Steady ship waves, wave resistance

Wave resistance drag on ship $D$.

$$\begin{align}\mbox{Rate of work done} & = \mbox{rate of energy increase} \notag ... ...{1 \over 4}\rho gA^2}\limits_{\mbox{\tiny {energy / area}}} \notag \end{align}$$

Question: Amplitude A = ? (depends on U, geometry)

Superimpose a bow wave ( $\eta _{b})$ and a stern wave ( $\eta _{s})$:

$$\begin{align}\eta _b & = a\cos \left( {kx} \right)\mbox{\ and\ }\eta _s = - a\co... ...sin ^2\left( {\textstyle{1 \over 2}\frac{gl}{U^2}} \right) \notag \end{align}$$

Steady ship waves (deep water)

$$\begin{align}U = & \mbox{\ ship speed } \notag \\ V_p = & \sqrt {\frac{g}{k}} ... ...t) \cong \rho ga^2\sin ^2\left( {\frac{1}{2F_L^2 }} \right) \notag \end{align}$$

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