Hi Frederik and everybody. Maybe this discussion is getting a bit too much for most readers on the list - but hey, feel free to delete this message instantly!

Note: all references to pedal position in this message refers to an upright bike.

Maybe you are right Frederik, maybe not. I am personally not convinced that we can pedal very much more efficiently than most skilled cyclists already do. I believe there are quite robust dynometer tests made on proffesional cyclists that prove this to be true. Look for instance at the graphs published by Powercranks ;). I admit that I haven't seen any of these test results myself but I have seen multiple references.

But lets assume you are right. Even if we can learn, with training and aids like the Powercranks, to produce good power on the up-stroke we still have a few questionmarks:

A: We still only use about half the cycle to produce power. In the 12-6 o'clock position we have nil torque arm if we assume that we have very poor power in the forward-on-top and rearward-at-bottom parts of the stroke. This still equates to erratic torque.

B. We have the issue of aerobic limitations. I.e. the cardiovascular system can not support an increase in power over any lenght of time even if we have the muscles to do it.

Comments on A: One could argue that there is a waste of energy in the bursts of power since the more erratic the powerflow is the more force is used to try to accelerate the bike (and rider) according to F=m*a. This component of force is missing alltogether if the force is constant. The momentum that you mentioned in your other message doesn't help a bit I'm afraid. Momentum doesn't add anything. In fact it is changing the momentum of the bike(accelerating) which is the problem. If momentum was good we would use heavier pedals ;). Powercranks does nothing to address this problem since it doesn't store energy. One could argue that it "only" prevents us from actually resting on the pedals on the upstroke and thereby counteracting the push on the other pedal. There is no telling how much power we actually add - it could well be nil. Bikedrive on the other hand does address the problem of erratic power. If we accept that we have an spike of force on the down stroke (or up stroke by the way) which is in part lost on trying to overcome the bike's (and rider's) moment of inertia (weight basically, in this case) we have an interesting opportunity here. By storing part of the access force (energy actually) in the spring instead of "burning" it on a fruitless attempt to jump the bike forward we can use that energy during the otherwise virtually powerless 12-6 o'clock part of the cycle. Thereby we would add no new energy, but we would waste less of what we have on fruitless short accelerations (F=m*a). BioPace used another principle, taller gear on maximum power. Clever really...

Comments on B: Your rowing bike is a good example of this. Even though you use a lot more muscles, you can hardly produce correspondingly more power right? I agree that there is probably some gains to be made by using more of your body, but other limitations will come in to play. The story of the two brothers is another good example of this. During the race the aerobic power is the limitation and the brothers were doing just as well. In a sprint the brother with the better technique can produce more anaerobic power (with more muscles) to win. The point is that he can't do this during the whole race. It is not obvious that endurance/economy increase by use of more muscles even if maximum power does.

Finally a word on your bouncy ride illustration: First of all 500W is a grotesque power for us mortals. I can myself (according to my Taxc) produce about 170W for 5 minutes or so (it's pathetic isn't it). This equates to 17kg's per leg in your equation. Secondly there are no blows. Stand on the floor and do a knee bend, there is your 65kg (in my case) blow! You are pushing, not recieving blows. It is cyclic, not sharp. Otherwise I think your little calculation was pretty good, and I believe that is indeed what you would see if you put a load cell between the foot and the pedal. I must turn this question around Frederik: -Where do you think the energy is coming from?