Service - performance and seakeeping trials on a car-ferry

ARCH lEE

SERVICE - PERFORMANCE and SEAKEEPING TRIALS

on a

CAR-FERRY

by

V. Ferdinande and R. De

LERE

197u

Lab.

_{v Scheepsbouwlwnje}

Technische Hogeschool

Deift

S:

III - 36

Ref: S III - 36 _{MAY 1970}

Le Ceberena es-t reconnu par le Centre de Recherches de l'Industrie des Fabrications Métalliques

-C. R. I. F. - Institution d'Utilité Pu.blique

-pour toutee recherches et investigations en rapport avec la construction, la propulsion et l'exploitation des navires.

Mémoire se rapportan-t aux investigations entreprises dane le cadre de l'activité de la section III

- Essais sur navires en rner

-et subsidiées par l'Institut pour l'Encouragernent de la Recherche Scientifique dane 1'Industrie et l'Agriculture

I. R. S. I. A.

CENTRE BELGE DE RECHERCHES NAVALES A.S.B.L. 21 rue des Drapiers - 1050 Bruxelles

SERVICE - PERFORMANCE and SEAKEEPIN TRIALS on a CAR-PERRY

° Ceberena

by V. Perdinande+and R0 De Lembre

SUMMARY:

The present analysis of performance data, gathered on the car-ferry m.s. ROl BAIJDOUIN, has been largely based on the properties of the apparent slip. The assumption of invariability of wake in this special case. of a twin-screw vessel enables the authors -to map out a generalised power diagram, -that remains unaffected by fouling of the hull. All available performance data, gathered by only one experimenter on board, and thus not quite simultaneous,

could be converted to values related -to a standard condition of loading and hull surface. These values are used to map the iso-weather curves in the delivered horsepower/ship speed diagram. For that purpose, however, an tIequivalen Beaufort number" had to be introduced, i.e. an index of total influence on added power at a given ship speed by wave height and

wind strength, which actually are not simply related to each other in coastal waters.

Seakeeping qualities have been investigated also. Waves, pitching and heaving motions, vertical and transversal accelerations, maindeck stresses amidships have been measured. Responses of ship motions, vertical accelerations, relative

vertical motions and velocities, bending moments to regular head waves have been computed theoretically and, on the basis

of the measured spectra, the statistical values calculated. The agreement with the measured values is satisfactory, except for vertical bow accelerations. The theoretical res-ponse, though, were considered as being sufficiently accurate

to investigate the seakeeping in severe sea states. A prediction of excessive bow accelerations, slamming,

shipping of water, propeller racing and main deck stresses

was atteum.p-ted. It could be concluded that exc.essif vertical

accelerations at the fore-end of the garage is the main cause of voluntary speed reduction. A criterion of maximum allowable bow acceleration, by which -the attainable speed can be deter-mined in severe head seas is suggested. In this way, it is pointed out that for this car-ferry no voluntary speed reduction is necessary up to a sea state Beau.fort 7 - 8

in the coastal waters under consideration.

+ Laboratory of Naval Architecture, State University of Ghen-t

INTRODUCTION.

The performance of cross-chamiel ships of the Belgian

State Line Ostend - Dover has already been investigated by Ceberena (Centre Beige de Recherches Navales) several years ago. Besides the analysis of measured-mile trials,

the results of extensive measurements concerning service performance of two passenger ships were published (Ref. 1) As part of a new sea-trials programme, service-performance and seakeeping of a car-ferry, the twin-screw uiotorship ROl BAUDOUIN, were studied during the last years in a wide range of service conditions. The analysis of the measured-mile trials is discussed in Ref. 2),

3)

and 4),.

Particular circumstances caused some difficulties in the gathering of the.data and in the analysis of ship's performance:

- the ship operates in coastal waters, where the usual Beaufort number by itself seems to be a rather poor index

of weather and sea conditions;

- the measurements were spread. over two years in order to

obtain enough data in a broad range of service conditions; This long lapse of time was unfavourable to the constant accuracy and even readiness of the measuring apparatus

on board;

- as during most crossings all data were gathered by only one experimenter, a rigorous simultaneity in recording of ship speed, horsepower and. engine revolutions was not

possible.

Nevertheless, the consideration of an "equivalent

Beaufort number" on one side, and some particular properties of the apparent slip of the propellers on the other hand, made it possible to overcome the above mentioned

SHIP CHARACTERISTICS.

The ship characteristics are given in Table I.

The car-ferry has two motorcar-decks, with an entrance by the stern. Por all voyages, displacement varied little,

an average draught being

3.50 in.

Trim by the stern was roughly always the same, about 0.20 in.

TABLE I

Principal ship and screw particulars

Length between perpendiculars, L , metres

110.62

Breadth moulded, metres 15.20

Design draught, metres

3.80

Average draught in service T, metres

3.50

Block coefficient at T =

3.50

rn

0.54

Displacement at T

3.50 in,

metric tons 3 300 Centre of buoyancy aft of midships at T =

3.50m

2.30 Half angle of entrance of waterline, degrE'

8.6

Shell plating welded

Diameter screw, metres

2.700

Pitch non uniform, mean, metres

_2.350

Thickness ratio.

0.053

Blade area ratio

0.738

Number of blades 4

Total nominal power of two engines, metric b.h.p. 9.600

Nominal revolutions per minute

₃₃₅

Maximum speed on trials, knots 21

Longitudinal radius of gyration

0.24

L

Natural pitching period, sec.

5.0

-4

INSTRUMENTATION and MEASUREMENTS.

A Siemens-Pord torsionmeter was installed on each shaft. Revolutions were counted on both Diesel motors. The r.p.m. of each propeller were determined during the period of torsionmeter readings by means of a stopwatch.

The speed through the water was measured by means of a Chernikeeff log. A mile counter made it possible to

determine the average speed during each observation period. The Decca Navigator offered a complementary means to

evaluate the ship speed, as far as the tidal current could be taken into account.

Wind velocity and direction were derived from repeated readings on anemometer and windvane dials respectively. The cup anemometer was installed on the mast behind the bridge. Previous windtunnel tests ensured a proper

calibra-tion.

Strain gauges were fitted amidships to the underside of the stringer plating of the strength deck.

Accelerometers were installed at several stations along the ship's length, measuring the vertical accelera-tions fore, aft and between, and the transversal and

longitudinal accelerations in the vicinity of the virtual axis of pitch rotation. The signals were recorded by

oscillographe, connected to carrier amplifiers.

Pitching and rolling motions were measured by means of Muirhead gyroscopes and pen recorded.

The encountered waves were measured by a Tucker ship-borne wave recorder. Heave was recorded intermittently, by means of this apparatus, after switching off the pressure

units.

The location of the pick-ups and apparatus is shown

5

EQUIVALENT , BEAU'ORT' NWI1BER

The, main object of the following analysis is the

determination of power-speed curves with the BeaiIfort scale

saparameter

In accordance with Prof.

Telfer'snomen-clature, thés.e will be called "iso-weather curvei"

In the present case, an adequa,te inde

of the severity

of environmental conditions should be,de'fined 'first-.

Not only coastal waters, in which cross-channel ships operate,

offer to the wave-induóing wind a limited fetch, but this

fetch is variable with respect to the direction of t?.e wind

blowing from the nearby coast, over the open North Sea (N.E

or from the Channel (S W)

Hence, not only wave heights

are lower, but their variability is much more pronounced

than in the open ocean, and a relation wave height-wind

velocity is more difficult to establish.

Significant wave heights, a

derived ±'rom, the wave

ecor4s .a'ter du-e eprrection, are pJrOtted verss wind

velo-city in

'ig 2. The correction was based on ,informat,ione

from. the o.w.s. " WEATHER REPORT

" tests, published by

the National Institute of Oceanoaphy, further on

compa-rison between statistical values derivdfrombe wave

records and from their corrected spectra, and on the mean

of periods of wave encounter

The scatter of the spots is

considerable

Nevertheless, an attempt was made to trace

through the spots a mean line, which might be regarded as

representing an average relationship between significant

wave heIght and wind velocity for the coastalwaters In

question.

