Those look very cool. I am amazed at some of the stuff we have managed to make.
My wife would think is says more about the "space" between your ears that you are interested in this stuff.
Well, if something cannot stretch, how does it absorb energy. Rigid body mechanics and modeling are mainstays of engineering to make these problems more easily solvable, IMHO.
Wait, you can't have it both ways. Perfect spring/bike capacitor? Choose one. Then do the math to show that it is actually possible (OK, I admit it is possible in the case of the perfect spring). I have already explained why the bike cannot act as this capacitor (plus the bike cannot give the energy back to the rider with a free wheel in the back, this could only work on a fixie). How does the bike act as this energy capacitor when there is a free wheel?

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Frank,
An original Ironman and the Inventor of PowerCranks

It doesn't. It only transmits it.



And the assumption of rigid bodies is accurate enough to allow those calculations to be useful.




Under a constant aero and gravity load (still disregarding the friction everywhere else) the chain doesn't go slack, does it?

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http://bikeblather.blogspot.com/

Frank wrote:
A perfectly rigid material would have no
capacity to absorb any energy so would
shatter at the first attempt to push
against it.

Frank, this statement is like fingernails on the blackboard. It is that painful to read.

Let's make this very simple. Forget the thighs. Take a fixie at rest; put a weight on one of the pedals. The pedal starts are 2:00. The weight goes down, the bike accelerates forward; the weight comes back up to 10:00 (okay, 9:59 in the real world), the bike stops; the weight goes back down, the bike accelerates backward.

If you acknowledge that this can happen without materials shattering (even if the materials are ideally rigid) -- which I think you must -- you have a problem on your hands. The energy in the system is a combination of potential (varies sinusoidally with crank angle) and kinetic (some of which varies with square of crank speed, other of which varies with square of bike speed). Yet energy is not lost (or it is lost negligibly -- and a real world measurable loss won't be heating the weight on the pedal, it will be bearing loss and air resistance).

From that exercise, move to a bike with initial forward velocity and one weighted pedal. The velocity will undulate by less and less for increasing initial velocity. The loss of energy will be negligible -- again, the usual bearing friction and wind resistance will explain anything you can measure.

From that exercise, it is a pretty small step to replace the inert weight with a leg, despite the linkages involved. If the squares of the speeds can be worked out with a lump of mass on a pedal, then they can be with a leg as well.

Notes that might help:
- what you perceive as imbalances of energy actually balance out (efficiently, mind you) in real time, as energy is transmitted from one place to another or converted from one form to another.
- as Tom A has pointed out, you should not be thinking that just because a material is non-ideal that there will actually be measurable losses due to the flexure of the material.

"It doesn't. It only transmits it."

Discounting kinetic energy, right? (Assuming the links have mass -- maybe we're thinking of different things.)

That only works when there is no need for energy storage. It cannot work in the case of the MMF because of the mass differences and the velocity ratio being fixed by the gearing. If KE is proportional to mv^2 these differences cannot work for all situations.

Of course, in most instances the losses are small. In this instance though we are trying to analyze where the losses are between the muscle and the wheel and how and where the cadence losses come from. Small (or smallish) losses may be important to this understanding so they shouldn't be ignored until they are demonsrated and understood to be trivial.

It would have to in the case of the MMF when the bike is trying to return energy back to the thighs and then when it changes back to the thigh providing energy to the bike and vice versa. It would have to go slack 4 times per revolution. In the case of the MMF the rider is providing no energy to keep the bike going. It is a perpetual motion machine, remember?

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Frank,
An original Ironman and the Inventor of PowerCranks

A rigid body can still have mass. The kinetic energy of a rigid link can increase or decrease by changing it's velocity. You also seem to be mixing your frames of reference in regards to the velocities of the leg masses, the tangential velocity of the crank, and the translational velocity of the bicycle.



Right, because in that scenario there are no frictional (including air friction) losses or hysteretic material losses. So, the first law of thermodynamics and Newton's first law of motion require it to keep moving with no external input.

