Papers on Shiphydromechanics, W. Beukelman. Volume 3

Ing.. W. Beukeirnan

Papers

on Shiphydromechanics

Voi. III

Reports of:

Deif t University of Technology,, Shiphydromechanics Laboratory,

Mekelweg 2, 2628 CD Deif t, the Netherlands. by: W. Beukelman.

Volume I

Bepaling van het

verband tussen goìfhoogte, periöde en pompstand van de goifopwekker.

W. Beukeiman.

April 1960, Rapport No. 65.

Voortstuwing in regelmatige en onregelmatige langsscheepse

golven.

J. Gerritsma, J.J. van den Bosch en W. Beukèlman. Juli 1961, Rapport No. 17-P.

IJking van golfopwekker nieuwe verlengde tank. W. Beukelman.

Augustus 1961., Rapport No. 78.

Excitatieproef met zevendelig model no. 41.. W. Beukelman.

December 1962, Rapport No. 107.

Over de bepaing van de demping van langsscheepse bewegingen.

Yu.A. Necwetajef. Vertaiing: W. Beukèlman. Februari 1963, Rapport No. 99.

Distribution of damping and addes mass along the leigth of a shipmodel.

J. Gerritsma and W. Beukeiman. February 1963, Report No. 21-P.

The influence of

a bulbous bow on the motions and the

propuision in longitudinal waves. J. Gerritsma an'd W. Beukelinan. April 1963, Report No. 20-P.

Een systeem van vergeiijkingen voor scheepsbewegingen, die

rekening houden met de koppeling tussen de doznp-, verzet- en rolbewegingen.

L.i. Pletneva-Machabeli. Vertaling: W. Beukeirnan. Oktober 1963, Rapport No. 108.

De analyse van de zig-zagproef voigens Nomoto. W. Beukelman.

Oktober 1963, Rapport No. 109.

Over de

opwekkende krachten die op het

schip werken in

regelmatige: golven.

B.E. Tosjef en W.A. Tjoskewi.ts_Verta1ingW.aeukelman.

Augustus 1964, Rapport No. 120-M

Volume I (continued)

The distribution of the hydrodynamic forces on a heaving and pitching shipmodei in still water.

J. Gerritsma and W. Beukelman.

-June 1964, Report No. 22-P.

Comparison of calculated and measured heaving and pitching

motions of a series

60, CB = .7.0,

ship model in regular

longitudinal waves.

J. Gerritsma and W. Beukelman. October 1966, Report No. 139.

Bewegingen van een schip in golven

(md.

dwarskracht en

buigend moment).

Beschrijving van programma I- 1433/Bertens-Beukelman. W. Beukelman.

Januari .1967, Rapport No. 168-M.

Analysis of the modified strip theory for the calculation of ship motions and wave bending moments.

J. Gerritsma and W. Beukelman. June 1967, Report No. 177.

Berekening vanj de bewegingen, dwarskrachten en buigende.

momenten van

een schip in. onregelmatige golven met. de

prograimna's JS-3509 en JS-4282.

W,. Beukelxnan.

Juni 1968, Rapport.. No. 206-M.

'Cömputed results .of ship. motions of a fast fruitcàrri'er'. W. Beukelman..

November 1968, Report No. 223-M.

Weerstandsmeting van twee f.innjoi1eno: W. Beukelman.

Juni 1969, Rapport No. 242-M.

Pitch and heave characteristics of a destroyer. W'. Beukelman.

August 1970, Report No. 257-P.

Stability of beaintrawlers in following seas. W. Beukelman and A. Versluis'.

January 1971, Report No. 295.

Resistance increase of a fast. cargo ship in regular waves. J. Gerritsma and W. Beukelman.

June 1971, Report No. 313-P.

Hydrodynamic forces on a surface piercing flat plate. J.B. van den Brug, W. Beukelman and G.J. Prins.

August 1971, Report No. 325.

Volume Ii

Zeilprestaties van drïe ontwerpen van een éénheidsjacht. W. Beukelman.

Analysis of the resistance increase in waves of a fast cargo

ship.

J. Gerritsrna and W. Beukelman,

September 1972, Report No. 334-P.

Description of a program to calculate the behaviour of a ship

in a seaway (named.: Tria]).

W. Beukelinan and E.F. Bijisxna.

August 1973, Report No. 383.

Full scale measurements and predicted seakeeping performance

of the containership "Atlantic Crown:n.

W. Beukeirnan and M. Buitenhek..

November 1974, Report No. 388-P.

Drag and sidef:orce measurements with a 1/6 scale model of the

yacht "Antiope".

W. Beukelman and A. Huijser.

March 1974, Report No. 395.

The effects of beam on the hydrodynamic characteristics of

ship hulls.

J. Gerri.tsma, W. Beukelman and C.C. Glansdorp.

June. 1974., Report No. 403-P.

'Zeilpres:taties van de ocean cruiser 16.

W. Beukelman.

Juni 1974, Rapport No. 404.

Comparison of seakeeping prediction methods

for different

ships.

W. Beukelman..

June 1975, Report No.. 420.

The influence of fin keel sweep-back on the performance 'of

sailing yachts.

W. Beukelman and J.A. Kéuning.

November 1975, Report No. 445-P.

Variation of, parameters determining seakeeping.

W. Beukelman and A. Huijser.

December 1976, Report No. 443-Pi

Handleiding

voor

het

.gebruik

vanhe.t

scheepsbewegingen

programma voor 6 graden van vrijheïd.

W. Beukelman.

April 1977, Rapport No. 449M.

Bottom inpact pressures due to f orced oscillation:.

W. Beukelman..

. .

February 1979, Report No. 479-P.

Hydiodynamic coefficients of rectangular barges in shallow

water.

-J.A. KeuningandW. Beukelman.

August. 1979,. Report No. 4.89-P.

Volume III

Seakeeping triais wIth }LMS "Tydeman". J. Gerri.tsrna and W. Beukelman.

March 1980, Report No. 494.

Added resistance and vertical hydrodynamic coefficients of

oscillating cyiir.ders at speed,.

W. Beukelman.

September 1980, Report No. 510.

Forced oscillation experiments With a segmented model

in

shallow water.

J. Gerritsma and W. Beukelman. November 1980, Report No. 513-P.

The distribution of

hydrodynamic mass

and damping

of an

oscillating shipfortn in shallow water. W. Beukeiman and J. Gerritsma.

March 1982, Repòrt No.. 546-P.

De verdeling van de hydrodynamische massa en demping over een in ondiep water oscillerend scheepsmodel.

W. Beukelman en J. Gerritsma. Maart 1982, Rapport No.. 546-A.

The longitudinal, distribution of low frequency hydrodyna.mic derivatives for lateral motions' in shallow water.

W. Beukelman. and: J. Gerritsma. September 1:983, Report No.. 562-A.

Cal culat ion methods. of hydrodynamic. coefficients. of ships

;fl'

shallow water.

W. Beu'kelnian, R.H.M. Huijsinans and P.J. Keuning. November 1983, Report No. 571-P.

Vertical motions and added resistance of a rectangular and

triangular cylinder in waves. W. Beukelman.

July 1983', Report No. 594.. '

On sway damping and added mass in. shallow water. W. Beukelman.

September 1984, Report No. 603-P..

Seakeeping_caiculationsfor_high_speed_roundbi1gedisplace -ment ships sub-series 1.

