Physics for finning in water

Question

On Scubaboard, people were discussing the reverse frog kick finning technique.

Someone mentioned that the propellant force has the square of velocity so it is important to apply a strong velocity during the propelling phase of the reverse frog kick and a slow one during the 'reload' phase where you bring back the fins in the original position.

Apparently, if you do not do this, you will cancel much of the speed obtained when you are propelling yourself.

So my questions:

• is that true that all things being equal, you will get better results if you increase the velocity during the pushing phase and decrease it during the reload phase

• I understand that the kinetic energy has the square of velocity in its formula but how does one translate this into the speed/acceleration caused to the diver when propelling yourself ? (maybe I am totally wrong and this would require some other equation)

Video of someone performing a reverse frog kick (also called back kick): link

TDI/SDI page about the finning techniques, bottom of the page has an explanation for reverse/back kick.

EDIT: tried to make the question clearer, added a link

Answer 1

Swimming at the human-scale is a large Reynolds number phenomenon (swimming is a complicated fluid dynamics problem even at low Reynolds numbers), so one can only make scaling arguments in a short answer. Physically, large Reynolds number means that inertial forces (fluid acceleration forces) are dominant over viscous forces. To answer your question, as a crude approximation we may neglect viscous forces altogether when the swimmer executes the swimming stroke. This is not to say that the viscous forces are unimportant; after all they bring the swimmer to rest ultimately.

If the scale for swimming-stroke speed is $U$, then the scale for the momentum flux of the fluid that moves in response to the swimming-stroke is $\rho U^2$, where $\rho$ is fluid density. The corresponding force on the swimmer, by virtue of Newton's third law, is then $\rho U^2A$, where $A$ is the fin area. The swimmer is pushed in a direction opposite to that of net fluid motion induced by the swimming stroke. So you can achieve net motion by using different speeds in opposite directions in a stroke-cycle. Also watching the video of the frog-kick you linked to, one can see that not only is $U$ different in forward and backward directions of the swimming-stroke, but in the backward stroke the fin is being moved in a streamlined manner so as to reduce the effective $A$.