A study on the form factor of frictional resistance by wind tunnel experiments

(1)

NO.4

A Study on the Form Factor of

Frictional Resistance by Wind

Tunnel Experiments

by

T. Tsuda

M. Takagi

March, 1968

HITACHI ZOSEN

TECHNICAL RESEARCH LABORATORY: OSAKA, JAPAN.

HITACHI SHIPBUILDING & ENGINEERING CO., LTD.

ARCHIEF

Lab v Scheepso'wkunde

Technische HogschooI

Dellt

(2)

SUNNARY

In recent years, there is a tendency that the hull form of the

tanker grows in size especially in breadth and fullness eventually

the Froude numbers in service speed reduce smaller and smaller.

In this kind of ship the viscous resistance constitutes a high

percentage of the total resistance. Therefore it is necessary to

research into the form factor of the frictional resistance not only for obtaining exact model and ship correlation, but also for

investigating means of the reduction of resistance. In this study

it was attempted to clarified the relation of principal form

parameters to the form factor and to develop hull forms of minimum

resistance by wind tunnel tests with twenty-one models. Besides,

wake surveys and flow observation were carried out for several

models. The results are as follows

(i) _{The relation of the form p&rameters to the form factor K is}

indicated by the following formula for the full load condition

of the normal hull form.

K (L)_2.o

(b)O

C66° ( 6.64 LCB2- 32 . 3LCB+13 9.2)

For the several models, the values of the form factors in ballast

condition were obtained.

For the reduction of frictional resistance, it iras confirmed

that the twin screw ship formwas superior to other forms, and

the round bottom hull form was favourable.

The results of the observation of flow patterns showed _{that there}

was evidence of separation in the vicinity of the stern of a

full hull form with

(3)

1 Introduction

In recent years, oil tankers are growing greater and greater

in size especially in breadth and fullress Consequently the valu

of the Froude numbers are becoming smaller In this kind of ships

the viscous resistance constitutes a high percentage of the total

rcsistance The form resistance, which forms a part of the viscou

resistance, is an important subject of the study in this field,

Usually a two-dimensional correlation method has been adopted to

estimate the required horse power According to this method the

total resistance is split up into the frictional resistance and tl

residuary resistance, the latter including a part of the form

resistance, The total resistance of the ship is calculated by add

ing a roughness allowance to the total resistance estimated from- t

model testj, However, when this method is applied to recent large tankers, the calculated results usually exceed the actual horse power measured at their trialruns Tri order to eliminate this

discrepancy, the idea of taking the roughness coefficient ¿GF

as negative has been adopted This idea requires, furthermore, to

modify appropriately the value of ACF according to the size and

form of the hu1l This fact obviously suggests some defects

existing in the method,

Now to cope with the situation, considering fully the form effect on the viscous resistance, Hughes and Lap separately have

CiJ C2J

developed new methods , which are called the three-dimensi

correlation method., When results of trial runs are analyzed with method,tCF becomes positive and maintains ari approximately const

values This shows that the three-dimensional method is superior es e he onal this ant to

(4)

the two-dimensional0 However, the problem involved in the application

of this method is that the form factcr must be clearly known0 The

investigation on the form factor also serves for the study of hull

f rm of minimum resistance0

The purpose of this paper is to present the form factors of some recent large tankers and to discuss what

full

_{form has minimum}

frictional resistance. For this purpose, seventeen tanker double

models were tested methodically in a wind tunnel and four special-form double models were tested in a way explained fully later,

In addition, Observation of the flow patterns and wake surveys were

made to investigate features of the flow around the _underwater

body0

Notations proposed by the 10T0T000 Presentation Committee _are

used in this paper0 _{Notations not involved in above list are used when}

they are usually used among the navalarchitects, _{e0g0 F0P0, A0P0, etc.}

The position of the longitudinal centre of buoyancy,

_LCB,

is expressed as a percentage of

Lpp

_{and as positive for the fore part0}

Details of Tests

1 _{Description of Models}

Twenty-one models were used; seventeen belong _{to the hull form}

which is generally in actual use, the other four had forms which

were a little different from the normal one _{as explained fully}

later0 Each form group is called the normal hull _{form and the}

special hull form respectively0

For the normal form, four form parameters _{are varied}

systematical-ly as follows:

_L/B

05705,B/

_21f-'-'3,O,

_{CB =}

_O78-O82,

(5)

-LCB=

0-?

