I don't know, where these numbers come from and if they are valid. Let's assume, they are ok.
Have you concidered the simple fact, that in order to make your muscles work you do not only need the muscles and some chemical energy, but you need your whole body with lots of other energy consuming organs like your heart, brain, etc...?

The force acting on the thigh via gravity is accounted for by the potential energy. If you will reread Papadapalous you will see they account for that then say there has to be further forces through the foot to drive the bicycle to dissipate this energy variation. Without the forces through the foot the energy dissipation cannot occur as they claim it does.

---

--------------
Frank,
An original Ironman and the Inventor of PowerCranks

Yes. That would reduce the overall gross efficiency some but it is not enough to account for the entire difference.

---

--------------
Frank,
An original Ironman and the Inventor of PowerCranks

But if we have some other numbers, let's say 35% and 25%?
I found exactly these numbers here:
http://www.lfe.mw.tum.de/...dyn_Muskelarbeit.pdf
(On page 5. Sorry it's in German.)

In fact I am surprised that the whole body needs that little energy!

You don't need to invent any magical energy losses. They simply don't exist.

Well, 25% is at the very high end of the usually accepted range of cycling efficiencies, so high as to be rare (even Lance's gross efficiency is only about 23%). A generally accepted range of cycling efficiencies is from 16 to 23% so 20% is a pretty good number to use as an average. We need to be able to explain the drop in all cases because this would allow those at the lower end of the spectrum to understand what makes them different so they can better improve.

---

--------------
Frank,
An original Ironman and the Inventor of PowerCranks

I can see it now. Lamb Cranks.

You've been in independent crank la-la land for so long, not only have you forgotten that people pedal against a load, but also that the cranks (and thus the masses) are attached to each other...

Stop trying to separate what happens individually at each leg and think about the structure as a system.

---

http://bikeblather.blogspot.com/

"No it is not, it is a simply because of the accepted definition of power. No movement, no power."
This is getting annoying. Show that this is the accepted definition of power. I agree that it is *an* accepted definition of power, but clearly in a discussion about efficiency, one would think that a participant could distinguish between power input and power output -- and the power input need not be mechanical. Before you call me ignorant, you should check the facts yourself.

"If you accept that it is a very complex question and that you don't understand it why are you here arguing as if you do?"
Re-read what I wrote; I think I answered that. If you make fundamental errors in physics, you might get the right answer sometimes, but you won't understand why it is the right answer, and shouldn't act as if you do.

"If you think it is irrelevant to racing... so be it."
Have you anywhere shown that the most efficient cadence is the optimal cadence. Slowman has convincingly posited (elsewhere) that it is not. Obviously efficiency is important; but is it the only factor to consider? No; and hence its irrelevance for this thread, which is about optimal IM cadence. You can try to change the subject all you want, but that is what the thread is about. Your line of participation is simply begging the question. I agree with your statement about minimising loss; I just have not seen you treat the subject properly in the context of this thread. In other words, if you knew the most efficient way in the world to pedal, what would you do about it? You might find that it is far from optimal for IM racing.

"As they say, ignorance is bliss." -- ad hominems ought to be below you. There ought to be some open-mindedness to learn something from the many that generously donate their time to try to show you that you are not being scientifically persuasive. I don't mind someone playing fast and loose with physics who knows his limits; but when you set yourself up as an authority, that is too much. You have said a number of patently incorrect things in this thread that relate to physics, and because I know something of the subject, I presume to speak. I happen to think that open-minded people can take correction and apply it, and by means of this process once-disparate parties can sometimes come to agreement, and deficient theories can be turned into better ones. Think about it.

Actually, they aren't valid, for the following reasons:

1) the efficiency of glucose oxidation (which is where the ~40% value arises) is calculated based on standard conditions, which do not exist in vivo. In particular, the actual delta G of ATP synthesis/hydrolysis is less than the assumed delta G zero prime, meaning that the actual efficiency of the initial energy 'capture' is <40%.

2) while the calculated efficiency of glucose oxidation may be ~40%, that is not the same as the efficiency of muscle contraction per se. The latter is difficult to determine, but must be less than 100% (2nd law of thermodynamics), meaning that the overall efficiency must be <40%, even if the conversion of force at the myofibrillar level to useful external work occurs w/o any loss whatsoever.

3) although whole-body efficiency when cycling is around 20-25%, that is for the body as a whole, not for the exercising muscles themselves. (As a general rule-of-thumb, the percentage of whole-body VO2 consumed by the legs during cycling is approximately equal to the percentage of VO2max, e.g., at 70% of VO2max the legs account for ~70% of whole-body O2 uptake.) If you calculate efficiency based on leg instead of whole-body VO2, you get a significantly higher value, i.e., around 30-35%.

Putting 1-3 together, the picture that emerges is that humans are actually quite efficient when pedaling a bicycle, something that makes perfect sense when you realize that the pattern of muscle use/activation when pedaling is quite similar to that observed when walking or running, i.e., we use our muscles to pedal pretty much the way they were evolutionarily-designed to be used.

Armstrong isn't particularly efficient, so I'm not sure why you use him as an example.

Reread Papadapolous. Their analysis presumes the cranks are connected but whether they are or are not, the analysis of the system is the same as the energy in each leg would be the same.

You were the one who threw the Papadapolous theory out as evidence that my assessment is all wet. I have simply pointed out that their analysis, while having some theoretical potential, cannot be true in real life, as stated, because the pedal forces required by their solution simply do not exist.

