Hull speed for Displacement hulls

Im hoping someone can answer a question about hull speed for me. Reading up about this a little I find that hull speed for displacement vessel is 1.33 x (lwl) 1/2 ... but I havent found out WHY this is or the calulations behind arriving at this formula. How can this hold true for every vessel. Shouldnt width, weight be factors?

 

This is a bit simple, but should get the idea across:
Think of a displacement hull as being limited in its speed by the waves that it creates as it travels through the water. Because it is a displacement vessel it does not climb its bow wave, and so it is sort of "trapped" between the waves it generates. The length of the wave the hull creates is the length of the waterline of the vessel. There is a formula for the speed of a wave (in many but not all conditions) that is
V = (g * L / 2 pi)^½, where V = velocity; g = acceleration of gravity (32.15 ft/sec.^2);
L = Wavelength (and vessel waterline length); pi =(3.1416.....). Solve this equation for V, convert ft./sec. to Knots and you get 1.34 * L^½. Hope this helps.

 

Michael's correct. The only qualification you would need to make, is that between a heavy displacement and a light displacement boat. In the case of the heavy displacement boat 1.43 * sqrt(WL) may be too high: depends on the prismatic coefficient as well. While for a lighter displacement boat this number may be too low. The more the boat can ride over it's bow wave the higher the number before the square root starts to climb, up until about 1.5 or 1.6 I guess, then you are near the onset of planing.

 

The " hull "speed formula is only for fat boats Lwl/ Bwl of 3 to 1 or 4 to one.

THATS why there is interest in multihulls , the 10-1 ++ L/B folks find the speeds far higher, on the same power.

The AYRS had a hull speed formula that included the beam (but its South & I'm North for the summer) that worked quite well.

A 3-1 or other fat boat makes so much wave resistance that eventually the bow is climbing a huge wall of water , and the stern is sucked into a hole .

For distance woirk a LONG boat can't be beat as at 1.15 -1 speed ratio the power required is very small.

Although oil tankers and big boats can only travel slow enough to have a wave amidships , or they would break in the middle.

 

Please, don't mix things. Hull speed is attained when the wave length of the vessel is equal to her waterline length.

Then V(kts) =1.34 * LWL^1/2 or metric V(m/s) = 1.25* LWL^1/2.

And that's it.

Hull speed is independent of L/B ratio, resistance or displacement. It just happens to be so, that heavy displacement vessels do have difficulties to overcome some 1.1 times the hull speed. Slender, light and/or powerfull vessels don't.

 

It would probably help to have two different words. The traditional formula is the speed at which the length of the bow wave, which depends on the boat's speed, is equal to the boat's waterline length. Any faster and the wave trough moves under the transom, so the boat has to plow through the water at an angle (bow-up attitude).

The reason some people say the "hull speed" can be faster or slower is that the bow wave may be larger or smaller depending on things like displacement and beam. Gerr's formula includes displacement, and it's well known that narrow cat hulls go faster without planing. It's the height of the bow wave that accounts for the differences. A light racing cat with narrow hulls has a small bow wave, a wide heavy freighter has a much higher bow wave. But the wavelengths are always the same at a given speed.