niiicholas
Posts: 319 Joined: May 2002

A Gonzaga student writes,
CONTINUED, AN ARISTOTELIAN DEFENSE ... ...based in part on the bacterial flagellum.
In PNAS:
Purcell, Edward M. The efficiency of propulsion by a rotating flagellum http://w3.impa.br/~jair/pnas.pdf
An important note:
Quote  The original version of this manuscript was completed by E.M.P. on April 26, 1978. It is an elaboration of thoughts presented in figures 13 and 14 of ‘‘Life at low Reynolds number’’ (1). A later version of the manuscript dated October 5, 1992, included an appendix in which E.M.P. worked out the propulsion efficiency of a rotating helical cylinder connected to a sphere (i.e., the power required to drag the sphere through a viscous medium, derived from Stokes law, divided by the power expended by the flagellar rotary motor). That work is not included here, because a similar calculation has been given by Childress (2). E.M.P. concluded that if the ratio of the viscous drag on a thin cylinder moving sideways at a given velocity to the viscous drag on the cylinder moving at the same velocity lengthwise were ‘‘a 5 2, which it is supposed to be . . . the propulsion efficiency cannot exceed 3% under any circumstances.’’ With more realistic values, he estimated a maximum of 1.7%.

Also by Purcell:
Life at Low Reynolds Number
Relevant to efficiency claims:
Quote  When you put all this in and calculate the efficiency, you find that it's really rather low even when the various parameters of the model are optimized. For a sphere which is driven by one of these helical propellers (Fig. 16), I will define the efficiency as the ratio of the work that I would have to do just to putt that thing along to what the man inside it turning the crank has to do. And that turns out to be about 1%. I worried about that result for a while and tried to get Howard interested in it. He didn't pay much attention to it, and he shouldn't have, because it turns out that efficiency is really not the primary problem of the animal's motion. We'll see that when we look at the energy requirement. How much power does it take to run one of these things with a 1% efficient propulsion system, at this speed in these conditions? We can work it out very easily. Going 30 micron/sec, at 1% efficiency will cost us about 2\times 10^{8} ergs/sec at the motor. On a per weight basis, that's a 0.5 W/kg, which is really not very much. Just moving things around in out transportation system, we use energy at 30 or 40 times that rate. This bug runs 24 hours a day and only uses 0.5 W/kg. That's a small fraction of its metabolism and energy budget. Unlike us, they do not squander their energy budget just moving themselves around. So they don't care whether they have a 1% efficient flagellum or a 2% efficient flagellum. It doesn't really make that much difference. They're driving a Datsun in Saudi Arabia. 
