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Re: cadence [Andrew Coggan] [ In reply to ]
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The contractile efficiency of the muscle is around 40%. The overall pedaling efficiency of the cyclist is about 20%. Account for all the losses without invoking losses from the pedaling motion itself.

I don't know, where these numbers come from and if they are valid. Let's assume, they are ok.

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.
Actually, the 40% number comes from some experimental studies. The efficiency of the muscular contraction varies substantially based upon the initial conditions. To reach 40% or higher requires pre stretching.

The purpose here is not to say that muscles contract at any specific efficiency when pedaling but to stimulate a discussion of where all the losses occur between the muscles and the wheel. No one seems to be able to account for all of these losses.

The numbers you give above seem pretty nonsensical to me since I just posted a link to a study that showed muscle contractile efficiency on the knee extensor varied between 26 and 28% depending upon frequency. I would love to see some references.

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Frank,
An original Ironman and the Inventor of PowerCranks
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Re: cadence [Slowman] [ In reply to ]
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Ok,

Let me be more specific. I went from a 40k TT in over an hour like 1:03 to 1:05 to an open 40k in 57 minutes and have held a 58 minute in an olympic distance race. This has also translated to faster half IM splits...2:11, 2:15. I am 6'1" 175lbs with an open marathon time of 2:46. This being said I haven't been able to run well off the bike...like no better than 1:30 in half IM. I did have a great race at Alcatraz in terms of my bike/run combo, but that was hardly a normal TT, since it was super hilly and I rode a road bike set up. Now that I am attempting to race Ironman distance I'm definately open to suggestions regarding efficiency. I don't use a HR monitor or power meter so either one of those would probably help. In terms of a drop in cadence, I went from trying to keep it 95 or above to low 80's with must faster times. Hope that is specific enough.

http://www.loopd.com/...pzuelke/Results.aspx
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Re: cadence [gciriani] [ In reply to ]
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> __________________________________________________________________________
>
> "the power input represented by the maximum kinetic energy of the thighs is
> in the order of 6-7W. "
> __________________________________________________________________________
>
> Please forgive me for asking, but I do not understand the physics behind your
> calculations.

Nor do I! My wording above was deliberately vague so as not to accept the notion that the thighs are absorbing the energy. I did the calcs that way for hypothetical reasons, hoping to exclude Frank's ideas on the basis of the numbers alone, since Frank is not persuaded by other arguments. But since my calcs were off I'm eating some crow. Still, Frank's assumptions continue to be wrong, and it may still be worth the effort to try to get him a glimpse of what he's missing.

The Power-Velocity curves may be useful (I haven't thought about it much), but I suspect that there are also other factors that make it more complex than just that.
Last edited by: Slowman: Oct 21, 09 17:33
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Re: cadence [LidlRacer] [ In reply to ]
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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".

Maybe we have differing conceptions of the "metal biker". I think of a metal man sitting on a fixie.
Why are the legs decelerated in some points of the movement? Because the pedals apply a force to them.
Maybe you have heard of actio = reactio.
When the pedal applies a force to the bikers leg, the bikers leg applies a force in the opposite direction to the pedal. This will acceerate the bike.
And vice versa.
As I said: Trivial.

@pedaller:
Now you get it right! The whole bike + biker constantly accelarates and decelerates a little bit. There goes the energy and nowhere else.
Sorry, you are wrong. Because of the differences in masses it is impossible for the entire bike/rider system to speed up enough to make up for the energy variation in the thigh. The problem is energy is equal to 1/2mv^2. if the masses are not equal how does the velocity variations exactly equal what is needed since the velocity of the thigh and the velocity of the bike have a fixed ratio on a fixie. It is simply impossible.

--------------
Frank,
An original Ironman and the Inventor of PowerCranks
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Re: cadence [pedaller] [ In reply to ]
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Frank: yeah, my numbers should have been quartered. Oops. How embarrassing. Thanks for the correction. Maybe I'll draw a picture next time, or else stick to dead reckoning (and heckling on that basis... ;-) -- obviously I'm not devoting the time necessary to get the right answers.