-'

In view of tracing iso-Weather curves 1n the

delivered-horsepower / speed diagram

PD

-

V ,

one immediately feels

the need of defining an adapted index, that might specify

an overall severity of the environmental conditions.

A usually convenient way in the case of

o cean-going vessels

consists in indicating the diferen

iso-weather curves by

-But, in fact, weather shiin the North Sea often make

mention of tWo Beaufort numbers, one corres.poMing to the actual wind. strength, axothercorresponding.better.to the observed sea state. The scatter in the spots in 'ig 2

demonstrates the necessity of making such a distinction. 'Some weather conditions are characterized by relatively

high waves .t a rather moderate wind velocity, others by lower wave heights, although a stronger wind is blowing.

To meet the wish o± unequivocalness in the indication of the different iso-weather curves, "equivalent wind

velocities" and "equivalent Beaufort numbers" are intro-duced here. Oneequivalent wind velocity is attributed 'to all simultaneous wind and sea conditions vhich induce an equal increase in delivered horsepower for this ship at

a given speed. It i.s the wind, velocity: corresponding to

the significant wave height on the representative curve of these two fàctorC (Pig 2), inducing together this

particular added 'power. The "equivalent Beaufo±t number", reiated to wind velocitr can be d.efinéd in analôgoüs

way.

Practically,, a spot "observed significant wave height - wind velocity" has to be shifted in ig 2 up to the

"average" curve along a well-define I direction, or line.

In view of the presumably unprecise weather data obtained (wind strength and sea state seldom seemed to be stationary in this area), a rather rough procedure for the determina-tion of these lines of eqiivalent wind velocity is adopted.

A given increase in deiivee&. hors ower colisists of an increase due to waves and. arióther due-to wind,

+ fPI

The increase due o wInd is the dIfference between the absorbed..power coresponding to wind resistance in

still air, v2) _Axa V ,and that caused by the relative wind,

+ V + w.)?)Ax V

7

or, if V is in Imots,

cp

71xI6[±v(v+v)2V3J

Axa

-The wind velocity V, is positive in case o± wind ahead, negative in case of following wind. The minus sign has to be used if (neg. V > V. The transverse projected area above the water, Axa , is assumed to be 224 sq.m.

The quasi propulsive coefficient used here corresponds to those values derived from the data in similar weather conditions given in ref 1). To the longitudinal specific wind resistance C a rough average value of 0.6 was attributed, apposite to wind ahead and astern within an angle of 30 degrees off the bow or the stern.

This average value of is derived from windtunnel tests, reported in Ref 6). The curves of added horsepower due to wind per unit of transverse projected area versus true wind velocity, for wind ahead and astern at different ship speeds, are shown in Fig

3.

As only a rough approximation is aimed at, they will be used at true wind directions up to 30 degrees off the bow or the stern.

It is Iiown that resistance increase in regular waves varies as the square of the wave height. This is not

necessarily so in irregular waves, for which the wave height has to be expressed by a statistical value, for instance the significant wave height 1 . In fact,

Fig 4 shows the plotting Of

(the increase in resistance due to waves tims a'onstant) versus

derived from the observed increase in resistance by

sub... racting the amount of resistance due to wind.

In head seas the following relation seems to fit on the average the experimental values:

DW =

18,75)+ 7.8J,

whereas for following seas V WV WI3

the relation seems rather linear:

i

DW

_29',,3

Influence of speed, in particular with respect to phase angles, is ignored.

8

This added resistance due to waves envoives also

stering effects and the incidental resistance caused by

the stabilizer fins. This may..explain the relatively high

amount pf added resistance in moderate following seas.

Notwithstanding the rather crude: assumptions and

esti-rnates

_'D

,for instance), the abQve mentioned relations

a'e siffic.iently accurate to. be usable in the following

procedure.

-Coaidering a gien. coistant value of SPD at agiven

ship: speed, &PDW

_{is calculated for different}

3

i

...

w13

Thus, the value ofàP

is determined, an

the

correspon-ding

V,

can be read off in Pig

3

Hence, one obtains

the relatiOn between

and

V. ,for which ±he increase

in power is constant

The curves of equal added power at

sOmë usual ship speeds are traced in 'ig? fo± head, and

for following seas. Por any spot, the equivalent 'wind-i

velocity, or equivalent Beau±'ort number can be found by

,line

... . f..

shifting it along a/parallel to the adjacent curves. Por

beam seas, a horizontal direction of hift seems to be

indicated.

ANALYSIS OP PERFORMANCE DATA.

A torsiônmeter was installed on the fore-part of each

shaft. Duing the measured-mile trials, torsiônmeter

readings Were taken at very low speeds, so. the

TE-POINCET method could' be applied and. the shaft losses

evaluated. These appeared to be 0.2 n

per shaft.. The, value

tof 'PD at each screW was obtained by sutracting'this.shaft

loss from the horsepower derived from the' torsionmeter

readings and the coiintedpi'qpeller ievoluti-on' fl

.

The numbei of revolutions of both motors differed very

little and the developed power could be regarded as being

equally distributed among both shafts.' nand

will

henceforth indicate the mean number of'revolü-t±ons Per

minute and the total deliveàd horsepower at the propellers

respectively.

. , ..

0/0

H.0°I

i66°

L0 I. 096 c66°

too'.

966° OO°1. 000° 1. L66° L6° 01.0° I. 9L6° i700°I. L6° 01.0° I.

90'

1.

996'

ii°L. L69 9O° I. 966° L6° 9000 1. L6°

coo'

1. 966° OO 1. 1.O°l. 9660 1.0° 1. c66° L66° 00001. 00° 1. c66° 1.

000

1.

00'1.

966° I. fr66° 900° 1. 000° 1. 66° L5° I- 96° frL6 i1.0° 1. L6° 066°

00

I. 66 61.01. L96° 066 c66° 096°

00°L

900° 96° 1. L6° 170°1.

00°1.

cg6°

660

96° 1.cO°1. cLO°1. 900°1.

00°1.

1.66°0 01.0'1. L01.

00°1.

966° 01.0° 1.

-

0660

-

cEa A tuaa mA 001. t'E°LI. cLOc

9'L1.

01. L6°91.

c9c

6691.

co91 0°91. L99 179'LL 01.L9 °L1. c1.L9 c9'L1. L99

1.°

91.

09

OL°L

L9

9°fl

c61

99'91. 99° 617 91. OL°91. c61.9 LL°91. c91.9 9L°91. cg1.9 9L°91.

09

09° 91. c61.9 LL°91.

09

tiL'91.

LL9I.

?9 cL°91. gj7ct7 01.°91. 0L 179°91. 9L9 17L°L[. cO1.L 0°9t.

69

017° 91. 0999

9'Lt.

cL1.c c9°91. 017L9

6L1.

01.9c LI. 01.99 ii9°L1. 09 i7i791. ci7L9 L8°LL.

06i7

9°91. 00 99° 91. c0179 9L°91. 0179 9L°91. coo9 c9°61.

09

9i7°61.

06c

c9'61. tnt a A 91.° cc1.c °L1. 9°1.L 091.' ci7llc 1.0°L1. 9°1.L L91.° 0917 0°L1. 017L 01.

-

17L1.

6LL

co°Li.

cc 0L 991.' 01.917

L6c1.

c9

o'

06179 09°L1. o6

90°

99

9°L1. °06

oK

0°1.6 09°LL.

09

ti0°

9I.° 060L 09°L1.

9°

176

9'

°1.

°1.

LL9

9°

cgE

1.° 091.17 09°91. °9 is 1.° 091.17 cL°91.

c°gc

99

cL°91. 0017 cc1.° 1.°

L9

I7L°9L

c°L6

a' 1.°

99

99°91.

t°1.6

I'

t°L6

9L°91. c9L9 V Is 1.° OL°91.

61.6

1.'

K9

LL°91. c°1.6

oK

17°1.6 OL°91. 9c1.° 9c1.°

099

c9°91. 6°1.6

9cv

099

L91.

9°1.6

oK

09

LL2

c9°cI.

00t

091.0 1761.' o9 00'91. 0°1.L o6

£0°

01.99

0091.

