Conditions for slamming free operation of a ship in waves

B.8.R.A. Translation No. 2W8

coffExTxoNs Boa sIvinRo.pg

_oPERATIoN OP A SHIP IN WAVES

G.S.Chuyjkoyakii

Budóstroenie,

No.6 (1965),

p. 10 (June).

When the bows of a ship slam against waves, this causes additional tynamic bending of the hull, and is very dangerous to its overall and local strength. This phenomenon

_(slmm11Ig)

is taken into account when strength is oaloulated by the approximate procedure given in aeferencea [1] and [2]; the procedure is based on the more accurate method of determiMng the magnitudes of the external forces acting on a ship, giv in reference [3], and involves mr(ig a number of assumptions.

Further research (for instanoe the test to find the hull strength and seaworthiness properties of the dieselelectric vessel

_{"Kuibyehevge&')}

has proved that these assumptions may sometimes cause greatly exaggerated data to be obtained for the dynamic bending momenta during

sln(ng,

_in particular when the length of the bows which leaves the water owing to pitching is not great. It beoaes necessary to obtain a more accurate idea of the extrapolated relationships between the dynamic bending moments and operating conditions.

Sletnm4ng prevents a ship from working up speed

in

waves. The establishment of the laws governing slaimn4ngfree operating regimes is therefore of independent importance, and is necessary not only for

finding a more accurate procedure for producing standard strength data for the hulls of seagoing transport vessels, but also for design4 them

effioieitly.

Certain .was of solving this problem are considered below. The problem amounts to investigating the operating regime with which the bow does not lOave the water. It can be assumed in practice

that sl1ml4ngfree operation is ensured if the bow does not emerge beyond the first frame station, since the lines of the hull forward of this

frame station are, owing to their sharpness, unable to cause any

appreciable hydrodnamio foroes when they enter the water. The amplitudes movernen.t:; of the hull at the first frame station relative to the aurfaoe of the water can be determined by. testing models meeting regular waves. The generalised dimensionless relationships for these amplitudes to the frequency of enwomter with the waves and their relative length are plotted in Pig. 1.

In this article A1 is the mó*emeát 1 amplitude at the first frame

station relative to the surface of the water (the greatest difference between the vertical movement

of the first frame station during pitohing and heaving and the vertical movement of the disturbed surface of the water at the same section);

h

r s , the amplitude of the waves;

the relative wave length;

) and h are the length and height of the waves; L is the length of the shj.p;

is the frequency of encounter with the waves (the apparent wave frequency);

5trnM

0

is the natural

ln

frequency for the ship, is taken as being equal to the natural frequency of pitching.

The curves in Fig. I have been plotted from the results of analysing a great number of tests on models, and can be applied to different types of ship with quite a wide range of different lines. We know that the

frequency of encounter with the waves to the natural movement. frequency of the ship during p'"sj. Then the magnitude of this ratio has been fixed, the effects of the ratios between the ma4 'i dimensions of ships, also the effeots of its hull linOs, and particularly those of the etern on the pitch4g parameters are of secondary importance (there is only a tendency forth. amplitude of pitching to decrease as the block coefficient of the ship is increased, owing mainly, to the inoreaeed fullness of the waterlines forward).

The requenoy Ci)e of encounter with waves is i

2

A (i)

where v8 is the speed of the ship;

is the speed of the wavee which is taken as being positive if it is opposite to the directiOn in which the ship is moving. If we substitute the speed of the ship, expressed in terme of the Frownumber, v8 - Fr in equation

Ci) (g

is gravity acceleration), and if we assume, as the basis of the theory for progressive waves of

, after earrying out transformations

2W

we gets

- +

rj;: Fr)/y/'.

₍₂₎

In order to calculate the natural longitudinal pi1tLrh1 frequency

3uq

nq

for a ship, the following appreimate equation oan be used, since it agrees well with the results if experimentsS

c-

(2.3+o.27-±_)

[1-0.38

(3)

here B is the breadth of the ship.

Instead of calculating and o using equations

₍₂₎

and (3), we can use the graphs in Pigs. 2 and 3 for the dimensionless magnitudes of these frequencies..

t the curves, in Fig. 1 shows that. for any fixed small amplitude, that

oncol!llilg wave length, the amplitude of movement at the first frame station reaches its mr4mu, in practice, with - = 1; it is particularly great if the relative length of the oncoming waves = 1.1-1.2. The worst s1a'"ng results from pitching in reaonanoe when the length of the waves is almost the same as that of the ship.

