In Reply To:
Modulus of elasticity has nothing to do with it. Regardless of modulus of elasticity, an elastic deformation converts work energy to potential energy and back again without loss.
In reality there is a small amount of loss, but that's no excuse to throw out the baby with the bathwater; the basic theory still holds. As to the applicability for this discussion, that's another matter...
And you can wave your leg of lamb all day, it will not cook (but you will warm up a lot!). Your challenge to explain the loss of energy should go back to you, since clearly you do not have sufficient grasp of the concepts to explain it.
Not that I'm pleased with everything your opponents have written, either; but they're closer to the mark.
On to another angle: the macro physics level is only one aspect of things. Work done is force integrated over distance from a macro point of view, but we all know that even statically applying a force in the human body requires power. So clearly there are inefficiencies at going at too low a cadence as well as pedalling too high. Determining the sweet spot is far too complex for me. I'm not saying your optimal cadence is wrong; I'm suggesting that you don't have calculations to support it, and in fact that no one has calculations to support it that are based on the macro physics of the thing; I think it's the sort of thing that is so complex that it would have to be determined empirically.
Well, when you combine modulus of elasticity with
elastic hysterisis I think you will find it explains the fact that there are losses quite nicely. At least you agree with me that there are losses here. You simply think they are too small to be considered.
Where is your data to even suggest what the magnitude of the losses actually are such that you feel they are too small to be considered? Do you feel the drive chain losses are too small to be considered? After all 1-2% is only 2-4 watts at 200 watts. I (and you) know those losses are there. I simply feel these losses have to be relatively large simply because I cannot find enough losses in other mechanisms to explain the totality of the losses without invoking them and their being relatively large.
One correction, statically applying a force by the body requires energy, not power, since no work is done. IMO, this phenomenon does account for some of the efficiency losses because the resultant force on the pedals is rarely tangential to the circle and applying force that does no work can only result in lowering the overall efficiency. I believe this could account for about half the difference in that 20-40% differential. If someone could apply a perfectly tangential pedal force around the entire circle I suspect they could get to a pedaling efficiency of about 30%. Of course, some here have held out that none of this stuff matters. Just ride your bike, don't worry about this efficiency stuff. Well, finally the Foss paper suggests that worrying about efficiency does or can make a difference in performance. These debates will never be the same.
You tried to put the burden on me to explain the losses but I have no trouble explaining the loss of efficiency between the cyclist overall and contracting muscle except I have to invoke losses the due to the pedaling motion I have mentioned to do it. If someone else can show that this loss can be explained totally without invoking a loss simply from the pedaling motion have at it. If this is so simple to explain where are the explanations showing me up for being so stupid?
Oh, and I agree that optimum cadence for anyone person must be determined empirically through testing. The principles are clear, I believe, as to what influences optimum cadence but the interactions and unknowns (muscle fiber type mix) are way to many and complex for any calculation. I think it is enough that people understand there is an optimum cadence for them and that they should endeavor to determine what it is if they want to maximize their performance. Even that seemingly simple idea seems to complex for many here.
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Frank,
An original Ironman and the Inventor of PowerCranks