Results of recent full scale seakeeping trials

Shipbuilding

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E X E C U T I V E E D I T O R S

Prof.ir. N . D I J K S H O O R N . Extra-ordinary Professor, Depart-ment of Shipbuilding and Shipping, Delft University of Tech-nology, The Netherlands.

Prof.ir. J . G E R R I T S M A . Professor, Department of Shipbuil-ding and Shipping, Delft University of Technology, The Netherlands.

Prof.Dr.Ir. J . D . V A N M A N E N . President, Netherlands Ship Model Basin, Wageningen, The Netherlands.

Ir. W. S P U Y M A N . Organization for Industrial Reseaich T N O , Delft, The Netherlands.

H O N O R A R Y C O M M I T T E E

Prof.ir. G . A E R T S S E N . Professor, Department of Naval Architecture, University of Ghent; President, Centre Beige de Recherches Navales, Belgium, (retired)

J . D I E U D O N N E . Ingénieur Générale du Génie Maritime; Membre d'Honneur de l'Institut de Recherches de la Con-struction Navale, Paris, France, (retired)

Prof.Ir. H . E . J A E G E R . Professor, Department of ShipbuU-ding and Shipping, Delft Univeisity of Technology, The Netherlands, (retired)

Prof.Dr.Ir. W.P.A. V A N L A M M E R E N . President, Netherlands Ship Model Basin, Wageningen, The Netheriands. (retired) Prof.Dr.-Ing. H . V O L K E R . Head Department of Naval Archi-tecture and Marine Engineering, Technical University, Vienna Austria, (retired)

I N T E R N A T I O N A L E D I T O R I A L C O M M I T T E E A . A N D R E O N I , Eng. Instituto de

Pes-quisas Technológicas, Naval Engineering Section, Sao, Paulo, BrasU.

Dott.Ing. G . B R I Z Z O L A R A . Admini-stratore Ing. G . Brizzolara & C , Genova; Consulting Naval Architect, Italy. Prof. J . B . C A L D W E L L . Professor, De-partment of Naval Architecture and Shipbuilding, The University of New-castle upon Tyne, Great Britain.

Prof.Dr.Ing. E M I L I O C A S T A G N E T O . Head of the Department of Naval Ar-chitecture, University of Naples, Italy. Prof.Dr.Ing. J E R Z Y W. D O E R F F E R , B. Sc. Technical University, Gdansk, Poland.

Dr. H . E D S T R A N D . General-Duector of Statens Skeppsprovningsanstalt, Göte-borg, Sweden.

J . G O R D O N G E R M A N . Partner German & Milne, Montreal, Canada.

Ing. A N T O N I O G R E G O R E T T I . Assis-tant Manager, Fiat Division Mare,Torino General Manager Grandi Motori Trieste, Fiat-AnsaldoG.R.D.A., Italy.

Prof. J . H A R V E Y E V A N S . Massachu-setts Institute of Technology, Depart-ment of Naval Architecture and Marine Engineering, Cambridge, U.S.A. Prof.Dr. J.W. H O Y T . Mech. Eng., Rut-gers Univ., New Brunswick. N.J., U.S.A. Prof.Dr.Ing. K . I L L I E S . Technical Uni-versity, Hannover, University Hamburg, Germany.

Prof.Dr. Eng. T A K A O I N U I . Faculty of

Engineering, University of Tokyo, Japan. Prof.Dr.Techn. J A N - E R I K J A N S S O N . Professor of Naval Architecture, The Technical University of Finland, Ota-niemi-Helsinki, Finland.

Prof.Dr. I N G V A R J U N G . Professor of Thermal Engineering, Institute of Tech-nology, Stockholm, Sweden, (retired). H . D E L E I R I S . Ingénieur Général du Génie Maritime, Paris, France.

Prof. J . K . L U N D E , B . S c , M.Sc. Chal-mers University of Technology, Sweden. S.T. M A T H E W S . Section Head, Ship Section, National Research CouncU, Ottawa, Canada.

Prof. L . M A Z A R R E D O . Director, The Shipbuilding Research Association of Spain, Madrid, Spain.

Prof. S. M O T O R A . Professor, Faculty of Engineering, University of Tokyo, Japan.

Prof.Dr.Techn. C.W. P R O H A S K A , Ship-building Department, Technical Univer-sity of Denmark, Copenhage; Director, Hydro- and Aerodynamics Laboratory, Lyngby, Denmark.