1.°6

69'1.

0069

tL°

9°69

99V

09c9

691.

1.6

ccc

°1.6 1.9°L1. 099 L61.° 1791.'

01.

gc°91.

9°L9

1.K

c6v

09179

0°9I.

o9

i'6L

ci'LI.

coLc cgi.°

L0°

O99

ç91.

o6

coK

L91.° 01.917

0'91.

o°6c

00K

1.°6

cc°L1. 0999

L6v

O1.t

'o9

01.°L1. 01.917

cv

Lv

01Z17 OOL1.

L'6c

0691.

O9

1.91.'

17°6

1.91.0 06179 O1.°61.

t°6

01.

9v

o66c cg°61.

9°c6

L1.°

cc

-

6?6

-

oL2c

91.'

o°c6

A U

po.xnsem

V9

°j

II

aav

-6-

u qg

L9'1.V01.

ii L L9 1.VL 9

L9°1.Vt

c U qj7 L9°1.1.° '8j7

L9°LV1.

£

L9°0V9

O U q.6 I. II 86!. U 91. II P91. as 091. II qg . II '891. 'I I. q.L1.

L9°0V1.

'8Lt. U 91. L9°O1.°91. c1. Ii 171. L901.°L1. u

L9°ovc1.

1.1. ii 0!. L9°0V17 6 51 9

L9°6°0

L II 9

L9°6°9!.

u 817 q L9°9°91. '8 'I U qi.

L99'

'8'.

oI

9q

I

PAT.IeP

I

ct1 tIlCa mA

'I.81fl

TDI A cEci A p8AT.Iep V9

I

cm

°,xem

°T inct mA

pa

jri.e em

mdj

U

Iv

o1I sq 6 0 I. 017:9

L°91.

1'9V 0339

o61.

c°1.63

63:

69Vi'1.

L17 1.1O' I.

96'

09t1

t'G1. ç9917

6°:3

93E u 917 L90°I. 91.0'1. O96i L9°9(. 1.LV 0L3 VL1.

0°L93

6G0'I.

H0'1.

0t:t

617i.

LI.°

01.'

0°03

93E

99'31.°L3

1717

6'

90°

I. oo61.

L9V

OLLI. 09°31. c°1761. 1.66°

oI.01.

0099 1.6°L1. o61.°

0i79

01.°91.

99'3V:3

317

9L6'

9°

1.

9l.t

1.:°91.

6v

cL01

oc°o3

'j73

Is 1.17

696'

6L'

ji9

00°LI.

1.i.°

091.9

0°

is L66°

9'

09

9'91. 91.?' 0039 is

q.ot

666'

"9°

09

1i9°91. 0039

03°i1.

1.' 1.93 3Q17 996° 0°1. 699

9°LL.

9I.°

99 9°L1.

0693

99'31.'33

6:

017° j799 91.

L°06g

9:

0939

6°063

093:

99°31.'L1.

L:

L9'31.°91.

0L3:

2°9L?

9°LL

0L:

9LL° Lt°L1. 900'L. 9L6°

9:

L9°31.'9

0L3:

0'17L3

3L1.

001. 091.' 17c°L1. 0L1. 666°

L96'

gtoi.

t66°

06179 9°91. OLV 0099

0°91.

c°1763

.0L3:

L9°31.' 9L6° iiOO'L. 00 09°91.

91.'

0L0 99°91. u L96° iiOO' 1. co L9°91.

9L.°

0t1. oG°g1. a is L96 1700° 1. 9°91. L?P1. ogLc 1.6°91.

0°:93

6:

L9'3V3

900'

L6'

1. 09L17

6°91.

I.° 0:917 017° 91. 1I17L3 P3E

996'

liOO' 1. 09Li7

6'91.

cv

06917

L:'91.

1766° 900° 1.

0Lt7

9°91.

l.'

03L17 017° 91.

q3:

1766' 1700'I.

:Lii

9'91.

1.° coL17

'9I.

6°:L3

L93L'1.

9'363

39'91.

6t9

u

L66'

I7QQ' 1.

01.9

0'9l.

OLV 06179 09°91. U ii

gco'

1. 096° 091.9 6°91.

0L.'

L91.

9°363

a 9O° I 096° 091.9 6°81.

0V

99

L91.

9°363

ss a P1.: 600 1. 966 09179 °9L 991.'

1.9

17°9L LL.01.

000L.

°9I. OLI.° c1799

oc91.

6363

0'

1. 66 06179 :9°91. 991.' 99 c°81.

3°:63

0173:

L91.VL1.

1. 66 091.9

L991.

L 3L°91.

V363

II II 1766

oo

I.

0:9

09°91.

V

061.9 9°91.

0363

II SI 1766' 0O' I. 01739 17L'91. L 0039 39° 91.

L'

1.63 U

L96'

00° I. 0L39 69'91. 6c1.' 61.9 QL'91. 9 1.63 II II 00° 096° I. 339 09°91.

V

001.9

0691.

0363

II II

P0:

600° 96 1.

:9

99°9L 391.' L1.9 39°91. 3° 363 LI ii

30:

996'

900° 1.

9:9

9'91. :91.° 0639 09°91. II

00'

L6° 1. 17:9. 9° 91. 391.' 091.9

L91.

1.°363 L9'I.1.'91.

0:.

P63 91. 176 639

3I.'

06'91. 039 00'1. 0'1. 1796' 01.0° I.

3:9

3991.

L1.

0339 £o'61. 90Q"I.

96'

01739 99'91. 171.° 091.9

9691.

1.00''.. 00'1. 061.9 96°91.

01.°

c039 90° 61.

L°363

L9'LVOI.

863 Pl-UOO

ii

aav

01.

-

-

Table II gives for each observation number the measured

values of r.p.m., ship speed and delivered horsepower,

(

n,

.V d

?

) at t

actual

i.splacemen.t..

They refer to different fouling conditions. The hll was

clean during the obs.n°

1. - 2

,

32 - 36

,

and. 51 - 59

,

and fouled to a considerable degree during the other obs.

The normal requirements concerning steadiness

f

weather conditions and constant engine .

performance

during the observations were not always fulfilled. The

non-isoclironous measuring (speed was measured over a length of

time overlapping a much shorter period of horsepower and

revolution measurements) may seem to be

other drawback.

Moreover, the torsionmeter readings had to be regarded

-with caution, because a shift on the dial oftheoint of

zero. torsion.ight occur during the crossings. Hence, the

measured data

and

_m

have to be considered here

merely asrouh estimates of the true valiiscbrresponding.

tothe measured revolutions per minute n. Only the error

on

n

may be regarded

as negiigible.Therefore, the

values of n in Table II will be considered. inithe

follow-ing procedure as a base fçr comparleon and calculation,

and regarded as a contant throughout varying environmental

and fouling conditions. I. fact this view agrees with the

actual situation on board of this vessel.

TABLE II.. :C011td.

48

_14.1.69

_{3290. 290.6 .19.50 6100}

49a 24.1.69

3280

_289.4

19.40 6060

.157 18.596095

1.044

.995

49b

288 .0

18.50 5980

.156 18.52 5990

1.000

.998

50

_24.1.69

3325

290.9

19.63 6010

51

28.3.69

₃₃₁₀

282.2

18.60 5130

.131 18.69 5270.

.995

.973

52

28.3.69

3285

283.0

16.70 5150

.133 18.70 5340

.893

.965

533i.3.69..3250

292.0

18.35 6675

.180 18.25 64Q0

1.005 1.043

54

291.0

15.35 6310

.176 18.27 6305

1.004 1.000

55

I.

290.8

18.00 6160

.138 19.10 5875

.943 1.050

56

_1.4.69

₃₂₅₅

210.4

13.80 2150

.1:48i3.66 2285

1.010

.940

57

223.3

-

2570

.144 14.57 2705

-

.950

.58

.12.4.69

3295

290.5

11.20 6560

.208 17.53 6495

.980 1.010

59 ., "

3345

2917

19.00 6010

.158 18.726250

101,4

.962

12

-The ship's master orders a certain number of revolu-tions and the engineer tries to maintain the requested r.p.m. in the arisen sea state. With respect to the calm water condition, both an increase in power and a loss.of speed occurs at the same r.p.m.