W. Beukelman.

April 1984, Report No. 616-0.

Trial, a computerprograni to calculate the behaviour of a ship. in regular and irregular longitudinal waves.

J.M..J. Journée and W. Beukeinian. November 1984, Report No. 451-M.

The high-speed' displacement ship systematic series hull forms-seakeeping characteristics.

J.J. Blok and W. Beukelman.

November 1984, Report No. 675-P.

Semi-planerende vaartuigen in zeegang, predictie van

inzetbaarheid. W. BeukeÏman.

Maart 1985:, Rapport Ño. 658-O.

Ontwerp serie modeÏlen ter bepaling van de inzetbaarheid op de Noordzee.

W. Beukelman.

April 1985, Rapport No,. 664-O.

Snelle depiacementsschepen in zeegang W. Beukelxnan.

April i985, Rapport No. 754-P.

Comparison of seakeeping calculation methods for model 9 of te high speed displacement ship series.

W. Beükelman.

September 1985, Report No. 689-O.

Semi-planingvessels in a seaway, comparative prediction Öf

operability.

A.M. van Wijngaarden andW. Beukelman.

-October 1985., Report No. 755-P.

Seakeeping calculations for high spee& round bilge displa.de-ment ships series of 20 models.

W. Beukeiman and J.A. Keuning.

-'November 1985, Report No,. 696-O..

Volume V

Prediction of operability of fast semi-planing vessels in a seaway.

W. Beukeiman.

January 1986, Report No. 700-P.

Bepaling van de inzetbaarheid op -de Noordzee van een sex je semi - planerende vaartuigen.

W. Beukelman en F. de Beer. April 1986, Rapport NOo 706-O.

Zeegangsgedrag als ontwerpparameter. W. Beukeiman en J.A. Keuning.

Mei 1986, Rapport No. 709-Pi

High speed displacement hull fOrm series.

Calculated influence of the pitch gyradius on seakeeping for

the paretrnodèI

W. Beukelman.

Volume V (continued)

Slarndrukken op cylinderviakken bij gedwongen osciliatie.

W.. Beukelman..

November 1986, Rapport No. 728.

Longitudinal di9,tribution of drift forces for a. ship model. W. Beukelman..

December 1988, Report No. 810.

Koersetabiliteit voor een ro-ro schip als fuñktie. van

waterdiepte, trim en sneiheid. W. Beukelman..

Juni 1989, Rapport No. 830-O.

Distribution of drift forces at 90 deg.ree drift angle. W. Beukelman.

July 1989, Report No. 839-O.

CroSs flow. drag. on a segmented model.

W Beukelman.

October .1989, Report No. 83i-P

De i.nvloed van trim op de :richtingssta'b.ilïtei.t vaneen Ro-Ro

schip op ondiep water. .

W.. Bukelman..

Januar± 1990, Rapport No. 854- P...

Added resistance and vertical oscillations -for cylnders at forward speed in still water and waves.

W. Beukelman..

August 1990, Report- No. :873-P.. .

Slaimning on forced oscillating wedges at fOrward: speed.. Part i: Tes.t results.

W. Beukelman.

May 1991, Report No. 888..

Slanuting simulation on penetrating wedges at forward speed.

W. Beukelman and D. Radev. .

. r October 1.991, Report No.. 888-P.

Hydromechanic aspects of marine, safety. W. Beukeiman.

June 1992, Report No. 921-P.

Hydrodynainic aspects of ship safety. W. Beukelman.

LABORATORIUM VOOR SCHEEPSHYDROMECHANICA

Rapport No. 494.

SEAKEEPING TRIALS WITH HNLMS !!TyDE4IS

Prof.ir. J.Gerritsma and ing. W.Bèukelman

Deift University of Technology

Ship Hydromechanics Laboratory Mekelweg 2

Delft 2208

Contents.

Introduction.

Description o measuring instruments.

Particulars of shio during trials.

Results of wave and wind measurements.

Comoarison of shio mötlon measurements and calculations. 5.1. Anti-rolling tank.

Acknowledgements.

References.

Introduction.

In the eriod of 13 - 22 March 1978 full scale seakeeping trials

have been carried out with the oceanograhic research vessel HNLMS !'Tydemantl. The purpose of the trials was to determine:

a1 the arniitude response functions for heave, pitch, roll and

for the vertical displacement 'of the. bowin longitudinal waves,

as weil as in oblique wave conditions, from wave- and ship motion measurements.

b. the influence of the free surface anti rolling _{tank on the}

rolling' motion in beam seas.

Most of the triais were carried out in a small area around

o ,

58 30 N 12 O0 W, but additionally two runs were done near

58°29' N 2°35'W.

After 'a small conversion of the after body of the ship a second

triai has been carried out in December 1978. On this _occasion

only the vertical displacement of thé bow has been measured

o , o ,

near 44 43 N 19 16 W in one head sea condition..

The trials included the measurement of the _{prevailing sea}

con-ditions by means of wave buoys, deveiooed _{at the Deift Ship}

Hydromechanics Laboratory. With regard to the choice of suitable

wave conditions for the intended seäkeeping triais, the _David

Taylor Naval S'hi _{Research and Development Centre (DTNSRDC)}

o.ffered valuable assistance through t'he Royal Netherlands Navy

by poviding wave and wind fore casts for the considered sea

area's., These, fore casts were madê by the Fleet Numerical Weather

Control. (FNWC) at Monterey, CA, for locations near the intended

trial area,. The wae fore casts have beén _{transmitted daily to}

-the ship at 0000 'and 1200 GMT.

On the basis of these forecasts _{the. March trials have been}

carried out near location 127 (58°18" N 12°18' W). The

predic-tion for the december trials has been _{carried out fó three}

locations, the nearest being 4.5900' _{N, 17°18' W.}

In total fourteen wave s'ectia have been measured with _{a recording}

time of forty minutes each, as well _{as corresponding ship motions,}

the average _{ower., the wind .soeed and.the. wind dÌr.e.ction...}

estimated by visual observation. During both trials the waves were not uni-directional, but no estimate of the angular spread of the wave energy could be made.

In this report the results of the wave and wind measurements are compared with oredicted values as a compliment of [i

Also the calculated amplitude. response functions, the measured

wave conditions and the motion spectra of the ship have been determined and comoared with the measured motion spectra.

2. Descriotion of measuring instruments.

The vertical displacement of the watersurface has been measured

with a wave buoy, which is described in some detäii in _{2 )}

.

The spherical wave buoy has a diameter of 0.43 meter and is half immersed when floating. The buoy is stabilized by means of a light tubular construction of about 1. meter length, a thin steel wire connected to this extension and a. stabilizing weight., see

Figure. 1. The length. of. the wire. deoendson. the.expected. wave ..

lengths which. have to be meas.ured . In a. seaway the buoy follows: the

wave surface with. sufficient...accuracy and the;stabilizing:system:

keeps the buoy, in a vertical position, within a few degrees.. ... -... .

-The buoy is equioped with an. an.teina. and.transmits:.a frequency.... moduiated signai of the vertical, acceleration: to the ship.:

The vertical displacement is found by numerical integration of

the di.gitiedacceieration recordïng. The effective range of the

transmitter is limited to about 9 - 20 miles depending on wave conditions. Digital data reduction methods have been used to compute the power density spectra of the wave recordings. Roil and pitch have been measured wïth a Sperry VG14 verticai gyro and for the determination of the vertical motion at the collision bulkhead and at the centre of gravity of the ship, vertical accelerometers on stabilized platforms have been used. The roll, pitch and vertical acceleration signals have been recorded on an instrumentation tape recorder, whereas for ship-speed, relative windsoeed,relative wind direction, torque and thrust a pen recorder has been used.

