A theoretical study on high speed ship hull form

Nomenclature

i . Introduction

When we design high speed displacement type ships, we think of making the resistance small at first. The resistance consists of frictional resis-tance and residual resisresis-tance. When a ship cruises

Read at the Spring Meeting of Kansai Society of Naval Architects, Japan, May. 27, 1994, Received June 10. 1994

\

University

TRDI, Japan Defense Agency

at high speed, the residual resistance takes most part of her resistance. Moreover wave making resis-tance is the largest in the residual resisresis-tance. lt is known from recent studies that diverging wave com-ponent is large in the wave making resistance at high speed. So it is important to reduce diverging wave component.

On the other hand, it is also important for high speed ship to reduce spray resistance. There is a the-

-ory that it

is necessary to make the pressure zero

ITEM DIMENSIONLESS ITEM DIMENSIONLESS

wetted length:Lw

derisity:p

coordinates

wave number

swell-up potential

wave making resistance

residual resistance another expression of each resistances 2 i (z', s", z') breadth:B veloc it y: V displacement

water plane area

pressure

spray resistance

water head resistance trim rise A B/LWL i Ç" V (z,y,z) = g(LwL/2) K (LLW/2)2 AÇq = = V2 A' P' A = LWL/2 D p pV3 D5 = = pV2(LWL/2)3 pV(Lw/2)2 n' DH "H DT pV2(LwL/2)2 D' pV2(LWL/2)2

r=tanr'

h'

h=

r = _pgV'/L.L

222-

Z69

J. Kansai Soc. N. A.. Japan, No.222. September 1994

A Theoretical Study on High Speed Ship

Hull Forms*

(Application for Practical Hull Forms)

By Masatoshi BESSHO** (Member) and Shun SAKUMA*** (Member)

When we design high speed displacement type ships, it is the most important to reduceher re-sistance. The faster a ship cruises. the larger wave making resistance becomes. This is the rea-son why designers want to search hull forms which give small wave making resistance.

More-over spray resistance is also large at high speed. Andit is known from recent studies there is water head resistance in a ship which has a vertical stem and a transom stern.

Hull forms which give minimum resistance components are studied, but obtained forms are strange and unrealistic. This report represents improvement of such strange forms and

applica-tion for practical hull forms. The obtained hull form has small spray at the bow. And this

form is enough to be realized.

at the edge of her water plane area in order to de-sign spray free hull forms. But there are few stud-ies what these hull forms become and how we make these forms.

A new resistan component is studied recently. It is water head resistance4. This component ex-ists in a ship which has a vertical stem and a tran-som stern. This component is studied very well on two-dmensional problem3'5. But we cannot ob-tain good result on three-dimensinal prob1em8.

We think that residual resistance consists of three components described before. But how do we design a hull form which makes these components

minimum? The authors try to obtain such

opti-mum hull forms on the condition which her water plane area is rectangle. The obtained hull form has very large difference between cruising draft and

still water draft. As the result of it, she cannot

run in free condition. This is caused by using pres-sure distribution which gives too small wave mak-ing resistance. But this hull form shows nice

perfor-mance at fixed condition. That is, there is no

steep wave which causes bow spray'°.

In this report, we obtain an optimum hull form in the practical region. We use optimum pressure distribution obtained from statical pressure

distri-bution. And the obtained pressure distribution

does not give so small wave making resistance. As the result of it, present hull form has very small

differen between cruising draft and still water

draft. Moreover curvature around bow is similar to previous optimum hull forms. So the bow spray is also diminished.

i Formulation of shallow draft ships The coordinate system is shown as figure 1. In this figure, F shows water plane area. CF shows forward periphery of F, and CA shows aft

periph-Fig. i Coordinate system

58-ery of F. We define p as pressure distribution, A as strength of swell - up potential4. In the linear theory, surface elevation is shown as follows

c

=

-

,y - ThO)dd17

+ J A(i')S(z - F, Y - 77p, O)diip (1)

Here T and S are kernel functions. In order to ob-tain numerical solution, it

is necessary to

inte-grate these functions in a divided

panel. This method is shown in referernces79. 1f we give hull offset to , equation (1) is regarded as integral

equation. So we can obtain p and A for given hull forms by solving

it.

Then Kochin function is

shown as follows H(k,9) = JJ p(z,y)e °'

_'dzdy,

₍₂₎ F H(k, 9) = H(k,

8)-i cos 9J A(yp)e" cøtø+yp ImD)dyF C,

So we can obtain wave making resistance.

