Seakeeping experiments

Seakeeping experiments

Prof. J. Gerritsma / University o f Technology, Shipbuilding Department, D e l f t

In the research on seakeeping qualities o f ships, model experiments have proved to be a necessary t o o l to stimulate and c o n f i r m analytical progress. Compared w i t h the classical resistance and propulsion ship-model test i n still water, w h i c h is used to improve the hull f o r m and to predict the power requirement o f newly designed ships, the seakeeping experiment is charac-terized by a larger number o f i m p o r t a n t parameters, such as the mass d i s t r i b u t i o n , the heading o f the ship and the wave dimensions. Consequently i n many cases seakeeping experiments, designed to study systematic variations o f ship parameters and wave conditions, consume too m u c h time to be acceptable f r o m an

economic point o f view. The very few exceptions carried o u t so far proved to be useful m a i n l y to determine the range o f the various m o t i o n responses.

Viscosity is not a dominant f a c t o r i n the m a j o r i t y o f ship m o t i o n problems. Therefore numerical methods based on potential theory could be developed, using the simplification o f the strip theory, because most ships can be considered as rather slender bodies. T h e strip theory, although i n this case based on rather intuitive assumptions, proved to be a very useful tool f o r prac-tical purposes.

Special experiments were designed to verify the sim-p l i f y i n g assumsim-ptions, i n c l u d i n g the linearity o f the p r o b l e m and the corresponding use o f the superposition principle, w h i c h is used to predict the ship's behaviour i n irregular waves.

The experimental determination and the analysis o f the h y d r o d y n a m i c properties o f an oscillating s h i p f o r m i n still water by using forced oscillation techniques was used t o supply essential data to check theoretical results. As far as k n o w n to the author the first forced oscillation test w i t h a ship model was carried out by M . D . H a s k i n d and I . S . Rieman [1]. It concerned the forced harmonic

heaving o f a simple mathematical ship f o r m at zero speed o f advance to determine hydrodynamic damping and mass as a f u n c t i o n o f frequency. Since 1950 similar testing techniques were used and f u r t h e r developed at the D e l f t Sh ip b u i l d in g L a b o r a t o r y , t o include f o r w a r d speed and coupled motions, such as heave and pitch and i n a later stage yaw and sway. D a m p i n g , h y d r o -dynamic mass and cross-coupling terms o f the considered motions were determined by measuring the i n -phase and quadrature components o f the e x c i t i n g forces on the ship model. I n particular f o r vertical motions the results agree satisfactorily w i t h strip theory calculations, using Ursell's method f o r oscillating cylinders i n a free surface [2] and a close-fit c o n f o r m a l t r a n s f o r m a t i o n procedure to cope w i t h the actual cross sections o f the ship [3].

The wave forces could be measured by using a fixed shipmodel i n a regular wave t r a i n . Here the calculation uses the F r o u d e - K r y l o f T hypothesis, which assumes that the wave pressure on the ship's hull is not influenced by the presence o f the ship. A f t e r w a r d s the result is corrected partly f o r reflection effects by t a k i n g i n t o account the relative water velocity and acceleration.

I n this way a more refined experimental analysis o f the merits o f the strip theory could be made than by a direct comparison o f calculated and measured m o t i o n a m p l i -tudes and phases. I n particular the d i s t r i b u t i o n o f the hydrodynamic forces along the length o f the oscillating ship is o f interest. By using a segmented ship model and measuring the vertical forces o n each o f the separate segments the d i s t r i b u t i o n o f the hydrodynamic mass and damping was f o u n d w i t h the forced oscillation technique. One example is shown in Fig. 1. The results revealed an i m p o r t a n t speed dependency o f the d a m p i n g force d i s t r i b u t i o n i n p i t c h and heave w h i c h introduces a hydrodynamic l o n g i t u d i n a l asymmetry. I n this respect

the symmetry properties o f the experimental cross-coupling damping coefhcients conlirmed an analytical result h\ R. T i m m a n and .1. N , Newman for a floating body mo\ ing w i t h constant f o r w a r d speed and perfor-m i n g sperfor-mall oscillations in a free siu-face [4]. Fig. 2 shous the result for a normal cargo ship f o n u .

To study the linearity o f pitching and heaving motions in longitudinal \\a\cs the frequency response functions for three dillercnt cargo ship-forms were determined by three different methods: 1 a direct measurement o f the ship model response in small amplitude regular waves, 2 a calculation o f the frequency response functions f r o m the second order equations o f m o t i o n , using tlie

/

2 3 . I. 5 6

CALCULATION.