But, while interesting, it doesn't matter much. Even if the total kinetic energy of the two thighs is not constant, you are not allowing for slight accelerations/decelerations of the bike+rider, which act as an energy reservoir. 5.7J if imparted to a bike+rider going 10 m/s will vary the speed by 0.007 m/s (25m/hr, ie, 0.025 km/h). You probably wouldn't perceive the energy being absorbed and released, which might lead you to think it isn't happening. But is it?

I'll read your link later. There is no doubt that contractile efficiency will drop with speed, but the point remains about defining how much and under what conditions that matters.
Of course there will be small speed variations during the pedal stroke but it is impossible for these to absorb the energy variations of the thigh since the masses are substantially different but the speed ratio of the two parts are fixed by the gearing. Since KE varies with the velocity squared it is not possible for this variation to absorb this variation since the speed variation of the thigh is huge and the speed variation of the bicycle is miniscule (and, to reiterate, in a fixed ratio).

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Frank,
An original Ironman and the Inventor of PowerCranks
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Re: cadence [Frank Day] [ In reply to ]
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It is simply impossible.

"You keep using that word. I do not think it means what you think it means..."

- Inigo Montoya

http://bikeblather.blogspot.com/
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Re: cadence [pedaller] [ In reply to ]
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> _______________________________________________
>
> "the power input represented by the maximum kinetic energy of the thighs is
> in the order of 6-7W. "
> _______________________________________________
>
> Please forgive me for asking, but I do not understand the physics behind your
> calculations.

Nor do I! My wording above was deliberately vague so as not to accept the notion that the thighs are absorbing the energy. I did the calcs that way for hypothetical reasons, hoping to exclude Frank's ideas on the basis of the numbers alone, since Frank is not persuaded by other arguments. But since my calcs were off I'm eating some crow. Still, Frank's assumptions continue to be wrong, and it may still be worth the effort to try to get him a glimpse of what he's missing.

The Power-Velocity curves may be useful (I haven't thought about it much), but I suspect that there are also other factors that make it more complex than just that.
You know, the thighs may only absorb the bulk of the energy when riding unloaded (this coming from negative muscle energy required to keep the pedal speed "constant". But, when riding loaded some of the losses may come from flexing and internal friction losses in the cranks and frame. Unless someone can convince me that there is a reasonable mechanism (that has some experimental support) to explain how this energy variation of the thighs is "conserved" I simply don't believe it exists.

--------------
Frank,
An original Ironman and the Inventor of PowerCranks
Last edited by: Slowman: Oct 22, 09 7:25
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Re: cadence [Tom A.] [ In reply to ]
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It is simply impossible.

"You keep using that word. I do not think it means what you think it means..."

- Inigo Montoya
I know what it means. It is impossible using everyday masses of the various parts of the system over the range of speeds normally encountered. (edit: if I am wrong someone should be able to do the math and prove that I am wrong)

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Frank,
An original Ironman and the Inventor of PowerCranks
Last edited by: Frank Day: Oct 21, 09 17:37
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Re: cadence [apzuelke] [ In reply to ]
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i hope you keep me updated on your experiments. i think high-90s is a great cadence for a 40k stand-alone, but it seems a bit high to me for a 40k in a tri. this, because, i think it's pretty evident in just watching cycling races from 3k to 3000mi that cadence rate trends up or down as effort trends up and down. a 40k in a tri is an easier effort than a 40k without a swim or run around it. so, i think 90-95 rpm, all things equal, seems about middlin'. in a half-IM, i'd think you'd go lower yet, maybe high-80s, again, all things equal. low-80s is more the typical cadence you see a top pro male using in an IM.

btw, i think a lot of people would take your not-very-fast 1:30 half-mary in a tri. otherwise, yes, i think a lot of folks here would say that using a power meter will teach you a lot about cadence and how it relates to your power.

let's keep this wine in the barrel for another year, and see what your best sense tells you then. i have a feeling your technique and tactics are still fluid, and you might say things in a year that you wouldn't say now.

