LOL Let's see. I propose that the energy variation found in the thigh when pedaling (which just happens to vary with the square of the cadence) must cause some pedaling inefficiencies because the energy variation must be dissipated. So, you introduce the little stick figure that by definition cannot exist in the real world and by definition cannot have any material losses as I propose (and the 2nd law dictates must be there to some degree) as evidence that my argument has no merit. I submit your submission of this model of the little stick man, for the sole purpose to make the arugment against my assertion, is what shows little understanding of the proper role of modeling and little knowledge of the physics involved in this motion.
LOL. Still don't get the deficiencies of your "model" do you. Unless your model actually is able to quantitate the losses you are simply guessing as to what they actually are when you say they are small. A good model needs to be able to predict reality. Your model ignores reality. My assertion better fits the data of McDonald than your model or your assertion these losses are small.

The only thing I have accepted where I might have been wrong is the fact that if one were able to actually build a perfect, frictionless, MMF that it might not violate the 2nd law. Maybe the way Einstein breaks down when things get really small. An exception to the general rule. Otherwise, I suggest you come up with other arguments when trying to rebut my assertion that in the real world the pedaling motion inherently involves energy losses. Again, we should not be debating as to whether these losses are there, only their magnitude.

---

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

Frank I was merely referring to your comments referring to Dr. Coggan's, which implied you caught him in a contradiction. I only explained it was not a contradiction, and here is why.

He wrote an excellent summary of how this argument evolved. He wrote that reverse dynamics doesn't prohibit internal losses. That didn't imply that the MMF model had internal losses, it only meant that dynamics modeling has a toolkit from which it can plug in internal losses; it's up to the person using dynamics modeling to add whatever is needed to understand the system. For instance you can model a vibrating system with a mass m and elastic constant k and determine that the resonance frequency is sqrt(k/m)/(2*pi). Then you can decide to see what the effect of a damping force f=c*speed, where c is constant, and by dynamics modeling find out that the resonance frequency has changed (I won't bother you with the details).

---

Giovanni Ciriani
http://www.GlobusSHT.com

Now through the 20 pages of rambling I've kind of forgotten what the point is, but I'm assuming it's to determine how the human engine affects final wheel horsepower via cadence, etc. If so, then if you really, really, really want to figure this out, what I would do:

1) build a dynamic model of the drivetrain which really isn't much more than relating pedal force to forward force of the bike (as simple as F=ma)
2) understand 1) with NO LOSSES
3) introduce drivetrain losses into the model
4) perform a parametric study of wheel horsepower as a function pedal force characteristics, drive train losses, rolling resistance, etc
5) neglect losses due to elasticity of the bike components (honestly, it's not needed)
6) once this model is well understood, move to the next step - model the legs and feet as a series of rigid bars and understand the kinematics of the pedaling motion
7) apply your torque at the hip and verify the model you created in steps 1-5 still works without losses
8) introduce those losses back in and verify it works still
9) take the losses out
10) do a parametric study of potential losses in the "legs"
11) add in the "bike" losses
12) from the hips up? Beats me. Consult an exercise physiologist

It all boils down to a building block approach. I've got some 20 years experience in modeling, yet when I make a new model I don't bite off everything at once. Baby steps and validation at each point. Even in this problem, the end point is just a premise. Without test data to back it up it's just a parametric study of what ifs.

Is it reasonable to neglect losses? You bet. We do it every day in engineering. From a structural dynamics perspective, we add "losses" in the form of structural damping mainly for 2 reasons: 1) make the system of equations more numerically stable and 2) to reduce the structural response/loads. Even with 2), we still use very conservative (i.e., low) damping. And things like hysteresis in materials (primarily due to plastic behavior) is only used when we are trying to pencil whip a bad stress issue, not as standard practice.

Fine. Did Dr. Coggan in his excellent summary point out that this little back and forth came about when he took Tom to task for agreeing with my comment that the up and down motion of the thigh actually involved energy loss. When I asked him to prove his assertion that it did not he provided the world the MMF model as his proof, a model that couldn't prove itself out of a wet paper bag if it had anything to do with the real world.

He has essentially denied that the laws of thermodynamics apply to bicycles.

Why on earth are you here defending Dr. Coggan? Do you believe in the MMF model as being worthwhile for anything other than an intellectual curiosity? Do you believe there are no losses associated with the pedaling motion? If so, what model do you propose to use to prove it? If not, why are you here defending this man and his preposterous claim and his weaseling attempts to avoid admitting he was wrong?

---

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

I submit you do not ignore the losses that you are interested in studying? That is what the MMF model does if we are talking about materials losses from kinetic energy variation and energy transmission, which was my claim.

---

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

Ummm...in the interest of accuracy, I didn't actually intend to agree with THAT portion of your original statement. As I wrote at the time, I had merely skimmed over that part and didn't fully comprehend your assertion on THAT point. Andy didn't "take me to task", he merely asked if that's what I really meant. The answer to that question was "no".

The other stuff though, I did agree with...