During the observation period

1967,

the log appeared to

be trustworthy. In view of the actual mean pitch ratio of the propellers, the apparent slip is given by

= 1 - 13.12 (1)

The values of _/

n3).106

are plotted versus the apparent

slip

5A in 'ig 5. The generally accepted hypothesis of

linear relationship (D / n3

).106

= a + b 5A (2)

in the most important range of 5A seems -to be confirmed

by the spots referring to the data from September, Octo-ber and NovemOcto-ber 1967. In this period the hull was fouled. However, this linearity seems only to be true up to

s = 0.19 . The spots with SA > 0.19 correspond to data

in adverse weather conditions, in which propeller emergence occurs frequently and variation in wake may be important.

Ignoring those last spots, one obtained by linear regression the relation

x

io6

155.0 +

617.4

SA n3

In ref 5), Telfer defined a torque constant

100 Q

Q = , assumed to be linear with

C

n

DZ

H1'

At the 100 percent slip condition this would become:

C =(8 +

Introducing the corresponding values, given in Table I, of propeller pitch H, diameter D, blade area ratio

and number of blades Z, one can express = 0.00823

-6 1

and C = 8.3 . Here, 0.02122 ---x 10 per screw

(since _D is the total delivered horsepower). Extrapolating the given relation between _D

/

fl3 and _{5A up to the}

100 percent slip condition, one finds a value of _D

/

13

-Applying the same procedure to the data of the

measured-mile trials at Polperro, one obtains following relationship: / n3)

x

io6

= 155.2 + 608.1

_5A ,which

is different but differs very little from the former.

Moreover, considering the data from December

1967

,just

after drydocking, one can see that the spots referring to calm water conditions lie, on the average, but very little under the straight line through the data of the fouled hull condition, at most indicating a very small difference

in _5A and thus in wake at -the propellers as well. 'om

these data, one can conclude that there is no considerable influence of fouling on the wake at the screw disc.

Ignoring this influence, a straight line has been drawn through the spots of September, October, November and December

_1967,

thus related -to data o± the fouled and

clean hull condition, by applying the procedure of linear regression. Relation

(2)

becomes:

x

i06

= 147.8 + 660.1 s

₍₃₎

-

A

which will be considered here as the basic relationship for the data of all periods in which investigations were carried out. The spots corresponding to following seas

don't appear to deviate substantially from this straight line. Moreover, Wave heights are moderate up to Beaufort

6.

So it was assumed that variations in wake were not suff i-ciently pronounced to alter the relation (3), except in the severer sea conditions.

This last relationship (3) corresponds to C

8.58

in

Telfer's representation. The good agreement with Telfer's formula, based on the open-water propeller performance, is remarkable. The discrepancies, as found by other investigators, do not seem to be considerable in the present case. Taking account of relation (1), the above mehtioned relationship

(3)

can be written under the form:

6 V

14

-Relations (3) and (4) determine the "generalised power diagram" as shown in ig 6, in accordance with

representatiqn.

Since it is assumed that fouling does not alter relation (3), this power diagram is valid for any fouling condition met with during the investigations0 Hence, it offers to

ship operators a convenient means of estimating the increase in fouling and its influence on

D after a certain period of service, by plotting the derived from the measured

V and n in fair weather0 As can be seen in Fig 5, the power diagram seems to be only valid up to

as far as the particular fouling condition during September, October and November 1967 is concerned0 Beyond

5A 0.19, a line with reduced slope, as traced

in Pig 5, seems to fit better the experimental spots. The deviation from the original straight line is believed to be due to heavy motions in worse sea conditions, leading to propeller emergence0 The latter may be considered as independent of the degree of fouling. Therefore, in the clean hull condition the original straight line defined by relation

₍₃₎

will be only valid up to (.19

-S ),

where i due to the fouling in question.

The - V curve, derived from the measured-mile trials at Polperro, was properly traced by means o± a procedure described in ref

_.3)

and 4).

Because of the actual schedule regulations on the line Ostend - Dover, the car-ferries are provided with less engine-power than the passenger ships are, but sometimes they still are in plenty of time to observe an opportune instant of arrival0 Por this reason, service-performance data are spread over a broad range of r0p.m. This last fact made the tracing of - V curves for calm water conditions quite easy. It was possible to determine from data in calm water the PD_value at certain speeds, in different fouling and clean hull conditions0 The tracing of the corresponding

15

-the whole speed range by comparison with -the "Polperro

cuive"

and assuming a variation of

_D

(friction) in

ratio of

V3

The

- V curves are converted to the

Polp'erro

isplacement (

3275 ton) by the relation

275

2/3

PD(Poip.)

₌ D )

at equal speed.

The different calm-water curves are drawn in Pig0 6

The

-V curve referring to the clean-hull condition,

as met with after each dydocking, lies under the line

derived from the trials at Polperro. A plausible reason

might be a certain degree of fouling during the stay of

the ship at' the yard in a seasOn Of high foulIng iate.

As can be seen on the power diagram in Fig

6,

_8A

with respect to any calm-water cu±.re,' remains alm.ost

constant over the raiige 'of usual ship speeds0 As'the

iso-weather curves are assumed -to be approximately pä±a1lel

to the ôal-water curve (according to Telfer, Aertssen,

e-t al),

_9A

not 'expected to vary substantially along

-these iso-weather lines

This fact gives a particular

significancE to the apparent slip0 It can be considered

ai "a means of indexing the influence of env±ronmental

conditions. This influence otherwise is usually presented

Tas a power ±crease at a given speed, or as a speid loss

at a given power, both in per cent of the corresponding

values in the calm-water condition

However, these

percen-tages greatly depend upon the considered ship speed itself

On the contrary, the increase in apparent Slip SSA

_{for any}

iso-weather curve with respect to the oalm-*ater condition

don't seem to depend considerably upon ship speed within

a broad range.

In order todraw.anadequate

_D

- V diagram by means of

the. limIted number of data, it is necessary. to convert all

the available information into values corresponding to a

standard service condition., for whi.ch will be chosen here

the clean-hull condition.af-ter each drydockii.g

(deteriora-tion of the hull, surface could not be noticed) at a

16

-A simple procedure was applied to reduce the measured data lIsted in table II. It was based on the assumption that, at a given displacement and degree of fouling, theapparent slip values are directly related to the environmental

onditions, indexed by the equivalent wind velocity and

by the wave dieo±pn0

The values of ship speed _Vm in the periods of Septem-ber, OôtQSeptem-ber, November

1967

(Obs. N° 5 - 31, ouled hull) and of December

₁₉₆₇

(Obs0 N0

32-36,

clean hull) have

been used.;to calculate

8A by mean of formula .1).

In- orderto reduce each value of to. the Polperro

displacement, one assumeS that, at constant horsepower, L

zi

V(Polp0) = Vm(

y4 '

As,however,the reduction is

preferred to be done along a constant n-line, the diagram in Fig 6 lets suggest that

Sv

= V(Polp ) - is

approximately one half of as derived from the above mentioned relation. Since the correction to for the relevant differences in A is small, this apprpxation

leads to an acceptable corrected value of SA for the

Polperro displacement A 3275 tons For each observation the corresponding sA-value in calm water is iown

(O147

over the usual speed range in the fouled condition

according to Fig 6) and hence, also due to ii.fluence

of wind and waves

Is

own.

These values of have been plotted on a base of equivalent wind speed , which is

derived for each observation from Fig. 2,and tabulated in Table II bis. A mean line could easily be traced

through the spots referring to head-9 beam-, and following seas respectively0 Only spots referring to heading within 30 degrees off the longitudinal and transversal axes of

the shifl were considered. These curves are shown in Fig. 7 It is further assumed tha.t, at a given equivàlen Beau±'ort

number, this increase ii equal in any condition of hull roughness 0Then, knowing

5A in thécalm wátSr and 5clèan hail condition at

A= 3275

tons, one can calculate1n the sea conditioné mentioned under the observation: numbers of Table II bie.

