Time-Domain Calculations of Drift Forces and Moments

When a ship is sailing on an ocean, it is exposed to several forces. These forces are due to wind, waves, current, and speed of the vessel. Especially the first three may cause the ship to loose its course, i.e. to drift away. Drifting forces can be very large, in particular the force due to the incoming waves. In this thesis this part of the drifting effect is studied, and the effect of forward speed of the vessel is taken into account. The drifting of a ship due to waves may be surprising. In the case of harmonic waves, the motion of the ship may be expected to be harmonic as well, thus no drifting would be expected. However, drifting does occurs, even in harmonic waves. This may be illustrated by two practical examples. When kids play football, it is very common, especially in Holland, that the ball ends up in a ditch or pool. A very practical way to get the ball out of the water, is throwing stones or dirt at the ball. The stones generate waves, which cause the ball to drift to the shore. This drifting even occurs when the waves are small. A second example is a ship lying at anchor in waves. If the waves do not come head on, the ship wants to drift away into the direction of wave propagation. Because this is prevented by the anchor, the ship will rotate until it lies in head waves. The examples show that drifting effects can be large and practical. They also show that the effect of drifting is important for both moored systems and freely floating objects. In the case of moored systems the importance of drifting may seem to lessen, when the system lies in head waves, as the example illustrates. However, the drift force is not a steady force, but may also include slowly varying components. The frequency of these components may be close to the eigen-frequency of the mooring system, thus possibly yielding severe damage to the system. This damage might for instance be breaking of anchor lines or the destruction of the mooring system. In the case of a freely floating ship a major contribution to the drifting effect is caused by incoming waves. However, from measurements it appears that the forward speed of the ship increases the drift forces considerably. Thus the forward speed has to be taken into account, together with existing ocean currents. But also in harbour circumstances the drift forces may be very important. Although the waves are in general not very high inside harbours, drift forces become large due to shallow water. Thus besides speed and current, bottom effects have to be considered. Before studying the combination of waves and forward speed, it is important to understand the forces due to waves and forward speed separately. The forces due to waves only are a special case of the problem we are going to consider, i.e. the forward speed is zero. Thus insight in these forces will be gained within this thesis. The forces in the case when no waves are present, however, are not part of this study, but knowledge about these forces is assumed. Therefore a short explanation will be given about the forces solely due to the forward speed of the ship. When a ship sails through otherwise calm water, it will generate a steady ship-fixed wave pattern. The generation of the waves leads to a power loss of the ship: the wave resistance. At low speeds, these waves have two distinct sources: the bow and the stern. The bow waves travel in a V-like shape, the so-called Kelvin-wave pattern. These waves can be observed when watching a water-bird swimming. This Kelvin-wave can be predicted very well using analytical methods. The second kind of waves are generated at the stern, see Figure I.1. They are very pronounced for sailing-boats at reasonably high speeds. These stern waves can not be predicted very easily; even numerical techniques experience difficulties trying to calculate these waves. To compute the wave resistance at finite speed, it is shown by Raven [25] that the complete non-linear free surface has to be taken into account. The results obtained by his method RAPID are very promising. For an extensive study of the wave resistance, the reader is referred to Wehausen [32].