Motions and resistance of a ship in regular following waves

TECHNISCHE HOGESCHOOL

_DELFT

AFDELING DER SCHEEPSBOUW- EN SCHEEPVAARTKUNDE LABORATORIUM VOOR _{SCHEEPSHYDROMECHANICA}

Rapport No. 440

MOTIONS AND RESISTANCE

_{OF A SHIP}

N REGULAR FOLLOWING

_WAVES

ir. J.M.J. Journée

September 1976

WI'

Deift University of Technology Ship Hydromechanics Laboratory

Mekeiweg 2

Deift 2208 Netherlands

Summary

In continuation of experiments in head waves an experimental program has been set up to measure vertical motions and added resistance in regular following waves. The results of these experiments are compared with theoretical

calculations.

Contents page

List of Symbols I

Introduction 2

Description of model and experiments 3

Analysis and presentation of the test results 4

4.1. Heave and pitch motions 5

4.2. Relative motions 5

4.3. Added resistance due to waves 6

Conclusions 8

Acknowledgement 9

References IO

T ab 1 es Figures

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1. List of symbols z z a e e a E w w e p A 2 k p g L B C V V

Fn7

VgL

instantaneous wave elevation wave amplitude

wave height (double amplitude) heave displacement heave amplitude pitch angle pitch amplitude phase angle circular frequency

circular frequency of encounter

wave direction (following waves : p0)

wave length wave number

density of water

acceleration of gravity

length between perpendiculars breadth

wave celerity forward speed Froude number

N' sectional damping coefficient for zero speed

m' sectional added mass

V amplitude of vertical relative water velocity

x,y,x _{right hand coordinate system fixed to the ship}

xb,yb, zb

RAW added resistance due to waves

s relative vertical motion

s amplitude of relative vertical motion

a

s crest or trough value of relative vertical motion

J

)

2

2. Introduction

To continue a research program with a model of a fast cargoship in regular head waves [1,2] a test program has been _{set up to measure vertical motions} and resistance in regular following waves.

The results of these experiments at several speeds _{and wave lengths have been} compared with computercalculations. These have been carried out with a program named TRIAL of which an earlier _{version has been described in [ 3 ]}

. Only heave and pitch motions are observed. The added _{mass and damping for the ship} cross sections have been calculated by using _{a Lewis conformal transformation.} Apart from heave and pitch motions the relative vertical _{motions of the}

afterbody at station O and station 2 _{are measured. By comparing the directly} measured relative motions with those calculated _{from the measured heave, pitch} and wave motions, the dynamical rise of the watersurface near the hull at these

two stations can be estimated.

At the same time the total resistance has been _{measured. By subt.racting the} still water resistance _{from this total resistance the added resistance due} to waves has been found.

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3. Description of model and experiments

The experiments have been carried out with a 3 meter model of the cargoship m.s. "S.A. van der Stel" in full load condition. The modelscale is 1:50, the main particulars are given in table I. Figures 1 and 2 show the bodyplan and the experimental set-up for these tests.

In case of head waves the influence of the surge motion on heave and pitch motions can usually be neglected as demonstrated in [1,2]

During the experiments in regular following waves, described here, the model has no freedom to surge for practical reasons. Especially at lower periods of encounter it is very difficult to produce a constant towing force or a

constant propulsion force which corresponds with the mean total resistance '- of the model. Also tank wall interference will be of more importance at a

surging model in a relatively narrow tank. The surging model introduces wave disturbances which make it impossible to measure the undisturbed wave motion. Five speeds in following waves have been considered corresponding with the Froude numbers 0.00, 0.15, 0.20, 0.25 and 0.30, while the service speed of the

ship corresponds with 0.26.

Heave and pitch motions have been measured by two low friction potentiometers at the centre of gravity of the model.

The relative motions with respect to the watersurface of the aft part of the model at station O and 2 have been measured by a conductance wave probe close

to the hull. The regular waves have been measured in the same way by means of a two-wire conductance wave probe which position with respect to the model is shown in figure 2.

All motions are recorded by an ultra-violet recorder.

The still water resistance and the average resistance in waves have been measured by means of a strain gauge dynamometer of which the output is integrated over a certain time or a full number of wave periods.