Prof. C E D R I C R I D G E L Y - N E V I T T . Pro-fessor of Naval Architecture, Webb Insti-tute of Naval Architecture, Glen Cove, New York, U.S.A.

Prof.Eng.Dr. S A L V A T O R E ROSA.Pro-fessor of Naval Architecture, Escola de Engenharia of Federal University, Rio de Janeiro; Vice-President, BraziUan Society of Naval Architecture and Marine

Engi-neering S O B E N A , Brasil.

Prof.Dr. A R T H U R S A R S T E N . Institute of Internal Combustion Engines, Norges Tekniske Högskole, Trondheim, Norway. Prof. K A R L E . S C H O E N H E R R . Consul-ting Naval Architect; Former Technical Director, Hydromeclianics Laboratory, David Taylor Model Basin (present U.S. Naval Ship Research and Develop-ment Center), Washington, D . C . ; Former Professor of Engineering Mechanics and Dean, College of Engineering, University of Notre Dame, Indiana, U . S . A .

Prof.Dr. H . S C H W A N E C K E . Head, De-partment of Naval Architecture and Marine Engineering, Technical University Vienna, Austria.

Prof.Dipl.Ing. S. S I L O V I C . Professor of Naval Architecture and Superintendant of the Ship Research Institute, Univer-sity of Zagreb, Yugoslavia.

Prof.Dr.Ir. W. S O E T E . Professor of Strength of Materials, University of Ghent, Laboratory for Strength of Ma-terials, Ghent, Belgium.

Dr.Ing. L O R E N Z O S P I N E L L I . Manag-ing Director, Registro Itahano Navale, Genova, Italy.

Prof.Dr.Eng. S H I N T A M I Y A . Institute of Structural Engineering, University of Tsukuba,Japan.

A. T O W L E , M . S c , C.Eng., F.I.Mech. E . Technical Director, Lubrizol Limited, London, Great Britain.

278

RESULTS OF RECENT F U L L S C A L E SEAKEEPING TRIALS by

Prof.ir. J. Gerritsma*

1. Introduction

During the last fifteen years the Delft Shiphydro-mechanics Laboratory has carried out seakeeping tests with a number of different ships. These activities star-ted after the Intemational Towing Tank Conference in

1963 which recommended to carry out:

'Accurate full scale data under conditions suitable for analysis to be used for correlation with model tests'.

In following conferences the ITTC did not continue the recommendation, or a similar one. I t could have been a general view that suitable conditions at sea are hard to find, or that the measuring or analysing methods were not sufficient for correlation purposes. Partly this is true according to our experience, but i t is also necessary to know where we fail and to what extend, for instance, standard sea spectra are reahstic for the comparison of computed seakeeping behaviour of alternative designs. Measured sea spectra show some-times double peaks and cross seas, resulting from sea and swell having different directions are quite often observed. Such sea conditions differ considerable from standard sea spectra.

Some of our seakeeping tests have been carried out in collaboration with the Dutch Navy, and this coop-eration had the advantage of more flexability in choos-ing suitable sea conditions and the possibihty of pick-ing up expensive wave measurpick-ing buoys. For economic reasons there are almost no possibilities in this respect on merchant ships and in general no drastic deviations in the ship's course are allowed to meet a desired re-lative wave direction.

A seakeeping trial with 'HM Groningen', a destroyer of the 'Friesland' class, has been carried out in 1965 (partly due to the 1963 ITTC recommendation), to compare measured motion amphtude response operat-ors with corresponding results of model tests and cal-culations. A prototype of the so called 'Waverider' wave buoy was available, which needed very careful handling, but provided satisfactory wave measure-ments. A second trial was carried out with the

'tic Crown', a fast container ship, on the North

Atlan-tic Route. A similar comparison of f u l l scale data with calculations and model experiment results was plan-ned, but this time the sea conditions and a fixed route on the North Atlanric as dictated by the ship's duty had to be accepted.

*) Delft University of Technology, Ship Hydromechanics Laboratory, Report No, 4 9 5 , Delft, The Netherlands.

It was also tried to determine the increased power due to wind and waves, because this was of interest for a project conceming the determinadon of sustained sea speed for optimal routing purposes. Increased resist-ance in a seaway is very important for large fast ves-sels, ( i - 200 m), because these ships reduce power much later than smaUer cargo ships.

For the tests with the 'Atlantic Crown' a disposable wave buoy has been developed by the Delft Shiphydro-mechanics Laboratory, which can be launched at high forward speed and from a considerable height, and in-dependent of the service duties of the ship.

