Optimal kinematics and morphologies for spermatozoa

We investigate the role of hydrodynamics in the evolution of the morphology and the selection of kinematics in simple uniflagellated microorganisms. We find that the most efficient swimming strategies are characterized by symmetrical, nonsinusoidal bending waves propagating from the base of the head to the tip of the tail. In addition, we show that the ideal tail-to-head length ratio for such a swimmer is $\ensuremath{\approx}12$ and that this predicted ratio is consistent with data collected from over 400 species of mammalian sperm.