec-

tively.

The

length

of

the model

is about

19.3

ft,

and

the depth

is

30 in.

The

beam

of

the

model

can be

varied.

Because

of the

gap

between

the

slotted

bilge

plate

and

the bottom

plate,

it was

thought

that

the model

might

have

to be ballasted

with

water

in

plastic

bags

in order

to

avoid

deforma-

tion of

the

rubber

sheet

due

to

the

water

pressure

underneath.

When

the

model

was

put into

the

water,

however,

no visible

indentations

of

the stretched

rubber

bottom

between

the

above-

mentioned

gap

were noticed.

For

all the

tests

conducted,

the

usual

ballasting

weights

were

used.

Figure 5

shows a

typical

plot

of a

set of

carriage

data.

The

test spots

were

obtained

by

going

over

the

speed

range

three

times.

There

was

a

lapse

of a few

hours'

time between

each

of

the

three passes

over

the speed

range. Each

pass

repeated

the pattern

of

the previous

CLrr~ra~

L I

---

-----

---- --

-__-_I--

-- sl I I

1

I --. ~s~Li


10/48

test

spots

very well. All the test

spots fell

into

a well-defined

curve. Figure 6

gives

a

series

of photographs

at

various

model

speeds of

a

typical resistance

test.

Under

towed conditions,

no peculiar feature of

this

model had

been noticed. No mechanical vibration

of any

part

of the

flexible model

had

been detected.

The flexible model

seemed

to

behave

exactly

the same

as

any

wood or wax

model under test.

THE

INITIAL

TEST

PROGRAM

The basic objective

of this

project

is

to find

the

effect

of change

of sectional

area

curves upon

resistance.

To accomplish this

objective

an overall

testing

program

should be

developed

to cover a

large variation in

sectional

area curves with a fixed

fineness

ratio and

overall

dimensions. To obtain

some idea

as

to

how and

to

what extent the area

curves

should

be varied,

some

probing

tests

were conducted in

the

initial phase of

the testing program.

In

this initial phase,

the

forms tested had the same

fineness

ratio, the same overall dimensions,

and

the same section

shape.

Nine

different

forms were

obtained from

this

flexible model. Each

form

was

tested for

resistance at

three different

displacements.

Altogether,

27

ehp

tests

were conducted.

These

forms had

the

same

Cp

value

of

0.66,

the

same

L/B value of 7.25,

and

the

same B/H value of

2.5 at the heavy

displacement

of

2473

lb. These

values

were the

same as those of

the Series

60, 0.65 block

coefficient

parent model,

Model

4211.

They were

chosen so

that the

work in

this project

could

be linked

to the work of Series

60.1

These

nine

forms

were divided

into

the three

groups shown

in

Table

1.

TABLE

1

-

Grouping

of

Models

Model No. Test

No. LCB

Location

4634-1

1,3,, 5

0.5 percent

A

Group I

4634-2 2, 4, 6 0.5 percent

F

4634-3

7, 8,

9 Midship

4634-4

10,

11, 12 Midship

Group

II

4634-5

13,

14,

15

Midship

4634-6

16, 17,

18 0.5 percent

A

4634-7

19 20, 21

0.5 percent F

4634-5

13,

14, 15 Midship

Group III

4634-8

22,

23, 24

Midship

4634-9 25,

26, 27

Midship

GROUP

I

This

group consisted

of three

models: Model

4634-1, Model

4634-2,

and Model

4634-3.

Model

4634-1 had

the

same area

curve

as

that

of Model

4211.

By

comparing

the

resistance

results

of these

two

models,

the effect

of

the extreme

U-section

upon

resistance

can

be inferred.

1References

are listed

on page

8.

- -

,

I

I I I I

II I

I

II

I

I I I

.

.,,


11/48

The

resistance

results

of Model

4634-1

are shown in

Figures

Ta and

Tb.

The area curve

of

this model is also shown in Figure Ta.

The difference of area curves for different displace-

ments

is not significant.

The effect of

LCB

location upon

resistance

was investigated in

this

group with tw o

additional

models,

Model 4634-2

and

Model 4634-3. Model 4634-1

had

an LCB location

at

0.5 percent aft

midship

section.

Model

4634-2

had

an LCB

location at

0.5

percent forward

midship section.