Dan Empfield
aka Slowman
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Re: cadence [Slowman] [ In reply to ]
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i don't think chrissie wellington, as fine an athlete as she is, can be safely placed in that paradigm shifting category yet. but, let's say she is a paradigm shifter. i'm sure that, as you say, and as sporting history illustrates, the other top pro cyclists and triathletes won't let more than a few months elapse before they start emulating her.
I wouldn't call dropping the cadence 15 or 20 or so a paradigm shift except for the resistance one sees from the so-called experts if one brings this up or in discussing that this might be an advantage. Because of this resistance by most of the guru's I would say it is a paradigm shift should it ever catch on. Especially since she has been doing this (and dominating) for 3 years now and it seems few have even noticed (or when they do it is a critical notice - see what started this thread), let alone caught on to apply it to their own racing.

--------------
Frank,
An original Ironman and the Inventor of PowerCranks
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Re: cadence [Frank Day] [ In reply to ]
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"I know what it means. It is impossible using everyday masses of the various
parts of the system over the range of speeds normally encountered. (edit: if I
am wrong someone should be able to do the math and prove that I am wrong)"

Frank, if your theory were true -- that the metal biker on the fixie must lose energy because of the fixed gearing -- then it should not matter to you that the members of the metal biker are made of an ideal material. So please provide a mechanism whereby accelerating the thigh link in the metal-man-fixie scenario will actually cause energy loss in the thigh in the form of heat. (You may want math, but that is putting the cart before the horse. No calculations can be done on something that is unspecified.)

Put another way, what are you trying to say? Are you trying to say that if the man-metal-fixie (MMF) is positioned at standstill with the thighs at top and bottom, that giving the bike a push will not cause the thighs to move? (Ie, that energy cannot be transferred from the bike to the thighs?) Are you trying to say that if the MMF is in motion and the thighs are next to each other, that as they begin to slow (by application of a drive force to the pedals) that the bike will not accelerate? (Ie, that energy cannot be transferred from the thighs to the bike?) As you answer, bear in mind that forces normal to the pedalling circle do not result in lost energy. If energy is being lost, where is it going, and how is it getting there?

How can you be sure that the 'impossible' doesn't happen all the time? What does a flywheel do, anyway?
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Re: cadence [pedaller] [ In reply to ]
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"I know what it means. It is impossible using everyday masses of the various
parts of the system over the range of speeds normally encountered. (edit: if I
am wrong someone should be able to do the math and prove that I am wrong)"

Frank, if your theory were true -- that the metal biker on the fixie must lose energy because of the fixed gearing -- then it should not matter to you that the members of the metal biker are made of an ideal material. So please provide a mechanism whereby accelerating the thigh link in the metal-man-fixie scenario will actually cause energy loss in the thigh in the form of heat. (You may want math, but that is putting the cart before the horse. No calculations can be done on something that is unspecified.)

Put another way, what are you trying to say? Are you trying to say that if the man-metal-fixie (MMF) is positioned at standstill with the thighs at top and bottom, that giving the bike a push will not cause the thighs to move? (Ie, that energy cannot be transferred from the bike to the thighs?) Are you trying to say that if the MMF is in motion and the thighs are next to each other, that as they begin to slow (by application of a drive force to the pedals) that the bike will not accelerate? (Ie, that energy cannot be transferred from the thighs to the bike?) As you answer, bear in mind that forces normal to the pedalling circle do not result in lost energy. If energy is being lost, where is it going, and how is it getting there?

