Limiting hull speed
Contents
| Section | Topic |
|---|---|
| 1 | Conditions |
| 2 | Derivation |
1. Conditions
- the bow sits at a wave crest
- the stern sits at a wave crest
2. Derivation
\[ \omega^2 = gk \qquad\qquad c = \frac{\omega}{k} \;\text{ and }\; \omega = \sqrt{gk} \tag{1} \]
\[ c = \frac{\sqrt{gk}}{k} = \sqrt{\frac{g}{k}} \qquad\qquad k = \frac{2\pi}{\lambda} \tag{2} \]
\[ c = \sqrt{\frac{g\lambda}{2\pi}} \tag{3} \]
For a transverse wave travelling at \(\theta = 0\):
\[ c = u = \sqrt{\frac{g\lambda}{2\pi}} \]
\[ u^2 = \frac{g\lambda}{2\pi} \qquad\qquad \text{set } \lambda = L \]
\[ u_{max}^2 = \frac{gL}{2\pi} \qquad\qquad u_{max} = \sqrt{\frac{gL}{2\pi}} \qquad\qquad \sqrt{\frac{g}{2\pi}} \approx 1.25 \tag{4} \]
\[ \boxed{\;u_{max} = 1.25\sqrt{L}\;} \tag{5} \]