To get information about the influence of a rotating propeller the vertical motions are measured too at a speed corresponding with Fn0.25 with

a "self-propelled" model restained in surge. Because the added resistance due to waves is very small the number of revolutions per second of the propeller has in this case been obtained from propulsion tests in still water. This number was kept constant by electronic control.

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T

-1-

-,m- ri +T

4. Analysis and presentation of the test results

The definitions and symbols of the vertical motions are shown in figure 3. The wave, heave and pitch motions are defined by

=

a cos Wet wave

z = z cos(w t+ ) heave

a e

e = e cos(w t + ) pitch

a e

where the frequency of encounter is defined by 2

w = w - - V cos p

e g

From this equation the relation between the frequency of encounter and the wave length-ship lngthratio can be found as shown in figure 4. In following waves p will be zero degrees,

At a certain speed two types of waves can be distinguished here

I . The model is overtaking the waves , which means

X

L

2. The waves are overtaking the model, which means

X

L

< 2 . (Fn . cos p)2

> 2 . (Fn . cos p)2

All experiments have been carried out in following waves which were over-taking the model. For these waves the frequency of encounter has a

maximum attainable value

e =

O.25\/'

g w max = Fn .cos p 4 V cos p

-4-

-5

)

6

T-n v cii i r T.717 e

rl-r

mi r' -rd- -

,- i i

- ,, Ç i ,, , ,- -t ,-

-at

=8

. (Fn.

cos)2

It can be found from reference [4] that in the towing tankused wall inter-ference will occur if

w . Fn . cos p < 0.43

e

However the maximum attainable value is

w . Fn .

cos0.25\J'

e

This means that it is not possible to do experiments with the model

considered in this towing tank without tank wall interference. During the experiments it appeared that wall effects became important at low frequencies of encounter, when the wave celerity decreased to the model speed.

4.1. Heave and pitch motions

The linear relation between heave and wave amplitude at each observed speed and wave length is shown in figure 5. It may be noticed that this linearity is very good. Figure 6 shows that the phase lag between heave and wave motion is not influenced by the wave amplitude.

In figure 7 and 8 the same is demonstrated for the pith motion. Experiments at Fn0.25 with a self-propelled model restrained in surge show that the influence of a rotating propeller on the heave and pitch motions can be neglected. This is also demonstrated in figures 5,6,7 and 8.

The average non-dimensional measured heave and pitch amplitudes, obtained by the least squares method, and the mean phase lags are compared with the

results of calculations made with the program TRIAL, mentioned before. The good agreement is shown in figure 9 and 10.

4.2. Relative motions

Because of potential flow effects due to the speed the effective freeboard in still water differs from the geometrical freeboard. Figure 11 shows the

measured relative displacement in still water at station O and 2 as a function of the model speed.

5 X

In regular waves dynamic phenomena will influence the immersion amplitude. The measured crest and trough values of the relative motions aft are

presented in figures 12-a-b-c-d-e versus the wave amplitude for different wave lengths and speeds. The experiments with a self-propelled model restrained in surge are shown here too. Besides a good linearity the experiments show that the influence of a rotating propeller on the relative motions of the af ter-body can be neglected.

The slopes of these lines, calculated with the least squares method, are shown in figure 13 versus the wave length-ship length ratio for all speeds. It may be noticed that, dust like for the relative motions at the forebody in head waves [2] , the average measured crest and trough values are not the same.

The undisturbed relative motions have been calculated from the measured heave, piteh and wave motions. The amplitudes are presented in figure 13 too. There is

a fair agreement with the values calculated by means of the program TRIAL. The differences between the directly measured relative motions and the relative motions calculated from the measured heave, pitch and wave motions are caused

by dynamic phenomena. In contradiction with the tests in head waves, this

dynamic phenomenonisnot only depending on the undisturbed relative motion and the speed but also on the frequency of encounter.

4.3. Added resistance due to waves

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The added resistance in following waves is obtained by substracting the still water resistance from the measured total resistance at the speed concerned. It appears that the added resistance in following waves is positive and very small. It varies as the squared wave amplitude. This is shown in figure

14.

