Resistance increase of a fast cargo ship in regular waves

Report No. 313 Deift Shipbuild.ing Laboratory

June

1971

Resistance Increase of a Past Cargo

Ship in Regular Waves

by

Prof.ir.. J. Grritsma

and

W. Beukelman

i. introduction,

om linear theory it follows that added resistance in waves is propor-'

tional to the square of the wave height. An accurate experimént with a

model of a passenger-cargo ship,. having a block coefficient of: 0B = 0.65, confirmed the square law to a large extend. Based on this

principle a prediction of the mean added resistance in a specified

irregular sea was in good' agreement with corresponding modél test results (1).

However, Sibul has found large variations in the exponent of the wave height; instead of a constant value of 'two his model experiments

indi-cate values, between 1.1 and 2.5. The average value is between .].7 and L8 for ships with block, coefficients bei ween

o6o

_{and 0.70 and a}

length-beam ratio of about

75o

There is a trend towards low exponent values for slender ships with a large ìéngth-beam ratio (2)..

To study the deviations from the square law for one particular oase extensive experiments with a model of the fast cargo ship "S.A. van der Stel" were carried out. The tests include wave resistance and motion

tests for a wide range of wave lengths, wave heights and forward speeds.

The influence of surge on the resistance increase in waves was investi-gated in 'addii ion to the wave resistance, experiènced by the model when lt was 'restrained in heave, pitch ard' surge.

The results of the measurements are given in some detail to allow compa-rison with theoretical results,

2. Test conditions and experimental set up.

in table I the considered ranges of' wave height, wave length and ship speed of the model experiment are summarized.

Table i

Wave oonditions

The waves were measured at a distanòe of

₄

_{mt ers In front of the model}

by means of a 'two-wire oonducianoe waveprobe. Additional measurements'

were carried out with' a sönic wave probe. (A very satisfaótoryaeement

between -ehe two kinds of measurement was fotthd..)

0..6

1750

0 8

:,

_.1/50

' 1/40 1/30 1.0

1/50

1/40

1/30 1.2. 1/150 1/5Q 1/40 1/30 1.4. '

l/5Q

1/40

1/30

1.6.

1/50

1.95

1/5Q

The test set up is given in Figure 1.

The majority of the rims was made

with

thé model restrained in surge,

but free to heave and pitch, as shown in Figure la.

The mean resistance in waves was measured by means of strain gauge dynamometers of which the output was integrated over a fixed period of time. A comparison of the results of this resistance measurement method with results of the more conventional system, using a dead weight as

shown in Figure ib, showed only very minor differences.. The

towing

arrangement, given in this Figure was also used to investigate the

in-fluence of surge. on the heaving and pitching motions and on' the added resistance.

The molions of the model were measured by wo low-friction potentiometers. Moderate wave heights were chosen in view of the applicability of the added wave resistance operators for superpositioñ purposes.

3.

Eerimental results.

The main,

particulars

of the ship are given in Table

2.

Table 2 Nain' particulars LV. S.A. van der Stel

in Figure 2 to. ₅ the experimental amplitude and phase characteristics

are compared with the corresponding calculated values. There is some indication of non-linearity in the measured motion amplitude. In pa?ti-cular a tendency to better agreement with the theoretical values in the

case of small wave heights is observed. The influence of surge was

.in-vestigatéd for one speed only: F =

0.25;

the results do not indicate

a marked, deviation from the results where the model is free to surge (Figure

4).

I4pp

-

152.5m

Lwi

154.7 m

B

-

22.8m,

T

-

9.im

-

17931

-

2431

m2 Ii -

2782993

m4 0B - 0,564 o,p -

0,580

LCB 1,68 a!t LCF -.

4,35

aft Vservice ''

19,5 1iots

'kyy

0,219

The added resistance in waves is shown in Figures

6-9

for the model

which is free to pitch and heave hut restrained in surge. Also the added

resistance is given for the case where the model is restrained for heave

pitch and surge motions. The results cover the various wave height

con-ditions as sunuitarized in Table 1. in view of the slight non-linearity

of the vertical motions, there is surprisingly little deviation from the squared wave height law. This also holds for the added resistance

of the restrained model. Figure 10 shows that the influence of surge

on the added resistance in waves is negligible. The validity Of the squared wave height law for this particular ship model is clearly shown in Figures 11-14, where added wave resistance for the pitching and heaving model and for the restrained model is plotted on a base of

waie height squarod.

The standard deviation from the assumed quadratic law is in the order

of

3%,

which includes measurements errors as wefl.