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http://bikeblather.blogspot.com/

The problem here is the amount of KE the rigid body can have is constrained by the amount of energy all the elements can have because they are all tied together. Unless you can show that the reduction of energy in one part is exactly balanced by increases in the energy in other parts when constrained by their various speed restrictions. I contend it is simply impossible since the masses are different and the energy varies with the velocity squared. You (or anyone else) has yet to show it is possible other than declaring it to be so. If it is not possible then a rigid body (a body that cannot absorb and store energy) cannot work in this situation where the total energy of the entire system must remain constant.
While I can accept the hypothetical of zero frictional losses when looking at other losses I cannot accept the zero material losses from hysterisis. I contend that there are such losses and that they are not trivial. You must concoct some half-baked additional hypothetical to the MMF, that can't possibly exist, to say it isn't so.

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Frank,
An original Ironman and the Inventor of PowerCranks

Yes...see my later response. He was referring to it "absorbing energy", and I don't consider a mass increasing it's KE as "absorbing energy"...it's important to try to be precise with the terminology so that we all don't spend multiple pages of a thread explaining relatively basic physics to someone who should already understand this stuff :-\

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http://bikeblather.blogspot.com/

@Frank
Big parts of your argumentation are so absurd, that I finally give up any hope, I could ever explain these quite simple things to you.

I assume, there must be some knowlageable people in your company you could talk to!?

This is what I was referring to in my post on Pros sitting up out of the aero position.

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wovebike.com | Wove on instagram

Perhaps you could be a little more specific as to which "big parts" are so absurd that you have given up any hope of explaining them. Perhaps you can't explain them to me but you can at least specify the parts you disagree with and which parts you agree with, if any.

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Frank,
An original Ironman and the Inventor of PowerCranks

You can't be serious, can you?
In almost every post I told you, what I disagree with.

Okay, I tell you again where we agree:

- Chrissies low cadence is good.
- And it is good for a reason.
- And at least part of the reason are higher energy losses at higher cadence.

But we totally disagree about the nature of these losses.
In fact there are losses, which get bigger with higher cadence
- because of the properties of human legs, which are neither nearly perfectly stiff nor perfect springs, but they are largly made of soft stuff which "absorbs" energy when it is deformed.
- because faster movements of the legs, pedals and cranks have aerodynamic disadvantages.
- maybe there are more reasons in the muskels, but I don't know much about this.

Almost everything you write about materials and energies is nonsense. I won't specify that futher again.

Sorry, I missed this. Perhaps you could show me where he connects the varying speed (energy) of the thigh to the exactly compensatory varying speed (energy) of the wheel/bike. (Because of the chain coupling, the speed (an contained energy) of each component is tied to every other component.) And, then show me where he shows that as the energy changes in in the thigh (the thigh sees energy changes even though the rotational speed of the cranks - and presumably the speed of the bicycle - remains constant) this results in an exactly equal but opposite compensatory energy change in the other coupled system components. In the MMF this is a condition that must be satisfied using rigid components for the MMF to become a perpetual motion machine as everyone wants it to be. If it can be shown the energy can be moved about the MMF with this condition being satisfied then I will surrender. I don't see where he does this and I don't think it is possible. That is the problem that I have and it is why I believe there is no solution to the problem which means there have to be energy losses imposed on the system and a perpetual motion machine is not possible using the MMF design.

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Frank,
An original Ironman and the Inventor of PowerCranks

Really??? Do you have any evidence to support such a statement?

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Frank,
An original Ironman and the Inventor of PowerCranks

So...does that mean that you still don't understand the first law of thermodynamics and Newton's first law of motion?

If, in this hypothetical case, there are no frictional losses and there are ideally rigid links, where else is energy being removed from the system that would require additional energy to be input to keep it moving? Since the energy cannot be lost as heat (again, no friction and no hysteretic losses), then the ONLY option is for it to be "moved around" between KE and PE of the various constituents to keep the total energy of the system constant.

You say that in this idealized condition that there still "has to be" energy losses. Where are they?

I accept your surrender :-)

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http://bikeblather.blogspot.com/

Sorry no wind tunnel data or something like that.

But I have this (sorry, again in German):
http://www.rennradtraining.de/kreuzotter

A bike speed calculator where you can change a lot of data, and see what effect it has on the speed.
There you can also change the cadence (= Trittfrequenz). In this model (nobody knows if the model is right), a cadence change from 100 to 70 leads to a speed increase of about 0.3 km/h.

I assume that might be too much, but I don't know.
But it is plausible that there is an aerodynamic effect:
The best case would be not to move on the bike at all.
When you pedal, the upper leg moves faster than the bike and will have more aerodynamic drag. Since the power necessary to overcome aerodynamic drag rises with the power of 3 of the speed (have I expressed this correctly?), the additional drag of the upper leg will be more than the decreased drag of the lower leg.
And even if the cranks are in the front - back position the vertical speed of the legs adds something to the horizontal speed (vector addition) of the whole bike.