In the case of 'HM Groningen' a reasonable long crested sea could be found, but during the 'Atlantic

Crown' trials the waves were certainly not

unidirec-tional and the main direction of the waves was hard to detect in some cases.

A third series of seakeeping trials has been carried out with the Oceanographic research vessel 'Tydemon', to measure ship motions in oblique waves. For the

'Groningen' and 'Tydeman' trials suitable areas could

be chosen and the ship could follow prescribed courses to meet waves from desired directions. The 'Tydeman' trials were carried out in 1978 (March and December). In both cases we had valuable assistance f r o m the Fleet Numerical Weather Central in Monterey, who send us wave forecasts for the trial areas, which could be com-pared with the measured waves at the considered locations.

A fourth series of f u h scale experiments concerned the container vessel 'Hollandia' to investigate the feasibility of a so called Operarional Performance System, carried out under supervision of the Nether-lands Maritime Institute by Lloyds Register and Delft. In this system the ship is considered as a wave height meter. By measuring continuously one or more mo-tion components as an input to a computer on board the ship containing the motion response operators, an estimate of the encountered significant wave can be made and any other motion amphtude or wave load parameter can be produced as output of the system. This system is designed as an aid f o r the captain to indicate dangerous wave loading of the ship.

In the procedure a number of assumptions is involved and therefore a check of the method in actual sea con-ditions was considered necessary.

In the following paragraphs the various trials and their results wiU be presented in somewhat more detail. It has to be emphasized that the results of this

work are not always satisfactory, due to the incom-plete information of the seaconditions.

2. 'HM Groningen'

The f u l l scale tests were conducted in 1965 on 'HM Groningen' of the Royal Netherlands Navy. This des-troyer was selected because of the large amount of seakeeping data already available from previous trials. A ship of this class was previously tested in the com-bined United States - The Netherlands seakeeping comparison trials as reported by Bledsoe, Bussemaker and Cummins [ 1 ] . The trial area was to the west of Marocco and Portugal.

The main characteristics of the 'Groningen' are summarized in Table 1.

Table 1

'HM Groningen': main characteristics of ship Length overah 116.00 m

Length between

perpen-diculars 112.40 m

Breadth 11.74 m

Draft 4.01 m

Displacement 3070 ton Blockcoefficient 0.563 Midship section

coef-ficient 0.827

Waterplane coefficient 0.801 Longitudinal radius of

gyration 26.2 m

Based on visual observation the wave conditions in the trial area looked rather good: a longcrested sweh which, apparently had only a small directional spread. Seven runs in head seas were carried out with speeds ranging from 11 to 28 knots in waves with significant heights from 2.5 meters to 5.5 meters and periods from 10—14 seconds.

In those days not everybody was convinced of the practical usefulness of linear strip theory and also scale effect was mentioned from time to time.

Fuh scale results with a scale ratio of 1 : 40 with re-gard to model tests, could reveil any significant scale effects i f present, but for such a comparison the ac-curacy of the f u h scale experiment is obviously a major factor in determining the validity of the correlation. For the greater part the accuracy of the comparison depends on the possibihty to measure the wave condi-tions and in particular longcrested waves are preferred because directional spread of the wave energy could not be measured with the available wave buoy which only measures the vertical displacement of the wave surface. Motions spectra were obtained for heave and

pitch and with the measured wave spectra the am-phtude response functions could be obtained, assuming unidirectional waves. The spectra for one particular speed are given as an example in Figure 1.

RUN 19 Fn = .28

Figure 1. Wave and motion 'HM Groningen'.

The response amplitude functions as derived from the motion and wave spectra are compared with model values and the results of calculations, see Figure 2. The agreement is satisfactory, although some scatter of the fuh scale values is present, in particular in the low frequency range [ 2 ] .

It should be emphasized that these rather ideal sea conditions could only be found because a Navy ship was available, which was able to spend some time in search for such wave conditions with the help of an oceanografie expert.

280

RUN 13 R U N 7 RUN 15

F n = .36 V = 2 2 . 9 1 K n . F n = .37 V=24.11 K n . Fr\ = M V = 2 8 . 1 6 K n .

0 0.5 1.0 1.5 2.0 0 0.5 1.0 1.5 2.0 0 0,5 1.0 1.5 2.0

Figure 2. 'HM Groningen'. Comparison of full scale measurement, model experiment and calculation.