This law becomes particularly apparent on evji1ng the curves in Pig. 4 for the different values of the relative amplitudes , plotted

r

on the oàordinates and (the continuous lines). Ifi an example,

C.')

relationships betwOen _A and _.._2 _{have been plotted on this graph for}

different Proude numbers for a ship with a ratio

-4- - 7.15

(the dashand--dot lines). Theae curves enable us to taoe variations in the relative

1.

amplitude - accompanying Ohangea in

_{A ,}

the relative onooin4g wave r

length, for different ship speeds (Fig. 5.).

The curves in Pig. 5 enable us to determine the maximum relative

A

amplili4e

[_t

_] (of all the possible values of this aáplitude with different ship speeds), and. to find the least favourable relative wave length ror, at which this maximum value of the relative amplitude is

A..

reached. Graphs for the variation in the quantities

or and [ _r max: with relation to the Froude number are plotted in Figs. 6 and 7.

The first frame station will not leave the water if ó., the amplitude of its movemmite relative to the disturbed surface of the water, does not exceed the draught T at this frame sta.ion in still water,..

If both sides of inequality (4) are divided by r -

4-,

after oariing out the same transformationB we obtain the following inequality, which defines the condition for the immersion of the first frame station'

2

5

If we have curves similar to those plotted in Fig. 5 for a

particular ship, by means of the inequality we can determine, for any operating conditions in regular waves and for any prescribed values of

A and the Pwcude number, the wave height with which the ba.

Will

not emerge beyond the first frame station.

The actual wave conditions at sea are a random process. On the belie of the experimental fact that the statistical parameters of waves alter slowly, modern oceanography considers this random process to be etady-,-, and uses mathematical statistics and the speotral theory of random functions for studying it.

To find the distribution of probabilities for the relative amplitudes of movement A1 at the-first frame station, we can use either the spectral method, which is based on representing the actual wave conditions in the form of the sum of an infinitely large number

of elementary sinuaO1dal wave systems, with different frequencies and amplitudes, or we can represent the actual wave conditions directly as a function of the distribution of elements in the visible waves, own from the results of statistical analysis of the wave conditions. Aesiun4ig

the reader to be aoquain ted with the fundamentals of probability thery, we will now set forth the principles of the method by whioh the problem will be solved.

Since waves at sea, caused by the wind, can be regarded as a normal random process with a relatively narrow spectrum, and ainoe the relation-ship of the parameters of movement by the relation-ship to wave height is linear, the distribution of probabilities of the relative movement amplitudes at the first frame station can be taken as following Rayleigh's laws

a2

A

₂

_D,

D

where D is the dispersion of the ordinates of movements by the first frame station relative to the surface of the water, considering these movements as a random prooess;. the dispersion is associated wiih the

mean amplitude of these movements (their mathematical expeotation) by the known relationship

D..-.(X)

2 ₂

(7)

With any particular spectral wave density P(Ci)), the dispersion

D of the relative ordinates of movement by the first frame station can be determined by the numerical integration of the equation

D

_{- /}

F

(w)

dW,

(8)

0

where f(W) is the amplitude-probability characteristic (the conversion

4

function) of the function

4,

and is the relationship of to the natural frequency Ci) of the waves encountered by the ship.

It is not difficult to obtain a relationship of this sort for any

ihip speed by

plotting a corresponding

'aph (Pig.

5),

neing the

equation

rr

C*) A I

'VVL

If we know the two-dimensional law for the distribution of the probability density p(h, )) as regards the height and length of the waves encountered by a ship, the mean relative amplitude 1 of the

movements of the first frame station will be governed

by

the equation

A h

11- /f

[__L)

_{-p(h,A)d) a,}

(10)

where [ ) is the relation:hip of

to the wave leh

X

(to

find this relationship it is necessary to plot a graph of the type shown in Pig.

_5,

using the equation _A

-

L).

The distribution function p (h,

A)

can be taken from referenoo [4). The dispersion D of the ordinates of movements at the first frame

station is determined using equation (7).

When the dispersion D has been determined, by one method or other,

wo can calculate the probability of any particular value of the relative

movement amplitude at the first frame station arising by means

of equation (6), and we can thus use inequality (4) to find the likelihoàd of this frame station leaving the water. Probability calculations of

this sort are interesting as regards research into desigu, in particular as regards investigating the most favourable operating regimes for ships.

