All fiber types (i.e., I, IIa, IIx) would be used in the latter two activities (although anyone who competes in 5+ h races would be rather unlikely to have a significant number of type IIx fibers).

You also keep "mixing" the mechanical forces with the muscular forces when you are discussing "efficiency"...

To be honest, I have no expectation of you ever understanding (or admitting that you understand) how this system all actually works, for obvious reasons...I just hope that others reading this will come to an understanding about the validity of your assertions.

I'm done for now since I think I've made my point.

If so, why haven't you come here and given everyone an accounting of where the losses occur between the muscles and the wheel. Until you are able to do that I don't think you have made your point. :-)

Frank, are you still looking for someone to... ahh, never mind. ;-)
A couple of things, though. I did some thinking about the kinetic energy of the thighs using some generous and round figures, and estimated that at 84 bpm cadence (the rate suggested by slowman) the power input represented by the maximum kinetic energy of the thighs is in the order of 6-7W. I used some simplifying assumptions, of course. If this is correct (and I am not infallible; I'd appreciate seeing if that's in the ballpark of what others get as well), it doesn't amount to much of the power loss. Eg, 200W output on the bike at 20-25% efficiency implies a possible 350W or so available biomechanically; and 6-7W is only 2% of that, not enough to account for some of the major losses you're looking for. This also means that slowing the cadence from 84 to 70 will only save about 3W in thigh-consumed power, which doesn't explain why Chrissie Wellington was so far ahead of the field. With higher muscle loading etc at that cadence, is the 3W gain worth it?
As a side note, based on my simplified model, the force of gravity was sufficient to slow the rise of the trailing leg before it got to the top, so no up-force on the pedal was required for this. (In other words, lack of upforce between 3:00 and 12:00 is no indicator of inefficiency.)
As for your question about losses, my suspicion is threefold. First, the muscles are to some degree working against each other for stability reasons (eg medial vs lateral). The second is that muscular effort is required to transfer energy without a gain in propulsive power; for instance, the ankle joint resists flexure by means of various muscles, when they are not adding [significant?] driving force but merely transmitting it. Third, the highest mechanical efficiency of the leg doesn't line up with the most efficient direction of force application at the axle.
Regarding the 'Largely tangential? LOL' comments: inefficiency is in the eye of the beholder. At rest, the mass of the leg will produce a downward force on the pedal, so you need to take that into account. Since there is a bunch of acceleration going on (of calf and thigh), converting kinetic energy from one direction to another, one would expect a significant normal (radial) force. (If you run a marble around a walled track quickly, the forces will be nearly radial. This does not indicate inefficiency, but conversion of the kinetic energy fron one direction to another, nearly losslessly, since the force and the motion are nearly perpendicular.) So you need to be clear about efficiency, and there is a difference between the strict mechanics of what is going on and the biologico-musculo-skeletal implications. It can be really confusing if you do not clarify terms and think through the implications with clear explanations. Otherwise it is nearly impossible even to interact effectively with your theories.

Pedaller
"the power input represented by the maximum kinetic energy of the thighs is in the order of 6-7W. "

@pedaller

I am not sure, what you tried to calculate here.
Did you assume, you have to invest the full energy to accelate the legs (or parts of them?) from zero(?) to maximum speed in each and every pedal stroke?

Frank, assumptions: thigh circumference of 60 cm, length of 50 cm, density 1.0, mass evenly distributed, rotating about endpoint with sinusoidal angular velocity, both legs, moving 35 cm (175mm x 2) at the knee. In general a thicker, longer, higher-moment-of-inertia profile, higher-peak-to-average-angular-velocity, longer sweep than the real thing, just to be conservative; the density is probably a little low, though (but there's plenty of conservatism to make up for that).
You are correct about cube of rate (as an approximation), as mentioned elsewhere in this thread (iirc), and the reason I gave nearly 50% away in going from 84 to 70 bpm. But again this is conservative because of energy conversion that is being ignored.