The principal particulars of these models are shown

in Table l The models No07, 8 and 9 differ from each other only

in CB and the models

No07, 9

and 10 only in LcB

Figs0l

and 2 compare the body plans and the prismatic curves with one another0 The body

plans of the other normal forms carl be produced from these figures

merely by enlarging or reducing the sections without altering their

spacing

The number of the special hull form is four One is the Myer

f:rm of which the frame lines in the forebdy are V-shape0 Another

one is the twin screw ship fors of which the frame lines in the

afterbody are V-shape0 The sha;es of the afterbody or the

fore-body of these two forms are the same as those of the model

No09.

nother two models of the four are secial forms, designed merely

to minimize the resistance and not intended for practical use0

They are called a round bottom hull form and an airship hull formO

The principal particulars, body plans and prismatic curves of these

four models are shown in Table 1 and Figs0 3

6.

For the round

bottom hull form and the airshi. hull form it is not considered

how to install the rudder, Therefore, it is difficult to decide

the position of A.P.. In the Table 1,

CB ,

etc0 based on the assumed position of A,P0 are shown with parenthesese.

The percentages of

Lpp

to LOWL of the round bottom hull form and the airship hull form are 97% and 100% respectively0 When they are

compared with those of the normal form, the value of Lpp 97% 11VL is not so improper but the value of

L= i00% LWL

is improper.

The assumed value of

L= 97% LWLiS

also adopted for the airship form; the particulars shown in Table i are altered as follows:

Lp=

1.9m,

L/B= 583,

CB =0.82,

LCB=3.kl%L.

(6)

Fig., ₇ compares the profiles of the normal forms and the special forms with one another

2,2 Items of Experiment

In this experiment, measurement of drag, surveys of wake and observation of flow patterns were carried out,

2,2,1 Measurement of Drag

There are various methods for obtaining the form factor but there

is not the best method confirmed., In this study, the wind tunnel test

was adopted from the following two reasons: (i) the pure viscous resistance can be perfectly measured (2) As the wind velocity can

be changed easily, a number of measured values are obtained,

The models used were wooden double models, 2m., Each model

was suspended by wire in the working section of the wind tunnel according to the method of three-component balances The drag was measured by a

six-component balance,

Two kinds of metal fixtures were used to join the supporting wire

to the model, _{One was shaped like a wing with a section of a symn.etrical}

circular arc, of which the length, the breadth and the maximum thickness were 600 mm, 50 mm and 6 mm respectively

This fixture was fitted at a position of 250 mm aft of FP; it passed

through the symmetrical plane of the double model. The other was of a

small ring-shape, and was fixed at the center line on the two bottoms of the model and at a position of I m aft of the wing shape fixture.

Supporting wires of 0.2 mm $, O,Lk mm $ and 0,6 mm $ _{were used.,} Two T-shaped rods were made to measure the drag of these wires., The drag

(7)

with the form factor of 0.4, for it was difficult to measure this drag.

Trip wires and studs were used as a turbulence stimulator.

The wire,

0,8

mm diameter, were fixed on the model at a position of lO mm aft of F,P, The studs were set up with the hight 1.5 mm and the

pitch 5 mm at the station 9Y2.

The wind velocity was altered at an interval of about 5 mm from

about 10 mm to 55 mm in readings of the manometer (corresponding to about 10 rn/sec to 27m/sec in velocity)0

Tests for the full load condition were carried out for all of

the twenty-one models. Additionally the five models, the models No.

4,5,8,14

and

15,

were tested for a ballast condition i.e. the 45%

full load condition with 2% trim.

The test were performed in the large wind tunnel of the

Gottingen type in the Osaka University. Figs.8 and 9 showed a sketch

of this tunnel and the lay-out of the model,

2.2,2 Surveysof Wake and Observation of Flow Patterns

For measurement of the velocity of flow in the plane of the

propeller, a wake survey rake was equipped on a stand installed

behind the model as shown in Fig. 10. This rake consisted of ten

Pitot tubes, 7 mm diameters, with a lateral spacing of about 30 mm, and is devised to be able to shift freely up and down or right and left.