The vertical displacements were obtained from numerical integration

of the recorded and digitized acceleration signals, as in the case

of the wave buoy measurements. For the determination of the power density spectra a sampling time of 1.4 seconds has been used., the length of each of the wave recorc being 2100 seconds with

the exception of the runs in Deceïnber 1978 where a record of 1120 seconds had to be used. The number of lags to compute the autocorrelation functions has been taken as 45 and a "Hann" filter function (0.25, 0.50:, 0.25) has beenused to smooth the raw

spectrum density estimates.

For comoarison with predicted wind soeeds the true wind seed and wind direction has been determined from the apparent windspeed, apparent wind dirèction, the apparent wind angle and the shio's heading.

Wind soeed and wind direction have been measured by means of a cup anemometer and a wind vane situated in the fore mast -of the

shp, where a minimum of air flow interference from th ship's

superstructure was exoected.

Particulars of ship during trials.

Main dïmen:sions.

Length over alI _LOA aooroximately 910.1.5 ut

Leigth construction waterline _LCWL 84.50 ut

Beam, moulded .1

B 14.40 m

Deoth to G deck D 10. 0:0 m

Draft förward _Tv 4.38 ut

Draft aft _{TA 4.92 rn}

Volume of disolacement in seawater 27916 ut

Longitudinal radius of inertia 21 .1 m

The ship is equioped with a passive free surface anti-rolling tank, situated midshios.

Results of wave and wind measurements.

Eleven wave soectra have been measured _{very neai to location 127}

and two soectra have been determined at 58°29' N,. 0203:5 ' W during

the March triais. In December 1978 wave spectra were measured at

38°05' N, 25°03' _{W, 4443' N, 19°16' W, 48°17' N, 8°41' W.}

InTab1e1 the signifiidant wave heights, as derived from the

spectral analysis of the wave recordings as well as the

corres-ponding, wind soeeds and wind directions are summarized for the March trials.

4

Table 1: Measured wave height, wind speed, wind direction.

sign.

wave

wave

direc-True wind 'True w±nd

speed 'direction

Date CMI Run Position height

non

1/3 in degrees rn/s degrees '16-3-78. 0815 BC 9 ,58°3VÑ

5.7

060 10.2' 034 11°30'W

16-3-78

0900 DE 9

58°35'N

5.5

060

13.4

041. 11°19'W

16-3-78

.0945 FG 9 58°28'N 5'. 1 060

13.8

059 1'1°20'W

16-3-78

1.100 'Hi 9' 58°38"N

5.0

. 060

13.2

038 11°30'W

16-3-78

.1200 CB 9 58°34"N

4.8

060 11.3 '050 11°'20'W

16-3-78

'1330.

j 9'

58°26'N

4.7

' 060

132

053 i1°2'8'W '

17-3-78

0830 BCl2. 5'8°35'N 3..9 Ö40

4.2

321 12°36'W ' ' ' .

17-3-78

0930 DEI2 . 58°42'N'

4.2

040

3.4

'297 12°24 "W

17-3-78

1030 FG12

5834'N.

. 4.1. 040

3.8

2.70. 12°20'W

17-3-78

1130 Hi12

58°43'N

3.7

040

4.7

248 12°42'W

17-3-78

1215 CBI2 5'8°41 'N

3.6

040

5.0

249 12°25'W

19-3-78

1505 BC 6.

58°29"N

3.9

170

15.6

192 02°37'W 19-3-78. '1550 CB '6 5'8°25'N

3.6

170

120

182 02°35 'W

the number following the two capitals being the nominal ship speed in knots of the considered run.

The th±rteen wave: spectra are shown ïn Figures 3a, 3b, 3c on a base of circular frequency. All of the spectra near location

127 were unimodal, where as for the runs BC 6 and CB 6, carried out near 58°29' N, O2:35' W, a bimodal spectrum has been found

(Figure 3a)

Similar information of the December trials is suiumarizçd in Table 2 and the Figure 4.

Table 2.

Measured, wave height', wind soeed,' wind direction.

December Trials.

Sign. wave

height wave True True

Date GMT Run Position

_ff

dire,c wind wInd

1/3 tion s:peed direction

(Y

degrees rn/s degrees

The main direction f rom' which the 'waves aproach as well a's

the angular spreading of the wave 'energy 'cannot be measured with the Deif t wave buoy.. Thereföre the main wave direction 'could only be estimated by. visual observation.

Although estimates of the''mai'n wave direction by independent

oservers d'id not differ greatly the relative wave direction with regard to the ship!s course remains as an uncertaiñ, factor in the considered trials.

This is also the case for the ämount of s'hort-crestthess of the seaway': in'some cases a secundary wave system, suer imposed on: the primary wave, but with a different main d'irectiön has been observed. For the trials on 16 March the observed main direction of the prïmary wave system was 060 degrees and the secund'ary wave system aporoached from almost the saine direction (040_60)

8-12-78 15,20 Al 38°05"N 2:5° 03 'W 5.1 045 11.5 266 '10-12-78 12,25 A2 4.4°43'N 5.4 210 18.;5 il3'5 1:9°16"W 12-12-78 10,30 A3 48°17"N 9.,,1 - 13,7 2,39 8°4l 'W

6

This is not in agreement with the forect, as can be seen from

Table 3, in which the wave and' wind fore casts of FNWC are

summarized. On 17 March the main observed wave direction was

040 degrees. However, on this day a windsea (visual estimate:

2½ - 3 meter) with a main direction of 320 - 290 - 280 -

250 -

260

degrees has been observed for the sequence of the runs

BCl2

through

CB12.

On

19 March a wave direction of 170 degrees has been òbserved in

acçordance with an estimated height of

2½ -

3 meters..

In the Figures

5

and 6 the windspeed and wave height fore casts

of FNWC are compared with the corresponding results of wave height

measurements. Windspeed is very well predicted and also the

pre-diction of the significant wave height on 16 March corresponds

satisfactory with the wave buoy data. The waves on 17 March have

been slightly underestimated.

From the visual observations on board of the "Tydeman" it was

concluded that the runs on. 16 March were the best for..analysing

the relation ,be,ttqeen. waveconditions and. ;shipmotions:....

However from the predicted. primary.. and.secundary..wave.:systems. as

given in Table 3, and from the observations it is clear that also

in. this particular case. the description, of the seaway. by a.

uni-directional wave' spectrum could be insufficient..for.ana'1yzing''

the ship motions, the difference of the two systems being'

aproxi-mately 180 - 210 degrees.. On 17 and 18 March the difference in

direction of the two. systems increased to' about

210 - 2.40

degrees according to the predictions. On 19 March the wave system

aPpeared to be very short crested and seemed not suitable

for seakeeing tests as further information about the spreading

of wave energy could not be obtained.

In the Fig.res 7 and 8 two measured wave spectra are compared with

the_corresponding_FC_forecastsInig.re7thefo.recas.t-made on

14

arch for poirt127 for 16 March

1200

GMT is compared with the

measured wave soectruin on run,

cB-12 1215'GMT.