-)bs true 10 _spe.ed kn. a lb a lb a

true sign .heading

dir.off height off

bow, deg a b a b 0 d e

a

b c

a

b

a

b c

a

b c d.

a

b

17

-TABLE Ilbis

Eq.uiv. Equ, Dir

wind Beau ection

veloc.'fort' of N°'. kn. B'. I 7.0 1455 0.25 - 7

2-3 foil.

.005

.128.

19.60

5965

18.0

0:25

-

8 3

.006

.129..

19.44

5855

3.0

0

_Q.25

0 5 -. 2

head

.00.3

.1.26

19 .70

5970

1:4;.0

25P

0.55

15P

13..5,"...4

head: .01.6

19.25

6040

45P

0.60

40P

13.5

4.

."

.01,6.

.139

19.25

040

24.0

?35

1.50P

"160P

0.45

0.40

140S

1505

10.5

3-4.

foil, II 9

3-4

.bo8

.007'

.131

.130

17.20

17.27

4100

4135

23.5

30P

1.40

30P

24.5

6

head

.049

.172

18.43

6340

19.0

170P

0.75

180

16.5

4-5 foil.

.

016

.139

16.99

4160

22.'Q

15P

1.70

15P 26.0 6-7 head .05,6. 179 18. .27 6390 16.0 0 1.20 0 20.5

5-6

.,034'

.1:57

11.95

5460

15.5

0

1.50

lop

IT

23.5

6 .0,45

.168

18.53

6330

165P

1.40

18QP 25 6

foil..

.03.2 .15.5.'

17.24

4805

30P

1 .50

50P

26, 6 bow

.048

.171'

18.39

6275

21.5

165S

0.90

140S

18 5

foil.

.019

.142

19.04

5970

41.0

85P

2.60

60P

36 8 beam

.125

2T48 16.60

6720

29.0

1605

2.50

'l,60S

_35.5

8 r'±'0ll"

.0.54. .1:77.

18.32

6380

25.0

15S 1.30 lOP 24 6 head

.047

1.70'

17.14

5055

125P

1.35

1355

25 6

quart.

_.033

.156'

16.57

4280

16,.0

loop

0.55

'60P

13 4 beai. .00.4

.127

19.40

5740

15.0

105P

_0.55

60P

13 4 II

004

.127.

_19?42.

5760

15;O

11.0

105P

90P

0',55

0.40

'6QP

60P

'.13.

₁₁

_3-4

4:

.9 o

004

.003,

.127

.126

19.38,

19.41

5730

5'T 20

11.5

85P

0.40

60P

₁₁

_3-4

II

.003.

.126

19.44.

5745

10.5

11.0

_:90P

90P

0.40

0.40

60P

'60P

I, 11

3-4

II

:11

3-4

.003

003

.126

.1.2&.

19.41

19,.41

5715

5 7-1,5

11.5

85P

0.40

60P

_11'

_3-4

If

003

1 26

_19.41,

5720

12.5

1005

_0.35

₁₃₅₅

_'3

quart..

0Q4 .. 127.

17.22

4015

2.0

1105

_.0.35

135S

8'

.3

.004

1,27

17.20

4000

11.5

1158

0.35

135S

8 'V 3

004

17 .20 -

4000

35.0

.. lOP

3.50

'20P

41.5

8-9 head.

..328

13.94

6020

30.0

"15P

2.65

30P

:35

8'

.128'" 2Q8.

_7.98

660

35.0

1703

1.45

1203

'25.5

6

quart.

.Q35

.158

1$ .

77

6275

22.0

_30P

1.70

30P

6

head.:

.056

17.9'

18.20

6320

21,0

0

1.70

0

26.5

_6-7

I! .0.59 .1.82

18.11

631 5

21.0

25..Q 0

1608

1.60

1.60

0

1508

I,

25.5

6

.27

.6-7 foil.

.054

036

.177

.1.59'

18 .22

16.55

6275

4320

1.,8.0

108

1.15

:15P

20.5

5-6 head:

.0.34'

.157'

17.48

5050

1.9.0

_95S

_130S

_{5, beam.'}

250

.405

1.05

35S

'22'

.5-6 head'.,

.039

.162

17.50

5180

27.0

70S

_0.95

505

19 5

beam;.

.0.12'

.135'

17.90..

₄₇₄₅

24.0

60$

0.50

.453

16

4-5 bow

.014

.137

17.86

4770

1'O:.O

1258

0.35

1208

10

3-4 beai

.002

.125

19.52

5775

100

1555

0.40

12OS

i'i''

_3-4

.

quart.

.006.

.129,

1,9 .41 582.5

'7;0

150P

0.40

1408

.'

3-4

.009:

.132'

19.38

5905

11.0

155P

0.45

140S

₇

_.3-4

Ii

_.004

_.127

_19.46

₅₇₉₅

18.0

-

I1OS

-0.90

1.00

70S

-

19.5

.0

5

beam

ft

.014

_.015

.137

_.138

_19,21

19.21

5935

5975

'1

kX.

p

Wjd

Waves'

3275 tons

c1eai

hull

0

T A .B L E

II Ms contd.

. '.. 'T' 3 17.5 115S 0.90 -' 19.5' 5 b earn _{.014 .137 19.22 59.5} 30d - 0.70 - 16 '45 II .007 .130 19.35 5820 30 e 30f 30g 30h 18.0 -18.5 1105

--"

905 0.8.5 0.80 0.70 0.45 65S 18 . 5 I, I, 17 5 I, 16 . 4_5 'I 13. 4 .011 .009 .007 .004 .134 .132 .130 .127 .19.24 19.29 19.36 19.43 5855 5830 5815 5770

31a 16.5 los 0.65 5P 15.5 4-5 head .020 .143 19.15 6105

31b 16.5 10.-s 0.85 0 17 4-5 It .024 .147 19.04 6150 31 c 17.0 205 0.75 155 Ot 16.5 '4-S .022 .145 19.04 6080 31d. 31é 31 f 15.0 los 0.85 1 .00 0.90 0 I, 17: 4-5 I, 17 4-5 'I 17 _4-5 '.024 .024 .024 .147 .147 147 19.02 19.02 19.01 6130 6130 6125. 3.1 g 32a 5.0 805 0'. 95 0.25 I,

-

4-5 8 .3 beam .124 18.28 4720 32b . 5.0 8QS 0.25 TI

83

.001 .124 18.30 4735 3'2c 7.0 905 0.25

83

'I .001 .124 18.32 4745 32d 7.0 90S 0.25 '8 ₃ U .001 .124 18.32 4745 33a, :4.0 205 0.15. 2 he ad '.003 .126 18.85 5235 33b 5.0 505 0.15 - 2 bow .002 125 18.83 5185 33c 34. ' 5.0 23.5 5'OS 355 0.15 1.35 -255' I,

52

24 . 6 head .002 ;047 .125 .170 18.82 18.63 5180 6490 35 19.5 1805' 1.65 180 28 6-7foli. 037 16O 17.54. 5170 36" 28.0' _{755 i.6S} 60S 28 6-7 beam .053 .176 17.47 5505 37 25.0 ,110P 90P - 6 8 32.b 90P 60 S - 7 .39 25.0 65P 1 .70 .35P 27.5 6-7 head .064 .187 17:90 6250 40a 30.0 0' :1.. '70 lop 28..5 6-7 II .071 .194 17.26 5790 4 Ob _29.0 0 1 . 60 0 27.5 6-7 II .064 .187 17.47 5805 40c 1 .45 0 26.5 6 It _.059 .182 1'7.63 5825 41 30.0 1605 0.90 1355 15 . 4 quart. .010. .13.3 16.81 3880 42 24.0 0 1.15 lop

22.5 5-6 head

.041

164

18.49

6170

43 15.0 1 70P 1.05 180 21 .5-6 foil. .024 .141 12.72 1770. 4* 33.0 50'S 1 .60 35.5 28 ,: 6-7 head .067. 190 15.43 40,60 45 28.0 75 S 1.15 70S 22 5-6 be am .021 .144 17.41 4620 46 32 .5 lisp'

1 .70

90P

28 6-7 II .053 .176 15.94 4190 47 12.0 8QP 0.55 30P 12.5' 4 head .014 '.137 19.17 900 48 0.30 9 3 49a 12.0 20P 0'. 15. 20P .8 3 head .007 .130 19:18 5660 4 9b' 9.0 5p 0.1 lop 7 2-3 It .006 .129 19.11 5565 50 0.2.5 9 3 -

.-

-

-.