The mean non-dimensional values of the added resistance, obtained by the least squares method, are presented in figure 15.

In [ i _{] Gerritsma} and Beukelman have introduced a method to calculate the added resistance of a ship in longitudinal waves. This method is based on the determination of the radiated energy of the damping waves. Neglecting the surge motion, heave pitch motions have been calculated with the strip theory. Added

mass and damping for the ship cross sections have been calculated by using a Lewis conformal transformation. In this way the added resistance will be

L k RAW _2w e o dm' 2 (N' - V -a-:-V dx, b a

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8

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As shown in [ i , 2

J there is a fair agreement between theory and experiments

in

case of head waves. In following waves the added resistance has been calculated in the same way. The results in figure 6 show a considerable negative added resistance. The significant deviation from the experirrnts will be investigated in the near future.

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5. Conclusions

From the analysis of the experiments and calculations for a model,restricted in surge in regular following waves it may be concluded

1. At each wave length and speed

the amplitude of heave and pitch motions varies linearly as the wave amplitude

phase differences between heave and pitch motions and wave motions are constant for varying wave amplitudes

crest and trough values of the relative motions of the afterbody vary linearly as the wave ampitude.

added resistance varies as the square of the wave amplitude

2. The heave and pitch motions and the relative motions of the afterbody of a model restricted in surge are not influenced by a rotating propeller.

3. Calculated heave and pitch motions are in very good agreement with the measurements.

4. The procedure to predict the added resistance in following waves needs further investigation.

5. Dynamic phenomena are of importance when calculating the relative motions of the after body.

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6 . Acknowledgement

The assistance of Mr. A.J. van Strien during the experiments and the preparation of the graphs by Mr. P.W. de Heer are greatfully acknowledged.

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7. References

E 1] J. Gerritsma and W.

Analysis of the resistance increase in waves of a fast cargo ship Netherlands Ship Research Centre, Report no. 169S;April 1972.

E2] J.M.J.

Motions, resistance and propulsion of a ship in longitudinal regular waves Delft Ship Hydromechanics Laboratory

Report no. 428; May 1976

L3] w. Beukelman and E.F. Bilsma

Description of a program to calculate the behaviour of a ship in a sea-way (named TRIAL)

Delft Ship Hydromechanics Laboratory Report no.383 August 1973

[ 4] T.

on the velocity potential in Michell's systemadthe configuration of the wave-ridges due to a moving ship.

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Table I Main particulars of the model.

L pp B T at even keel V Cb Lcb/Lpp

k/LPP

3.050 0.456 0. 83 0. 1434 0.564 -1.10 2 1 . 88 m m m 3 m

heave meter relative wave height

7

meter s b V LL.I'4¼J I il II '.JLL¼JVV lI'j VVP-V

Figure 1

Body plan

7/

FIG.2 Experimental set up.

%tank wall7////////%

I

li

L /

0.50

4 Vt

WeEncos It. 0.25

z0

L O

z

Zb X

wave -

= aC0kXo0

-

wt) in

x0 y0 z0 ç = a

cos(wet)

in X y z ,x=O heave - z = Za cos(Wet +Ezç)

pitch -

e

_{Oacos(Wet+Ee)}

WeW

2Vcosp.

FIG.3 SYMBOLS OF DEFINITIONS.

AIL

2

(Fn cas

FIGL.. RELATION BETWEEN FREQUENCY OF ENCOUNTER AND WA'/E LENGTH IN FOLLOWING WAVES.

a-v- ship speed

C - wave celerity

_L

A J o II j_ u o (J > I u,

ici

ti

j

WI 01 o >1 WeW_k.V.COSJ. IL<gO0 b 211 10 20 811 30 LO

)

(cm)

(cm)

. EXPERIMENTS WITH TOWED MODEL WITHOUT SURGE MOTION.

. EXPERIMENTS WITH SELFPROPELLED MODEL WITHOUT SURGE MOTION.

FIG.5 RELATION BETWEEN HEAVE AND WAVE AMPLITUDE IN FOLLOWING WAVES.

=

i

=2.0 5 O

-5 o 5 s 5

.*-

-

'a.--.