The measurement were carried out only a range of a quadrant in the plane of the propeller because it was expected that the wake distribution was symmetrical both vertically and horizontally in view of the shape of the model. Points measured were twenty in a vertical spacing of 15 mm and eight in a horizontal spacing of 20mm,

0cL, ref,

(3) p.408,

Fig.142.

(8)

and the total were 160 points. Models used for this purpose were

five the model No.2,

3, 7, 9

and the twin screw ship form.

The two models,

_No.3

and the round bottom hull form, were also

tested in a circulating water channel of our technical research

institute and the flow around the body was recorded by still

photographs and observed with the naked eye.

These double models were fully submerged, The observation

of flow patterns was made by twin tufts fastened to the surface of

the models. The twin tufts constitute of wollen yarn (white and

black), are fixed to small pieces of vinyl with a tiny hole, and

are attached to each vertical wire through the hole. The white

one was attached to the surface of the model and the black one

was located in the plane at a distance of 25 mm from the surface.

3,

Test Results and Discussion

3.1 Form Factor

For the calculation of the form factor, Hughes' frictional

formula was used.

The form factor K obtained from one of the measurement results was, as an exampe, plotted against Reynolds number as the

abscissa, and is shown in Fig,ll. _{The points are distributed over}

a wide range, In the case of R> 3.0 x 106, however, they indicate

approximately a constant value and each average line is shown by a

solid one. The average value of K thus obtained for each model is

given in Table 2 for all models.

(9)

Table 2 V&lues of K for Full Load Conditions

Si : the round bottom hull form

S2 : the airship hull form

S3 : the Myer form

SL : the twin-screw ship fcrrn

These values are plotted against , C11

,LCB

ar1dT

and shown in Figs 12, 13, l and 15 respectively; each solid

line indicates the mean curve of these average values These

K-curves against , CB and

B,,

have a trend expected, but their values are considerably higher as compared with values which

are obtained for ships commonly in service estimated from the

results of their model tank tests This fact is related to the

value of

LCB,

as noticed from

Fi'l4,

which shows the effect of

LCB0n the form factor According to this figure, the K -curves have a minimum value at a position of LCB= 2% The values of

LCB

of actual ships are usually

LO

2O%L

while those of

the models corresponding to Figs 12, 13 and 15 are nearly o%

Therefore, it is natural that the K -values in these figures are

higher In the vicinity of

LCB=

2% the values in Fig014 almost agree with those estimated from the tank test results;

thus the valuos obtained from our wind tunnel tests and from the tank tests are consistent with each other

-8-M.SNc 1 2 ₃ 4 1 6 7 8 9 10 11

K

0,67 079

0,92

O59

0.65 O52

06l 073 O43

O52

0.61+

I'hSONd 12 13 14 15 16 17 Sl S2 S3

(10)

Most of the models used in our tests have hull forms of

_LCB=O%L0

Therefore, it is inconvenient to use the results obtained from the

test directly in design or for reference,, In order to eliminate

this inconvenience, the authors tried to develop a formula for *

these results0 It is helpful to use a power formula for this

purpose, because constants of the formula can be evaluated easily and effects of each parameter can be followed clearly. However, if this formula is expressed by the products of only power functions of the parameters, the effect of LCB can't be contained adequately0 Therefore, we assume a quadratic equation

for _LCB, as follows:

L

Bß

_r

K=

()

_{CB (p' LCB2+ q'}

a

_,

_{fi, r}

_,

p

, q and

r

_{are constants and the values can be}

evaluated uy the method of least-squares from the experimental

results0 They have the following values:

a =

-2.09,

fl= -0.157,

= 6.60

p=

6.6/+,

q = -323,

_{r =139.2}

Values of K _{calculated from the formula (i) are shown by}

dotted lines in Figs0 i2'-l5. It is desired to notice that these

curves agree fairly well with the mean curves of the experimental

values,,

The results of our tests show _{that there exists the optimum}

value of LCB , in which the value of K becomes _{a minimum, as}

evident from Fig. l4 _{When this value is calculated from the formula (1),}

a value of _LCB =

2,43%

is obtained, On the other hand, according

to the results of tank tests for tanker models with _{a bulbous bow,}

* cf0

reference

(4)