Ummm...yeah...I'd like to see the basis for that calculation used in that model...

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http://bikeblather.blogspot.com/

Well, your explanation makes some sense but it would be nice to see some experimental support, especially for the aero position where the forward moving upper legs get some shielding. This would be a very simple experiment to perform. If it hasn't been done it should be. Plus, there have to be plenty of people here who have been to the wind tunner who might have some experience with this but most of them have probably given up on this thread by now. Let's see what happens. If not, maybe I will start another thread and see if we can get some to post their wind tunnel experience with this.

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Frank,
An original Ironman and the Inventor of PowerCranks

Just found an english version of the calculator
http://ntucyc.twbbs.org/~hansjoerg/leistung/espeed.htm
and the faq:
http://ntucyc.twbbs.org/~hansjoerg/leistung/espeedfaq.htm

As you can see, the author assumes that at a (hypothetical) cadence of 500 the air resistance doubles. Obviously this can only be a very rough estimate, but maybe he has some real data supporting that. I don't know.
At least some other data in the calculator are based on real measurements with an SRM sytem.

One of several reasons why I don't put much faith in that calculator...

(BTW, I am aware of at least two wind tunnel studies examining the effects of cadence on aerodynamic drag, with neither being able to detect any effect. This makes sense when you consider the relatively slow speed at which the legs move relative to passing air.)

Is it possible to give some references. I couldn't find anything on a google search

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Frank,
An original Ironman and the Inventor of PowerCranks

Try typing "cadence aerodynamic drag" into the search box and look at the 3rd link. ;-)

(The other research of which I am aware - but, surprisingly, the authors of the above study apparently were not - is work done by Chet Kyle back in the mid 1990s, which was described in Cycling Science.)

http://www.hupi.org/HPeJ/0014/0014.html

The usefulness of both coast-down and wind-tunnel tests is improved when test results provide the best insight to actual cycling conditions. In order to understand the effect of leg position and cycling cadence on the drag of a cyclist, a short wind-tunnel test was completed to measure the drag of a cyclist with the legs in several static positions, and with the legs spinning at different cadences.
Discussion
It is not surprising that the cyclist's drag was significantly affected by crank position. The highest drag occurred for the case of the crank arms normal to the ground. This position would present the rider with the largest frontal area. It was somewhat surprising that the case of the pedals in the horizontal position was not the smallest drag value, although the positions near the crank arms being horizontal resulted in lower drag. The standard deviation for each test was quite small.
The difference in drag between pedal positions varied from 1 - 5%. As coast-down tests with the rider in a static position are sometimes used to measure the effect of equipment changes, the results of this test show that controlling crank arm and leg position is quite important. The variation between crank arm and leg positions could be larger than the result expected from a change in equipment.
Pedaling cadence showed little effect on the measured aerodynamic drag, with only a 1% variation between test conditions. Thus, any desired pedaling cadence can be used for wind-tunnel testing.
The drag measured for a rider when pedaling is not influenced in a significant way by the speed of pedaling, in the 40-100-rpm range. The drag measured while the rider is pedaling turned out to be a little smaller than the average of measurements taken with the rider's feet stationary at various positions around the pedaling circle. We do not know the reason for this difference, but it is quite small. We conclude that it is valid to take wind-tunnel drag measurements with the rider pedaling anywhere in the 40-100-rpm range.

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"Competetive sport begins where healthy sport ends"

i guess this shows the value of actually doing testing to support or refute what seems logical (or not). :-) It would seem cadence has a trivial impact on aerodynamic drag. Why this calculator thinks it does is anyone's guess.

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Frank,
An original Ironman and the Inventor of PowerCranks

you beat me to the link. i knew i'd seen it somewhere.

I've been trying to follow the thread but haven't read it all so i don't know if this study was quoted or if it has any relavance.
Have you see it and is there anything in here that would add to the discussion of optimal cadence.
thanks

Local and global factors affecting the optimal cadence in cycling (U. Emanuele)

I also found this by the same person

A Holistic Mechano-physiological Model To Explain The Optimal Cadence In Cycling

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"Competetive sport begins where healthy sport ends"