From later experience i t appeared that we have been very lucky to find such wave conditions.

However i t is not very satisfactory that the result of an experiment depends so much on luck.

For a continuation of the seakeeping trials the Delft disposable wave buoy has been developed, the wave rider buoy being too expensive and to delicate to handle, see Figure 3.

The spherical buoy has a diameter of 0.4 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. The length of the wire de-pends on the expected wave lengths, which have to be measured. In a seaway the buoy fohows the wave surface with sufficient accuracy and the stabilizing system keeps the buoy in a vertical position within a few degrees.

The buoy is equipped with an antenna and transmits a frequency modulated signal of the vertical

accelera-tion to the ship. The vertical displacement is found by numerical integration of the digitized acceleration recording. The effective range of the transmitter is limited to about 9 - 2 0 miles depending on wave con-ditions. The transmitting power is 1,5 Watt. The card board cyhnder on which the steel wire is stored before and during launching appeared to be one of the most important parts for the satisfactory operation. The total weight of the buoy is about 250 Newtons and launching is possible in almost every weather condi-tion by two people as shown on several occasions [ 3 ] .

3. 'Atlantic Crown'

During a voyage of the container ship 'Atlantic

Crown' in 1972 the Delft buoy proved to work

satisfactory under adverse conditions on the North A t -lantic. Heave, pitch and waves have been measured as weh as torque, revolutions speed and power and also wind, because wind resistance of containerships can be

Table 2

Container ship 'Atlantic Crown'

Length over ah 212.42 m

Length between perpendiculars 196.00 m

Breadth 28.00 m

Draft 8.15 m

Displacement 26708 ton

Block coefficient 0.576

Midship section coefficient 0.969

Waterplane coefficient 0.724

Longitudinal radius of gyration 50.12 m

Figure 3. Delft wave buoy.

quite substantial. The main dimensions of the ship are given in Table 2.

Three runs have been analysed and the results in the form of measured and calculated response spectra for heave and pitch are presented in Figure 4 for one typical run. The calculated responses are based on the measured wavespectrum, transformed for the ship's speed (V = 16.8 knots). The main direction of the waves with respect to the ship for the data in Figure 5 has been estimated as: n = 150 degrees but the

cal-culations have also been carried out for = 130 de-grees and = 170 dede-grees to show the sensitivity for errors in the estimated wave direction. The correlation between the f u l l scale results and the calculations is not impressive. In particular the determination of response amphtude operators from these data did not seem an useful exercise.

For pitch the computed response spectrum shows a shift towards lower frequencies, but this cannot be explained by a reahstic error in the main direction of the waves. The motions of the ship were rather violent (pitch - 3 degrees. Length 212 meter), and the ship's speed showed very large fluctuations (a few knots). This may be another cause for the observed discrepancies between measurement and calculation. Therefore a more detailed analysis of the motion spectra has not been carried out.

From a calculation i t can be concluded that the in-fluence of heading on added resistance is not very large.

The ship maintained full power (30000 hp.) during this run with a speed drop from 24 knots (service speed) to an average speed of 16.8 knots in head waves with significant height of 7 meters.

In Table 3 the power for wind resistance, still water resistance and added wave resistance are given for the three runs which were analysed.

Except f o r run 4 the prediction of added power due to waves agrees reasonable with the measured values. The calculation of the added resistance in waves is based on the detennination of the work done by the

Table 3

shaft horse power metric units

Run still wind waves total measured diff. knots degrees m water

4 20.6 135 4.1 17987 2139 3710 23836 30600 - 2 2 % 6 23.0 10 2.9 26186 141 1330 27657 30040 - 8% 7 16.8 150 7.1 10279 3089 15089 28457 29600 - 4%

282 75 m^sec SrK)| ^ 5 _ V = 0 m / s e c T R A N S - J n = 1 5 0 ^. v = 8.627 m/fe.c FORMED I (1 = 170° , 7,5 Degr sed Sg (Ue) P R E D I C T I O N V= 6,627 m / s e c • Vsec

Measured wave spectrum for run 7 with spectra transformed Measured pitch spectrum for run 7 and predictions for direction for speed and direction of wave travel fx = 1 3 0 ° , 1 5 0 ° , 170°. of wave travel n = 1 3 0 ° , 1 5 0 ° , 1 7 0 ° .

