I believe the relevant point about biopace rings (and it is not intuitive at all, at least not to me), is that since the ring is symmetrical, the same number of teeth, and hence the same amount of chain, are always engaged by the ring. that implies that the amount of chain between the cog and the ring is always the same. The amount of chain between the cog and the ring does NOT go up and down as the chain ring turns. the only variable is the "apparent diameter" of the ring; as that changes, distance from the engagement point of the cog and the ring varies ever so slightly, as if the chainstay length were varying a tiny amount with each revolution of the crank.

In a back-of-the-envelope calculation I think this might result in a change in cog-to-chainring distance of about 1.5 millimeters... which is probably with in the range of acceptable chain tension that most of us maintain.

Does any one happen to know the high and low radii of a biopace chain ring (yes, I know, that will depend on the size)? My winter bike has them... but its at home and I am not.