On squat calculations for vessel going in shallow water and through channels

21 t'1F1973

ARCH1EF

ON SQUAT CALCULATIONS FoR

_{VESSELS GOING}

AND THROUGH CHANNELS

ab.

y. Sheepsbouwkund

Technisce HogechooI

EDeift

C) 3

a-f,LET1A/o,'.

PI qNv0'rw'

A wide

ogam of theoretical and

experi-research of the motion of vessels stcain ing in a restricted fairway has becit carried out at the

Institute of Marine Engineering of

Odessa (U.S.S.R.) (luring some last years 11, 2.J

A great itiamber of tests for measurements of

squats at Various sliips speeds Iii shallow water ami t hiritiaghi channels have heeti carried (mt in

a model hasiit of t he I tist it iii r h tt h iii st ill water

aii.l iii saVeS.

TABLE I

IN SHALLOW WATER

Eight models of siii!le-s(rew niereliaiit sliii)s

(Series 60 f trm) atiil lmr flit ilels 'f in ut -sinn merchant ship have heeti invest igateti Itotli in still water conditions and iii waves.

Shi P pa ri i(ular. are slit iw u in Tal tir t.

The experiinciits were earrid out in vari',ns dept lis in shialkiw waler. iii four fuIl -haiikn.I

channels and

¡ti .5 deep t rallezoidal shapesi

channels. The sizes of eliatitiels auth t lit dept

Ii-draft ratios are shown iii Fig. I. Model'a title 'Length L, m Breadth B, m Draft T, ra Block Coefficient ô L

-B B T No. 1 1.068 0.364 0.1433 (t.6 - 3.3 _2.3 No. 2 1.968 0.280 0.1143 (1.6 7.11 2.3 No. 4 1.008 . 0.364 0.1433 0.7 3.3 2.3

No. j

1.968 0.286 0.114.5 0.7 7.0 2..5 No. 7 1.008 0.384 0.1433 0.8 3.3 2.3 No. $ 1.068 0.286 0.1143 0.8 7.0 2.3 No. 9 1.968 0.235 0.094 0.8 8.3 2.3 No. IO 1.968 0.286. 0.0933 (1.8 74) 3.0 No. II I)rv-enrgn ship 1.968 0.288 0.0817 0.8 7.0 :1.3 2.678 0.303 0.16(1 (1.62 7.33 Tanker 3.196 0.-$30 0.173 0.713 7.43 2.48 I)ry-cargoship 2.06 0.280 0.123 0.63 7.35 I)r-.eargo ship 1.678 0.240 0.111) 0.67 7.43 by GULIEV U. M.

18

k.M _{I 1.01 1.0} l.5 11.5 I 0,8

Igl'

'14

t'

' 6

t

=

= 0,22

0,81;

F =

Fig.1

Models speeds corresponded to Froude

num-bers Fr

= -= =

0 0,8.

U VgR

During the tests the sinkiiì of two points. of a model, on fore and aft perpendiculars, was

measured and the largest one was taken into

consideration.

The main results of model tests in still water

areas follows.

3

These tests in shallow water showed a great

effect of the water depth and the model speed

upon squat.

There exists ali universal

for all models

relation between a relative squat and Froude numbers in depths Fr,,

--f(Fç1) (i)

where .

T'

is the squat

B the beam amidships

s the ship's sclo(ity

IJ water depth.

So the ratio is independent from the

giontit rica I characteristics of models.

o

V

- O

0,8

The results of the model tests in fully-banked channels also showed an

universal for ail thé'

models relation:

&Twiiz

= fi (Fr0, p) (2)

where p = that is channel cross-section Si submerged ship's midarea ratio Sc.

The curves representing relation

(2) are shown in Fig. 2. It's necessary to notethat the curve of the Fig. 2, which bears the inscription

p > 26 coincides with the curve obtained for shallow water.

Evidently, the existence of universal relations

such as (1) and (2) proves that the squat in

still water is effected by wave forces.

It should be noted that C. Sjostrom 'in his work [si also gives an universal formula of a

type (2) based upon the results of a few model

tests.

lt was proved that in the channel of a

deep-trench form we may use the same relation (2) aitil the samecurses as had been used in

cal-culations for models in the fully-banked

chan-nels. 4

'i

4

à

1,0 1.0 1,5 1.5 2,0

tg

b,u 1/4 0,075 1/ 0,075 1/4 11'/8 0.07510.075 1/4 0,075

The only difference is in d'termiiiing p for

the channels of a deep-trench form by the

s formula.

where pS

«U«5

Ftg. 2.

of such a fully-banked channel which is formed

by. prolongtion of the slopes of a deep-trench

form channel t, its, crossing with the 'water

level (dotted lines in Fig. ib).

K is the coefficient dependent upon the

rela-tion h/H and p* determined upon graph,Fig. 3.

ro'

Ihi

II iIUlIUIIE1P2U

FI

SIIIUII

.a.miiuiisiivqi

IISII4d#

¶

aumuu

_lulls

usuisi.

lus

'r

d

ill

«

iaua

s

__

p=K.p*

(3) *

Mt''

L

e ti)

I

z

So the practical calculation of maximum

squats ir motion in still shallow water and

through .èhannèls may be effected by means

of two gphs: Fig. 2, 8.