-:'''<<

Fn= 0.00 Fn = 0.15 Fn = 0.20 Fn= 0.25 Fn = 0.30

Fn= 0.00 Fn = 0.15

(cm)

. EXPERIMENTS WITH TOWED MODEL WITHOUT SURGE MOTION.

s EXPERIMENTS SELFPROPELLED MODEL WITHOUT SURGE MOTION.

FIG.6

RELATION BETWEEN PHASE LAG OF HEAVE AND WAVE AND WAVE

AMPLITUDE IN FOLLOWING WAVES.

Fn = 0.20 Fn= 0.25 Fn = 0.30 80 O a -a 80 O

0

80 O a s . 80 O s a -

I.e

-80 O s

,

_w

____

180 O s

I

SS

a

.

.

o 80 O

s

S

. -

I

i 180 O

IS

.-..

.

I

e

o 5 0 5 0 5

ß

5 .0 5

)

i

'T

(degr) =0.5 =0.8

L

i.o L

(degr)

(cm)

. EXPERIMENTS WITH TOWED MODEL WITHOUT SURGE MOTION.

. EXPERIMENTS WITH SELFPROPELLED MODEL WITHOUT SURGE MOTION.

FIG.7 RELATION BETWEEN PITCH

AND WAVE AMPLITUDE

IN FOLLOWING WAVES. =0.8 = 1.0 =i .4 . = 2.0 5' 5

T

₌

_

_Q-.--_______

----7

Fn = 0.00 Fn =015 Fn = 0.20 Fn= 0.25 Fn =0.30

(degr) 4 2 2 4 (cm)

. EXPERIMENTS WITH TOWED MODEL WITHOUT SURGE MOTION.

a EXPERIMENTS _{SELFPROPELLED MODEL WITHOUT SURGE MOTION.}

FIG. 8 RELATION BETWEEN

PHASE LAG OF PITCH

_{AND WAVE AND WAVE AMPLITUDE}

IN FOLLOWING WAVES. L L L L L L 70

II.!

i

i

i i

z

-i -i

_i

..

:

I

I

i

u

I

u

g0u..I.

70__

iìii.

IUI

I

:

_!:

Fn = 0.00 Fn= 0.15 Fn= 0.20 Fn= 0.25 Fn = 0.30

. MEAN EXPERIMENTAL VALUE

CALCULATED

JLJ'

FIG.9

MEASURED AND CALCULATED CHARACTERISTICS OF

HEAVE MOTIONS IN FOLLOWING WAVES.

s s s o s

;:

s s o

_;

s s s s s

1/

55

_

sJ

O 1

20

1

20

1

20

1 2.0 1 2 Fn = 0.00 Fn = 0.15 Fn = 0.20 Fn = 0.25 Fn = 0.30 1.5 1.0

Za

0.5 o ₁₈₀ O

£z

180

(degr) - 360

ea

ka

1.5 1.0 0.5 O 360

Ee

180 ( d egr) O

. MEAN EXPERIMENTAL VALUE

CALCULATED

FIG.1O MEASURED AND CALCULATED CHARACTERISTICS OF PITCH MOTIONS IN FOLLOWING WAVES.

.

_.

.

I

I>

.__

Fn 0.00 Fn 0.15 Fn = 0.20 En = O .25 Fn = 0.30 1 210 1 _{210 2 IO 1 210 1 2}

5 h 3 2

i

o STATION O STATION 2 Fn

FIGli

RELATIVE DISPLACEMENT

OF THE

AFTERBODY IN STILL

WATER.

o 0.10 O. 20 0.30

so's2

0.8 1.2

(cm)

-. EXPERIMENTS WITH TOWED MODEL WITHOUT SURGE MOTION.

1 .L. 1.6 2.0

STATION O

STATION 2

FIG.12a RELATION BETWEEN CREST AND THROUGH VALUES OF RELATIVE MOTIONS AND WAVE AMPLITUDES IN FOLLOWING WAVES.

(Fn =0.00)

:

(cm)

. EXPERIMENTS WITH TOWED MODEL WIIHOUT SURGE MOTION.

FIG.12b. RELATION BETWEEN CREST AND THROUGH VALUES OF RELATIVE MOTIONS AND WAVE AMPLITUDES IN FOLLOWING WAVES.

