The influence of freeboard on wetness

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See note inside cover

NATIONAL PW( SICAL

-LAB 0 RA rO1 Y

SHIP DIVISION

ThE INFLUENCE OF FREEBOARD ON WETNESS

by

G.J. Goodrkh

This report is a reprint of a paper presented at the

5th Symposium on Naval Hydrodynamics

organised by the US Office of Naval Research

and the Norwegian Ship Model Experiment Tank

In Bergen, Norway,. lOth-12th September, 1964.

Lab. v .Scheepsbouwk.uncle

Technische HogescI$

REP. 0

Deift

A Station of the

Department of Scientific and Industrial Research

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Crown Copyight Reserved.

Extracts from this report may be reproduced

provided the source is acknowledged.

Approved on behalf of Director, NPL by

Mr. A. Silverleaf, Superintendent of Ship Division

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ThE INThUENCE OF: FREEBOARD ON WETNESS

by

C., J. Goodrich

Abstract

Model experiments in regular waves and. probability theory. have been used to

pred.iot the probability of ocourrenoe of wetness at the fore end. of a ship of

given type.

Calculations made for ships of d.ifferent fullness have suggested

that the frequency of occurrence of wetness varies with block coefficient as

well as with length for a

ven freeboard ratio.

Introduction

The prediction of the probability of occurrence of wetness from model

experiments in regtilar waves has been attempted by Newton

using statistical

sea data to represent full scale conditions.

Newtonts work suggested that for

a given freeboard ratio a 200 ft ship would be drier than say a 2-O0 ft ship

under North Atlantic conditions.

This general conclusion seemed contrary to

what would be expected and. consideration was given to the possibility of using

model data and. probability theory to predict the probability of occurrence of

wetness for ships of. different fullness and.. length.

The intention of the present paper is not to provide detailed design

information but to indicate a method of analysis which could. be used. for

specific design studieá ath tO showthetrend-bf the va±±ation of wetness with

ship length and. block coffiôient.

Wetness definition

When considering the prediotion of the probability of occurrence of wetness

it is sufficient to say that if the motion of the bow relative to thö water

surface is such that the water rises above the deck level at the fore end, then

the probability of wetness exists.

No attempt is made to say how wet the deck

wil

be, nor to what height the water will rise above the deok.

Model. data

The most systematic model data available at present are those of Vossers

and.

swaan(2)

and. these have been used in the present analysis,. Measurements

ware made of the relative bow motions of a series of models and the response

curves presented. as the ratio of the relative bow motion to wave height on a

base of block coeffioient and. for a range of speeds.

Cross curves have been

derived. of the relative bow motion to wave height ratio for constant wave lengths

to a base of Froud.e Number,

Some account has been taken of the loss in speed

due to wave action by assi.ing a

oss in speed curve for each model.

The

responses have then been obtained. from the cross curves for the speed. corresponding

to the particular Beaufort scale being considered.,

Typioal response curves

are given in Figs. Ia and. lb for the 0.70 GB

form.

pesentation of the sea

Sea spectra are nee.ed

±he analys

in order. tp obtain

tion response

spectra and a modified form of the Darbyshire formulation has been used..

The

curve of significant wave height against wind. speed. shown in Fig. 2 was used and.

the three .Darbyshire spectra are shown in Fig,

3.

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Where H2

u2

f

Hf2

d.f =

23.9 exp

= Z Hf = spectral ordinate

-2-The equation of the Darbyshre $peotrum

is:-2

,,

(f-fo,

\O,OO8l.7 (f-f o) + o,O1.2

f frequency

fo = frequency of the peak value of the speotru. = 1.6511.

.This latter value of lit is that derived by Da±byshire from his analysis.

The pectr in this foz'm cannot be cobined directly with response ope±ätors

which are expressed in terms of wave length to ship length ratios, nor in

frequencies of encounter, If the response curves for one ship speed and for

vaxying wave length are used they can be combined with a speotru transformed

from the frequency base to a wave length base. The transformation

is:-2 112

_i

d.X,Hf

d.f

4.

df\HJ

aid includes the .chmge from the enerr expressed. in terms of wave height, to

the enerr in terms of wae amplitude.