Figure 8 compares

the 16 March. forecast for 17 March 120:0 GMT with the measurement

taken during the

run CB 12'.

In this case the FNWC values appear

to have a shift in frequency, to the left, but in general the

two forecasts show a positive comparison, .including the 48 hour

11), peak at 6' sec

2.) broad 11 - 15 sec, very small height

principally swell, very smafi wind sea

very broad'

peak at 12 'sec:; waves at location 127' will decrease to 4.3 meters by 1200 GMT on 1.7 - 3 - 78

'small

1 = primary wave system

.8.) 2 = .secund'ary wave system.

.7), '8)

Wind Wind sign. direction period direction period

Date Q4T speed direction wave 1 1 .2 ' .2

height

rn/s degrees m degrees ' sec degrees sec

14-3-78 0000 FO.. 3 116 5.. 3 1 86 4' - 7 none -14-3-78 1200 8.7 065 3.7 246 .16 '036. 6 15-3-78 0000. 7.7 033 3.0 246 18 036 11' 2) 15-3-78 1200 5.5 042 3.2 036 11 - 12 246. 12. 15-3-78 0000 1.5 294 3.. 3 246 18. 036 l'I 15-3-78 1200 4.0 1107 3.2 216. - 246 15 '036 8 -. 9 16-3-78 0000: 1.1.3 :064 5.1 036 11.-' 1'5 '216 15 16-378 1200 '1i6.2 028 5o7 036 10 - 16 246 12 16-3-78 0000 6.6. '05.7 3.3 246 1:5 036 .:; 16-3-78 1200' 1.2.3 '033 3.6 036' 9 246, 18 17-3-78 0000. 12..6 007 3.8 :036 ' '9 276,2.: 14. 17-3-78 0000. 8.7 006 3.. 7 036 9 2.76 ' 16 17-3-78 1200 4.6 292 3.0 246 - 276. 12 006 6 18-3-78 0000 '9..8 218 3:.3 246 - .276 1,2 0,36e 1F 18-3-78 1200 14.9' 1195 4,5 .1816 - 216 ' 11 186 -216 ' 6

Table 4.

Significant values of wave

height,:pitçb,

ha.ve

aU

amplitudes.

* calöulated without anti-rolling tank

i inasurement 2 calculation RUN _T1

a,()

2

i2

i9

O 4.9 3.1 3.3 1.8 1.9 2.8 .3.1 6.1 0.0 DE9 60 5.5

25

2.8 2.3 2.4 3.0 3.3 11.4 9.0 FG9 90 5.1 2.6 0.2 .2.2

25

2.9 2.6 9.1 10.7 KJ9 9Ó 4.7

23

0.2 2.2 2.4 2.7 2.5 5.9

94*

HÏ9 120 5,0 2.6 3.1 2.1 2.4 2.7 3.6 7.1 8.8 BC9 180 5.7 4.1 4.9 1.8 2.4. 3.4 4.4 2.8 0.0

carried out, but only on the 10 December run the vertical accelera-tion of the bow has. been measured. The 8 December run has been

used for other technical experiments with the ship,. whereas on the 12 December run the wave conditions were too confused and too severe for an analysis of, Ship motions based on spectral

ana-I.ysis.

5. Comparison of shio motion measurements and calculations.

The results of the motion measurements of. the 9 knot runs on

1.6 Marchare given as anmiltude spectra in Figures 9a

-

9f..

Ps a reference the corresponding wave spectra are gIven ±n this Figures on a base of. the frequency of encounter.

In Table 4 the ignifican,t values of wave .height,.pitch,heave,

vertical displacement at the bow and roll are. suirimaiized.. In the Figure 9 and in Table 4 the results of strip theory

calculations are given as well The calculations are based on the

following assumptions: .

-The motion amplitudes are linear with respect to wave .ampIitude. The wave spectrum is strictly uni-directional.

The wave direction with regard to the ship's course is defined by the observed main direction of the seaway.

For the calculation of, the motion spectra, the actual measured wave spectra have been uséd, a's well as the measured mean speed

through the water of the ship, as given in Table 5.

Table 5..

Mean shin soeed of runs on 161 March.

In 'Figure 10. the measured wave and the vertical displacement _of

the bow spectra are given as well as their significant values

for the runi 10 December. The ship

was in a head sea condition

with a mean speed of aproimately 6 knots, but large _fluctuations

in sneed hàve been observed.

BC9 DE9 FG9 H19 CB9

speed 8.7 9.1 8.8 9.01 9.6 9.1

12.

10

-Table 4 and the Figures 9 and 1.0 show that there. is not a very close agreement between the experimental and calculated signif i-cant values of the motion amplitudes, but the differences are not large. it should be noted that there was appreciable rolling in

the head sea and following sea conditions (runs BC9 and CB9)

and quite some pitching in beam sea conditions (runs FG9 and KJ9), although for unidirectional waves these motions should be zero, resectively. very small.

This indicate'. a short crestiness of the seaway and for an

error in the estimated main direction of the wave spectrum, which

was not taken into account in the calculation procedure.

With respect to a possible inaccuracy in the estimated main direction of the seaway the runs in the beam sea condition are of interest. The H19 .and FG9 (Figures 9c ànd 9d) calculated roll spectra show a shift in modal frequency in comparison with the corresponding measured values. The shift is approximately 0.2 radIs, but this difference is.too large to exolain from,..,an..err.orin the:'estimated: main direction of: .the..wave.syste.,.when..ònly one'. uni-directional... wave spectrum .is.'cons'idered..

-For run BC9 ( = 180 degrees) the influence of the 'main:direction.:

and the soreading of the: wave energy has.been.analysed..'Acosin'e.... squared.. soreading' function: has: been used: :for. .this ourposefor -an:...

angular range convering;

to.-Four main directions have been considered.: 180, 165, 150 and 135 degrees. The comparsion öf the results concerns the pitching motion and the vertical displacement of the bow.

In Figure lithe amplitude response functions for these motions are given. In Table 6 the significant values' of pitch and vertical disolacement amplitude are given for the varïous main directions of the seaway with respect to the ship. In this case the

measured wave spectruni and the computed amplitude

response function were used to 'determine the response spectra. Two cases have been considered for the analysis namely a cosine

squared wave energy spreading

function,

as well as a

uni-directio-nal wave system.

Influence of main direction and spreading of waves Run BC9, V = 8.8 knots.

S(.i,w) = f(,ji) S(w)

but it should be realized that this is also. an assumotion which is not based on the actual measurements.

Furthernore there is little experimental evidence to support the

assuinition that f(p.) = cos p,

although it is widely used to calculate the relative merits of different ship designs. Lt should not be excluded that. f(p) could have an asymmetric form.

Also a saway comnosed of two or more wave systems with different main directions could have been existed during the trials., Such wave systems are frequently reported by ship's officers

It seems not r)ossible to get more insight in the angular soreading

of wavé enerqy from measured ship motions and

a corresoondng

From the results it could be concluded that rather large

corec-tions and/or

a wave energy soreading function is necessary to

get a closer agreement with the experimental values. See f or

instance the results for p = 135° and f (p) = cos2 p,.

Generally theirectional wave snectrum is written as:

point spectrum of the seawaves,. Due to its dimensions the ship is not a satisfactory directional wäve measuring device.

p. f(,p) = . cos2p f(p) = .1 measurement

degr _ZB

O/3

Z

a]1

m

. degr. in degr. m degr.

