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ond order parts. We investigate various information on the diffraction and radiation waves observed by the improved technique of wave measurement particularly for seeking any explanation of the discrepancy of added resistance of shallow draft ships.

We then propose a linear analytical approach to predict the fluid pressure on ships particularly due to the diffraction wave. This approach accounts effectively for nonuniform steady flow which is prominent in the vicinity of the blunt bow and is supposed to have large influence on accurate prediction of the wave pressure on the bow part.

We test the accuracy of our analytical approach by comparing the diffraction wave field predicted with the measured with our improved technique. We presume that if the prediction of the diffraction wave elevation around the bow is accurate, then the prediction of wave pressure on the bow part will be accurate and the added resistance, on which the wave loads at the bow is the most influential, will be predicted accurately.

2
Measurement of Radiation and Diffraction Waves

Neither radiation wave nor diffraction wave field generated by a ship advancing in waves is visible at tank test because of the coexistence of other waves such as steady wave generated by the forward speed of the ship on otherwise a calm water and incident waves. So we need a technique to separate each of those waves.

It is relatively simple to exclude the effect of the incident waves. We measure them upstream where they are not yet disturbed by a ship model and extrapolate them to near it. The extrapolated incident waves are subtracted from the measured wave.

Another problem is that instantaneous distribution of wave elevation around the model is not a full information of the radiation and the diffraction waves. One can obtain a complete picture of the radiation and the diffraction waves only when the distribution of the amplitude and the phase of the wave motion is measured.

Our method to overcome this at tank test is to place several wave probes on fixed positions to the water tank and on a line parallel to the track of the ship model with an equal spacing Δx. When the ship model advances in the tank, each wave probe comes to a location relative to the ship model at different time instant. In other words the wave probes record the wave elevation at every location on the line parallel to the ship model's track on several different time

Figure 1: Coordinate System

instants whose interval is Δx/U. U is the speed of the ship model.

Temporal and spatial variation of the diffraction or radiation waves generated by the ship model running at forward speed in the monochromatic incident waves or sinusoidally oscillating is given to the second order by

ζ(x,y,t)=η0(x,y)+η1(x,y)eiωt2(x,y)ei2ωt (1)

where the coordinates fixed to the average position of the ship model are defined as a right-hand system shown in Fig.1.

The first term on the right of (1) is the steady wave elevation corresponding to the Kelvin wave pattern. Naturally it includes the second order steady component. The second term is the linear oscillatory part and the third the second order oscillatory component.

If the interval Δx/U is small enough and the number of the wave probes is large enough, we fit measured wave elevation on several different time instants with equation (1) at every x of the line y=constant to determine η0, η1 and η2. Fig.2 is an example of the fitting of the wave motion in the vicinity of a ship model at midship; this example is the radiation waves of a Series 60 model of CB=0.8 at ballast condition forced to heave at relatively large amplitude (amplitude-to-draft-ratio is 0.9). We used



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