Dw = - f

H(Ksec2 99)2 sec5 8d9 (4)

ir io

And we define as strength of singularity of pres-sure at bow

= ):!,

[(z/i

()2]

So spray resistance is

= o2(y)dy. (6)

Then water head resistance is

=

_{i I}

_{A2(y)dy. (7)}

2 Jc,

-Thus we can know various things due to solving in-tegral equation (1)8). But if we give p and A to

right hand of equation (1), we can obtain corre-

-sponded surface elevation. So if p and A is opti-mum, obtained surface elevation is regarded as

hull offset of an optimum hull form.

Now let us discribe conditions of an optimum hull form. At first, we can easily find from equa-tion (7) that water head resistance becomes O by setting A0. Secondly, let us think of spray resis-tance. we can also easily find from equation (5)

Ctuinzed

pressure

di stri buti ori

Usirig infli.ence function

calcu)us of vari atioris

If water piare area is

1.rectarigie 2. ellipse

3.rectangle+eilipse.

If water piare area is arbitrary.

Fig. 2 Methods for pressure optimization

Now let us consider detail of influence function. \Ve can integrate equation _{(4) with respect to &} on the condition of equation (9). So we can obtain Wave making resistance as follows

D =

.JJJJP(z,y)P(e,'T7)

P_5(KT, Ki

,, 0)deddd1, (10)

here P_ is _{very complex function defined by}

Bessho2 shown as bellow.

59--P_5(x,y,0) = fcos(zsece)cos(ysec9sin8)

xsec59d8 (11)

Now let us consider the variation of D, that is,

¿1Dm, when

varies p+p.

Dw±Dw =

P_s(Kz -,

0)ddi7dzdy 2K2

+ ¡f

p(z,y)dzd,x ir JIF JJ p(,i)P_5_F (12)

Here the second term of right hand is zlDw. We can define influence function as r.

2JC,

r(z, y) = _{ir Jjp}1 p(, i7)P_5(K ¿, KjT, 0)

xddi7 (13)

So the variation of wave making resistan is repre-sented as follows

=

il

y)r(x, y)dzdy (14) This equation is very intresting. If we can find

pres-sure distribution which gives r = constant, r

goes to the front of integral signs of equation

(14). In general, we optimize pressure distribution on the condition which the displacement is con-stant. So right hand of equation (14) becomes O.

Namely, it shows the pressure is optimum and

gives minimum wave making resistance. This is the reason why we use influen function for pres-sure optimization. Wave making resistance is

Dw

.ffp(z,y)r(,)dzd

(15)

It is convinient for numerical computation to inte-grate P_5 in a devided panel.

K2

___

Jj(z,y; 77) =

P 5(K,KjT,0)

ir

Jill

xdedi7dzdy (16)

-The integration method of this equation is

repre-

-sented in references79. The integration of influ-ence function in a panel is represented as follows us-ing Ji

Hi 6 that spray resistance becomes O by using

rsure distribution which gives p=O at the edge tvater plane area. This condition is very

effec-. We verify that this condition realizes spray

t hull forms in our previous work.Thus we can optimum conditions for water head resistance

spray resistance shown as follows

p(z,y)=O 0nCA+CF (8)

A(y)=0 OflCF (9)

or a next step, we must optimize pressure dis-:ributiofl which gives small wave making

resis-hice.

How to obtain optimized pressure distribution There are two methods for pressure optimization shown in figure 2. Firstly, it is calculus of varia-tions. It is very effective when water plane area is one of three shapes shown in figure. We use this method on rectangle water plane area in our previ-ous work. Secondly it is the method using influ--'nce function. It is effective when water plane area is arbitrary. We use statical pressure distribution of series 64 model no.4793 as initial value. So we

optimize pressure distribution using influence func-tion.

Now let us vary pressure distribution using this function. In this work, pressure is varied in propor-tion to this funcpropor-tion.

p(z,y) =

cjr(z,y) + C2

(18)

The negative sign of C1 shows characteristic of pre-sent method. If P is negative in a panel, pres-sure is increased. If positive, prespres-sure is decreased.

We assume that displacement is constant. So we can find easily,

ILp(z,)dzdy

=

_c1JJr(z,y)dxdc3JJdzd=o (19)

Substituting equation (18) for equation (14),

=

C1 J' r(, )r(, y)dzdj+

c2JJr(z,)dzdy

(20)

Each integration about r and

r* is defined as

follows

A1 =

JJ r(,)dzdy

=

(21)

Here s,,,,,

is area of a panel.

A3 =JJ r(z,,)r(,y)dzdy

=

r.2(,

) (22)

A3

=JJ r(z,y)dzdv= (23)

So the reduction of wave making resistance is

repre-sented as follows

¿D _{cA2_AlA3,1} C1

Dv,

-

a

Here a is arbitrary positive number and A is wa-ter plane area. Following condition is necessary in order to reduce wave making resistance.

A3

A3> -

_iw

So we can easily obtain coefficients C1 , C2.

If we use these coefficient,

ip can be obtained.