---

--------------
Frank,
An original Ironman and the Inventor of PowerCranks

I've been reading this thread and have one quick question; if the majority of pros ride at avg C 84, what are the TBB women averaging in an ironman? does this vary on terrain or do they try to keep C constant? Thanks. Sorry if I missed this in previous threads.

Let's see if we can simplify this enough for you...gravity slows the rise of the rising leg, the load slows the fall of the falling leg. The energy of the total SYSTEM is all accounted for...

---

http://bikeblather.blogspot.com/

I don't know how the average TBB woman rides. We have been told that Brett trains them to ride at low cadence. Chrissie seems to always be at a lower cadence than most but we only see snippets.

---

--------------
Frank,
An original Ironman and the Inventor of PowerCranks

Are you blind? Do you see all of these largely tangential forces being applied by the foot on the downstroke? Do they not need to counteracted by largely equivalent reaction forces supplied by the LOAD? Stop with the unloaded pedaling nonsense...it's just confusing you.

---

http://bikeblather.blogspot.com/

I believe the energy lost in muscles is due the mechanism in which myo-fibers create force. They repeatedly contract and the slide against each other during the same muscle contraction, in a round-robin fashion. For 10 myo-filaments belonging to the same myo-fibril, first no.1 contracts, then 2, then 3 ... then 6 contracts; then as no.7 contracts, at the same time myo-filament no.1 slides back; the same with 8 contracting and 2 sliding back; similarly for 9 and 3, and 10 and 4. So in this simplified example only 6 fibers are contracted at the same time. The friction resulting from the filaments sliding back is what wastes the energy produced. If this is true, overall muscle efficiency will never be 100%, and will be 0% in an isometric effort. Every little radial component of the pedaling force will be responsible for a component of isometric effort, i.e. for a component of athlete effort that results in 0% cycling efficiency.

However, the above will not help deciding what the optimal cadence is. I believe cadence must be different from individual to individual, and there is a way of figuring it out either experimentally, or in a lab setting. Actually I believe that rather than determining the optimal cadence, we would rather determine maximum power output for that individual in a predetermined race and optimal pedaling foot speed; from max power we would determine his/her maximum bicycle speed; for each individual then we would be able to determine cadence, crank length, gear ratio and wheel diameter that yield that foot speed and power.

---

Giovanni Ciriani
http://www.GlobusSHT.com

Yes, and as I noted in an earlier post above, if the "load" on the falling leg is not tangential to the pedaling circle then most of it is still being lost as heat. So, when pedaling unloaded the inefficiencies are taken up by the muscles in the leg and when riding loaded they can be transferred to the crank arm and frame of the bike but little is transferred to the wheel to drive the bike because there is little evidence to support that these forces are anywhere near tangential to the pedal circle. Some energy transfer may occur but it certainly is only a small portion of the total that needs be transferred so the Papadapalous argument is certainly incomplete and misleading. So pedaling dynamic losses do occur whether they are lost in the leg or the crank/frame or some combination and the amount of the loss is going to vary with the cadence.

---

--------------
Frank,
An original Ironman and the Inventor of PowerCranks

Largely tangential? LOL.

The area of interest here is the area where the thigh is decelerating (after 9 o'clock on this diagram) and expecially the area where it is decelerating the most rapidly (where the forces are the greatest - between 7 and 8 o'clock). In this area of most interest the angles from tangential vary from about 45º to about 80º by my eye. The energy transferred to drive the bicycle would be equal to the load times the cosine of the angle. Not very efficient in my opinion. And, of course, some of that is being diverted to push the trailing leg over the top.

---

--------------
Frank,
An original Ironman and the Inventor of PowerCranks

Giovanni, that is exactly what I had in mind, but I backed off in the realisation that my [mis]understanding of muscle contraction could be wrong. I haven't looked at it in a long time.
I agree that off-tangent forces are inherently inefficient (that the radial component is 0% efficient). However, an apparent fix to this (by pedalling with only tangential force at the pedal axle) is not necessarily a fix, as it concentrates the problem farther up the leg. The muscles apply force at some angle relative to the desired force by means of different levers, and they invoke other muscles for stability; making the force tangential at the pedal may actually result in lower efficiency due to the muscle setup than leaving it as-is. By the same token, lifting the rising leg may or may not be more efficient than using the down force of the falling leg to lift it; discussion of the benefits of lifting the rising leg should consider the tradeoff. And then, beyond efficiency (it may be more efficient to 'mash'), we come back to what is better for an IM, which may not be the most efficient, but rather the most sustainable and the most suitable as preparation for a run.
Thanks for your thoughts.

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.

---

http://bikeblather.blogspot.com/

Pedaller,
Absolutely, optimality has to be looked in the contest of what is sustainable in a particular race/effort. Keep in mind that the Power-Velocity curves I posted earlier can be obtained for:

• 1 minute sprint in which one utilizes all fiber types, slow-twitch type I, fast-twitch type IIa (aka intermediate), and fast-twitch type IIx;
• or a 30 minute race, in which ono ae utilizes fiber types, slow-twitch type I, and fast-twitch type IIa (aka intermediate);
• or a 5 hour race, in which one presumably utilizes, slow-twitch type I, and to a much lesser extent type IIa;
• or a 9 hour race, in which I guess only slow-twitch type I fibers are utilized.
  

I'm sure the four curves would be quite different and would lead us to very different (sustainable for that race) speeds, and different optimal cadences.

---

Giovanni Ciriani
http://www.GlobusSHT.com

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).