51 14.0 1 20S 0.70 1105 15.5-4-5 beam .007 '.130 18.71 5255 52 6 0 0.50 30P 10. ' '3 "head '.010 .'133 18.70 5340 53 2.9 .0 55P 1 .60 40P 27.5 6-7 bow '.057 .180 18.25 6400 54 30,0 70P' 1 65 70P 28 6.7beà.m .053 .176 18.27 6300 55 25.0 75p. 1.00 75p 20. 5 .015 l38 19.10 5875 56 1.4.00 160P .1 .35 655 24 6 " _.030 .148 _13.68 2280 5.7. - - . 1.15 705 22 5-6 " .021 .144 14.'56 2700 58 32.5 3QP 1.90 .20P 30.5 7 head .08.5 .208 17.5.1 6500 59 ' 28.Q 160.S 1.40 130.S 25 : '6 quart. ;033 ' .156 18.76 6210

19

-The corresponding value5bf ship Cpeed V, for each value of

the actually measured rp0m., weie subsëduenIr alcuiated

br means of formula i). For the hull OondiOn ii the period

September, October an

November 1967, the Ooxr&spdnding

values of

were dErived from the forulä. 3),: but only for

8A up

to O19. In severer' sea states the abOv-mëitIoned

linear relationship was seen not to be valid anrore, and

was derived from the estiniated line show±i in Pig. 5.

The deviation from the straight basic line inFig

5 is

assumed to occur beyond a value of 5A'= 0.04, due to

'weather influexce. This value is independent of fouling.

Hence, the b4sic line reresenting relation 3)'will only

be valid up toa certain value of

lower tháx

0.19 for

the clean hull c-tion, but higher for a sore pronounced

fbuling(Decembervfor instance). The respective' lines

repre-'sénting the relationship

_{1'D/ n3}

' SA

are'derifE'

from

the line "September, October, November, Deeeber 1967" by

shifting the latter parallel to direction 3) by a certain

s(fouling)on the sA_scale. For instance, see Fig. 6,

= 0.123 - 0.147 = - O024 for the clean b,u]1 cóñdition,

and.'sA

0.150 - 0.147= 0.003 for thè'foüiiñg condition:

in December 1968. The relationship

D/

3 "A ±ôr these

three conditions of hull rouhnese

et With are Shown in ri

.

Pig 5. The lów?et line (àlean hull) is. used to derive the

values of PD for each obeervation, as giveniri. Table II bis.

After plotting all vaIue

of PDand V, the isO-Weather

curves "clean hull,.= 3275tons" in. head,:

and.

following seas can now be traced, Fig0 8. BoW àn.d

tiartering

s.ea8 under heading angles of 45;degrees off the ship's axis

are not presented in Pig 8, but listed in Table II bis.

The influence of weather appears to be more prOnounced

'in foli6wing'Waves than in beam seas if the Beäufoxt number

is lower than'6, while for higher seas the' contráiiseems

to 'be true.

Because of the assumptions made In this procedure, some

dQuht wight be thrown upon the ultimate accuracy in

deter-ininin

iso-weather curves in such a way.

20

-Therefore, the values and V in the "clean, hull,

A= 3275 ton" condition have been converted by the inverse procedure to those goirg with the actual fouling and dis-placement. The results for each observation. axe: listed in

Table II. A comparison with the primary measured, values can now be made. The ratios _Vm/V and _PD/P are listed in Table II, and plotted in rig. 9 versus equia1ent wind speed. This figure gives an overall picture of the "errors" the measured values may be subjected to. One can. notice

that the discrepancies are scattered alost eqaliy about

the base line (ratio 1) and only toa reaonable extent. The accuracy of most measurements seem to be within.., the

following limits of error: about 2 % for ship speed, and about 6 % for delivered horsepower. The balance of the

discrepancies suggests that the foregoing procedure of

analysis gives acceptable results, and that the information the measured values could offer has been igbtly processed.

0

0 0

FOULING

The former analysis of performance data leads to the conclusion that the effect of fouling on _SA was about the same for observations done in September, in October, and in November 1967, and thus, that fouling had not increased in a great meure during these months. Hence, since the ship was drydocked at the end of May. 1967, it may be

concluded that fouling occurred at the highest rate in the period from May till August.

In order to get some more information on, the increase in as far as it may be attributed to fouling, the authors persued the log books of the ROl BAUDOUIN. The time and revolution readings are noted by ship officers at the moment the ship encounters buoys on its way, Prom the

1iown distance between selected buoys in deep water, the speed could be calculated. After correction for tidal currents the speed through the water could be estimated and, lmowing the mean r.p.m., the value of *as derived.

-21-.

Oniy crossings In calm weather up to Bèáufort3, in a sea

state. denoted bf"Smooth",'ripplèd1oi' "caiiñ" \ère considered.

Plotting the estimated values of

_s

on a time base,

One is confronted with a large scatter of the .äpots, due to

errors from diverse source, Nevertheless, mean, lines have

been traced through the numerous spots, connected by a

dotted line over the periods in whicb, calm-water data were

scarce0 Fig. 10 presents these lines, showing the trend of

variation in

s

with time. The rapid increase in

from Ma

_{till September, demdnstrati.ng a considerable}

growth

of organic fouling, seems Lo be confirmed

An apparent decrease in

_S

during autumn

ouid

indi-cate a partial disappearance of fOuling.. As t1.eiogbooks

me,rely could offer some crude information, aid,

ptwith-standing some observations done by biologists adescribed

further, the authors at this moment restrict themseives

to the statement that no increase in fouling i.s likely to

occur from October till April0

Wenn the ROl BAUDOUIN was drydocked in. Noveey. 1967,

in April. 1968 and in February 1969, the fquiing..condition

of the. hull has been examined0 The general picture consists

of. a belt of green seaweed near -the waterline, .o

disparsed

zones of brown seaweed underneati this belt, an& ..of

dispar-sed patches of barnacles lower uxder the waterline0 The

ship's bottom, however, was clean. In N0vember 1967

dispar-sed p'atches of barnacleswere noticed only at the fore and

aft ship. In April 1968 no presence of barnacles had to be

mentioned. In February 1969 patches of barnacles were more

n.ü.erous at fore and aft ship,and in the vicinity of the

bilge keels.The averae diameter and height of the

aspe--r±ties were 5 ani2 mm respectively, although ateome spots

7 and 4-'mm-respectively had to be reported. Déisity of

barnacles reached locally 100 to 200 per sq0ft.- Because the

patches of barnacles werè sparóe over the huil surface, the

overall fouling could be regrded as being rather moderate0

No fouling of the propeller blades ever was noticed,

- 22

All dates of drydocking are indicated in Fig. 100 A general conclusion would be that drydocking were the most efficient in September0 However, service schedules might urge to choose another date. Moreover, the state-ment as made above does not exclude as yet the necessity of drydocking in early spring0 Fouling on immersed plates in the harbour of Os-tend has been investigated by Leloup

and Polk (Ref, 7). Iediately after the immersion of the

plate, they observed the appearance of a primary film, containing bacteria and forming a proper base for the growth of fouling organisms. After the formation of this film, the growth of barnacles (Balanus. Balanoides) was noticed Indeed. Hence, it is possible that, if the ship were not docked inearly spring and this basic film not

eliminated, the growth of baxnacles dur-ing the subsequent summer months would be much more extansive,

The above mentioned report further states a posterior covering of the plate by a particular kind of mud,

"Polydora cilia-ta", in June but also in October, with calamitous cOnsequences to the existing barnacles, which

die soon and. leave their caleareous skele-tons-o'Examination

of the plates by the end of August gave evIdence Of the disappearance of the PolydOra mud and of most Balanus

skeletons as well.