(11)

which had been conducted in our Institute, the optimum value of

LCBwas

about 2,8 3.0%. The value corresponding to the above got

from the wind tunnel tests is somewhat smaller., It is right

qualitatively that the optimum position of a longitudinal centre of buoyancy of the hull form with a bulbous bow is somewhat more forward than that of the normal hull form, because the flow over

the bow is improved by the bulbous bow., On the basis of the above

facts, it is resonable that the optimum value of LCB is about 2.5%

Lpp

in the normal hull form.

Next we will discuss about the form factor of the special

hull form., In order to minimize resistance these hull forms were designed after full consideration; items considered are as follows.

In order to ease all the flow around the body, the hull forms were stream-lined not only in the shape of the water line but also

in three-dimensions. In particular, we took full notice of shapes

at the places where the water flowed down under the bottom from

the side, or flowed up in the inverse direction.,

Values of K

of the special hull

forms based on

this

consideration are shown in Table 2, It follows that the values of

K become smaller in the order of the twin screw ship form, the round bottom hull form, the airship hull form and the Myer form, We will compare the special hull forms with the model No.9, This is the normal hull form having the same values of the form

parameters as the twin screw ship form and the Myer form., The value

of K of the twin screw ship form is lower than that of the model

No.9, as expected. This value of the I1yer form is higher contrary

to expectation. As the values of the form parameter of these three

(12)

-hull forms are equal to each other, such differences are mainly due

to shapes of the frame line0 Transverse sections of the forebody

of the Myer form are V-shaped and its shoulder is rather abrupt0 Therefore it is believed that the downward flow around the forebody

is improved but that the side flow becomes unfavourable0 It is

thought that such flow has a bad effect upon the form resistance0

It appears to be imprcper to apply the Myer form to the super tanker0

The test results of the Myor form and the twin screw ship form suggest that the effects of stream-line fairness in three dimensions to the

form resistance are greater in the afterbody than in the forebody0

The round bottom hull form and the airship hull form are

different in shape from usual ones0 Their hull forms are unsuitable

for practical use as they are0 However, they are remarkable hull

form0 In particular, the round bottom hull form is possibly a

favourable one from a wave making point of view0 It is possible to

reduce the form resistance by shifting the position of the longitudinal center of buoyancy farther rward0 On the other hand, it seems that

the airship hull form is not so favourable from a wave making point

of view because of the very large entrance angle0 However, if a

value of

_O97

is adopted as becomes O82 as mention-ed in the section 2l According to these facts this form is more

full-bodied one ini substance0 ihen the k -value of the normal hull

form corresponding to this item is calculated with the formula (i), a value of O63 is obtained0 It follows that the k -value of the

airship hi1l form is reduced to about 70% in comparison with that

of the normal one0 In addition, this form has the characteristic

of a small displacement-wetted surface ratio0 The fact shows that

(13)

is a desirable one for the full low-speed ship. It is hoped that

these two special hull forms will be further investigated in detail

regarding their applicability to the actual ship.

Fig0 16 compares values of K obtained from the authors' formula (i), Prof0 Sasajima's foru1a and results of some

tank tests with one another; the solid line, the dotted line and the symbols o +, etc0 correspond to the authors' formula, the Sasajima's formula and the results of the tank tests respectively0 The form factor of the Sasajima's formula is based on the Schoenherr

Mean Line0

ihen

K and K'indicate the form factors based on the Schoenherr Line and the Hughes Line respectively, the relation

of K'= K

+ Ol2 holds approximately0 This value of K' is addopted

as the form factor of the Sasajima'sforrnula in this paper0

This figure shows that the effect of CB is different between the

formula (i) and the Sasajima's formula0 That is, a gradient of

K-curves againstCB of the formula (i) is larger than that of the

Sasajima's formula. This discrepancy becomes considerably remarkable

in the range of larger L/B

Next we will compare the two curves with the values obtained

from the results of the tank tests0

In the range of/ß6o5 the

values of the two curves are not so much different from those of the

tank test. In the range of L/> 7GO, however, the Sasajima's curve

better agrees with them than the authors' one0 It appears that the

authors' values are

too

low in this range0 The accuracy of the approximation of the formula (i) appears to become worse in this

range of , because the number of the models in the range are very

small0 However, there is room for réexamination in the results of

(14)