---

http://bikeblather.blogspot.com/

So, in view of what has transpired recently are still asserting that there are no energy losses associated with the pedaling motion? If so, what are you using as evidence to support your assertion? Certainly, not the MMF model? Or, are you still holding to that as being valid?

---

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

Is it really that difficult to understand?
A simple mechanical pedaling motion
- with ideal material and no friction has no losses
- with nearly ideal materials like metal has insignificant losses
- with materials like bones has still small losses
- with muskels and other soft stuff has more losses

You don't need rocket science or thermodynamics for that.

Yeh, but you do need a model that takes them into account. Without it you are simply guessing as to the effects or worse, saying the effects are non-existent, which has been done in this thread multiple times. I didn't see you objecting to the assertions.

---

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

Being a coupled, balanced system, there are no losses due to JUST the motion of the constituent parts. Any losses dowstream from the production of the actual power are from frictional and hysteretic losses, which as Andy has pointed out to you ad nauseum, are exceedingly small.

The evidence to support my assertion? As it's been all along, just basic physics and the results of modeling efforts that very closely match actual data, many of which have been shown in this very thread.

---

http://bikeblather.blogspot.com/

That is correct, but we don't go for the whole ball of wax at the start. It's that building block approach. Baby steps so you know what's going on. When you start tossing out laws of thermodynamics, equations you only see in continuum mechanics courses, and other stuff at the start, it shows you are merely pulling stuff out of thin air and grasping at straws. You can't understand anything when you try to model every part of the problem from the start.

Also, without test data to correlate the model, the best you can do is make a trade study and show what *could* happen, not what *will* happen.

See...that's where you get wrapped around the axle. You NEED the simple model as the starting point. For example, THAT'S what tells you what the forces are in the constituent members so that you can figure out what the hysteretic losses would be based on knowledge of the material properties. It's the underlying framework that the more complex model can be built upon.

In any case, all of this bluster about the validity of the simplified, idealized model is really just a way to get the attention off of the point that your initial assertion that just the motion of the pedaling ITSELF required losses irrespective of friction and hysteresis is incorrect.

---

http://bikeblather.blogspot.com/

But, the MMF model doesn't go for anything. It just ignores all the possible areas that might cause some pesky energy loss leading people to make outrageous claims that the pedaling motion does not inherently involve energy loss (in violation of the 2nd law) and, worse yet, people actually believing them.

Maybe the Naval Academy did alright by me after all.

---

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

Go to the chalkboard and write 100 times: "This is where the model starts."

Baby steps Frank. Baby steps.

Here's a perfect example of progressing from easy to harder: mass-spring-damper system in atmosphere in the presence of gravity and an initial velocity. What's the response? The prudent practitioner would likely go through these steps:

1) solve m*d^2x/dt^2+k*x=0 to understand the natural frequency
2) resolve 1 with x(0)=x0 and see if you understand that
3) resolve 1 with v(0)=v0
4) add a constant body force acting on the mass and resolve
5) add damping (and make the decision on what kind of damping it is) and resolve
6) implement a drag force as a function of the speed of the mass

Now if you tried to solve this nonlinear problem from the start I submit you'd be scratching your head for hours. Hopefully they taught you in the Academy a systematic way of solving problems.

I don't deny the sinple model can be a starting point. But, it is not the ending point as has been asserted here many times. I made the point that the pedaling motion itself involves some energy loss. I have been subject to many many posts questioning my intelligence for not understanding the MMF model, which supposedly proved my assertion to be wrong. I believe you were one of them who posted that view. It was nothing but intellectual bullying by people who had never really thought the problem through. I feel vindicated even though, as yet, not a single "opponent" has had the courage to admit that they were wrong.

If you really think my initial assertion was "that just the motion of the pedaling ITSELF required losses irrespective of friction and hysteresis" it is you that is incorrect. I simply have said the pedaling motion involves losses. I have only specified the nature of those losses when pressed. If you will go back you will see I thought the losses were due to hysterisis, mostly, not that there were additional losses beyond friction and hysterisis as I don't know what other losses there could be. This is just more back tracking on your part to avoid admitting a mistake. It wasn't me, but you and Dr. Coggan who claimed there were no losses associated with the pedaling motion. I suspect my statement is more correct than yours as mine doesn't violate the 2nd law.

---

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

I think you should be directing your comments to Dr. Coggan, not me. Why weren't you instructing him on proper model design when he was touting the simplified MMF model as being appropriate to analyze this problem? Dr. Coggan, and others, didn't even take the first step beyond the "simplified" approach which made his solution nonsensical. Yet it has taken us several hundred posts for you folks to figure it out. Doesn't anyone here actually think about this stuff? Why are you lecturing me on model design? I "got it" all along. I may not have articulated it well, but I "got it".

---

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

Ummm...here was your first response to me after I "corrected" myself:




Here's one of your responses to Nicko:


Shall I go on? Also, when I continually asked you where the additional losses would be if there was no friction and no hysteresis, why did you not answer that question and instead just keep blustering that "It's just not possible!" ? That's a rhetorical question...no answer necessary.