The comparison of squat calculations by

the proposed method and methods of C. Sjos-tram [4) and Sogreah laboratory [8) is shown

in Fig. 4.

x-I

Ssywcfr

O-I

CSjàtri.

B-if

S'vI?

.-

Sqiwuá

L-I ¿Jsstr.,i

121 4. V _f PI& t

For shallow water all

the methods show

practically identical results. For fully-banked

channels our results are similar to those obtained

by the method of Sogreah.

Calculations by C. Sjostrom's graphs give with Frs> 0,8 values

greater than those by the curves of Fig. 2.

For the deep.treneh form channels with

Fr > 0.3 the Sogreab method shows greater

squats than by our method.

lt's necessary to bear in mind that Sogreah's

method is founded upon the interpolation of

test results in the fully.banked channels and in

shallow water; the curves of Fig. 2, 3 arc

obtained as a result of model tests directly in

the dccp-trt.neli form channels.

- Experinientail investigation of squat of models

in regular waves (head and following seas) was

carried out both in shallow water and in'deep- .

- trench form chanñels for various depths.

Comparison of. heave and pitch records with

those. of squat in calm water proved that the '

models oscillate round a position they occupy'. -moving in still water under the same conditions' .

as in waves. ..

This conclusion enables us to determine the total squat A Tmiiz as a sum of two components: the squat in still water A T'mii and the maximum squat due to ship's motions A T"mn.

AT_ =AT'__+AT"__

(4)

Model tests in waves showed that the squat

caused by pitch and heave A T"miuiz measured in shallow water and in deep-trench form chan-nels is nearly the same under the similar

condi-tions.

So when calculating squat due to the motions

of a ship moving through channels by

for-mula (4) one can use the values A T".az deter-mined for shallow water.

The dependence of a squat due- to motion

on the ship's particilars and speed, water depth, waves dimensions and direction is investigated

by using the wellknown equations of the

lon-gitudinal motions.

(M + a) Z" + bZ' + cZ .d4,' - .e4' f+

=FxCos(t+e)

(5).

(J + A)

_V'

+ B4i' +

DZ" - EZ'

= Mn Cos (t ± Ci.)

where Z is the vertical displacement of the

ship's centre of gravity + is the pitch angle

aK is the circuit frequency of encounter. Calculation of ship's motion under the equa-tions (5) gives resultf sufficient enough in deep water.

In literature one can find little information

on the influence of water depth upon the

coefficients of the left sides of' the equations (5)

and the amplitude and phase of the exciting

force and moment of the right sides of the

equations as well.

Model tests were carried out to determine

hydra-dynamic coeflicients of added mass and

the damping coefficients a, A. b and B and

coupling coefficients d. e, D, E ¡n shallow water.

1

Ii

---a-

--a-

-a---a

aa-a-

_-aa-a

Q,

-pv&-o

The influence of water depth upon the

and g

of the exciting fozee and "'it wes

amplitudes F and M

and phases of s,

experimentally investigated too.

a e 7

I

s e I s

In Fig. 5 there Is an example of some graphs, frein which one ein find outs that the added

mess a and the damping eoffli't b are

greaUy influenced by the water depth. But the

- depth praetieaBy does flot influence the

- f

lie resulta of the tests wore u

for

det'-mination of squat amplitudes due to pitch and

tve T"n and the wave amplitude

ratio for varima wave qn...1!vPL The fonction

T"

was need fUrther for calculation of

sqàat due to pitch and heave in irregular waves

by means of wellknown formuli by the atatic.

ti -.

The squat calculations In irregular waves were

carried out by a digital computer

fl"

for various types of vessels and their speeds,

water depth and wave dimensions.

The results of these calculations showed that

squat due to pitch and heave motions depends mostly on the ship length, wave height h$%, velocity of the ship and water

depth.-Vasaais

* '7àa

W

TaW

P*g. 6.

s

It should he noted that sqùat in _{head waves}

is larger thaui that in following _{waves ;} T"ni*z Values decrease with

_{the depth tinder the}

nsta,it ships velocity.

The curves shown in Fig. 6 may be used for

determination of _{T".nir values for different}

T

' -

t ratios and Froude numbers.

REWERENCES.

Vorabiev J. L... Oullev J. M.. and others. Experknental rearch on variation of the water line of oen going ships in shallow waters and channels. - Scientific and technical oullection Construction and repairs ot ships, part 1. O.I.I.M.F. Edition. 1967.

Oulier J. M.. Elia J. M. Influence of the depth of

water on the additional weights and on amortization onefficlents in case of ship rolling. - Scientific and technical oullection Construction and repairs o! ships.

part 2. O.I.I.M.F. Edition. 19.

Dickson A. P.. Underkeel Clearance. The Journal oji The Institute of NavIgation. October 1967, vol. 20. No. 4.

pp. 363-385.

Sjostroin C. H.. Effect of shallow water on speed and trim. Naval Engineers Journal. April 1967. Pp. 271-274.