Since the

flexible model

had

the same

end profile for

the bow

and

stern,

Model 4634-2 was

obtained

by towing Model 4634-1 backward.

The resistance

results and

the area

curve of

this model

are

shown in Figures

8a

and 8b.

Model 4634-3 had

an

LCB lo-

cation at the midship

section. The

area curve of this model

was obtained by

taking

the

mean

values

of

Model

4634-1 and

Model 4634-2. The

resistance

results and the

area curve of this

model are shown in Figures

9a

and 9b.

GROUP 11

This group

consisted of four models:

Model

4634-4,

Model

4634-5,

Model 4634-6,

and

Model 4634-7. The

basic

model of

this

group was

Model 4634-4. It was

derived

from the re-

sults

of

Weinblum's work.

2

The

sectional-area

curve

of this

model

is expressed as follows:

withy

= 1

-

(A

2

X

2

+A

4

K4

+46

X

6

+ A8X

8

+ A10X)

[1]

ydx=

[2]

y

(1)

= 0

[3]

There

are five arbitrary

constants

in Equation

[1].

With

the conditions of

Equations [2] and

[3],

two of

the five

constants

can be

expressed

in terms

of

the

remaining three

constants,

which in

turn are

determined in

such a manner that

the wavemaking

resistance

of

this form

would be a minimum at

F

=

0.267 V/V/L-= 0.795).

The

sectional

area curve so

obtained

is

shown below:

y

= 1 -0.86104 X2

+ 0.14966 X

4

-4.683

X

6

+9.6816 X

8

-5.28722

X

10

[4]

The

plot of

this

curve is shown in

Figure 10a.

Because

of

the large

tangent value

of the

area

curve

at the ends, the side walls near

the

ends

could

not

be easily bent

to

conform

with this

curve. Wood and

wax

were patched to

the

side

walls

near the

ends and shaped to

obtain the

desired form. The resistance results

of this model are

shown in

Figures

10a

and 10b.

During

the test of

this

model,

a

large spray

of

water,

due

to the

blunt angle of entrance,

was

noticed.

This model was modified

locally near the

ends, from

LWL above

in an effort

to

reduce

the amount of

spray. The

resistance

results of

this

model,

designated

as Model

4634-5,

are shown in

Figures

11a

and 11b.

. Ylurr

5 -rn~~ I= ---- IW~


12/48

The

effect

of

shifting

the LCB location of Model 4634-5

was

also

investigated with

the

two additional models,

Model

4634-6 and

Model

4634-7.

Model 4634-6 was

obtained by

adding

the asymmetrical

portion of

Model

4634-1

to Model

4634-5, which

was symmetrical.

It had

an

LCB

location at 0.5

percent aft midship section.

The

resistance

results

and the area curve

of

this model are shown in Figures 12a

and 12b.

Model

4634-7 had an LCB location

at 0.5

percent forward midship section. It was obtained by towing

Model 4634-6 backward.

The

re-

sistance

results and the

area curve of this model are shown in

Figures

13a and

13b.

GROUP III

This

group

consisted

of Model 4634-8, Model

4634-9,

and Model 4634-5 which

was com-

mon

to Group fl.

All the models in

this

group were arrived at from the

work

in

Reference

2.

Model

4634-5 has already

been mentioned

in Group

II.

Model 4634-8

was optimized at

F =

0.316

V/xii

= 0.942).

Its

area

curve

is

expressed

as follows:

y =

1

+

0.088603 X

2

- 9.05356 X

4

+ 20.9267

X

6

-

17.86922 X

8

+

4.90748 K

10

[51

The

resistance

results and the

area curve of

this model are shown in

Figures 14a and

14b.

Model 4634-9 was optimized at F

=

0.2235 V/VTL

= 0.666). The

area

curve of this model

is

expressed as follows:

y = 1 - 0.4524

X

2

- 0.8437 X

4

- 5.0840

X

6

+ 11.1729 X

8

- 5.7929 X

10

[61

The resistance

results

and

the

area curve

of this model are

shown in Figures

15a

and 15b.

DISCUSSION OF

TEST RESULTS

Only a few models were

derived from the flexible model and tested in this

initial phase

of the

experimental

work, and they

were chosen at

random. They

served

the

purpose of test-

ing

the

feasibility of the flexible model; at the same time,

these

tests probed

the ground

upon

which future

experimental studies will

be developed. Since only a limited number of

models

have been

tested

so

far,

and they

were not

systematically related

to each other, no important

conclusions

can be made

from

these

results.