It. must be apprec±ated. that although a unique cirve of significant wave

height versus wind speed has been usea, wide variations of wave height exist

in practice for a given wind speed. It is assumed that using this "mean cirve" and. deriving the resulting response spectra results

in

mean values of the

root mean square response for a ven i.nd speed or Beaufort Number. Method of Analysis

A number of gross assumptions have been made ,n the analysis as

follows.:-It has been assumed that for the extreme motions the oond.itions remain linear, The model experiments were

carx'ie4

out for a constant height-ship

length ratio of

It has been assumed that. the motion is regular about the mean still w.ter

daught of the Bhlp.

(o) For comparative purposes it has been as5umed. that the sl4ps are in the head.

sea oond.itión 1O of the tine,

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C )

-3-By combining the response curves such as in Fig. I with the sea spectra

given in Fig. 3, the response spectra are obtained and by integration of these spectra, the mean square response is derived

2

()2

2

m

Z--[r(?.)]

(h)

The d.erived. curves of root mean square response amplitud.e 5m for a range

of Beaufort numbers are shown in Fig. for 0,70 GB ships of 200, 00 and 600 ft lengths.

It has been assumed. that the short term distribution of the variation of relative vertical motion of' the bow will have a Rayleigh distribution,. With this distribution the probability of exceeding a specific value of relative bow

motion Si is

ej2/Sm2.

In order to obtain the long-term distribution of S,

a weighting factor for weather distribution must be included. As was st.ted

earlier no weighting factor has been included in this analysis to take account of variations in the sea direction. The probability of exceeding a specific.

value of S is therefox'e3- 2

y

.

where P. is the weightg factor for the general weather probability

distribution, The weather distribution used is given below over -the range of weather groups I to 5,

The mean value of 5m for each .group has been used. in the caJ.ulation of

with values of S of 10, 20 and 30 ft for all lengths of ships. om the

calculated. values of for specific values of S. probability curves can be

drawn such as in Fig. 5. 1±' freeboard. at the fore perpendicular is substituted for S then these curves show the probability of the water rising above the

freeboard. A non-dimensional freeboard. ratio can be used, (defined as the ratio of the freeboard. at the fore perpendicular to the ship length) rather than absolute freeboard and. the results for the. 060, 0.70 and O.8OCB are given in terms of this ratio in Figs. 6, 7 and 8, The curves for the 0.80

B ships include lengths of up to 1000 ft since there is a growing interest

in the behaviour of bulk cargo carriers of such lengths,

Figs. 9, 10 and. i'1 show the freeboard ratio required for various ship lengths for equal probability of wetness.

G-roup Beaufort Number Distribution %

1

0-3

52,0

2

L1-

.5 29.0

3

6-7

15,0

8-9

3.5

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AF

Discussion of results

The results show that for equal probability of ocourrence the freeboard.

ratio decreases with increasing ship length. The results for the 0,60 and. 0,80 CB

ships are similar but the analysi8 shows that the 0.70 CB ships require a

greater freeboard.. This result is a direct consequence of the hIgher resppnses obtained for the O.7OCB model tests, In Fig. 11, the 8lQpe of the 1-inea of freeboard.. ratio for constant probability of occurrence of wetness indicate that for ship lengths In excess of 600 ft a constant freeboard. gives equal probability.

The question arises as to that is an acceptable level of probability of

wetness, At this stage it is difficult to say what is acceptable but ship

which are lmown to be good sea ships could. be plotted in the diagrams in order to see what level of probability would be expected for them.

it is the intention to run. models of the 0.60, 0.70 and. 0.80 block coefficient in irregular wave systems to check the number of times wetness occurs in a given ttain of waves. The system of generating irregular waves in the ship Division's No.3 Tank is such that the scale of.the spectrum is easily modified. A constant length model can therefore be used with varying

scale of speotrurn to simulate different ship lengths.

Ac1mowleduent

This work has been carried out as part of the research programme of t}e

National Physical Laboratory and. the paper is published, by permission of the Director of the Laboratory.

References

1, iEWT0N, R. N. - Wetness related. to freeboard and. flare. ioy-ai Institution of Naval Architects. Vol. 102,