: Does anyone know of a formula or calculation for the minimum water depth
: required for a boat of given length to reach its theoretical maximum
: speed? Certainly below a certain depth the wave characteristics change in
: relation to the hull and inhibit maximum speed.
The standard definition for "shallow water" for waves is water that is less than half the wavelength deep. "Shallow" is water that slows down the wave. The "hull speed" of a boat occurs when the wave length of the wake equals the waterline length of the boat. From this you can say that a boat will start feeling the bottom when the water depth is less than half the waterline length of the boat.
If you assume the boat will have trouble going any faster at the point where it starts to feel the bottom and the boat speed will be equal to the wave velocity at that point: the wave velocity (C) is equal to the square root of (g*d) where (g) is the acceleration of gravity and (d) is the water depth.
This is not a perfect assumption because you can probably force the boat to go a little faster than the wave velocity, but it may be a good approximation.