-the tank tests, because th tank tests weren't necessarily carried out

for the purpose of obtaining the values of K This problem must be

fully investigated hereafter0

The values of K in ballast conditions were measured only for the five models described in the section 2.2l As the data aren't

obtained so much fully as we car0 discuss in detail, the results are

only shown in Table 3 for your information0

Table ₃ Values of K in Ballast Conditions

In the ballast condition, the amount of ballast and the trim need to be taken up as factors influencing the form factor besides the

form parameters0 It becomes a difficult problem how to arrange the

results of tests0 Additionally,, in the full load condition, fairly

reliable values of K can be obtained from the results of tank tests; in the ballast condition, the accuracy of the K-values obtained from such tests become worse inevitably because the effect of wave-making

becomes greater0 As mentioned above, it is difficult to obtain

reliable values of K systematically so as to be available in the

design of a shíp However this problem is so important that it is

hoped to investigate this one at the earliest opportunity.

32

Wake Distribution

Fig _{17 show the wake distribution of the models}

_{No0 2, 3, 7, 9}

and the twin screw ship form0 _{The wake distribution of the models No02}

and _No03 _{are quite similar to each other; only the thickness of the}

13

-M0S0No0 ₅ 8

l

15

(15)

boundary layer of the model No03 is greater than that of the other0 These figures show that the wake values don't necessarily decrease gradually outward from the center plane, and that iso-wake contours

are projecting around the middle of the draft of LOWOL., This

feature is related with flow separation and vortex formation around

the stern which were observed by flow observation explained later.,

In the model No07, the projecting of the iso-wake contours becomes

smaller, but it seems that vortices are formed0 In the model No09

with LCB = 2%L, the wake distribution is pretty fair as a whole except iso-wake contours of W _00/i and

O5

In the twin-screw

ship form, the wake distribution isn't always smooth, but the wake

values decrease gradually outward from the center plane0

When the wake distributions are compared with the form

factors K obtained in the section 3,1, the following are noticed:

the lower the value of K is, the fairer the wake distribution is and the narrower its extent is, as expected0

3.,3 Flow Observation

Flow

patterns around the sterns of the models No03 and the round bottom hull form were taken by a camera with a shutter speed Y

second0 These photograph are shown in Figs0 18 and

l9

In the model No.,3, black threads (at a distance of 25 mm from the surface) don't show uniform one0 The formation of flow separation was

observed clearly with the naked eye0 As the photograph is not so

clear, the flow patterns of the whìte ones are sketched, and shown

in Fig.20. The arrow of a dotted line in Station shows that its

thread rotated sometimes., The arrow of a solid line indicate that

small bubbles in the water adjacent to the model surface formed a

spiral flow., The flow around the bow also was observed, nothing 1/i

(16)

-- 15

abnormal was noticed and the pattern was fair. As the forehody of the

model No.3 is comparatively fine because of LCD= 0%, it is believed

that the flow around the bow becomes easy. However, in the models

with LCB

4% Lpp,

it is probable that the separation may occur at

the bottom of the forebody in view of the tendency of K - values.

It

is hoped to confirm this phenomenon at the earliest opportunity. The flow pattern of the round bottom hull form was very smooth and

the confused flow was not noticed anywhere. _{This fact also suggests}

this form is excellent on resistance performance.

4 Concthsions

The results of the tests are summed up as follows:

(i) The form factors Ko±' the nornai hull forms in the full load

condition were measured systematically, and the formula of K related

to the form parameters was developed.

K=

(2.09

.

(-°.'

C6°

(6 .

64LCB2-32

.

3LCB+l 39. 2)

The value of K calculated from the above formula agrees very well

with that obtained from the result' jf the tank tests for the wide and

full hull form in the range of

_6,5.