"Well, I checked your work and I calculate an energy loss at a cadence of 60 rpm of about 20 watts. At a cadence of 84 rpm the loss would have to be (1.4)^3 higher or about 55 watts."

Frank, I should have thought more about the number before I posted it; it must take more than 3W to flap a leg around. I think I slipped a decimal place somewhere and maybe did worse than that (the price for working in my head... maybe I shouldn't do that!) So I think your number is somewhat right, but don't forget that this is only the basis for an outside bound and we have no agreement on the meaning of this number.

Now let's look at this more closely. At 84 bpm with our assumptions there is 22.63J max kinetic energy in one thigh. However, each thigh is started and stopped twice for each revolution of the pedals, and there are two thighs, so to be consistent in the assumption that this is lost energy, you would need to count them all. So for each revolution of the pedals, the left thigh requires 22.63J to make it go, 22.63J to make it stop, 22.63J to make it go, 22.63J to make it stop. Similarly for the right thigh. So each revolution must cost 8x22.63 = 181J. And since one revolution occurs in only 60/84 of a second, the equivalent lost power is 181*84/60 = 253W.

At a maximum muscle-level efficiency of 40%, this amounts to 634W required by the body. This would involve burning 545 calories per hour moving the legs only. At 100 bpm, that would be 919 calories per hour. (Note that although the model is conservative, we haven't factored in the calves yet, and the 40% is really high...) Clearly this cannot be, and the idea that the thighs are absorbing energy just because they are moving must be fallacious. There must be legitimate conversion of the motion of the thighs into work, otherwise cyclists would be even thinner than they already are.

So now for the hard part. Identify how much of this kinetic energy supplied to the thighs is converted into propulsive energy, and how much is not. It is a subtle business from the dynamics standpoint, as I hope I conveyed well in the previous post.

Nice. But there is no use in calculating this energy because the energy is NOT lost.
It is simply transferrred between the parts of the legs, the cranks and the whole bike and rider.

Maybe you should have a look at this double pendulum:
http://www.mathstat.dal.ca/~selinger/lagrange/doublependulum.html
It's parts continously change speed in an amazing way.
But it never stops because it does not lose energy.

Again: A hypothetical metal biker with fixed gear and without friction will roll forever!

Maybe I should better talk to a wall ...

Rather than talk to a wall perhaps you should reanalyze the problem. They are different problems. In your double pendulum problem the total energy of the system remains constant although how it is distributed between kinetic and potential energy is constantly changing. You won't find that to be the case in the hypothetical metal biker. Do the math and pay special attention to the "thighs". It simply cannot be (see the above posts).

Pedaller:
At 84 bpm with our assumptions there is 22.63J max kinetic energy in one thigh.

Of course the pendulum is different, else it would be a bike. :-) The bike + biker is a bit more complex because of more moving parts and a bit more simple because the parts can't move freely. Still the effects are the same.
What happens in the double pendulum only is more obvious than it is in the bike(er). Energy is transferred between different parts moving with varying speeds.

Why don't you understand, that the "metal biker" simply has no possibility to lose energy, since there is no friction or any other energy consuming effect anywhere? It can do nothing else than transfer energy between it's different moving parts. When the legs move slower, the whole bike moves a little bit faster. When the legs move faster, the bike moves a little bit slower. You don't need math for that. It's trivial.

The metal biker has to have the possibility to lose energy since the energy of the system cannot be constant (simply add up the energy of the various parts throughout one revolution) without energy being put in or taken outside of the boundaries. Since your biker doesn't allow energy to be put in, everytime energy is taken out, the bike, as a whole, must slow down.

The reason I "don't understand" why the metal biker "has no possibility to lose energy" is because such a statement is pure nonsense if one actually analyzes the problem, which you clearly haven't. See the above discussions about the energy variation associated with the thigh movement then apply them to your "metal biker".