The official term for that is 'Prone Recumbent' (lying on your front)
And it's much less popular for the simple reason of being very difficult to find a comfortable position, with the added bonuses of:
1) Compacting the front of the torso when you need to breathe very heavily
2) With the knees having to extend downward instead of upward every stroke, the entire body needs to be placed higher to compensate, so you are in fact forced to raise the centre of gravity (or worse, in a bike, give yourself a higher aero profile, reducing or even negating the chief benefit of a 'bent).
3) You force the body to work harder in the rest phase of the stroke - to illustrate this, sit down on the edge of a raised surface (bed, sofa will do fine). Lie on your back, stick your legs out straight, and hold them there for a few seconds. Now roll over and do the same on your front. You'll see the muscle and bone structure make it naturally much easier to do on your back than on your front.
(, Fri 13 May 2011, 22:23, Reply)