180 4.2 4.4 , 4,4 i 4.9 3.4 4.1 165 4.2 4.4 4.3 4.8 i - -150 4.0 i '4. 4.2 4.5 -135 3.4 3.2 4.0 4.1

-In general it could be concluded that it would be desirable for

shio performance studies to have more. information concerning the.

directjonai spreading of wave .enegy which occu in practice.

5.1. Anti-roiling tank.

The influence of the free-surface tank on the roiling motion of the ship could be estimated by a comparison of the runs in the beam sea condition.

During the KJ9 run the anti-rolling tank was in operation, whereas durIng the FG9 run (and on ali other runs) the tank was empty.

The wave

conditions

during this two beam runs showed sufficient

similarity, with a somewhat lower signif.icant wave height for KJ9 as shown in Table 4. Therefore a comparison of the rolling motion in both cases can be made using the significant roll

amplitude in degrees per meter significant wave height.

In Table 7 these.vales..are.gIvenfor..both runs:in.,adaition.:to.::.. the. similar.. expressions. for. the: signïficant. pitch amplitudea.:;

Table.

Influence of.: free-surface tank: on roll and pitch.

The Table shows a roll amplitude reduction of about 30%. The. dfference in the pitching! motion is too small to conclude thát the anti-roiling tank had an influence on this mode of motion.

6. Acknowledgements.

The authors wish to express their appreciation to DTNSRDC and

to the crew of H'NLMS Tydeman' for' the, cooeration in erfbrming

12 -Run nr. H 1/3 I3 KJ9 1.26 0.49 FG9 1.78 0.51 Free s.urface tank filled empty

the described test's..

Moreover they are grateful, to M. Buitenhek, J. Ooms and

C.W. Jorens who were responsible for the instrumentation, and the data reduction of the measured signals.

7. References.

1J Gerritsma, J., M. 'Buitenhek and C.W. Jorens,

"Wave and wind measrements during HNLMS "Tydeman" full scale triais",

Shi Hydromechanics Laboratory of the Deif t University

of' Technology,

Retort no. 464, May 1978.

2)

Buitenhek, M.. and J. Ooms,

"An updated design of a disosable wave buoy",,

Ship Hydromechanics Laboratory of the Deift University of Technology,

14

-8. Nomenclature.

B beam motilded

deoth to G deck

H wave height

k longitudinal radius of inertia

yy

LOA length over alI

LCWL length construction waterline

S spectrum

Tv draft forward

TA draft aft

V ship's speed

z heave displacement

ZB vertical displacement at the bow.

p wave direction

V volume of displacement

w circular wave. frequency

We circular wave frequency of encounter

roil angle

O oitch angle

ç instantaneous wave elevation

Subscripts :

FIßURE1

DELFT WAVEBUOY.

.c) stiff 3-iegg tail

iron wiré with length of 2.5 to 40 rn cardboard case

way e d'i!rection

buoy: location

1:

2 u,

w

»- rad/sec

i=3.89 m

0.5 1.0 1.5 20

Figure 3a: Measured wave spectra March trials

Ci w UI

L

o o =3.56 m I I 0.5 1.0 1.5 w rad/sec 2.0

'E --.- FlCFIst RUN KJ-S. L7Im

j.2

w.. rad#IIC RUN 1114 q.,sozm

Figure 3b: Measured wave spectra March trials

i:

W.

riEf is

RUN .o

OS 0 1.6 3D O.S IO LS 3D 05 10 LS 3D

Figure 3c: Measured wave- spectra- March triais

1.0 LS 2.0

lo-RUN Al R? =Sim I

- I

0.5 1.0 1.5 W - radis 20 15 u' E 5 o D 2.0 'n 1. RUN Ä3 9.1m 05 tO l5 W

-

rad/s

Figure 4 Measured wave spectra December trials

2.0 RUN A 2 ii =5.4m I I. rad/s 05 1.0 1.5 2D

t

w

>

4

I

z

4

C-) IL

z

(D (n

15 MARCH

16 MARCH

MARCH

FORECAST DTNSRDC LOCATION 127

MEASUREMENT HNLMSTYDEMAN 1978

Figure 5 : Comparison of predicted and measured waves.

20

s

1-

I 15 MARCH

FiIure 6

;

Cornjrisn

FORECAST DTNSRDC LOCATION 127

MEASUREMENT HNLMS TYDEMAN 1970

nf predicted and measured wind.

C-) w V'

«

L

7 6 5 4 3 2,

i

I I I (D

FNWC H'i3=5..72cn

1200 GMT

o

CB-9

'/4.8'Om

12i5 GMT

sec

FIGURE 7-

Comparison ofmeasured and predicted

wave spectrum C B 9

(J)

17 March 1978

O CB-12

Ñ:i13= 3.59m

12'I5GMT

FNWC

'/3'.:O24m

1200 .GMT

5

1.0 1;.5 2!Q

w

sec

FIGURE 8 Comparison cf measured aúd predicted

j -05 w. 1 = ca1cu1ated 2 = measured

Figure 9a: Wave and motion spectra on a base of frequency

- of éncounter. AaL

/

w. 1.0 0.5 lo to os to '5 03 iO 1.5

g. rad/sec se PITOl v.P. N MI R M 120' .102e' 2 .2ec-I. = calculated---2 = measured

Figure 9b: Wave and motion spectra on a base of frequency of

encounter. I w. to t i RUN 14.9 .S.02m 01 1.0 LS 20

E A T O 05 iO LS 20 In- raa..c 3 /

HEAVE AT TIE W RUN NE lu O

Il R*.&71n. 2 I 's.. r s. --s. In.

i

1 20 J =.calcuiated 2 = measured

Figure 9c: Wave. and motion spectra on a base of frequency of

encounter. w, to tE. w. as

-

In, Lo LE I. 3

3-A :03 1.0 LS LO w r;d,$e RUNFG-I JN NS 909 I. 9O 906m I 0át.2 2 R.LS1.--N I calculated 2 = measured

Figure 9d: Wave: and motion spectra on a base of frequency of

encounter. R0(

(J

RUN NS FOR iI W 006m -2 Q OES to LS

10 I

--I

OS to 15 20

Wi - rid/I

¿j

HEAVE AT ThE '.0

I'

w poni,e 099 rn 4.2 .aion. 2 2.ZStn. 2 1,LLf-L, L 60 ¿0 00 LS I, JI 6- 2-00 I = calculated -2 = measured

Figure 9e: Waveand motion spectra on a base of frequency of

encounter. t 2it.2.27i LO LS 3 t OES LS

I = calculated

-2 = measured

Figure 9f: Wave and motion spectra on a base of frequency of

encounter. w. raft 0 .5 PITDI RUN N! CR! i', Il I, S ê.10! I i i Ip I tI i, j ZU.. RUN NRCB9 £0 -2a.&I3 20

SZB

10

j',

/

i

I

t

1

/

../

_t t

j

s. (measured)

/

j fl'1

5.4m

i

measurement

ZBII=3.6m

ZB=4?Om calcuLated

Z

_B

(calculated)

t

Z B (measured)

..rad:/s

FIGURE 10 Wave spectrum and vertical dispLacement

of. the

bow., measurend on 10 December 1978..

i 4%

I

ZB

Ça 1.0 2.0 1.0 o

i= 180°

0.5 We O 0.5 1.0

We

FIGURE 11.