S,(ü)e)| 5 V = 9,627 m / s e c PREDICTION _<"V3 . ( 1 = 1 3 0 ° Z a , ^ ^ = 3,08m-- H= 1 6 0 ° Z^^^^ = 2 t 9 m , ( 1 = 1 7 0 ° Zo,^^= 2 25m 150 Ton seel V = e.627nysec (1=150° R^^^ =86,7 79 ton (1=170° R^^^ = 80,806 ton ^100 '

Measured heave spectrum for run 7 and predictions for direction Predicted added resistance spectra for run 7 and direction of of wave travel/Li = 1 3 0 ° , 1 5 0 ° , 1 7 0 ° . wave travel M = 1 3 0 ° , 1 5 0 ° , 170°.

\1 r 160° F n : 15 E X P E R I M E N T 0 FUJII ' • NAKAMURA J 5 RAW CfJ 0 11 I 180° / Fn = 20 5 7 0 y , o 1 c 1 2 10 H = 1 5 0 ° EXPERIMEfJT Fn = 15

Figure 5. Added resistance in oblique waves.

damping forces of heave and pitch, using linear stiip theory, which ignores three dimensional effects at the bow and the stem of the ship. The radiated damping energy is set equal to the work done by the force correspondmg to the extra wave resistance. Model results have proved the practical usefulness of this approximation (see Figure 5) also when the influence of lateral motions is not taken into account.

Wind resistance is estimated by using windtunnel tests and the total propulsion efficiency has been es-timated by using propeller data and model experiment results in still water.

The very large amount of power due to waves in run 7 (50%) is noteworthy.

In this particular wave condition there was no volun-tary speed reduction and the prediction of the speed loss due to waves was rather satisfactory. Recent trials with the container ship 'Hollandia' seem also to confirm the method.

The 'Atlantic Crown' trials clearly showed that actual wave conditions may differ considerable from assumed unidirectional waves: from visual observation it was

clear that there was an appreciable amount of direc-tional spreading [ 4 ] .

4. 'HM Tydeman'

'HM Tydeman' is a Dutch oceanographic vessel of

which the main dimensions are summarized in Table 4.

Table 4

'HM Tydeman'; Oceanographic Research vessel Length overall Length on waterline Breadth Draft Displacement Block coefficient

Midship section coefficient

90.15 84.50 14.40 4.75 2977 0.498 0.837 m m m m ton

The 'Tydeman' trials were carried out to measure ship motions in oblique waves for comparison with calculations.

Two sets of trials have been carried out in 1978. In March the Rockall area. West of Scotland was chosen for extensive experiments and a limited ex-periment has been carried out in an area North West of the Azores in December 1978, where a severe storm interfered with the testprogram. A very low air pres-sure has been meapres-sured on that occasion (956 mbar) and a German container vessel 'Miinchen' was lost with all lives several hundred miles from the trial area. Again FNWC provided us with wave forecasts f o r loca-tion near the trial area's.

Figure 6 gives the run program for the March trials and relative wave directions with regard to the ship's course were: 180, 120, 90, 60 and 0 degrees, 180 degrees being the head wave condition.

The main wave direction had to be determmed by visual observation. This has been done by two indepen-dent observers. The difference between the two

es-w a v e direction

buoy location ^

J K Figure 6. R u n identification 'HM Tydeman' trials.

P I J C H RUN NO BC 9 p = 180° H i = 5,6im. b e r : Ü a j = 4.84° gem:5„i. = 4,13--r \ I \ I \

timates was small (approximately 10 to 20 degrees) and checked by radar observation, but this could not be verified by a more objective measurement.

Three ship speed's were considered 6, 9 and 12 knots. During the six 9 knot runs (each appr. 45 minutes) the wave spectrum showed only a slow change to lower wave heights (H^i^ = 5.7 m 4.7 m) whereas f o r the 6 and 12 knot runs the sea looked very confused and bimodal spectra were measured. In total 14 wave spectra, with corresponding motion spectra (pitch, heave, acceleration at the bow) have been measured, but only the 9 knot runs have been analyzed in some-what more detail. In Table 5 the significant motion amphtudes of these six runs are compared with the cal-culated values assuming unidirectional waves and an energy distribution as measured.