_{It seems that the value of}

the formula becomes too low for the slender hull form _{in the range of}

7.

It is hoped to reexamine this point.

In the ballast condition, the form factors of the five models were

measured. -s data got from the tests are only a few, any conclusion

can't be obtained. _{It will become necessary to introduce the form}

factor for the estimate of the horse power in this condition.

(17)

It was confirmed that the twin screw ship form was superior to other forms on resistance performance and the round bottom hull form

was favourable

According to the wake survey and the flow observation, there were evìdences of flow separation near the stern of the models with

L/B=55,

C8 =O82 and

LCB =

Acknowledgements

The authors wish to express their appreciation to Prof K Senda and Prof S Nakamura of the Osaka University for their

approval of using the wind tunnel, and to their assistants for

their help in the tests

Special mention must be made for the encouragement of

Dr, S Okada of Hitachi Shipbuilding & Engineering Coo, Ltd.,

The authors are deeply indebted to the guidance of Mr, M, Fukui

for preparing this english manuscript.,

(18)

-Re ferenc es

(i)

G0 Hughes : 'Frictional and Form Resistance in Turbulet Flow,

and a proposed Formulation for Use in Model and Ship Correlation' L

N0 p., l954

A. J,, W,, Lap : "Frictional Drag of Smooth and Rough Ship Form'

L N

A0 l956

Goldstein "Modern Developments in Fluid Dynamics'

Vol0 II, l957

P. R0 Crewe ¡ The Hovercraft - A New Concept in Maritime

Transport' I N0 A 1960,,

H, Sasajima, M0 Nakato, T0 Suzuki ¡

'On valves of K,w, t

of full-.oëied hull form "

given at the meeting of the Kansai

Society of Naval Architect, Japan

_1964,

autumn0

-

17

(19)

Remarks:

Table 1

Principal Particulars of Models

* LCB

is expressed as a percentage of

and the fore parts as positive.,

** Wetted surface of naked hull without appendages. ** A.P. does not always means the rudder position for the ship form is not suitable for installation

of rudder. M.S.No. 1 2 3 4 5 6 7 8 9 lO 11

L/B

505

5.5 5,5

5.5

6.0

6.0 B/T

2.7

2.7 2,7

2.7

2.7 2,4

CB 07795

.7964

8186

.7988

.7975

.7799

.7970

.8185

.7982

7977

.7971

GM

.9920

.99no

.9920

9920

LCB(%)*

0.05

0.04 0.21

1.99

4.06

0.32

0.18 -0.16

2.00

4.02 -0.02

V (ne)

.07635

.07801

08019

07825

.07812

06421

.06552

.06739

.06574

.06568

.07381

s

(iif)

1.0363

i.023

1,0698

1.0522

1,0364

.9512

.9611

.9823

.9616

9622

1,0209

L(m)

2.000

2,000 2,000 n,000 2.000

2.000

2.000 20000

2.000

2.000 B(m)

.3636

.3333

j .3333

T(rn)

.1347

1347.1235

.1235

1235

.1235

.1389

M,S, No. -12 13 14

--

15 16

-17 1ound*** BottOni Air *** HuUMYer win Scr Forrnh Foi'tn

L/B

6.o

6,5

6.5

700

7.5 (6.o)

(6.0)

6,0

6,o

B/T

3.0 2,7

2.7 2,7

(2.7)

(2,7)

2.7

CR

.7975

.9920

.7789

9920

7968

.9920

.8188

.9920

.7966

.9920

.7971

.9920

(.7950)

.9800

(.7968)

.9800

.7999

7985

.9920

CM

0,05

0.06

-0.01

0.09 0003

0.05

(

o

)

(4.81)

1.90

1.94 V ( n)

.05907

.05465

.05591

.05745

.04816

04201

.06545

.06560

.06586

.06573

S (m)'

.9202

.8770

.8912

9047

.8233

.7648

.9784

.9265

.9594

9551

L(m)

2.000

2,000

(2.000) (2.000) 2,000 2.000

B(m)

3333

.3077

.2857

.2667

03333

.3333

T(rn)

.1111

.1140

.1058

.0988

.1235

(20)

B.A.P i 136 2 236

//

i'ig0l Models No6,7 and 8

M.S.No.7₀ 9 Prismatic Curves io BA.P½ 1 136 2 2½ 3 4 5 6 7 736 8 8½ 9 936 F.P. Body Pisms (. =2.7) Body Plans 2.7)

19 -Fi2 Models No7,9 and 1O

7 736 8 836 9 936 F.P.