How can you be sure that the 'impossible' doesn't happen all the time? What does a flywheel do, anyway?
Yes, you can push the bike and start the wheels and the thighs in motion. At that point the sysem contains x amount of total energy. But, once in motion the energy variation of the thighs must be absorbed somewhere in the system or it must be lost to the system because the total energy of the system can never go up once external forces are removed. It cannot be transferred to the speed of the bike because the different masses and speeds cannot be made equal because the gearing is fixed. A perfectly rigid material cannot absorb the energy because it would fracture. It would take a perfect spring in the leg or crank or somewher to absorb the energy as potential energy and then return it without any loss. As far as I know, that material does not exist. Hence, even if this device could be made frictionless, it would not be a perpetual motion machine.

So, where is the energy lost to? Energy must be lost through materials distortion and hysterisis losses (heat), the only place it can go in a frictionless system.

--------------
Frank,
An original Ironman and the Inventor of PowerCranks
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Re: cadence [Frank Day] [ In reply to ]
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"I know what it means. It is impossible using everyday masses of the various
parts of the system over the range of speeds normally encountered. (edit: if I
am wrong someone should be able to do the math and prove that I am wrong)"

Frank, if your theory were true -- that the metal biker on the fixie must lose energy because of the fixed gearing -- then it should not matter to you that the members of the metal biker are made of an ideal material. So please provide a mechanism whereby accelerating the thigh link in the metal-man-fixie scenario will actually cause energy loss in the thigh in the form of heat. (You may want math, but that is putting the cart before the horse. No calculations can be done on something that is unspecified.)

Put another way, what are you trying to say? Are you trying to say that if the man-metal-fixie (MMF) is positioned at standstill with the thighs at top and bottom, that giving the bike a push will not cause the thighs to move? (Ie, that energy cannot be transferred from the bike to the thighs?) Are you trying to say that if the MMF is in motion and the thighs are next to each other, that as they begin to slow (by application of a drive force to the pedals) that the bike will not accelerate? (Ie, that energy cannot be transferred from the thighs to the bike?) As you answer, bear in mind that forces normal to the pedalling circle do not result in lost energy. If energy is being lost, where is it going, and how is it getting there?

How can you be sure that the 'impossible' doesn't happen all the time? What does a flywheel do, anyway?
Yes, you can push the bike and start the wheels and the thighs in motion. At that point the sysem contains x amount of total energy. But, once in motion the energy variation of the thighs must be absorbed somewhere in the system or it must be lost to the system because the total energy of the system can never go up once external forces are removed. It cannot be transferred to the speed of the bike because the different masses and speeds cannot be made equal because the gearing is fixed. A perfectly rigid material cannot absorb the energy because it would fracture. It would take a perfect spring in the leg or crank or somewher to absorb the energy as potential energy and then return it without any loss. As far as I know, that material does not exist. Hence, even if this device could be made frictionless, it would not be a perpetual motion machine.

So, where is the energy lost to? Energy must be lost through materials distortion and hysterisis losses (heat), the only place it can go in a frictionless system.
Frank, prove this and there is a Nobel prize with your name on it at the horizon. Seriously.

Your bragging rights would finally equal your panache and you wouldn't have to be the Don Quijote of ST :-)


Hint: This guy Newton thought about these things some 350 years ago. He even made a little 3-step "rule-book" to stick to when in doubt. He has since been called the most influential man of science ever. Maybe you can replace him?
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Re: cadence [Frank Day] [ In reply to ]
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Frank,


"But, once in motion the energy variation of the thighs must be absorbed somewhere in the system or it must be lost to the system because the total energy of the system can never go up once external forces are removed. It cannot be transferred to the speed of the bike because the different masses and speeds cannot be made equal because the gearing is fixed."

No one said the energy of the system in free motion had to go up. Why do you think the different masses and speeds need to be made equal? There will be a proportionality based on crank position, but so what? The rate of change of bike+rider speed is influenced by its inertia when viewed as a single mass combined with the inertia of the thighs. The rate of change of the thighs is influenced by their own inertia combined with the linear inertia of bike+rider. That inertia of bike+rider is a relatively large reservoir of kinetic energy which is added to or taken from, as appropriate. I think you must be thinking of the thighs and the bike+rider mass partly as independent systems, but they aren't. (Maybe you've spent too long thinking about independent cranks?)