The correlation is not too bad, but in the beam sea condition (FG 9) a significant pitch amphtude has been measured and a roh amphtude of 6.1 degrees is found in the head sea condition. In some cases the cal-culated response spectra show quite some differences with the measurements as shown for instance in the Figures 7a (pitch, 180 degrees), Figure 7c (heave, 120

Table 5

Significant values of wave height, pitch, heave and roll amplitudes Run m (m) W Run m 1 2 1 2 1 2 1 2 CB9 0 4.9 3.1 3.3 1.8 1.9 2.8 3.1 6.1 0.0 DE9 60 5.5 2.5 2.8 2.3 2.4 3.0 3.3 11.4 9.0 FG9 90 5.1 2.6 0.2 2.2 2.5 2.9 2.6 9.1 10.7 KJ9 90 4.7 2.3 0.2 2.2 2.4 2.7 2.5 5.9 9.4* HI9 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 1 measurement 2 calculation

* calculated without anti-rolling tank.

degrees), but heave in beam seas is predicted quite weh: Figure 7b (heave, 90 degrees). From the com-plete set of results i t is not clear whether the differen-ces are due to an error in the estimated main direction of the waves or due to directional spreading of the wave components. The wave conditions were not ex-treme for the ship during the March trials.

During the December voyage only the vertical ac-celeration at the bow could be measured due to other commitments for our instrumentation. There is a large difference between the measured and calculated ver-tical displacement of the bow, including an unexplain-ed large peak at low frequency in the measurements. Wave conditions were not stationary because of an approaching storm and significant wave heights in ex-cess of 9 — 10 meters. In the head sea condition the ship speed dropped to very low values and no further experiments were carried out.

In view of the unsatisfactory correlation the in-fluence of a change in heading and of a change in directional spread of the wave energy has been in-vestigated for the March BC9 run.

The pitch and heave response operators are given in Figure 8 as a function of heading, and these were used to see i f a change in heading and the inclusion of a cos squared spreading function could bring the calculation and the measurement closer together. A combination of a 45 degrees shift in the main direction and cos squared spreading improves the correlation for the heave response spectrum and for pitch a shift between 30 and 45 degrees could give an improvement, see Figures 9 a,b,c,d, 11 and 12. This is a rough trial and error method but i t could indicate some of the possible sources of error and show the importance of heading and spreading of wave energy.

It is not impossible that predicted significant motion amphtudes, as given in Table 5, are of practical value and interest, including their differences with measured values, but a more systematic investigation of the wave direction problem seems necessary.

10 3a/ 1 1 1 = 190° 1 = 165° ^ = = 5 1 = 1 50° ~ 1 = 1 3 5 ° " " " " ^ ^ v = 120° = 9 0 ° 1 1 ^ 2.0

%

\

Figure 8. Amphtude response functions for different wave directions.

The 'Tydeman' trials gave the opportunity to check wind and wave forecasts with actual measured values. Figures 10 and 11 show the predictions by FNWC for the period of 15 March — 19 March in comparison with the measured values (location 127). The Figures show that the forecasts are extremely good, also taking into account the quick changes in the weather condi-tions during the time of the year.

A satisfactory agreement is also found for the more difficult prediction of a wave spectrum as shown in the Figures 12 and 13.

286

10

\ HEAVE AT THE BOW

1 RUN B C - 9 Measurement Calcutation M-=180° Unidirectional | I = 1 8 0 °

• - • | I = 1 6 5 ° Cosine squared directional spreading

HEAVE AT THE BOW RUN B C - 9

Measurement Calculation M- - 1 5 0 ° 1

Cosine squared directional spreading M- = 1 3 5 ° ' | I = 1 3 5 ° Uridirectional Se PITCH RUN B C - 9 Measurement Calculation = 1 5 0 ° M- = 1 3 5 ° | i = 1 3 5 ° Unidirectional

Cosine squared directional spreading"

Figure 9. Measured- and calculated motion spectra for different main directions with and without cosine squared directional spreading.

Figure 10, Wind speed. Figure 11. Wave height. 16 March 1978 0 1 1 1 O CB-9 H/s = ABOm 1215 GMT I A FNWC H'/3= 572m

- •

\

J

sec'

Figure 12. Comparison of measured and predicted wave spec-trum CB-9.

'Hollandia'

Wave directions and wave energy spreading func-tions are very important for the 'Hollandia' project. In cooperation with Lloyds Register a feasibility study is made of an Operational Performance System.

With the increase of ship size during the last decades and the corresponding increased distance of an obser-ver on the bridge to the wave surface, i t has become more difficult to estimate the wave conditions by visual observation. On large ships i t is also more

dif-17 March 1978

Figure 13. Comparison of measured and predicted wave spec-trum CB-12.

ficult to sense the response of the ship to various sea conditions, in particular with respect to the magnitude of structural loads. In some quarters it is believed that it would be desirable to have some kind of warning system, based on actual measurements of the ship's response, to provide the ship's officers with relevant information as a base for a decision to reduce speed and/or heading in adverse conditions.