The experimental results will be used for comparison with calculated

values of the added resistance in waves.

4. Conclusion.

For the considered ship form the resistanöe experiments in waves indicate

that added resistance in waves varies as the wa'.re height squared in the range of wave conditions which was investigated.

5,. References.

(i) Prof.lr. J. Gerritsma, Ir,. J.J. van den BosCh and W. Beuke1nan Propulsion in regular and. irregular waves.

International Shipbuilding Progress 1961

(2) 0.J. Sibul

marease of Ship Résistance in Waves Report NA -

67 - 2, 1967

Resistance

dyna mometer

t

A

a.

Weight

Resistance

dyn a m o met er

i: 5

LC)

Figure 1.

Arrangement

for

resista ncetests

in

D

1.0-o _°__b_ O O

o"

'O

0--

1.0--U)

w

w

(D1OO-w

300-O O

-- - -. -o u

- - - CALCULATION

--.ce

N

'J

o

o

2

= L f50

.

EXPERIMENT

WITHOUT.

SURGE

\

_\

Figure 2

_{Frequency characteris't ics at}

_Fn=i5

C

N

o 1.0 U)

w

loo

300

A

t

o

_o

\

rEe

EXPERIMENT

WITHOUT

SURGE

2

= L/150

o

L/5O

o

L/40

= L/30

- CALCULATION

\

Figure 3

VL/x

Frequency characteristics

_at

_{Fn = 20.}

1.5 1.0

o,,

1,0

1.5-1T

U)

w

w

CD

w-1:00-

300 300

-- -- -- -- CALCULATION

EXPERIMENT

WITHOUT SURGE

Figure 4

1- e

O

_2a

_L/50

1.

EXPERIMENT

L/40

_f

WITH SURGE

'5

D D

N

D

1.5-i10

U)

w

w

w

-300-o

o

o

.

- - CALCULATION

L/150

= L/ 50

= L/ 40

L/ 30

-- O-.. ,Q _

-'

s'

EX PE RI M E NT

WITHOUT

SURGE

'o

0

'5

VL/x

2-2a./50 RESTRAINED MODEL.

-- I _I I I I i - i - I I i - - t

0.5

1.0 1.5

VL/x

t

VLÍx

RESTRAINED MODEL.

\IL/x._:

ç

0.5

VL/x

Figure 9

.

Added

res

ance.

in

waves

at

Fr

.30

t

2-0 2a L/52-0

WITH SURGE.

L/40Ç

RESTRAINED MODEL.

WITHOUT SURGE.

1.0 1.5

VL/x

'

2

cm2

0

5 1O

_cm2

20

₂₅

o 5

_.1-cm2

20

25

Figure i3

Added

resistance in waves

X/L =12

-O- WITHOUT SURGE.

i-D- RESTRAINED MODEL.

i

.5

RGE

TRAINED P'IODEL

o

-.

s

Figjf

_{clecf resistance ¡}

_M

a

Cm2

Waves

A/Le i4

The test set up is given in Figure 1. L

The majority of the runs was made with the model restrained in surge,. but free to heave and pitch, as. shown in Figure la.

The mean resistance in waves was measured by means of strain gauge

dynamometers of which the output was. integrated over a fixed period of time.. A comparison of the results of this reistanöe, measurement method

with results of the more conventional system, using a dead weight as shown in Figure lb, showed only very minor differences The towing

arrangement,. given in this. Figure was also used to investigate the

in-fluence of surge on the heaving and pitching motions and on the added resistance.

The motions of the model were measured by two low-friction potentiometers. Moderate wave héights were chosen in view of the applicability of the added wave resistance operators for superpositioñ purposes.

3.

perimental results.

The main particulars of the ship are given in Table 2.

Table 2

Nain particulars N.y. S,A. van der Std

-

_l52.5m

Lwi

-

,154.7m

B -.

22,8m

T

9lm

- 17931 m - 2431 m2 Il - 2782993 m4 CB -

0,564

cp

-

0,580 LOB - 1,68 aft LOF

4,35

aft Vservice -

19,5

knots - 0,219

In Figure 2 to 5 the experimental amplitude and. phase dhazracteristios are compared with the corresponding caloiïLated values. There is some ,indloation of non-linearity in the measured motion amplitude. In

parti-cular a tendency.to better agreement with the theoretical values in the

case of small wave, heights is observed. The influence of surge was

in-vestigated for one speed only: F = 0.25; the results do not indicate

a marked deviation from' the results where the módel is free to surge. (Figure

4).