Arniitude

response functions for different wave

directions.

1200 135°

moo

165°

1800

10 5 o

5-o - - Measurement

__Ll50ei

IL. 135°°°° iLa.Id drectimal sedtng

-IL.135à UrCirectiona(

05 We

-12

Meaied àilcuiatdmotjon

_{specra it and withut}

cosine squared directional spreading.

PITCH

- - Measiement

Calculation

- -

I.L=150.i

3L 1350jCoine suared directional

L.135° Unidirectional RUN BC

t

529 A Calculation.

-

- L180° Urg1iretiont

801085

TECHNISCHE HOGESCHOOL DELFT

AFDELING DER SCHEEPSBOUW. EÑ SCHEEPVAARTKUNDE LABORATORIUM VOOR SCHEEPSHYDROMECHANICA

ADDED RESISTANCE AND VERTICAL HYDRO-DYNAMIC COEFFICIENTS OF OSCILLATING CYLINDERS AT SPEED.

W. Beukeiman

September 1980

Rapport n'o. 510

Deif t University of Technology

Ship Hydromechanics Laboratory Mekelweg 2

2628 CD DELFT

The Netherlands :Phone:015 7B6882

Summary.

Nomenclature.

i. Introduction.

Experiments.

Calculations..

Discussion of the resu1,ts 4.. I. Added resistance.

4.2. Hydròdynamic coefficients.

Conclusions and recommendations.

Acknowledgements.

References.

Appendix.

ADDED RESISTANCE AND VERTICAL HYDRODYNAMIC COEFFICIENTS OF OSCILLATING CYLINDERS AT SPEED

by

W. Beukeiman

Summary :

With a rectangular and triangular cylinder forced oscillation

tests ïn the vertical mode. have been cairièd out fór two

speeds of advance. The added resistance due to oscillation has been measured while at the same time the hydrodynaiuic coeffi-cients have been derived from the measured vertical forces. The results have been compared with computations for both resistance increase and the hydrodynamïc coefficients.

it appeared, that the resistance increase is very small and not comparable with the predicted values. The diff:erence between experiment, and calculation for the hydrodynarI c coefficients has shown to be very small for the triangular cylinder, but very large for the damping of the 'rectangular cylinder.

Nomenclature.

A,B,C,D,E,G hydrodynamlc coefficients of the equations

a,b,c,d,e,g J of pitch and heave respectively.

B beam

wctcri.r,

CB block coefficient

Fn Froude number

g acceleration due to graiity

H. depth

k vertical longitudinal radius

yy

of inertia of model

L' effective length of model

L length of model

rn added mass

T draught of model

Te period of oscillation

V forward velocity

V vertical relative velocity with respect

to the water

Xb,yb,Zb right hand coordinate system fixed to the

model with the origin situated in the water-line of the model and the port side positive half width of waterline (z=O)

z heave displacement

phase angle

V volume of displacement of model

We circular frequency of oscillation

p density of water

e pitch angle

Subscripts

a amplitude of d'enoted parameter

Superscripts

i. Introduction.

In the past extended oscillation tests have been carried out by

Ueno et aL [1,2,3,4,5] , to determIne the added resistance for

different ship models and for several modes of motion. These authors refer to the calculation method of Maruo [6 ] for the determination of the part of the added resistance in waves due to t'he ship's oscillations only. Also Goeman [7] performed a ver-tical oscillation test with a ship model to measure the added re-sistance.

Many experiments have been carried, out with respect to the resistance increase of a ship model in waves. Measurements and a simple calculation procedure for the determination of the added resistance in waves have been presented by Gerrit:sma and

Beukel-man in 8

With respect to the determination of the hydrodynamic coefficients many oscillation tests have been carried out from which the

great majority was related to models of ships [9,10,1]].

Only a few number of oscillation tests have been performed for cylinders, so for the two_dimensional case. These experimeñts were mostly restricted to zero speed of advance. For this case it is important to mention the work of Vugts [12] whose tests are related to cylinders with different beam/draught ratio's for circular, triangular and Lewis-form cylinders.

For rectangular sections the experiments of Keuning and BeUkelman

[13] may be used Their oscillation tests with a barge at zero

speed delivered hydrodynamic coefficients for both deep and shallow water.

For two-dimensional shiplike bodies oscillation tests at shallow water have also been carried out by Takaki [14]

The methods for the calculation of vertical hydrodynamic

coeffi-cients for a ship at speed are well-known [1.0,15,16] and mainly

based on the work of Urs-eh

[17]

for oscillating cylinders in

a free surface.

The main purpose of this work ïs to measure the added resistance

due to vertical oscillation for _{a rectangular and triangular}

clinder at speed, for_whi.ch_dïffersnt_types of damping may be

from a calculation procedure based on the method resented

in

[15]

Furthermore the verticb.l hydrodnaIic coefficient's have been

derived frOm the hydrodynamic forcesa Comparïson with' the

calcuia'tèd' rsu1t's shöws the difference in damping, the ïnfl'uenc.e

of speéd., amp1iüde of oscillation and form of the cylinder on these 'oefflcients.

2. Experiments.

For the experiments two cylinders consisting of polyester reinforced plate had been manufactured.

One of these cylinders had a rectangular transverse section and the other a triangular, one. An. equal section form was maintained over 2 rn, while fore and :af t the ends had a length of '0.2.5 m. At these ends the breadth was linearLy reduced to

zero. For the dimensions of these cylinders see table i and figure 1.

Table i.

The length L' may be considerdd as the effective length for determination of thè F'roude number and the dimensionless hydrodynarnic coefficients.

The models have been forced oscillated by the PMM (Planar Motion Mechanism) for vertical motions as described in [ 9] The models were connected to two rods of the oscillator by means of two strain gauge dynamometers for each rod.. One of these dynamometers was sensitive in only the vertical direction while the other was sensitive in the horizontal direction for the determination of the resistance.

Two speeds of advance for both cylinders were taken into con-sideration viz.. y = .0.74.3 and 1.238 rn/s.. FO the'rectangular and for

the 'tr...angular cylinder...withFn'=- 0.16 and'0.-2'7. . .

Rectangular cylinder Triangular . cylinder L . 2 .50 rn 2'. 50 rn B 0.2.5 m 0.25 in 0.

25

p _. I rp T 0.1.5 m 0.15 m H 0.25 rn 0.25 m V . 0.8438 m3 0.2419 ni3 kyy/L 0.2,5 0.272 L' 2.33.3 m 2.167 in

4

= 3,5,7,8,10 andi:2

TheTfoiiowing circular frequencies were djus.ted for the heave

and pitch oscillation

The amplitude of oscillation was for heave

r ₌ °°'Ê .0.02 and 0.03 ni and for pitch

r 0.01 and 0.02 ni

At first the stili water resistance R had been measured for

both cylinders as shown in f 1g. 2 and 3.

Afterwards the models were forced to carry out a heaving and pitching oscillation for the above mentioned frequencies and amplitudes. For these situations the total resistance RT had been measured and after reduction of.the still water resistance

the added resistance RA could be established.

The measured. values for the added. resistance are. for both cylinders. shown in. fig. 4 - 11.