In order to predict the effect of these changes on the ship's motions and stresses it is necessary to have ac-curate information about the sea state and the cor-responding ship response.

For experimental purposes, wave buoys are suitable, but these are not practical for normal ship operations.

288

On the 'Hollandia' an experimental system has been installed to provide a warning capabihty for critical response levels, but also to give information on the effects of changes in speed and heading on the various ship responses.

In the present set-up the system works as follows. Heave, pitch, roh, vertical acceleration forward, and bending stress at the midship section are measured continuously and the recordings are digitized to ob-tain the corresponding spectra by means of a Fast Fourier Transform processor. For each response com-ponent the signals of the last 20 minutes are used and the spectrum determination is carried out each two minutes. From these spectra the significant response amphtude R^^^-m and the characteristic response period T^ —m are calculated, which can be shown on a visual display unit as a function of time.

Than, these monitored response data are used to der termine the significant wave heigth H.^i^ and a charac-teristic wave period T j by using a calculated data base of the ship response. Two assumptions are introduced here:

1. The dominant wave direction can be obtained from visual observation of the sea or from a radar picture. 2. The wave spectrum can be described by the two parameters Pierson-Moskowitz formulation with a cosine squared wave energy spreading function. When these assumptions are not in accordance with the actual wave conditions five different and/or un-reahstic sea state informations from the five measured ship responses whi result.

The calculated response data base, stored in a disk system, consists of significant response amplitudes per

unit significant wave height: '1/3

H

, and of response 1/3

periods Tj^ for a range of wave periods, headings, ship speeds and loading conditions.

With the considered ship speed and loading of the ship and the observed main wave direction a search and interpolation procedure, carried out with a P.D.P. 11/34 computer on board the ship, gives for each measured response the corresponding significant wave height and the corresponding characteristic wave period, as shown in Figure 14. The diagram in this figure is entered with the measured response period to find the characteristic wave period T^- This wave period provides the corresponding calculated signifi-cant response amplitude per unit signifisignifi-cant wave height. With the measured significant response ampli-tude this finally results in a equivalent significant wave height.

The equivalent sea state now can be used to predict the effects of change of heading and change of speed on the ship responses with regard to motions and stres-ses in the construction.

I t is also possible to store data on r.p.m. power and fuel consumption in the data base, to analyse the ef-fect of changes in heading and ship speed on these quantities which are important for the economy of the ship's operation, and in particular for the saving of fuel.

In the Operational Performance System the ship is used as a wave buoy, but many assumptions have to be made for the procedure as described. Three succes-ive trials from Europe to the Caribean have been made on the 'Hollandia' to check the operation of system. A typical example of the recorded wave height and wave period, based on measured pitch, roh, heave, ver-tical acceleration forward and bending stress at the midship section is given in Figure 15. The sea condi-tions on which Figure 15 is based were not ideal for the evaluation of the system, but the results are not discouraging. More favourable sea conditions were met during the last trial in January 1980 and the measure-ments are now being analysed.

^ c a l c u l a t e d )

t2

Figure 14. Scheme of the determination of the equivalent sea state from the response measurements.

lo 5 k ( s e c )

-

Figure 15. Sea state information derived from the ship's responses.

Conclusions

It may be concluded that the influence of the main heading of sea waves and the spreading of wave energy is most important for studying ship responses at sea. A systematic study of the sensitivity of the ship res-ponse for heading and spreading wih therefore be car-ried out, using a six degree of freedom computer pro-gram to calculate shipmotions in oblique waves with certain spreading functions, including conditions re-sulting from two wave systems with an appreciable difference in main direction.

In the 'Hollandia' trials main heading and directional spreading of the wave system are assumed to be known. Probably these assumptions do not give ac-ceptable results in ah cases.

It could be of interest to investigate the possibility to use the ship as a wave height recorder without such a priori assumptions. Computers, suitable for use on board ships, as well as calculation methods for

ship-motions in six degrees of ship-motions are available for this purpose.

A systematic series of full scale trials with one ship during a reasonable long period seems very useful to get more insight in the various problems as mentioned. The results of this research whi be of high value for the profession.

