  In a classic paper, Edward Purcell analysed the dynamics of flagellated
bacterial swimmers and derived a geometrical relationship which optimizes the
propulsion efficiency. Experimental measurements for wild-type bacterial
species E. coli have revealed that they closely satisfy this geometric
optimality. However, the dependence of the flagellar motor speed on the load
and more generally the role of the torque-speed characteristics of the
flagellar motor is not considered in Purcell's original analysis. Here we
derive a tuned condition representing a match between the flagella geometry and
the torque-speed characteristics of the flagellar motor to maximize the
bacterial swimming speed for a given load. This condition is independent of the
geometric optimality condition derived by Purcell and interestingly this
condition is not satisfied by wild-type E. coli which swim 2-3 times slower
than the maximum possible speed given the amount of available motor torque. Our
analysis also reveals the existence of an anomalous propulsion regime, where
the swim speed increases with increasing load (drag). Finally, we present
experimental data which supports our analysis.
