Well, if someone is sharp here, then it is certainly you, Ted :king - you figured all this long before us. Additionally I really admire the professional approach you have to the testing, construction, and manufacture - it is absolutely incredible!
OK, so I went to sleep with the problems in my head, and run hundreds of laps with Lunocet and other fins on my legs during the night (what an exhausting sleep
). And it proved useful - now I believe I understand it perfectly. I see in fact, Ted and myself, although opposing, we were both right. Let me explain it (sorry, it is long, but I tried making it comprehensive even for those not aware of all the details):
Let's simplify the propulsion model maximally - let's ignore all non-substantial factors like the turbulences, induced drag, vortices, variable speed and variable power during the kick, the asymmetry of the kick and human body anatomy, diverse knee and ankle flexes, and let's forget even the lever Lunocet works with. Let's say we have an ideal case where there is a constant kicking force in both downward and upward direction, and where the hydrofoil support moves only vertically without any lever angle, with a constant amplitude, just like a piston in a cylinder of a car engine. I also assume that the tension of the bungee is already adjusted to the available kicking force and that we neither over-power nor under-power it.
In this case, the vertical kick force against the hydrofoil acts against two reactive forces - the speed induced pressure (the bigger the faster you go) and the pitch-controlling bungee resistance (constant, more precisely growing with the angle, but considering it constant will work for this simplified model). So now, if your available kicking force is constant (you push with the maximal force from the start to the end), and if we consider the bungee resistance constant, the kicking force is directly in reaction with the speed induced resistance reducing the pitch. So here, Ted is perfectly right, that you do not need any stiffer bungee at high speeds, because the hydrofoil will always travel in the right angle of attack as a result of balance between the kicking force and the speed induced frontal pressure on the hydrofoil.
Now, the resistance force of the bungee is not constant, but rather growing with the foil angle, hence smaller at higher speeds (smaller pitch). So at higher speed, there is less resistance which you then must compensate for with lower kicking force to avoid overpowering the fin. Although it is already an argument for increasing the stiffness with growing speed, let's ignore this factor for now.
The above simplified example assumes a constant amplitude of the kick. Now that will work fine if the support of the fin is always perfectly horizontal as we assumed. As Dr. Fish (what a Nomen Omen if it is his real name!) told Ted, that's indeed the case at dolphins - not only the lever they use is quite longer than at humans, but due to the flexibility of the body and tail, and due to the muscle control of the tail fin, they are able to keep the fin in the ideal angle of attack during the entire kick.
Unfortunately though, humans with a Lunocet fin are close but still not entirely like dolphins. The lever is quite short (especially if you have a bad style and bend your knees while kicking), and we are not able to keep the hydrofoil support in a horizontal position, but rather moving it on a lever under a variable angle. Let's say it is +-20 degrees. Now let's look at the serious consequences it has:
At the start (speed zero), the ideal angle of attack is roughly 45 degrees. You adjust the tension of the bungee so that with your kicking force the hydrofoil moves to the angle 45 degrees at zero speed induced frontal drag. So far so good. The pitch is 45, the lever angle is 0, and the angle of attack is 45 too. Now the kick continues upwards, the lever angle grows until the max of 20 degrees. Lets assume the pitch angle is constant at given speed - 45 degrees. In fact the kicking force is not entirely constant, and we would also need to use trigonometric functions to calculate for the change of the forces and change of the pitch, but those changes, at the small angles are relatively unimportant for our calculation. So (still standing) we have a constant pitch of 45 degrees, but a lever of 20 degrees - the resulting angle of attack is no more 45 degrees, but just 25. Well, that's not too bad. Especially assuming there are many other factors affecting the efficiency, the relatively small reduction of propulsion due to less than ideal angle of attack in the extremity would not make a big difference. We can still tell - so far so good.
Now we start gaining speed and the necessary angle of attack falls down and the blade indeed sets in position automatically due to the speed induced pressure. In the moment we reach the speed when the needed angle of attack is 20 degrees, we are getting into real troubles - it will be 20 in the middle, but at extremities it will be zero - so far still not too bad: with angle of attack equal zero you are simply gliding when in the extreme positions (up and down). But when you get even higher speed, and the pitch lower than 20 degrees, in the extremity the angle of attack will be negative, meaning that you start braking and won't be able to get over this critical speed.
You have two basic ways for solving this problem - either a technically challenging system keeping the hydrofoil support horizontally all the time, or voluntarily reducing the kicking amplitude with growing speed. Already here, I believe that the possibility to adjust the bungee tension on the fly would help with reducing the amplitude - the growing stiffness would help you naturally reducing the amplitude. But even if you think you do not need that and that you can learn the right style without it, let's look what happens:
The angle of attack falls from 45 (minus the angle of the leading foil side to the chord) at zero speed to zero at high speed. Yes, at high speed you can have a immobile solid hydrofoil and still propel with it, thanks to the angle the opposing sides have. The great advantage of the solid hydrofoil is that it has dead space close to zero. Hydrofoil with an angle of attack needs to flip to the opposite direction, hence losing the propelling power in the dead points of the kicking cycle. The bigger the angle is, the bigger the dead space.
When you go faster, the pitch falls down, and consequently the dead spaces too, but since you also need to limit the amplitude to avoid kicking out of the zone of efficient angle of attack, you need to reduce the dead spaces as much as possible. And that's exactly what you achieve by increasing the bungee tension. Although by making the foil stiffer, you under-power it slightly (kicking with a less than ideal angle of attack), it allows you greatly reducing the amplitude (staying so in the most efficient zone) while minimizing the loss during the foil reversion.
So my conclusion is that indeed the possibility to control the bungee tension on the fly, making the fin stiffer at higher speeds (while reducing the kick amplitude in the same time) would help the efficiency and reaching higher speeds better than without it. On the other hand, with the progressively stiffer fin, you really need to decrease the kick amplitude at high speed, otherwise you get easier into the negative efficiency zone at extremities of the kick.