In order to estimate the sl.imn4ng_free operating regimes for ships approximately we can uoe the graphs in Figs 6 and

7,

assuming that the relative amplitudes of movement by the first frame station in irregular waves does not exceed the amplitude of movement by this frame station

in

regular waves and with the least favourable relative

oncoming wave length This assumption does not contradict available experimental data.

Let us use nor to denote the ratio of the length Aor of the most unfavourable wave to its height h01,. Then

XL

or or

h -

-or n

or

If we substitute this equation for the height of the most

unfavourable wave. in inequality (5), and note that when the ship meets this wave the relative amplitude of movement at the first frame station will be

[-3

, we get the following oondition for no slamming

r or

AL

_or 2T

L)

r max cr' where A -2 (14) r

The coefficient A is plotted against the Froude number for ships with different ratios

-4

in Pig. 8.

A The ratio nor

- her

Pr

_0.175.

L

highest waves with a length Acr which the ship ma in practice encounter during operations in particular wave conditions. It is recommended that n01, should be taken as between 15 and 20 inclusive for ships operating in condition(3 of unlimited severity. We must recall that the Proude number from which the coefficient A must be determined should be calculated on the basis of the actual speed of the ship through waves.

Let us clarify the use of jpequality (13). Let us suppose, for instance, that we wish to determine the maximum speed which a ship

L

iJeatkr

with a ratio -'v-' - 15 can develop in ww of unlimited severity without

slammliig tJilring plao (a tanker fully laden).

Asa"4e

that

cr -we get A -

0.75,

and we find from the curves

in

Pig. 8 that, with

a ratio

-4- -

7, the relative spóed for the ship under consideration

with whioh ther, is no danger of elama4ag is given by a Proude number

the greatest speed at which there will be no

sl1nittg

corresponds to a Proude number Pr - 0.22.

This example confirms,

in

particular, the situation, which we know from our experience of using tankers, that when these ships are operating fully laden practically no slamming

000ure,

for the values of the

nonelafmniiig speed are suffioiently high.

Inequality (13) and the curves in Fig. 8 can also be used; when ships are being desigeed, for selecting the optimum ratios

-4-

and

with which the ship

will

be able to attain the specified speed through

waves without any sliunmii taking place.

Using these curves and the inequality we can determine the maximum wave height in which a ship can sail at a given speed without

al'4g

tAiring place. In this latter case the permissible value of the ratio

cr must be determined, and the zimum wave height which is required is found using equation (ii).

I Sirongth standards for steel seagoing vessels. USSR

Register.

Seagoing Transport, Leningrad,

1958.

USSR Register strength standards for seagoing vessels, seaond edition. Morskoi transpobt, Leningrad,

1962.

Manual of engineering meohanies for ships. Ed. by Loademician Tu.&.ShiianBkii, vol. XII, Seotion T, Sudpromgis,

1960.

Krylov, Tu.M. Theory and aalculatiofl of waves raised by the wind in deep parts of the sea. Trudy Gas. Okeanografioheakogo Ins titutá,

r

10

-uUIU

/jr4A4

0_{aa as £0 U} .4L p. UC. _B

Fig. 2. Relationship of the frequency of enootmtr with waves of different relative lengths to the speed of the ship.

Fig. I Relationehipa of the amplitudes of movement by the first frame

station to the relative frequency of encounter with waves of different relative lengths.

f:i im...aa.

Pig. 3. Relationship of the natural longitudinal pitching frequency for a ship to the ratio .4. for different Proude numbers.

Pig. 4. Curves for different values of the relative amplitudes

'4)

(the continuous lines), also for the relationship between and

-(the dash-and-dot lines), for different Proud. numbers and a ship with a ratio -

_7.15.

Pig.

_5.

Relationship of the relative amplitudes

1'

onooming wave length, .with different ship speeds.

Pig. 6. Relationship of the least favourable relative wave length to ship speed, for different ratios

-4-to the relative / A.p 2 0

-

p.

-484.4f.

42

,

41

-

13

-42 43 Fr

Pig.

_7.

Ratio of the relative aiplitude to ship speed for different values of -4-.

L

A

Pig. 8. _{Relationship of the coeffiajent A to the Proude number for}