-The results of these observations demonstrate that the fouling condition of a ship's hull might vary over the year in a complicated manner. \irther and more systematic

research In this field is needed.

The increase in due to fouiing can be rea.d off in

Fig. 6. For instance, at V =

_18.5

i this Increase is

900 hp, i.e.,

_18.5

per cent of the the clean-hull condition.The ship presumably met severer fouling

condi-tions, as 'Fig. 10 can show, In _19.68,

8A would have

increased by 0.05, corresponding to an Increase, of = 1700 hp, i.e., ₃₅ per cent.

23

-SEAIEPING ..

The ship:.is provided With DNYBR0% stabilisers,

which are ut. into op:era-bio; as soon as weather deteriorates

and the sea state reaches Beaufort 5. Rolliiig did not exceed a sigiifican.t value o± 6 degrés double amplitude

dul'ing the obsvations, and-do not seem 'to pbsean

parti-cular problem on thi vessel.

Pitching and heaving motions at' several ship speeds in regulã.r head waves have been calculated ±èoret±cally, according to the classic linear strip theory

The coefficients of he coupled differe.t1a1. equations

are in the form as presented by Gerritsma and Beukelman

The sectional addedmass and dam±ng ceff±c±ents .have the values given by Grim. The computer prograe, although

adapted t the existing facilitiesat the State University of Ghent, is substantially the. one-resented by the

Department of Naval Architecture and Marine- Engineering of M.I.T. (Massachusetts Institute of Technology, U.S.A.). .inRef. :8).

-Thé computations have been carried óutfàr only one particular displacement,

A

= 3275 ton, with a trim by the

stern of 0.20 metre. The loading conditions ó±'such

car-fèrr vane very little, displacement, for instance,

not much more than 10.0 tons.As a check, the same calcula-tions have been started over again for a displacement of 3385 tons. By eomaning the results'of both caldulations, differing but in displacement by about 3.5 per cent,

one can state that. the differences betweer the motion amplitudes, and between the phase angles.as *eii are

negligible. . . .

-The range of the ch.sen ship speeds(5, 8, 11, 13, 15,

17, 19 knots) covers all particular speeds measured on board in diverse sea states, and thf considered range of wav lengths cthitents those believed to be of any

24

-The theoretically calculated amplitudes and phase angles of pitch aid beave.otions are presented .1in

Fig0

11 and 12

respectively. Tue ratios motion/wave ampiitude are plotted a base of _{wave length/ship length . Although no explicit} representation of the ration pitch/rnaximu wave, slope is

given here, the traced line of maximum wave slope clearly indicates the relative smallness of the pitch magnification factor. .The damping of pitch motions is considerable.

The damping of the heaving' motion is even more pronounced. The vessel is characterized by a large BIT ratio and by

flared shape of frames. Actually, damping of heave might be larger"than 'Fig. 12 lets one presume, because the exis-tence of appendages and stabiliser fins was ignored in the theoretIcal cã1cilations.

- During the first period pf the full-scale observation

programe,. pitching motione

ai4

ep.cQuitered waves have been

.reeQrded simultaneously. The heaving.motions, however, had to be measured before and after the w.ve recording,

because the same apparatus was used.for'botb.-jneasurements.

Some characteristic observation records were analysed with a view t comparing with the theoretical results. These

observations are among those numbered in Table II, though they are not covering exactly the same length o± time. For this reason they are 'abelled by another observation number, as listed in Table III In order to provide infor-mation on environmental conditions, the corresponding

numbers referring to Table II are given also0

Records of waves and motions have been analysed by means of Tukey's aitocorrelation ethqd. The spectra presented here are amplitude spectra, i.e., the area under the spectra

is twice the variance of the, record. Hence, the spectral density of the waves will be denoted, by 2 ( one

dimensional spectrum), the variance by E and the area

under the spectrum by 2E. The area under the motion spectra which equals twice the variance of the motion record, will be denoted by _Re ,

R

, etc.

25

--. By. deiding at any chosen encounter frequ.nc.y the motion

àmi3litude

-spectral.densi.ty by 2S , th squared responsevoperator

has been found. Taking due accop.nt of heading d ship

speed and assuming a long-crested sea, one. couldderive the motion response at the corresponding wave length -ship length ratio.

. -;

For the.purpose comparison, 'ozily easesofhead- of

:..nely headseas have been chosen.The heád-ihg *

estima-ted. by visual, observation of the wave tterh and' therefore

-' only rou, round figues cold be listed. .Coparing the

curves o.f "measured" and "theoretical" valtieâ thé shift of

0

the curve"apparent maximum wave siopev/1(18O degrees

head--.ing) shouldbe taken into conideration. Figi3a & b ;.show two exampie.s of simultanedis wave and pitch spectra,

and the derived, pitch reponse törguiar-waes.''

The:compar±son of this "measu'ed respbnse" With the

.':Itheoretical response" show a fair agreement A.a-analogous treatment of the heaving motions waâ only posib1e- by set-ting against theheave spectrum the "mean'! Of two wave spectra from-records obtained before-and-after the heave

record. .Fig.. 14 shows an example-of-..stóh heáe analysis, for which the sea state hadbeen ttiona foralong. time.

:- The measured heave response appears -to be smällei than the theoretically calculated espise, presumablbeOaus'e of

damping due tó'appendages and stabiiiser fins.

One caii compare statistical values also. The ean of the

double amplitudes (peak-to-trugh), measuredon the motion

records, is assumed to be directly related to

\Ji.

Ofi-theother hand, the Iue of R hóuld equal the area under the motion spectrum that is derived from the

theore-tica]Lly calculated response (sq.iiared response amplitude

operators) by applying the superposition principle to the coriesponding measured wave spectrum A "theoretical"

can. be obtainedin this way.

-0) _{(at the particular heading)with respect to the} "maximum wave slope"

-26-In general9 wave heights and the ship motion double amplitudes are assumed to be Rayleigh-distributed, and. the relation ba-tween the statistical averages and the variance then is given by Longuet-Higginss formulas0 In view of the particular character of sea patterns in this coastal areas, this assumption must not be accepted without being checked.0 This check, however, is impossible to be done for wave heights0 The wave recorder writes down but amplitudes

to be corrected. yet0 A proper correction can only be applied to the components of the spectrum, resulting in a corrected

2E0 Hence, a correction factor is included in the relation between 2E and the statistical average values as read. off. However, since t1s correction factor is dependent upon the wave period, it is different as far as mean, significant or average of one-tenth highest wave heights are concerned. On the contrary, the recording of responses like pitch and vertical acceleration, for instance, is exempt of frequency dependent attenuation, and. a direct comparison between the actual and the Longu.et-Higgins coefficients is possible. For -that purpose, the area under the measured pitch spectra has been multiplied by

1.77

_2Q83 and 3.60 , and the

results compared. with the mean, significant and. average of

one-tenth higheat pitch amplitudes as read off, respectively.

The values derived from the spectra were,igeneral, about

5 per cent higher than the oorreeponding statioIea&ies

read off, but the ratios seem to be equal for the mean,

significant

and average of one-tenth highest.

Hence, it may be assumed, that the pitch (and heave) motions follow the Gaussian law, and that the Longuet-Higgins

coefficients may be applied., without to big an error to result, even if the exciting waves , especially in moderate

sea conditions, appear to have an unusually broad spectrum.

Hence, -the "measure

\ft

= 1/1.77

(mean of 'double amplitudes).

27-A good agreement between easured and ôalculated vertical accelerations is less probable, because of the involved

combination of pitching and heaving motions and their phase angles The vertical accelerations in regular waves at different stations along the ship's length (the P,

midships, the APand the locations where the accelerometers were installed) have been calculated theoretically.

For example, Tig 15 presents the results pertinent to

station EP. The vrtica1 accelerations at a station 10 metres aft of the FP, where bow accelerations have been measured, are presented in a somewhat different form in Fig 16,

suited to read off -he respone at any ship speed.

The results of the calculation can .elp one to visualise

the variation of vertical acceleration along the ship's

length, as 'ig 17 shows, for example, in the important case of regular head waves with

_{)= L}

at various speeds.