However,

the following observations

are

noteworthy.

The effect

of LCB location upon

resistance

was

explored,

both

in

Group I

and Group

II

models.

Figure

16

shows the composite plot

of

the

results

of

the

Group

I

models.

The

effect of

the shifting of LCB location upon

resistance in

this

group

agrees

very well with

the

results

found

in Reference

3. Figure 17 shows the composite

plot of

the results

with

the

Group

II

models.

In

this group, the

improvement

in resistance

by

shifting LCB

aft

is

negligi-

ble, whereas

the penalty for

shifting LCB forward is very pronounced.

The area

curves of

the first group

are very

similar

to

those

of the

corresponding Series

60

models,

and the

area

~

a a a

_

Illill

lih

'


13/48

curves

of

the

second

group

are

very

different.

This

seems

to indicate

that

the effect

of

the

shifting

of LCB

location

upon

resistance

depends

very

much

on

the

area

curve

of

the parent

model.

The

result

of Model

4211

is

also

shown

in

Figure

16.

By comparing

the

results

of

Model

4211

with

those

of Model

4634-1,

it

is

noted

that

the extreme

U-section

model

shows

larger

resistance

than does

Model

4211,

which

has more

normal

section

form.

However,

this

difference is not

big

at

the

service

speed

V/I

=

0.8).

Since

Model

4634-5

was optimized

at V/j

=

0.795,

the

results

of

this

model

are also

shown in

Figure

16.

At lower

speed

range,

this

model

has higher

resistance

despite

the

fact

that

it was

optimized

at V/I/

=

0.795.

However,

at

higher

speed

range,

this

model

is

far

s dperior.

Figure

18 shows

the

composite

plot of

the

results

of Model

4634-4

and

Model

4634-5.

This

plot

shows

the improvement

obtained

by

reducing

the angle of

entrance

at the waterline,

as

mentioned

above.

The

results

of

Group

III

models

are

all plotted

in Figure

19.

This plot

gives

a

rather

pessimistic

picture

regarding

the present

theory

of

wavemaking

resistance.

At

V/I =

0.795,

Model

4634-5

should

have

the

lowest

resistance

according

to

the

theory.

However,

the test

results

show

that

Model

4634-9

has the

lowest

resistance

at

that speed-length

ratio.

At

V/IL

= 0.942,

Model

4634-8

should

have lowest

resistance

according

to

the

theory,

rather

than

Model

4634-5.

The

computed

resistance

results

of these

three

models are

superimposed

on

the

corresponding

experimental

results,

as

shown

in Figure

20. Again,

this

figure gives

a

pessimistic

picture

of the

reliability

of

the present

wavemaking

resistance

theory.

The effect

of

change

in

displacement

upon

Rr/A is small

for Group

I

models. This

ef-

fect

is larger

for

the

mathematically

derived

models.

The

plots of

versus

are

some-

what misleading

in showing

this

effect

because

of the

large

change

in 0 values

as

the result

of

change

in

displacement.

CONCLUSIONS

The flexible

model

has

proved

to be a

very

useful tool

in finding

the

effect

of

the

changing

of waterline

shape upon

resistance.

With this

model,

an extensive

test program

may

be accomplished

within a

relatively

short

time and

at

substantially

less

expense.

The

results of the

initial

phase of

the

experimental

work

clearly indicate

that at

high

speed-length

ratios a

great

improvement

in

resistance can be

made

by

changing

the shape

of

waterlines

without

reducing

the

fineness

ratio

and the beam.

At present, ships

of high speed-

length

ratio

are always

designed

at

reduced

fineness

and

increased

L/B

ratio.

Both

of

these

factors will increase the cost of construction. The test

results

also

show

that the mathemat-

ically

derived

models give

far better

resistance

results

at high

V/T,

as

shown

in

Figure 16,

even

though

the computed results did not agree

with the experimental

values.

