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post #7 of Old 11-14-2004
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What can you tell from the numbers?

Thanks for the kind words.

You have asked a question that I had avoided discussing because there is not one cut and dried answer to this issue and it would make an already long answer much longer and I wanted to get out sailing for the day. There has been a lot of study of the issue of draft and wave surface speed and like so many sailing dynamics issues thewre are a lot of factors at work beyond the simple draft and the results of testing suggest that there is a lot at play here.

To begin with, the phenomina that you mention is related to the fact that the surface of a wave can be moving at a substantially greater speed than the center of the wave which can be moving at nearly a zero speed. I have seen this described as ''surface sheer'' and ''gradient surface sheer''.

In theory the deeper a vessel extends into a wave the greater the difference in speed will be experienced between speed of the water at the tip of the keel and speed at the waterline.In principle that difference in speed can and does induce a roll moment (We can see wave driven roll even in passing power boat wake or lying cross wise to a chop.)

The current thinking is that it takes a wave at least twice the height of the beam of the boat to induce sufficient force to be considered to be a contributing factor in a capsize or roll over. To some extent that minimum height is related to fact that greater surface speeds are experienced as a wave gets taller. But that is not the whole story because open ocean waves that are twice the beam of the boat are rarely steep enough to cause a roll over. A wave of twice the beam of a boat needs to be at or near breaking for a wave to capsize or roll over a boat.

This is because a wave near breaking is as steep as it can be before the shape of the wave fails due to gravity and the top of the wave simply falls off (breaks). The steepness of the wave also affects its surface speed with a steep wave having a greater surface speed relative to the center than a flatter wave. That relative speed comes from the fact that waves get steeper when they encounter friction. When a wave train encounters friction, the spacing of the waves get closer together and the waves get steeper. Friction comes in the form of a current running in opposition to the wind direction or the bottom of the wave dragging on the ocean bottom in shallow water. It can also occur when a strong wind builds suddenly. To understand this it should be understood that normally when there is a strong wind blowing for a period of time, the wind creates a surface current of water that is moved along with the wind. When a strong wind comes up suddenly there is no surface current so the waves that form experience friction between the wind at the very surface and the still water below making a very steep chop. As the water below begins to move with the wave trains the friction decreases and the wave steepness will flatten.

I mention the frictional aspects of steep waves to explain why there steep waves have a greater difference in speed between the surface and the center and therefore are more dangerous.

Which brings is back to the original question at hand. In theory your question should have a simple answer. All things being equal a deeper boat, with the same VCG as a shallower boat, should be heeled more and therefore be more likely to trip. The only short coming is that boats rarely have all things equal.

For example, a deeper keeled boat is likely to have less keel length (fore and aft) and keel area than a shallower keeled boat because the deeper keel is more efficient and does not need as much area. Its shorter length means that it is more likely to stall at high incident angle and absorb less energy than the shallower longer keel which is less likely stall and therefore absorbs a lot more energy. A lighter boat is more likely to heel and slide down the wave (in effect surfing sidewards.) A heavier boat is likely to stand its ground be rolled by moment created by the difference in speeds of the surface sheer. A boat with a high roll moment of inertia, is less likely to be rolled. That said, it is far less likely to be rolled if that the high moment of inertia occurs due to weight that is below the instantaneous roll axis. A boat that has a high roll moment of inertia that includes a lot of weight aloft builds up a lot of kinetic energy that would tend to continue the roll of the boat towards a capsize even after the energy of the wave has ceased to propel the boat. In fact as the boat encounters the back flow on the other side of the wave, the inertia of weight aloft can cause the mast to dip into the face of the back of the wave further guarantying the capsize or roll over.

In any event, it is easy to argue either side of this one. Deep is good vs deep is bad, high moment of inertia is good vs high moment of inertia is bad. Fin keel is good, vs fin keel is bad and the reality seems to be that there are situations where each can be good or bad but a deeper VCG is always good.

As to this morning''s post. I wrote most of it this morning but some of it was editted from a draft of something that I was writing for another venue.

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