Abstract
The hydrodynamic effects of non-uniformities in cross-section and wavelength of three-dimensional flagellar waveforms are investigated. Estimates of propulsive velocity obtained by the use of mean constant wave parameters are close to the more precise calculations except where the wavelength varies more than twofold during wave propagation. Energy expenditures against external viscous forces are appreciably greater than the estimates based on mean wave parameter assumptions. Rotation of an inert head attached to a flagellum contributes a significant proportion of the total power dissipation. Energy requirements of an individual bull spermatozoon are greater than previous estimates. There is little difference between the energy supplies necessary to propel bacteria by rotating rigid flagellar helices or by propagation of helical waves.
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