From these

considerations,

the immediate future work

should follow

the

outlines

listed

as follows:

,

lc-------

-s~-- I Ir 1 111~~


14/48

Phase

I: Choose

a

speed-length

ratio,

say 1.2,

and

derive

a theoretical optimum

model

at

that point by using the following expression

for

area curve:

y

=1 -(A

2

X

2

+ A3X

3

+A

4

X

4

+A

6

X

6

)

[7]

The

higher powers in X are omitted

at

high

Froude

numbers.

With the

conditions of Equations

[2]

and

[3],

A

4

and

A

6

can

be

expressed

in terms of

A

2

and 43.

Besides

the

set

of

A

2

and

43

values

obtained

at

optimized condition, the

values

of 42

and

A

3

should be

varied

system-

atically.

Keep A

2

fixed at the optimum value; A

3

should

be

varied

in

three steps.

Then for

each of these

three

43 values, A2 should be

changed

in

three steps.

Altogether ten forms

should be

tested.

Phase II: From the results

of Phase I, a new

parent symmetrical

model will be chosen.

The asymmetrical

portion will

then

be

introduced into this

new parent model

systematically

in

several

steps. The details in this

phase

should be

decided upon

as the

experimental

work progresses.

The

results

obtained should

definitely indicate

the

effect

of

systematic

change in the

area curves

upon

resistance,

from

which

useful conclusions

may

be

drawn for

practical

de-

sign

purposes.

ACKNOWLEDGMENTS

The author

wishes

to thank Mr.

John W. Hill

for his assistance

in conducting

most of

the

test

work.

The assistance

of Miss

Mary Cavanaugh

in preparing most

of the figures in

this

report

is also greatly

appreciated.

REFERENCES

1.

Todd,

F.H.,

Some

Further

Experiments

on

Single-Screw

Merchant

Ship

Forms -

Series 60,

Transactions,

Society of

Naval Architects

and

Marine

Engineers,

Vol.

61 (1953).

2. Weinblum,

G.P.,

A

Systematic

Evaluation

of Michell's Integral,

David Taylor

Model

Basin

Report

886 (May

1954).

3.

Todd,

F.H. and

Pien,

P.C., Series

60 - The Effect

upon

Resistance

and Power

of

Variation

in LCB Position,

Transactions,

Society

of Naval Architects

and

Marine

Engi-

neers, Vol.

64

(1956).

^I--------

------------

I I r Il ~


15/48

Figure

1

- Metal

Portion

of

the Midship

Section

of

Model

4634

Bilge

Plate

l Separation

I

IPoand S

-6 Rubber

Sheet

4

x8 I Beam

Bottom Plate -.

Cont.

Weld to

I

Beam

Figure 2

-

Details

of

the

Bilge

Piece

rrrxg*~rrn~

~--...^----ill--

--1I~~~ ---


16/48

Figure

3

-

Inside

View

of Model

4634

I

-- ~I

'


17/48

Figure

4 - Outside

View

of

Model

4634


18/48

O

)A

Model 4634-4

Test

10

Displacement

2473

Ibs

Pass

Through

Speed

Range

0

First

L Second

O

Third

O

O

C

5

A

O 00

0

AOZ

E

2.5 3.0 3.5 4.0

Speed

of

Model

in knots

4.5

5.0

5.5 6.0

Figure

5

-

Plot

of

the

Test

Spots of

a

Typical Resistance

Test

(

0

.0

u I I I I I II I I I II


19/48

4 bO

KNOTS

S5.00

KNOTS

I

Figure

6 -

Typical

Wave

Profiles of the

Flexible

Model

under Towed

Conditions

Model

4634-4

Test

13

Displacement,

2473

Pounds

Bare

Hull

-- ~ ~--


20/48

0

Stations

10

r

I I I I I

1- L I

I

I

I

__

__

\

__/

/

t

_

7L

/_

_

_______

/

/

_

_ _

I

/

I01

Model

4634-1

Test

I

-

.-----

-

Test 3

Test 5

--

I 1

I

I

2.0 .5

0

Figure

7a - Sectional Area

Curve and (D

versus

0 Curves, Model

46

2

1 0

,

0.8

0.6

A/A

x

0.4

0.2


21/48

16

12

/

/

Model

4634-1

...

Model 4634- Displacement

..

