Optimal pitch of a helical microswimmer
= Optimal pitch of a helical microswimmer
{title2=$\tan\phi=\sqrt2,\quad U_{\max}=\omega b/(2\sqrt2)$}
When head translation is weakly resisted compared with the flagellum but head rotation is strongly resisted, $A_0\ll A$ and $D_0\gg D$. Then $U\simeq-B\omega/A=\omega b\sin\phi\cos\phi/(1+\cos^2\phi)$. Maximizing this expression gives the displayed pitch and speed for the chosen handedness and positive $\omega$.