EXPERIMENT

Fig. 1 Caiculated and measured disti'ibutions of tfie damp-ing coetficienl /; and the dampdamp-ing cross-coupfdamp-ing coefficient

c of a ship model (fength 2.3 ni).

190

• c J ^EXPERIMENT • E,e CALCULATED

Fig. 2 Damping cross-coupling coefficients E and e as a function of forward speed. Length of ship modef 2.3 m.

experimental determination o f coefficients in the equa-tions and 3 an analysis o f tests i n irregular waves to arrive at the frequency response functions by using spectral- and cross spectral-analysis. The very satis-factory correlation o f the three results showed the applicability o f the assumptions and the use o f second order equations o f m o t i o n although these have frequency dependent coefficients.

I n F i g . 3 a result o f the irregular wave tests is compared w i t h the corresponding values derived f r o m experiments i n regular waves, w h i c h confirms the applicability o f the superposition principle.

A f u r t h e r development concerned the comparison o f the

2 7 0 " 1 8 0 ' U 9 0 ' P H A S E 1.0

"As.

Fig. 3 Frequency characteristics of pitch and heave de-termined by spectral analysis of the motions in irregular waves.

calculated pitching and heaving motions, using no empirical data at a l l , w i t h the results o f model experi-ments and f u l l scale measureexperi-ments at sea.

The ship trials were carried out w i t h a destroyer o f the Royal Netherlands N a v y near the coast o f M a r o c c o , where a reasonable uni-directional swell was f o u n d . The wave spectrum was measured by a floating wave buoy and the corresponding irregular pitching and heaving motions were reduced by spectral analysis to amplitude response functions. A g a i n a satisfactory agreement w i t h the calculated values as well as w i t h the experimental model results was f o u n d .

I t may be concluded that a theoretical prediction o f pitching and heaving motions i n irregular head sea conditions is available f o r practical purposes. Similar w o r k is i n progress f o r the other modes o f m o t i o n , although f o r rolling, f o r instance, i m p o r t a n t viscous effects necessitate the inclusion o f empirical data.

A n o t h e r i m p o r t a n t part o f the seakeeping behaviour is added resistance due to waves. I n the case o f linear motions, theory predicts that added resistance in regular head waves divided by the squared wave amplitude is constant f o r constant wave length and ship speed. M o d e l experiments c o n f i r m this property o f the so called 'added resistance operator' to a certain extent. Con-sequently the mean added resistance in a long crested wave spectrum can be f o u n d by integrating the product o f spectral density and the added resistance operator over the range o f frequencies under consideration. Similar procedures may be used f o r propeller thrust, torque and r . p . m . As an example, F i g . 4 shows the c o m parison o f the predicted and the observed power i n -crease i n a seaway o f the passengerliner ' M A A S D A M ' . The numerical or experimental determination o f ship motions and resistance increase i n specified wave con-ditions can be used to predict the sustained speed o f a ship at sea.

I n adverse weather conditions the ship's speed is reduced deliberately to avoid excessive hydrodynamic impact forces, shipping o f green water, large m o t i o n amplitudes, racing o f the propeller etc.

These phenomenae are related to the ship response due to wave conditions and are to a certain extent predic-table f o r a given wave spectrum. F r o m statistical analy-sis o f ship trials, the amount o f slamming, wetness and 191

racing w i i i c l i is accepted by the commanding officer w i t h o u t speed reduction can be determined i n the f o r m o f realistic probabihty levels. By using such criteria the m a x i m u m ship speed in given sea conditions can be determined. These methods may be used i n o p t i m a l ship r o u t i n g procedures or f o r o p t i m i z a t i o n o f different ship designs w i t h regards to their seakeeping qualities. However, there is still a need f o r f u r t h e r experimental research i n this field, f o r instance to establish i n more detail the relation o f ship motions and the above men-tioned speed l i m i t i n g phenomenae.

5 0 0 0

1 0 0 0

THE NUMBERS AT THE DATA POINTS CORRESPOND TO THE NUMBER OF OBSERVATIONS ON WHICH THE AVERAGE IS BASED

PREDICTION

2 3 4 5 SIGNIFICANT WAVE HEIGHT ( m l Fig. 4 Comparison of the calculated mean increase of power (PAU ) in a seaway with service performance data.

References

1 M . D. Haskind and I . S. Rieman. Bulletin de I'Academie des Sciences des U S S R . Ciasse des Sciences techniques, 1946 no. 10.

2 F. Ursell. Proceedings Symposium on the Behaviour of Ships in a Seaway. Wageningen, 1957.

3 B. de Jong. Report 174. Delft Shipbuilding Laboratory, 1967.

4 R. Timman and J. N . Newman. Journal of Ship Research, 1961.