'

Test I

- -

2473

Ibs

0

Test

3

2054 lbs

Test

5

1752 Ibs

-2

1

L_____

i I

i 1

0.6 0.7

0.8

0.9 1.0

1.1 1.2

1.3

Figure

7b

-

Rr/A versus

V/U-

Curves,

Model 4634-1

11-1-110iii14-'M-wffl0fl-q -- ft

~

-11111(~1


22/48

Stations

1.5

2.0O 2.5

3.0

Figure

8a -

Sectional

Area

Curve

and

C

versus (

Curves,

Model 463

A/Ax


23/48

~~1~ /

//

//

/1

//

/,

-I-- 1

I

I

L I I I

0.8

0.9

Model

4634-2

Displacement

Test

2

-

2473

Ibs

Test

4

2054

Ibs

Test

6

-----

1752

lbs

I

I I

i

v/ C

Figure

8b

- Rr/A

versus

V/j/

Curves,

Model

4634-2

Rr/A

-2

0.

6

nanr~~~ll

uL

~a~U-

r--

I --

rr

-- ----

~xLd


24/48

Stations

I0

0

1.0 -

0.8

0.6-

A/A

x

0.4

-

0.2

0

1.5

Figure 9a - Sectional Area Curve

and ( versus 0 Curves, Model 4

2.0 2.5

3.0


25/48

6

12

8

4}

Model

4634-3

Displacement

...-

Test 7 -

2473 Ibs

Test 8

2054 Ibs

0

Test 9

1752 Ibs

_____I

I

.

I I

I i

-2

-

_

_ _ _

_ _

_ _ _ _ _

_

_

0.6

07

0.8

0.9

1.0

1.1

1.2

1.3

v/W

-

Figure

9b

- Rr/A

versus V/IT Curves, Model

4634-3

I~a~~rxl~

CC

'~ e*UIII.~~~~

~

~--~-

- I -- -

-------..

rrr-~-~~l~

rr~*lrrrn


26/48

Stations

10

/ \0

/

___________________________

____ ____ ____ ____ I I

_____I ___________

2.0

2.5

Model

4634-4

Test

10

Test

II

Test 12

Figure 10a

- Sectional

Area

Curve and

0

versus (

Curves,

Model

4

0

1 I1 T 17 r T f

, . .

2 (

1.0 .

0.8

0.6

A/A

x

0.4

0.2


27/48

Rr/A

16

Test

10

- 2473

lbs

0

Test

II

2054

Ibs

Test 12

. 1752

Ibs

-2

1 1I__j

0.6

0.7

0.8

0.9 1.0 1.1 1.2

1.3

Figure-

Rr/A versus

V/

Curves,

Model

4634-4

Figure

10b -

R./A versus V/

- Curves,

Model

4634-4

,

L I- --

yl-

I II --

~i U' ~

' '-'


28/48

Stations

I0

Figure 11a -

Sectional

Area Curve and

(

versus

(

Curves, Model 4

20

1.0

-

0.8-

0.6-

A/Ax

-

0.4-

0.2-

0


29/48

Rr/A

1/

8

___

.

........

.

......