Thus pressure is optimized by iterative computa-tion from equacomputa-tion (17) to equacomputa-tion (26).

3. The computed results

The optimization is carried out at K=2.5. Fig-ure 3 shows behavior of wave making resistance and optimization parameter as iterative number

in-creases. Though we designate a =0.4, ¿1D/D

does not become 0.4. This is because C1, C2 is con-stant over the water plane area.

Fig. 3 Behavior of parameters for iterative computation

Figure 4 shows influence function and surface ele-

-vation which are computed with given pressure dis-tributions. The given pressure distributions are statical pressure distribution which is obtained with hull ofset and the computed pressure distribu-tion which is modified from statical pressure distri-bution using the iterative computation method de-scribed before. Firstly let us consider variation of pressure distribution. There are not so obvious dif-ference as iterative number increases. Observing longitudinal distribution, we find pressure shifts

gradually to fore and aft end. This trend agrees

with optimum C

curve theory'. But it is

suspi-cious that wave making resistance is reduced so much, because center of lift shifts to aft end

gradu-ally.

Secondly let us observe influence function distri-bution. We can find easily that the curves become

= JJ

r(,)dd

= 2 (17) C1 = aß, C3 =

ZETR

-L

PRESSURE DISTRIBUTION (BODY PLRN)

(c-2.500 LRIIDDR. .525 PuRe- .2894

990

PR55URE DISTRIBUTION (BOOT PLRNI -2.5DO LAF1BDA- .128 rIlRx- .1471

I :x0.990 2: 0.952 3: 0.875 4: 0.769

5: 0.631 6: 0.469 7: 0.289 8: 0.098 9: -0.098 10:-0.285 11:-0.469 12:-0.531 13: -0.759 14:-0.578 5:-0.052 16:-0.990

BURFRCE ELEYRTION IZETRI BOOT P1..RN

ZI1RX. .07664

PRESSURE DI8TRIBUTION (PROFILEJ

(c-2.500 LRrISCR. .128 PflRX- .1471 ZETA O ZETA O -L

PRESSURE OIBTRIBUTION PROFILE(

((-2.500 LRflBDR- .125 PIRX- .0394 a:y0. 017 b:0.049 c:0.075

d: 0.101 e:0. 118 f:0. 125

2 -2 0

SURFACE ELEVATION IZETRI PROFILE

¡flAc. .07594

INFLUENCE FUNCTION (GRrlrlRc PROFILE

0LiRe- .00L3L P14-5.55

L-L

statical pressure

distribution

INFLUENCE FUNCTION IQArrnR PROFILE

0LIRe- .001009 RM-2.37

6 times iterative computation

Fig. 4 Optimization of pressure distribution and obtained surface elevation

oath and thier absolute value becomes small _as rative number increases. But distribution _shape not so different. This is because the water plane

a is fixed.

astiv we compute surface elevation. It is notice-e that aft and fornotice-e notice-end bnotice-ecomnotice-e dnotice-enotice-epnotice-er as

itera-

-61--tive number increases. In present work, _{we draw} body plan using 6 times iterative surface _elevation.

The obtained body plan is shown in figure _5. There are unevenness in the computation result. _So we carry out fairing boldly. The curvature of fore

part is similar to previous forms. \Ve think the

3 14 IS IS

i&

I 2 3 4

LL

5618 1211 log e ¡ _d

/1

/11

r:

fi' V. 13141516 ¿p

cá.4

1 2 34 l2

f

\

IO 6 7 8 -L 5 0.531 9: 0 098 3: -0. 159 2: 0.952 6: 0.469 10:-0.289 14:-0,818 3: 0.878 7: 0.289 11:-0.459 15:-0.952 4: 0.769 9: 0.098 12:-0.531 16:-0.990 L a:y0. 017 d: 0.101 b:0.049 c:0.078 e:0. 118 f:0. 126 -L O O 2 0 2

SURFRCE ELEYÑTION LZETR( BOOT PLRN _{SURFACE ELEVATION (ZETA! PROF ILE}

L = 1500mm B = 192mm V = 0.01538 FP 2' f,

/ /

s'

Fig. 5 Body plan of the obtained hull form

spray

free condition gives such curvature. We

draw the bow shape such as a destroyer shown in figure.

There is small spray strip in fore part. This is be-cause previous optimum hull forms have much lager spray strip. It is caused by negative pressure for transverse direction. There is no negative part in present pressure distribution. So we have found spray strip is not necessary in present case.

Finally we compute displacement of this hull

form. The cruising draft is almost equal to still

water draft.

Fig. 6 Observation of bow spray (present hull form, Fn0.447)

62-0.04 0.02 -0.04 20 lo -o 4 . Experiment

The experiment is carried out at circulating wa-ter channel in West Japan Engineering Laboratory Co., ltd. The items are measurement of resistance and dipping and spray observation.

