Some time ago I tried to calculate what would be the optimal speed in dynamic. I created an equation from the O2 consumption while not moving (static) and the consumption while moving, presuming that the consumption of the O2 that is used to moving varies with the square of speed. So basically: consumption (dynamic) = consumption (static) + consumption (the oxygen needed for moving). And the consumption of the oxygen needed for moving goes up with the square of speed. For example, if you go two times faster, you consume four times more energy and oxygen, and if you go three times faster, you consume nine times more energy.
From that basic idea I got into the final equation, which is in the attachment, where you insert your static PB (this tells your oxygen consumption when you are not moving), the diving speed of your DYN (or DNF) PB, and the duration of your DYN (or DNF) PB. After that you put there some other diving speed, and the equation tells you what your distance would be with that new speed. The reason for putting in your PBs is that it kind of sets the baseline by which the increases in oxygen consumption are calculated. Other option would be building a hydrodynamical model.
Couple of points and notes:
1) According to this formula, the duration of the DYN or DNF should always be half of the static PB. If you go faster than that, you consume too much oxygen for moving, and if you go slower than that, you consume too much oxygen for just holding your breath that long.
2) Your static PB and DYN/DNF PB should have had the same level of hypoxia at the end. I.e. if you don't really train statics and your PB is 4 min but you still do 200 m dynamics that last 3 min, the equation is clearly not going to work, because the static PB doesn't relate to your real capacity and thus gives wrong resting oxygen consumption.
3) The formula assumes that all the work done during the dive is aerobic. This is not how it goes in reality, as anaerobic energy mechanisms are very important part of dynamics. The equation doesn't actually calculate the oxygen consumptions, but energy consumptions. To make it more realistic, it should include anaerobic energy and the diving reflex. But that is kind of tricky, as they depend on person and also vary with speed in some way. So, as the formula gives suprisingly reasonable results, the reality is still more complicated.
Feel free to suggest how to make it work better.