Model

4634-5

Displacement

Test 13

-

2473

lbs

Test

14

2054 Ibs

Test 15

1752 lbs

-2

I

I p

I

I

I

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Figure

lb-

/

versus

V/

Curves,

Model

4634-5

Figure

11b - R./A versus

V/ LCurves,

Model 4634-5

'~ (-Cxiui~ __

I

C- i~lyw


30/48

Stations

Figure

12a -

Sectional

Area Curve

and

( versus ®

Curves,

Model 463

A/A

X


31/48

16

5

z

12

//

8

/

4/

0.7

0.8

Model

4634-6

Test 16 -

Test 17

Test 18

I I

I

Displacement

-2473 Ibs

-2054 Ibs

1752

Ibs

i

I i

0.9

V/V,

Figure 12b -

Rr/A

versus

V/JvL-Curves, Model

4634-6

R

/A

-2L

0.6

-------------

--

I-

I


32/48

Stations

I0

2.0

2.5

@

Figure 13a

- Sectional

Area

Curve and

0 versus

) Curves,

Model

20

1.0

r-

0.8

0.6

A/A

x

0.4

0.2

0

.01


33/48

16

.-

1

_

2

b

12

000J

0

Test

20

2054

lbs

Test 21 - - --

17

52

lbs

0.6

0.7 0.8 0.9

1.0

.I1.2 1.3

V/

Figure

13b -

Rr/A versus V/ Curves,

Model

4634-7

Model

34-7Displacement

Test 19

- - 2473

lbs

0----------------Test

20

2_054 lbs

Test 21

17

52 bs

0.6 0.7

0.8 0.9

1.0 I.

1.2

1.3

Figure

13b - Rr/A

versus V/vi-L Curves,

Model 46.34-7

---1L1YC-II -I


34/48

Stations

1.5 2D 2.5

3.0

Figure 14a

-

Sectional

Area

Curve and

(

versus

( Curves,

Model 4

A/Ax


35/48

R

r/A

/

16

/

12 Oe

4

.0

Model

4634-8

Displacement

Test 22

- 2473 Ibs

0

Test

23

2054

Ibs

Test 24

----- 1752 Ibs

-2

I

I

I

1

1

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Figure

14b

R A

versus V/L

Curves,

Model

4634-8

Figure

14b

-

Rr/A versus

V/C Curves,

Model

4634-8

_

~urmsaa - - -I - -

I

I-~ -- -- I

II~ IILlcs~nllllZliMI-


36/48

Stations

20

18

16

14

12

10

8

6

4

1.0 --

0.8

SModel

4634-9

S0

/Ao

/,

)

0.2

° // '

,0.8

Figure

15a - Sectional Area

Curve

and

0 versus (E Curves,

Model

4


37/48

32

-

28

24

20

Rr/A

/

----

Model

4634-9

Displacement

Test

25

-

2473 Ibs

STest

26

2054

Ibs

Test

27 1752

Ibs

-2

_

I-

1

i

0 6

0.7

0 8

0 9

1.0

1 1

1.2

1.3

V/l

Figure 15b -

Rr A

versus

V/-

Curves Model 4634-9

_ _

- -

mmmmmmi-v

i


38/48

Rr/A

/

16

-/

0

0

.2

VI

/

12

Figure

16

-

Composite

Plot

of

Rr/A

versus

V/v/LCurves

of

Group

I

Models

4

0.6

0.7 0.8

0.9

1.0 1 1

1.2 1.3

Figure

16

- Composite

Plot of

R./A versus V/V

1

iCurves

of

Group

I Models

I I

I II II

I

F


39/48

30

I

/

26

X,

14__

__

_

-2-1

V/rL

//

///

Figure

17

-

Composite

Plot

of

Rr/A

versus

V/

Curves

of

Group

II Models

n-r~~

i

- II---- -Illr~

-1 I -- I I _ ~I_


40/48

3

4

-,

-

--

%.

1%0

Displacement

2473

lb.

30

26

22

-

8

-

- -

14

10

0.6

0.7

0.8 0.9

1.0

1.1

1.2

I.

V/

Figure

18

-

Composite Plot of Rr/A

versus

V/JE

Curves

of

Models 4634-4

and 4634-5

__

?I

1

111 1

I _

l]llp


41/48

34

4634-9

25 ----

Displacement 2473 lb.

I

-fr

00I

---- I -

I

2

0 6 2.7

0.8

0 9 1.0

1.1

1.2

1.3

-4

-

/V/

Figure

19 -

Composite Plot

Of

Rr/A versus V/ Curves

of

Group

III

Models

/

_ __/

0.6 0.7

0.8 0.9 1.0 1.I 1.2

1.3

viyi?

Figure

19

- Composite Plot of Rr/A versus

V VE Curves

of Group Ifl

Models

Ir

-rr~*m-xiqn~s-

-~ - L - - -- I I I -


42/48

0.6 0.7 0.8

V y C

0.9

1.0

1.1

Figure 20

- Composite Plot

of R

r /A vers

us

of the

V/lE

Experimental

ana Theoretical Values

of

Group

III

Models

2L

0.5

i I I I T ll

i

.__~__~~__~~~ ___~_

_~____~~~~_

_~__~ ~ ___ ~_ ~~_~_ ____________~____~~_~~__________________ ~__~_~_~_ ~1~

10illiia, l1

1


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tech

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in

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Webb

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Exper Nay

Tank, Univ of

Michigan

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of NAME, MIT

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General Dynamics

Corp,

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England

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des Carenes, Paris,

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Skeppsprovingsanstalt,

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45/48


46/48


47/48

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Documents

PIEN Flexible Hull