---

http://bikeblather.blogspot.com/

In going through the baby steps you understand where the losses are and what are worthy of being modeled. In the example above, my fidelity of modeling depends on what I'm after and also the effect parameters have on the response. If the effect is minimal, why include the behavior? Does it affect it physically? Sure. Does it affect the bottom line? Depends.

This seemed to have started with your instance in modeling losses, no matter how big or small. The discussion was derailed from the start.

Frank,
I think I wrote down the equations representing the MMF model at post #336, and provided equation used, input data, calculations and a graph. Also thanks to the observations of a few, the numerically results were corrected. I've been enjoying this thread, because in the process I've learnt from the contributions of others, you included. However, I didn't see you proposing to replace the equation I wrote with a different equation. So who is it here who hasn't really thought the problem through? The one who has proposed a working equation, or the one who just wrote that equation was incorrect without producing one more correct?

---

Giovanni Ciriani
http://www.GlobusSHT.com

So, my biggest mistake was to not specify I was talking about real world conditions? I simply could not tell you where the losses would be if there was no hysterisis and no friction because the 2nd law says there had to be losses. But I couldn't tell you where as the only possible losses I know about are friction and hysterisis that could account for the required loss. Therefore, it would be impossible. What is wrong with my understanding.

You knew I was talking about real world conditions. Why was it you kept denying that energy loss would be inevitable, even when I pointed out the 2nd law required it?

My initial post on this point was about a real world condition. You and Dr. Coggan had to resort to some crazy scenario that was both hypothetical and impossible to try to make me look like I didn't know what I was talking about. At least I think the few who are still following this thread now understand this.

---

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

Huh? I simply stated a fact. I made no mention of modeling losses. My belief is based upon my personal experience and an energy analysis. I do not have sufficient math skills to develop a workable model although I know it has to contain two additional terms beyond the MMF model to be a reasonable model, a term for friction (or several terms for friction - there are several frictional elements) and a term for material losses (or several terms as there are several material loss elements from the legs, pedals, cranks, frame, and more).

It is incontrovertible that the real life pedaling motion involves energy losses. This has been shown many times in unloaded pedaling where it is reasonably easy to separate pedaling losses from other losses as many losses, such as bearing and chain friction are pretty well known. The only variables which cannot be separated involves both leg friction and dynamic material losses. These two losses have been shown to be substantial in many studies - just look at what Papadapalaous wrote and the McDonald study. What is crazy is that somehow Papadapalous, Coggan, Tom A., Martin, and others seem to think that just because you load the chain that all these losses can be made to disappear and then they point to the MMF model as "proof". You were much better qualified than I to call them on this yet it is left up to me and even you were critical of me doing so and are now addressing your modeling criticisms towards me, not them. Yet, despite it being incontroverticle, I spend 100 posts or so defending the fact that the pedaling motion actually involves losses. It is crazy. Even now, those who were arguing the opposite still have not been able to bring themselves to agree with my original assertion. Rather, they are arguing that I don't understand modeling, the losses are small (for which they have no evidence), or any other myriad things.

---

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

Yes you did and it was the interactions with you that caused me to determine that the MMF could actually work if it were actually possible to build. I also have changed some of my thinking as a result of this thread. However, your equations again were misleading for the analysis of the problem because there was no provision for materials loss. You wrote the equations for the MMF with the implication that they applied to the problem. The MMF model requires the transfer of energy between the parts. In this instance the second law requires energy loss. Energy transfer requires material deformation and, hence, hysterisis loss. The MMF was being represented as representing a real world solution. While it is true that some of the KE could be moved around such that the losses are probably not as high as I, at first, anticipated, a reasonable model would account for them until modeling, confirmed by experiment, truly showed them to be so small as to be inconsequential. The data from unloaded pedaling, however, suggests the losses are too great to ever be ignored and, probably, not much can be done about it because a lot of the loss is probably coming from the hysterisis in the soft tissue of the leg, tissue that is constantly being accelerated, has a lot of mass and doesn't have a lot of springiness. Without a proper model though, we are all just guessing.

---

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

I think we are getting somewhere. By unloaded pedaling, you mean passive muscles in which shortening and lengthening muscle fibers cause the sliding myo-filaments to generate friction against each other. Am I interpreting you correctly?

---

Giovanni Ciriani
http://www.GlobusSHT.com

Unloaded pedaling is simply pedaling that is doing no external work so no net force/work done by the pedals. This means the muscle are not passive but contracting but only to the degree necessary to replace that losses from the motion. Internal friction in the joints and muscles would be one source of loss but this cannot explain all the loss because the shape of the loss curves are curvilinear and a friction only based loss would be expected to follow a straight line. Therefore, material deformation losses must be present also and these woudld be expected to vary with the square of the cadence, causing the losses to follow a curvilinear path.

---

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

Frank,
What curve do you mean, and why should it follow a straight line? There could be viscous losses as well. Perhaps dr. Coggan or the rest of the camp can illuminate.

---

Giovanni Ciriani
http://www.GlobusSHT.com