M S No 6

0 ₇

(21)

Prjmatjc Curve

r i i j i

A.P. )i i 1)6 2 236 3 1 ₅ ₆ ₇ ₇₎₆ ₈ _8)s 9 ₉ F.P.

Body P1rn

;i3

Round Bottom Hull Form

Prismatic Curve

N

FigL Airship Hull Form

20

-AP.} i lS6 2 2)6 3 5 6 7 736 8 836 9 9)6 FP.

(22)

A.P.

F'ig07 Profiles of Models

- 21

me

Normai Hull Form _J».

/

'S.-Bound Bottom Hull Form Air Ship Hull Form

¡

I

-

_MyerForm 0.5 Base L i -'s "s' 's' 's

Normai Hull Form

4

Round Bottom Hull Form

Air Ship Huil Form Twin Screw Ship Form

2 I- - --0.5 - - Ba se L A.P.36 1 1½ 2 2½ 3 4 5 ₅ 6 ₇ _7½ ₈ _8½ ₉ ₉₃₆ _F.P.

Prismatic Curve Prismatic Curve

Body Plan _{Body Plan}

(23)

1.350rn.-4

<2

Fig.

9 5.200m

22

-i . 800

Fig8 A Sketch of the Wind Tunnel and a

Double Model

(24)

1.0 0.8 0.6 O.* 0.3 1.0 o.8

o.6_

0./k 5.5

Fig0ll

Some of the Measurement Results

6.0 6.5 L/B 0.80 - CB 0.82 23 -7.0 -7.5

7ig.l2 Effect of L/ß ori the Form Factor K

AUTHORS' FORMULA

igl3

Effect of Cß on the Fonn Factor K

C8 8/i' LCB D

0.82

2.7 0

-

0.80 2.7 0 0.78 2.7 0 L/B

B/F

LCB

_-r--

5.5 2.7 0 6.0 2.7 0 -,-- _6.5 2.7 0 1.0 0.8 ₀₉ 0 o 09 00 _{M.S. No.2} o 0.6 o M S No.7 9 9 -OfrM.S. No.14 0.4 .0.3 2.0

30

4.0 iO6

02

0.78

(25)

0.2

5.5 6.0 6.5 7.0 7.5

L/B

'ig016 Form Factor K of Authors' Formula,

Sajj]as Fcronila and Some Towing Tank Tests0

1.0

0.8

0.6

02

-LCB (%)

Fig0lL

Effect of LCB on the Form Factor K

Fig.15 Effect of B/T on the Form Factor K

-J- C = 0.84

o 0.82 RESULTS OF SOME TOWING

0.80 TANK TESTS 0.78

-

24 -AUTHORS' FORMULA AUTHORS' FORMULA SASAJIMA'S FORMULA L/B B/T CB 5.5 2.7

0.80 o--

6.0

2.7 0.80 CB L /B LCB

6.0

0.80 -o---AUTHORS' FORMULA 2.7

-

B/T 3.0 0.8 0.6

(26)

0 1 2 3 4

(a) Model No.2 (KO.79)

(e) Twin Screw ship Form (K=0.39) 4 3 2

/

/7

I I I 0 1 2 3 4 5

(c) Model No.7 ( K -o.6i)

5 4

-3

2 i ()

Fig017 Iso-wake Contours

25

-0 (b) 2 (d) Model No.9 3 4 (K= 0.43) 5 5 ¡I. 3 2 ç) 5

-4

:3 i

j

0 1) .1 2 3 4 5 Model o.3 (K 0.92)

(27)

A.P.

Fig.18 Model No03

Figl9 Bound Bottom Hull Forma

26

-Fig020 A Sketch

of Flow Patterns on