Now let us cosider bow spray. The result is

shown in figure 6. We can find easily there is no steep wave which causes bow spray. This trend is the same as previous optimum hull forms. Figure 7 shows bow spray observation of series 64 model no.4793. Though she cruises at lower speed, there is high steep wave. Obseving these two photoes. we can find it is very effective to use spray free con-dition which is eq. (8) in spite of her ship type wa-ter plane area. There is a little wave such as mus-tache from the tip of present hull form. This is be-cause the entrance angle is smaller than Kelvin

an-computed trim

£ computed rise

measured trim trim of series 64 no.4793

measured rise

L

rise of series 64 no.4793

rrieasured residual resistance measured residual resistance

of series 54 no.4793

computed residual resistance

Fig. 7 Observation of bow spray

(series 64 no.4793, Fn 0.447) Fig. 9 Residual resistance

trim

5 x rise o

.0.02

0.2 0.3 0.4 0.5

froude number

Fig. 8 Trim and rise

-0.5 04

0.2 0.3

r

O-1

p

O

PRESSuRE DISTRIBUTION (BOOT PLRN(

N2.500 LRIISUR- -128 PIIRI- .1980

-1

PRESSURE DISTRIBUTION (BOUT PLRNI

N-2.500 LRflSQR- .128 PTIRX. .1415

Fig. 11 C and C curves of present hull form and

series 64 model no.4793

gle. _{It is necessary to round the tip of the water} plane area in order to vanish this wave.

For a next step, let us consider trim and rise. It

is shown in figure 8. Trim is larger than that of

series 64 model no.4793. This is because cetner of floatation goes to aft end. Rise is also large. This is because diminished spray causes low bottom pres-sure around the bow. We can compute trim and rise at only design speed. We cannot succeed in

solv-ing integral equation (1) perfectly.

Lastly let us consider residual resistance.

lt is

shown in figure 9. Though we attempt to reduce wave making resistance using influence function,

ex-perimental data is very negative. Why is not wave making resistance reduced ? Firstly we verify that

pressure can be optimized truely with influence

func-zion. Figure 10 shows this result. We compute opti-mum pressure with both calculus variations and in-fluence function on ellipse water plane area which ad the same displacement as present hull form.

\VO different methods shows almost same result.

-1 0

X

PRESSURE DIETRIBUTION (PROFILE!

K-2.500 LR(1BOR- .128 PuRI- .1335

PRESSURE DISTRIBUTION (PROFILE)

c-2.500 LRI1SDR- .128 P(1RX- .1415

Fig. 10 Pressure optimizations using calculus variations and influence function on same ellipse water plane area

33-Using influence function Iterative number is 9.

Using calculus of variations Trans. series number is 1. Longi. series number is 4.

So we think present method is effective. But we can not obtain the complex pressure distribution which is obtained easily with calculus variations,

though we carry out the iterative computration

many times. This fact shows that it is effective to use influence function when we improve pressure

dis-tribution slightly.

Secondly we check C,, and C, curves. It is shown in figure 11. C. curve of present hull form is the same as that of series 64 model no.4793. But C,, curves are different. C,, curve of present hull form is affected significantly by C curve. We think wa-ter plane area is bad. This fact shows it is impor tant to optimize water plane areá before we try to optimize pressure distribution. We think these are the reasons why wave making resistance is not

re-duced.

Finally we computes residual resistance. As de-scribed before, we cannot solve integral equation (1) perfectly. Though the computation is not per-fect, there will be some swell-up potential.

Be-cause if we add water head resistance to wave mak-ing resistance vhich is obtained from statical

pres-sure distribution, the

results shows about the

same order as measured residual resistance. But the detail is not yet known.

Conclusions

The present work shows some results shown as bellow.

If we design optimum hull forms using pressure

making resistance, she cruise at a draft which is

almost equal to still water draft.

The spray free hull forms are obtained on the con-dition that pressure is zero at the edge of water plane area even if her water plane area becomes slender at fore part. And such water plane area is very effective for designing bow shape

properly

-It is convinient to use influence function in order to improve pressure distribution. And it is neces-sary to use calculus variations in order to obtain

optimum pressure distribution.

It

is very important to optimize water plane

area in

order to search more optimum hull

forms. But we don't know yet how the water

plane area is optimized.

Acknowledgement

The authors express their

gratitude to Mr.

Kiyoshi Morohoshi and Mr. Shigeo Watanabe, Sum-itomo Heavy Industries. They gave us the chance of this experiment and very effective discussions.

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forms in view of the wave-making resistance

theory, Memoirs of the Defense Academy,

Japan, vol.111, No.1, 1963, 19-38

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Memoirs of the

Defense Academy, Japan, vol.111, No.1, 1964, 19-38

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