(Fn =0.15) STATION O STATION 2 '

<

<

Ib

50

lo

(cm) S2m

(cm)

lo

.-=O.5

0.6 5 0.8

. EXPERIMENTS WITH TOWED MODEL WITHOUT

0

FIG. 12c. RELATION BETWEEN CREST AND THROUGH

(Fn =0.20) 1.0 1.2

l.I

1.6 2.0 STATION O STATION 2 WAVES. (cm) o 5 MOTIONS 0 5 AND WAVE 5 AMPLITUDES 5 IN FOLLOWING SURGE MOTION. VALUES OF RELATIVE

=0.5 10 5 O 5

10

5 O 0.6 0.8 1.0 1.2 1 .L1 1.6 2.0 STATION O STATION 2 (cm)

L

I EXPERIMENTS WITH TOWED MODEL WITHOUT SURGE MOTION.

u EXPERIMENTS WITH SELFPROPELLED MODEL WITHOUT SURGE MOTION

FIG. 12d. RELATION BETWEEN CREST AND THROUGH VALUES OF RELATIVE MOTIONS AND WAVE AMPLITUDES IN FOLLOWING WAVES.

0.6 0.8 1.0

. EXPERIMENTS WITH TOWED MODEL WITHOUT SURGE MOTION.

1.2 1.6 2.0

STATION O

STATION 2

FIG.12e. RELATION BETWEEN CREST AND THROUGH VALUES OF RELATIVE MOTIONS AND WAVE AMPLITUDES IN FOLLOWING WAVES.

(Fn =0.30)

b 5 O

5 05050

5 0 5 0 5 .0 5

3 2 asm

aa

o 3 2

i

210 1 210 210

Sa J

CALCULATED WITH MEASURED HEAVE, PITCH AND WAVE MOTIONS.

__l CALCULATED WITH PROGRAM

TRIAL.

asm J_a_ MEAN MEASURED CREST VALUE.

aa i_v_MEAN MEASURED TROUGH VALUE.

i

210

FIG. 13 MEASURED AND CALCULATED CHARACTERISTICS OF RELATIVE MOTIONS IN FOLLOWING WAVES.

2 STATION O STATION 2

,'

j&

\A

S% V 'V

.'

'

"p

.-

\

4tlP_&_IlP2

,

,4

__v

'.

_.

I I

-. /&, A/li

£#/

'y,,

_y

fl/.r

_/

,

k-.

'

_I

'V..ß-J-.

.'

-Ps _w

'&_,-g

'iIr'

,

_ s %

&IAA__

_v_y _::

i

-::1¼

-4- _

. 4

:

"_'__*__41___{y__1,__,_____}

_

.-y--.\ L En =0.00 En = O 15 En = O 20 En = O 25 Fn= 0.30

e

0.100 O 0.100.

O7

0.100 RAW O 0.100 (kg) O 0.100 Fn =0.00

SW

Fn=O.15 Fn=O.2O Fn=O.25 Fn=O.30

//

_/

S

(cm')

NOTE: AT Fn=O.00 THE NEGATIVE

ADDED RESISTANCE HAS BEEN GIVEN.

FIG.0

RELATION BETWEEN ADDED RESISTANCE AND SQUARED WAVE

AMPLITUDE IN FOLLOWING WAVES.

L

-t- =0.8

2_

_{=i .o} L

1 o

1

o RAw

PgB2/L

o

1

i

o

i

i

o

i

i

FIG.15 NONDIMENSIONAL MEASURED ADDED RESISTANCE IN FOLLOWING

WAVES.

..

_s.

.

s

s s. s

s s

5555

₅ s s

s 55 s

s s o 0.5 1.0 1.5 2.0 Fn = 0.00 Fn=0.15 Fn=0.20 Fn= 0.25 Fn= 0.30

s

RAw

PgB2/L

o 0.5 i .0

FIG.16

NON-DIMENSIONAL CALCULATED ADDED RESISTANCE IN

FOLLOWING WAVES.

9635

relative wave

height

_A

meters J L

02

pitch meter

resistance

dynamometer

¿xpenmental set

up.

q

1.880m

wave height meter