Hull Speed
The hull speed equation can be used to give an estimate of the maximum speed obtainable by a displacement hull if having enough power.
\begin{align}
v_{hull,max}=\sqrt{\frac{L_{wl}\times g}{2\pi }}
\end{align}
with Lwl being the waterline length in meters and g being the gravitational acceleration i.e. 9.81 m/s2.
The speed obtained by the equation equal the speed at which the bow wave length equal the waterline length or a Froude Number of 0.4. This is however a fairly rough estimate and displacement hulls have been developed that without planing can obtain higher speeds.
The equation is do to its short comings not used by Naval Architect today as far as I know. Instead Naval Architects rely on the Froude Number instead.
It is however still a reasonable good for a first rough estimate.
Calculator
Graph and table
| Waterline length | Hull speed | |||
|---|---|---|---|---|
| m | ft | m/s | knot | mph |
| 2.0 | 6.6 | 1.8 | 3.4 | 4.0 |
| 4.0 | 13.1 | 2.5 | 4.9 | 5.6 |
| 6.0 | 19.7 | 3.1 | 5.9 | 6.8 |
| 8.0 | 26.2 | 3.5 | 6.9 | 7.9 |
| 10.0 | 32.8 | 4.0 | 7.7 | 8.8 |
| 12.0 | 39.4 | 4.3 | 8.4 | 9.7 |
| 14.0 | 45.9 | 4.7 | 9.1 | 10.5 |
| 16.0 | 52.5 | 5.0 | 9.7 | 11.2 |
| 18.0 | 59.1 | 5.3 | 10.3 | 11.9 |
| 20.0 | 65.6 | 5.6 | 10.9 | 12.5 |
| 22.0 | 72.2 | 5.9 | 11.4 | 13.1 |
| 24.0 | 78.7 | 6.1 | 11.9 | 13.7 |
| 26.0 | 85.3 | 6.4 | 12.4 | 14.3 |
| 28.0 | 91.9 | 6.6 | 12.9 | 14.8 |
| 30.0 | 98.4 | 6.8 | 13.3 | 15.3 |
| 32.0 | 105.0 | 7.1 | 13.7 | 15.8 |
| 34.0 | 111.5 | 7.3 | 14.2 | 16.3 |
| 36.0 | 118.1 | 7.5 | 14.6 | 16.8 |
| 38.0 | 124.7 | 7.7 | 15.0 | 17.2 |
| 40.0 | 131.2 | 7.9 | 15.4 | 17.7 |
| 42.0 | 137.8 | 8.1 | 15.7 | 18.1 |
| 44.0 | 144.4 | 8.3 | 16.1 | 18.5 |
| 46.0 | 150.9 | 8.5 | 16.5 | 19.0 |
| 48.0 | 157.5 | 8.7 | 16.8 | 19.4 |
| 50.0 | 164.0 | 8.8 | 17.2 | 19.8 |