The measured: vertical förces were reduced into an in-phase.

component and. a 9.0. degrees out-of-phase component with. .thê adjUsted motion by means of an. analoque-Fourier-transformer, mechanically

linked with the osciliatòr.

rom these for.ce components and the known particulars of the

model the hydrodynamic coefficients could be. derived as denoted in appendix 1.

They are shown in a dimensionless way for both cylinders in fig. 12 - 25.

3. Calculations.

According to t8 it should be possible to determine the added

resistane for a ship oscillating instill water. This.method is based on the principle that the energy radiated by the damping 'waves is equal to the energy performed by the added resistance

to maintain the adjusted speed of advance.

Thé following general equation should therefore be used:

RAVT

fjT

b'V2dtdx

in which:

the relative vertical speed of across. section Xb is given by:

V =V

cos(.wt+)=-Z _Za e y and: + VO (2) added resistance T = oeriod of o:scillation e

-b' =

N' - V- = the sectional damping

b

coefficient at speed

N' the sectional danìping, coefficient for zero speed

Z = Z COSWt

= the heave motion

O =. O Öosw t = the pitch motion

a e

From (1) follows 'the added resistance for the general case of oscillation:

RA = ½V

f

b'.v2 dxb

.

.

According to appendix i it may be evaluated from (3) that for a pure heave oscillation the added resistance will be:

2 2

w. z

e a

b

"A - '2V

in which b = the damping coefficient for heave of, the total

model at speed..

In

the .sarne-wa-y--the-added-re

sis-ta.nce-f-or--the_pu-re'_p.itch:ing_ösc.i.l.la-tion

may be dètived from f3 as shown in appendix i--and

ïs-written-then as:

-6

RA ₌

3

w2 (B + 2VD + V2b}

in which:

B thedamping coefficient for pitch

D = the mass. coupling, coefficient for pitch

The calculations of the added resistance have been carried for

the pure hèave- nd pitch oscillations in agreement with '(4) and

(5). These calculations were related to both the calculated and measured hydrodynamic coefficients.

The results for 'both cylinders are shown in fig. 4 - li.

wIth respect to the calculation of, the hydrodynaiT. ic coefficients

reference should be made to E1'5 where a thet'hod is presented

to determine these coefficients for two versions according to the. strip theory.

The expressions for the different hydrodynamic coefficients

according to i5], are presented in appendix 2.

The calculated. hydrodynamic coeffïcieitsare:'for both cylinders and both ver.s'ons shown in fig. 12 '- .23.

4. Discussion of the results.

4.1. Added resistance.

The calculated and measured added resistance have been plotted in two ways:

a. dimensionless as

rzpg',iL frequency parameter:

See fig. 4 - 7.

on basis of the dimensionless

b. as a percentage of the measured still water resistance, so

RA _L

- x 100

also on basis of the frequency parameter w

-R3 g

For these results see fig. 8 - 11.

The experimental results for added resistance show remarkably low values with one exception for the case of pitching at the lowest speed.

Table 2 gives an impression of the average measured resistance increase as a percentage of the still water resistance for both cylinders and speeds.

It is quite clear that the highest values may be expected at the lowest speed, because of the relatively low still water resistance. Comparison between measured and calculated values shows unreasona-bly high differences. Evidently one should establish that the

flow of energy is directly from the oscillator into the radiated damping waves so that no resistance increase will be caused. The small values which have been observed may be due to non-linearity because of viscous -i-nf1uence.

Table 2 _{RA 1000}

/RSx

Heave Pitch Fn=0.16

Fn=Q26/027

Fn=0.16

_Fn=°26/O27

Rectangular cylinder Triangular cylinder 2.1 0.9 -0.4 0.1 7.4 8.6 2.4 1.3

8

The same tendency has been observed by Goeman. 'in

6]where

no,

sometimes even small negative added resistance was found with a ship model forced oscillated in still water. This model was

equal to the one described

in8]with high added resistance in

waves.

This all means that it is impossible to determine the oscillatory part of the added resistance by means of forced oscillation of

ship models. Therefore it is worthwhile to consider the measured results of peno L1Ê2,3,4,5J in this respecta

The deviation between the values of added resistance determined with calculated - and experimental hydrodynamic coefficients is very significant for the rectangular cylinder and is caused by the high viscous dámping for this cylinder as shown in figa 18.

4.2. Hydrodynamic coefficients.

For added mass and the cross coupling coefficients for added mass

it appears. from fig.. '12 -. 17 that in general there. is a. good.

agreement for both cylinders between experiment and calculation. The strongest deviation but stili rather small could be established for the.rectanguiar cylinder with. respect to the added mass moment... of inertia.

From the figures.. also.. follows, no preference: for one of the two versions as result of comparison with the e.xperiments.

Furthermore. it appears from. the figures that there is a good proportionality for added mass with respect to amplitude. of 'oscillation.

The speed influence has shown to be negligible.

Considering the damping of the rectangular cylinder it is clear 'from fig. 18 and 20 that there is no question of any agreement

between experiment and calculation as already said before.

Also a rather strong proportional influence of the amplitude of oscillation may be observed from fig. 24-25 at lower speeds. Damping increases with the amplitude at increase of frequency of oscIllation. The viscous darnpihg' because of the sharp edges of the rectangular cylinder appeared to' be mos:t important.

The'spe'ed. influence is also rather significant for the rectangu-lar cylinder and may be characterized a's 'an .inci'ease with speed. In general it may be observed from fig. 26 that for the rectangu-lar cylinder the experimental data tend to the calculated curve, so the potential dampingif t'he amplitude of oscillation an.d

This phenomenon is in agreement with the calculated and measured

values presented.in [12j arid [13]for a pontoon at zero speed and

deep water.,

In a reversed way one may put it so that for the rectangular

cylinder the viscous damping i.ncrea:se with amplitude of oscillation and forward velocity squared (fig. 24 - 25 - 26).

The agreement between èxperimen't. and calculation for the damping cross..coupling coefficient is somewhat 'better than for the damping coefficient 1h the case of the rectangular cylinder, see f igo

22-23. The proportionality with amplitude, and frequencyof

osóillation is also smaller than for the. normal damping coefficient

as: shown in. fig.. 24-25.

With respect to 'the triangular cylinder a nice agreement between experiment and calculation could he observed, fo,r the damping at heave from fig. '19. It is obvious that for this case t'hee is only poten'al damping and almost no viscous influence.

The proportionalityo damping with amplitude is very small for

the whole frequency range.

For pitch. the agreement between measurements and calculations is.,,

worse just a for the damping cros,s coupling coefficients as shown

in fig. 21-23.

It is remarkable tiat the damping cros:s coupling coefficients show a better agreement between experiment and calculation for the, rectangular cylinder than for the triangular one.

Concerning: the speed' influence it is clear from fig. 18-19 that for the triangular cylinder t:here is a small decrease of damping with speed just reversed 'in tendency as, for the rectangular cylinder.

lo

-5. Conclusions and recoinmendat ions.

From the preceeding experiments and calculations the following

conclusions and recommendations may be derived with respect to the added resistance due to forced vertical oscillation and with réspect to the hydrodynamic coefficients:

1. Almost no or only a small adde. resistance may be measured for a model forced oscillated at still water, which values

are not comparable with those ¿f the calculations and those

measured in waes.

2 The 'f icw of energy appears to be directly from the oscillator

into the damping waves so that no resistance increase arises. The measured and calculated values of added mass and the

mass cross coupling coeffici'ent are in good agreement.