References

1. Bledsoe, M.D., Bussemaker, 0., and Cummins, W.E., 'See-keeping tnals on three Dutch Destroyers', S.N.M.E., 1960. 2. Gerrhsma, J . and Smith, W.E., 'Full scale destroyer

measure-ments'. International Shipbuilding Progress, 1966.

3. Buitenhek, M. and Ooms, J . , 'An updated design of a dis-posable wave buoy'. Delft Shiphydromechanics Laboratory,

1978.

4. Beukelman, W. and Buitenhek, M., 'Full scale measurements and predicted seakeeping performance of the containership 'Atlantic Crown", International Shipbuilding Progress, 1974, Vol. 21, No. 243.

290

ON T H E PARAMETRIC E X C I T A T I O N O F NONLINEAR R O L L I N G MOTION IN RANDOM SEAS

by

M.R. Haddara*

Abstract

The nonhnear equation of roUing motion in random oblique seas is analysed considering parametric excitation caused by transverse stability variation in realistic seaway. Use of Bogoliubov-Mitropolsky's method o f slowly varying parameters together with Stratanovich-Khasminsky's stochastic averaging is made to obtain an equation describing the variance of the amphtude o f roUing motion as a function o f time. The condition for stable motion is then derived. Furthermore, stationary variance is expressed in a closed form.

1. Introduction

Transverse stability variations in waves and non-linear static cross couphng are known to be sources of parametric resonance in ship motion. The phenome-non of parametric excitation in regular waves has been considered by many authors. Grim [ 1 ] and Kerwin [2] investigated rolhng instability caused by transverse stability variations in following seas. While, PauUing [ 3 ] , Nayfeh [ 4 ] and Mook [5] investigated motion instabUity caused by nonlinear cross coupling between roUing and pitching motions.

More recently, the phenomenon o f parametric excitation of linear rolling motion caused by the varia-tion in the transverse stability in random seas has been considered by Haddara [6] and Price [ 7 ] . Haddara showed that the equations describing the mean and variance of roUing motion retain the time-dependent coefficients character which is known to be associated with the parametric resonance phenomenon. I t has been shown also, that unstable motion occurs when the function describing the variation i n the transverse stabüity has large amount o f energy centered around one of the Mathieu's equation frequencies enough to overcome the effect o f damping. Price, on the other hand, showed that stability is govemed by the value of the variance of the function describing the trans-verse stability variations and that stability is ensured i f the variance does not exceed a certain value related to the damping coefficient also.

In the present note, the problem o f nonlinear rol-ling motion in random seas is analysed taking into consideration the effect of transverse stability varia-tion. The approach used in a combination o f the slow-ly varying parameters method of Bogoliubov and Mitropolsky [ 8 ] and the stochastic averaging tech-nique of Stratonovich and Khasminski [ 9 , 1 0 ] . I t is shown that stabüity in this case is related to the spec-tral density of the function describing the variation in the transverse stability evaluated at twice the natural frequency of roUing motion. Furthermore, an expres-sion for the variance in the stationary case is derived.

2. Stability analysis

The rolling motion of a ship sailing in random obhque waves can be represented mathematically in the following form:

^+N((P)+D((P,t) = K(t) (1)

where

(j) is the roll angle,

Af(0) is the damping moment, Z)(0,O is the restoring moment.

Kit) is the exciting moment, t is time,

and dots indicate differentiation with respect to time. A mixed hnear-plus-cubic model is used for damping. This has been shown to be reasonable both quahtat-ively and quantitatquahtat-ively [ 1 1 ] . Also, a nonlinear restor-ing moment which reflects the effect of transverse stabüity variation in random obhque waves is used. Thus, the dampmg and restoring moments are expres-sed as

7V(0) = 2 f w ^ ( 0 + e i 0 3 )

= c o 2 ( 0 + e 2 0 ^ ) ( l + 0 ( 0 )

Since, roUing motion is a narrow barid process, one can assume that

4>= R cosn -I- ey

. (3)

(}) = — nR sinS2 -I-ey

where, n = + 9, = (1 + SejO^), and is the variance of linear rolling motion i n beam seas. I t is assumed that R and 0 are slowly varying random pro-cesses.

From equation (3), one can deduce that

R cosn - è Rsin = 0 (4)

Substituting equations (2) and (3) in equation (1), one finds that for a first order analysis in e, and e j

-nR Sinn - nè R cosQ, - 3 e^Ria^ - y'iR^)cosn -l^u^nRH+YAe^n^R^) s i n f i + Vie^^co^n^R^ *) Suez Canal University, Port Said, Egypt.