From 'ig 18 it appears that these variations are not in quite the same proportion for any wavelength...

A similar comparison beeen the area underthe spectra

Ra. and thesta.tis.tical averages derived fom.the record readings, as done. for the pitching motions, hos that the

LonguetHiggins -coeffi,cien.s may be applied in, order to derive

:0m he mean of measured. dQuble apitdes of

the. vertical -bow. acceleration record. The -response tO

regu-lar waves-was derived- from verticalbow acceleration and -wave spectra, and compared with the theoretically calculated

response to regular head waves. 'ig..9a& b g±v examples

of "measured" and. "theoretical!'curves.

5c0mpa1' Wit1 pitching motions, the agreement is less

satisfactory. No speci-fic bias with.re.spect to, the,

theore-tically calculated curves could be determined, -Discrepancies in theoretical and actual phase sngles, shortcrestedness of the irregular waves, and shock effect in the foreship

und.ou.btely are causes of a rath.er poor correlation.

The discrepancies can be figured out by matching the

statis-ticalivalues, for iiistance,

- 28

-mean of double amplitudes with the Va from the bow

acceleration spectrum that is calculated by means of the theoretical response curve and the corresponding wave encounter spectrum0 The measured wave spectra, converted -to zero speed, are shown in Pig. 20. As can be seen in Table III, the discrepancies between "measured" and

"theoretical" values of Va are considerable, in some

casea even up to about 30 per cent. However, as these disarepancies with respect to the theoretical values seem to be in some degree balanced, the curves of theoretical acceleration response should not be rectified on the

ground of the experimental data. It seems opportune to use them in the further investigations.

Pig. 21 shows the variation of Va along the ship's

length, on the one hand the theoretical values in the sea states from Obs. III to VIII, on the other hand the measu-red values at the stations A ' , 8..fld P ,

where accelerometers have been installed during the last phase of the research programme. The proportional trend of all curves is nearly identical. To evaluate the ratios of values at some stations with respect to a particular

one, at 1P , the curves derived theoretically will be used.

These ratios are not expected to be invariable at a given station for diverse sea states. However, the scatter seems to be small. The minimum vertical acceleration varies

between 20 and 24 per cent of the acceleration at the

P, on the average 225 per cent. The location of minimum vertical acceleration lies between 063 L (higher seas)

and. 0,6 I (moderate seas) aft of the FP, The vertical acceleration at the AP varies between 66 to 77 per cent of the corresponding value at the P , on the average

70 prcent.

The accelerometer in the foreship was located at station P (to m aft of YP), where also the response has been

cal-culated -theoretically. Special attention should be paid to the vertical accelerations in the garages.

29

-In fig. 21, fore and aft bulkhead of the garage are indi-cated. It can be seen that in all weather conditions

considered, the vertical acceleration near the fore bulk-head varies between 87.5 and 89.5 per cent of the value

in station F. In the oliowing, the vertical acceleration inthe garage is assumed to be 89 per cent of the,measud or the calculated 'value in rp

-Pig. 22 shows the increase in measured vertical bow

acceleration at P with wave height. It isremarab'1e that

in beam seas the accelerations seem to reaOh the same leyel a?.in head sea?.,.Above a significant wave height of about 2 metres, as a rule, no further increase in vertical acce-leration seems to occur. The yertical bow. acceacce-leration in anr âea state depends upon the ship Speed, and the latter has to be reduced deliberately in order to lmt this aces-.

-leration in. severer wave pa±terns. This speed reduction was

'ordered by the captain, relying on his own experience, but it apparently led, in fact, to the observing of an upper limit of vertical, bow accelerations. This upper limit will not 'make necessary any speed reduction in heavy quartering or following waves, but the 11n5 traced for head and beam seas in Pig. 22 is believed to enclose the accelerations at the highest safe, or attainable ship spee.

Thedotted..lines in the same Pig. 22 represent an average of transversal accelerations in beam and in head seas.

Assessing the safety of motor-carson the garage deck? with respect to sliding, one has to take account of the simulta-.. neOus transversal accelerations as well. The longitudinal

accelerations have been measured also, but the±r.rnagnitude appeared to be small, and can be ignored.

The apparently allowed limit of bow accelerations at sta-tion P corresponds to

V'a 0.22 g , or \1'a = 0.20 g

at the fore-end, of the garage. Of cours, with respect to sliding of motor-cars, only upwards directed inertial forces are of importance. Besides "double amplitudes" of vertical

acceleration., the upwards and the downwards directed

"ampli-tudes" have been read off systematically on. the records from

3Q

-TABLE III

30.9 3.11 4.11 '67 '67 '67 2152 2320 0012 7 24a 24b 58 21 20 - 1.3 -18.25 17.19 171918,07. 536 11.00 13.00 15,00 13OO 13,00 165 180 180 160 150 . 18O 160 180 140 180 1.37 1.48 1.57 1.54 3,00 3.233.23 3.23 3.48.4.20 PITCH . . . . . measue,degrees 0.62 0,36 0.62.0.57 -. 1.60 1.86 - 1.66 -theoretical, " 0.60 0.270.50 0.46 0.82 1.54 1.78 1.82 1.83 2.14 2.35 HEAVE . &.Tmeaurë.d,metres - - 007 0.14 .0.14 -

058 -;

0.65 fR theoretical.,. " 0:30 0.10 0.17 0.16 0.33.0.45 0.60 0.65 0.69 0.76 0.86 VET .ACCELERATION, P.

(:1.maft of P

. .

rRa.measured, times0055 0,051 0.137 0,120 0,162O,O95 -. 0175- - 0,215 -\rRatheortical," g.O.071 0,056 0.092.0,088 0.1.24.0,115 O.193.,Q216.Q239 0,252 0.270

Theoretical values

vert.accel.a times

AP 0,055 0049 0076 0,074 0097 0,105 0i55 0j71 0184 0195 0212 M1:(17.7m. aft:M. 0.024 0019 0,027 0.026 0,038 Q0350.0500056 0064 0.062 0,071 M amidships .0,027 Q.019Q029:Q028.0,044,Q,031 Q057.Q067-0,077 0,076 Q083

M

(11.7m foeM 0,036 Qb2'6 0.0420,040 0.060'Q048 0,086 0.0990.111 0.114 0.124 pp : . 00820,066 0108 ,O.1O30,14$ j36 Q26 Q255Q2.80 Q295 0,317

II' III

IV t vi (vii) vii (vii) Viii 310

1.29 1.241271.89 2,102.30 2.22 2.75

1.40 .1.48 1.76 2.45 ?,66 2.85 2.93 3.43 42.1 35 0 57.0 64.7 64 2 63 8 61 3 77.5 1.553 1512 ;283430753ii1 3149 3477 3884 Rel.vert.inotionV rn A (2.2m aft ofAP 0.34 0.45 .S opellers _{0.29 0.45} 0.22.0.48 -.

M

0.20 0.46

'-0.2L aft of IT-

0.47 0.58O75

01L aft ofIP

0.63 0.63 0.87

pp.

0.79 0.63 0.89

Helat ,vert .veloçty

-msec 0.2L aft of IT O,69 1q25 124 0.1L aft of I? 0.83 1.29 1.37 Shear, M, tons 14.3 29.0 38.7 Bending Moment,

-M

, m.tons . 774 934 1420 Observation number I Date: 4.10 '67 Hour 1636 O'bs.N.°Table.I ... 9 .

Ship speed, knots ₁₈₃₀ Headings, degrees 170 Sea state 2.83iE,rnetrè 1.07 12.4 2.1® - 28.10 - 17.10 -'69 '67 - '67 - '67 -1303 0516 0434 - 0447 -- - _{- 1.37 - 1.25} - 1.69 - - - 1.03 .- 1.40 -- -. 0.87 - _0.83 - 1.08 .

-0.71-

0.70 - _0.91 077 0.-8.51-O7 1.49 1.601.70 1.78 2.02 0.86 1.10 1.66 2.08 217 2.25 2.49 2.75 0.86.1,29.2.20 2.57 2.65.2.72 3.10 3.38