the forces on the stalled surfaces the area is much more important than other geometrical properties, so a long keel yacht will have more damping than a fin-keel one. This is an important conclusion, which speaks in favour of traditional designs and against more modern ones with a small lateral area.
It should be pointed out also, that forward speed increases damping considerably, particularly for fin-keel yachts. If the speed is high enough the keel starts working properly and the forces get much larger. Fig 4.17 shows how the roll amplitude decays with time for Grimalkin in still water. At zero speed the decay is much smaller than at high speed, where the rolling is rapidly damped. It is.therefore important, especially for fin-keel yachts, to keep the speed up under critical conditions.
Fig 4.1 7 Influence of speed on roll damping -fin-keel yacht
The righting moment is influenced by waves in two ways:
• The wave profile along the hull changes the waterline shape
• The centrifugal forces on the water particles change the pressure in the wave
As regards the wave profile, two typical cases may be distinguished. These are shown in Fig 4.18. Hogging is when the wave crest is at midship, and sagging when the trough is at this position. For a sailing yacht, with some flare at all sections, hogging means that the submerged part of the hull gets thinner at the ends and beamier at midship. Since the water plane moment of inertia and the metacentric radius depend on beam cubed (Figs 4.8 and 4.9), this results in an increase in stability. In sagging the opposite occurs, with an increase in beam at the ends and a reduction at midship, ic a more even distribution of beam, which causes a reduction in stability. (It may be
Influence of waves on the righting moment
Time gHSSa waw
Roll amplitude [dag] k initial heel angle
Fig 4.18 Hogging and sagging
mentioned that the effect is often the opposite for a ship with vertical sides at midship.)
For the wave profile effect to be significant the wavelength has to be of the same order as the hull length. This is not the case at sea, at least not under difficult conditions, where the waves are much longer. On the other hand, the waves generated by the hull itself often have the same length as the hull (as we will see in Chapter 5). The hull is then in a sagging condition and this may reduce stability considerably, particularly for hulls with a shallow draft, where the maximum beam may be much reduced in the wave trough. A formula for this effect will be given in the final section in this chapter.
To understand the effect of centrifugal forces some knowledge is required about the particle motion in the waves. This is explained in Fig 4.19. When the wave passes a certain point on the surface the water particles exhibit an orbital motion. Thus, when the particle is in a wave crest it moves with the wave, while the opposite is true in a wave trough. It is easy to compute the orbital speed, since the diameter of the circle is equal to the wave height, and the time to complete one full turn is equal to the wave period. For ocean waves this speed may be several metres per second.
The centrifugal effect on the water particles is explained in the lower part of Fig 4.19. In a crest the centrifugal force is directed upwards, ie opposite to the gravitational force; while in a trough the two forces are in the same direction. An extreme case is when the two forces are equally large, which may happen for short and steep waves. Gravitation is then cancelled in the wave crest and the water will no longer be continuous, but break down into droplets. A hull in this position will lose all its stability. A relevant question is whether it will still stay afloat, and the answer is yes (provided it does not capsize). It will, in fact, float at the original waterline. This is because the hull loses as much weight as the water due to the circular motion.
Complete loss of stability is, fortunately, very rare, but significant
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