The results of the experiments and the calculations agree- very well for the damping coefficient of the triangular cylinder, which means that' for thi's 'case viscous influence. J.s almost'

negligible.

The measured damping coefficients of the rectangular cylinder are véry high in comparison with the calculated values with 'a strong proportionality related to the amplitude at: the

higher frequencies and' lower speeds.

The.large differences between measured and calculated damping coefficients for the rectangular cylinder should be due to viscous influence on account of the sharp edges.

(J

7. The speed influence is mainly measured for the damping coeffi-cients with a strong increase with speed for the rectangular cylinder and a moderate decrease with speed for the triangular cylinder.

The viscous damping for a rectangular cylinder increases with the amplitude of oscillation and with forward velocity squared. The damping cross coupling coefficients for the rectangular cylinder show a better agreement between experiment and

cal-culation than those of the triangular cylinder.

lO.it should be valuable to gain a better insight in the flow

of energy with respect to the added resistance of ship in waves.

The author owes a great debt to the various, members of the staff of the Ship Hydroinechanics Laboratory of the Deift

University of Technology for their assistance n running and

conducting the described experiment.Speciai thanks are due to mr. A. y. Strien who carried out the experiments.

7. References.

Ueno, K. 'et ai,

Some experimentá of heaving effect on aheàd re's'stànce of ships,

Journài of the Society of Naval Arôh'itects of Wést Japan, No. 37, February 1969 and 12th ITTC, p. 112, 1969.

I]

2]

t

Ç6]

12

-Ueno, K.et ai,

Some experiments of pitching effect on ahead resistance of

shi.ps,

Journal of the Society of Naval Architects of West Japan, no. 37, February 1969 and 12th ITTC, p. 114, 1969.

Ueno, K. et al,

Some experiments of yawing effect on ahead resistance of ships,

Journal of the Society of Naval Architects of West Japan, No. 23, March 1962.

Ueno, K. et al,

Further experiments of yawing effect on ahead resistance of ships,

Journal of the Society of Naval Architects of West Japan, No. 27, March 196;4

UenoÉ K. et al.,

Some experiments of roiling effect on ahead resistance of ships,

Journal of the Society of Naval Architects of West Japan, no. 31, March 1961.

Maruo, H.,

On the increase of the resistance of a ship in rough seas, Journal of the Society of Naval Architects of' Japan, no. iOi

1.957.

[7]

Goeman, A.,

Weer.stan'ds- en voortstuwingsproeven met een nLodel van de S.A. van der Stel osc'illerend in vlák water (in Dutch), Ship Hydromechanics Laboratory of the Deift University of Technology, report no. 402, July 1974,.

Grr:itsma, J. _{and W. Be.ukelman.,.}

Analysis of the resistance increase in waves of a fast cargo ship,

International Shipbuilding Progress, vol. 19, no. 2.17, 197.2 and 13th ITTC, vol. 2, 1972.

Grritsma, J. and W. Beukeiman,

-The distribution of the hydrod.ynamic frces on :a heaving and pitching. ship model in stil watér,

Fifth Symposium Naval Hydrodynamics, 1964..

[io] Gerritsma., J. and W.

Analysis of the. modified stri,p theory for the, calcUlation of . ship motions and wave bending moments,.

rnternational Shipbuilding Progress., voI. 14,

no. 1.56., 1.967.

Beukelrnan, W.,

Pitch- and heave characteristics of a destroyer, international Shipbuilding Progress, no. 192, 1970.

The hydrod:ynamic coefficients for swaying, heaving and. rolling oyiinders in a free

surface,-Netherlands Ship Research Centre TNO, Report no. 112S,

May 19 68..

Keuning, J..A. and W. Beukelman,

Hydrodynami.c coefficients of rectangular barges in shailow water,

Second' inteinational Conference -on Behaviour of Off-Shore. Structures (BOSS'79), August 1979, voi. 2, paper 55-.

[14] Takaki, M.,

Wave induced forces and moments as acting on the two dimen-sionai bodies oscillating in shallow water,

Res. Inst.. f Appi. Nech., Kyushu Universi.ty,Japan, vol. 25

14

-15 Gerritsma,J, W. Beukeiman aiidC.C.. Glansdorp,

The effect df beam on thehydrodynamic 'characteristics of

ship hulls,

Tenth Sympos'ium Naval Hydrbdynamics, 1974.

16] Salvèsen, N., E.O. Tuck and O. Faltinsen, Ship motions and sea loads,

Tran'sàctiOfls of the SNME, 1970.

UrseIl, F.,

On the heaving motion of a cIrcular cylinder on the surface of a fluid,

Quarterly Journal of Mech. and Appi. Math.,

We

Ib.

Further evaluation yields the general expression for the added resistance due to oscillation:

RA =

f

b' V

dcb

For pure heave oscillation it holds that in (2):

O

= c =

O so that

VZ = _W _Z

a

ea

Obviously the added resistance due to pure heave oscillation may be written as: W2Z 2

e a

2V 2

e a

2V Appendix I.

As generai equation for the added resistance due to oscillation

is given:

RAVT

fe

b'V2dt

dxb

(1)

Lo

and with:

V VZaCOS

et + c)

=

-

XbU + VO

(2)

follows:

RVT

=

/

¡b'

VCOS2Wt

Cv)d(Wt + c)

y

2

dx

Z b

J

b'dx L b (4)

For pure pitch oscillation it holds that

in

(2) Z = O so that

VCOSC

=

V

_za

s1nc

_y

= X

bea

Q

or:

from which fóllows:

V _{= eXb0'a)} 2 + (V0'):'2

Substitution 'f (6) into (3) dëiivèrs for the:, added resistance die to pitch oscillation:

with: and' RA =

02

a 2.V 16

-e2 / b'xb dxb + V2 ¡ b'dxb)

= (7)

b' '= N' - V (see 3') and thé hydrodynami'c coefficients.

B

¡NXb2d,b

- 2V

_fm'xbdxb

- V _xb2dxb

D J rn" _{Xb dX}

L

it is pössible 'to reduce '(7)' 'to:

.RA

02

je2 + 2VD) + V2b ( 5')

This expressïon. is valid for both versions. as. presented in appen'-:

dix '2.

Appendix

For convènience the hydródynamic coefficients, as they are. derived

in appendix I of [15] for both mentioned versions are presented

here: Heave a =

!m'

dxb +

[ç ¿'

dx].

L

b

J

(N' - V ) dxb L h c = 2pg

wb

=

Im'

_xbdxb +

[r

f

-

XdX]

e

f

N'xbdxb - 2V

f

m!dxb L

f dN'

L L dxb 2pg

J

XdX

L Pi.tdh A = fmtxb2clxb

+[2]_Y-r

f+J7

_'e

b [L. L _ç

J

= i N'

xbdxb - 2V

_J

_.mxbdxb L

rV2

_{f dN'}

L - L L b Xb dXb. = 2pg y xb2dxb D

_fm'xdxb

+

C

E = N' x1.. dx V L u b L dxb G. 2.pg

J

;z X

dx

J N'

L fN ' dxb _-

_{;:- /}

dxb + V2

T

e

xbdxb

+ xbdxb + L xbdxb + V ,, din' L b b]

- 18 -'

When the terms between the brackets are left out one f in.ds the hydrodynamic coefficients according to version 1; if not these coefficients according tö version 2 are presented.;

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