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The most obvious reason that you don't see stabilizers on planing yachts is that the loads on the blades and their stocks would be way too high at higher speeds. You would not be able to build the stabilizers strong enough to handle the loads. Also, the blades would cause a lot of drag at higher speeds and therefore they would reduce speed considerably. I am talking probably a few knots here, which is a lot.
Control is another matter. Stabilizers get their power from the speed of the water going over them (actually, the load is a function of speed squared) and the angle of attack of the blades to the flow. The faster the boat goes, the less angle of attack is required to obtain any given amount of lift. So as the boat goes faster and faster, the angle of attack gets tiny, and very small shifts of angle of attack can cause enormous amounts of heeling force. You don't want that at high speed. It would be too difficult to contol the proper angle of attack at high speeds, I believe. The alternative to this is to design very small stabilizers (small planform area) to do the job, but then they would be worthless at lower speeds. And you still have a control and drag problem.
A planing boat achieves a lot of dynamic stability from the hydrodynamics of a well designed bottom. You should not need stabilizers to adjust the roll or trim of such a vessel. That is usually handled sufficiently well by the trim tabs. Stabilizers are intended primarily for displacement and semi-displacement vessels where the speeds and loads are relatively low and easy to design and build to.
Eric
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Eric W. Sponberg
Naval Architect
St. Augustine, FL
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