Would it help to conceive of the MMF as a single-legged rider? Then gravitational potential energy enters the issue, but surely you can see that the rate of fall of the leg will be limited by the need to accelerate the bike+rider, and the leg will rise again by taking kinetic energy out of the system. Actually, in the first half of the descent, the rate of fall will not only be limited by the bike+rider acceleration, but also by the acceleration of the thigh; the rate in the second half of the descent will be limited by the bike+rider acceleration, but assisted by the deceleration of the thigh; and so on. Does that help?

I think it also might help you to make a simple Excel model and for small delta-angle of the crank work out pedal force, effect on bike speed and thigh speed over the related time interval, and work your way around the crank circle. Keep track of the sum of kinetic energy of the thighs and kinetic energy of the bike+rider. At some point the light will go on, surely. The 'work done' (component of pedal force tangential to the circle times the distance covered over the iteration cycle) is what adds to the kinetic energy of bike+rider and subtracts from the kinetic energy of the thighs. The same number is used as a basis for both.


"A perfectly rigid material cannot absorb the energy because it would fracture."

Well, if you are talking about mechanical deformation, then it would be undefined. That is obviously what was being excluded. There is still the possibility of thermal, gravitational potential, kinetic, and chemical potential energy (maybe I've missed some other types as well).


"As far as I know, that material does not exist."

Obviously. The point is to isolate different things to enhance discussion and understanding.


"So, where is the energy lost to? Energy must be lost through materials distortion and hysterisis losses (heat), the only place it can go in a frictionless system."

So the implication is that an ideal MMF could not move? The pieces would just shatter?
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Re: cadence [Slowman] [ In reply to ]
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"It didn't take long for people to adapt to the new high jumping technique as soon as it was understood. What is so difficult about understanding this cadence issue?"

i agree that paradigm shifts in technique occur. in my lifetime, i can think of these: fosbury flop, bill koch skating an entire xc race; discus spin replacing the glide shot put; underwater dolphin kick replacing surface swimming in fly and back; i'm sure there are others, but, i just can't think of them. they're rare. there are also aborted tries, like, doing a front somersault during the long jump.

i don't think chrissie wellington, as fine an athlete as she is, can be safely placed in that paradigm shifting category yet. but, let's say she is a paradigm shifter. i'm sure that, as you say, and as sporting history illustrates, the other top pro cyclists and triathletes won't let more than a few months elapse before they start emulating her.

"What top athletes do" as much reflects orthodoxy as what's best. Go back and look at some IM videos from the early 90s..... Allen, Welch etc are spinning away at cadences of 90+.
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Re: cadence [gciriani] [ In reply to ]
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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.

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).
But don't fibers IIx get fatigued, therefore you are not able to utilize them after a while?
During exercise at a mild-to-moderate intensity (such that it can be maintained for 5-9 h), type I motor units would be preferentially recruited, with initially limited recruitment of type IIa and especially type IIx motor units. As the initially-recruited type I motor units fatigued, additional motor units would be recruited to maintain the force/power output. Ultimately, essentially all motor units will have been extensively utilized, as evidenced, e.g., by the near-uniform depletion of muscle glycogen at fatigue.
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Re: cadence [Frank Day] [ In reply to ]
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Here is a link to a study looking at contractile efficiency in human muscle at different frequency. From this data it is clear that gross efficiency can drop as cadence goes up simply because of the contractile velocity. While I knew this I didn't expect it to be so large in this narrow range. This loss would be in addition to any losses we are discussing above.

Such losses are not in "addition to", they are the primary "energy sink". Once the limbs are actually set in motion by muscle contraction, there is very little additional loss (cf. Jim Martin's studies using inverse dynamics).
Last edited by: Andrew Coggan: Oct 22, 09 7:42
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Re: cadence [tim_sleepless] [ In reply to ]
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"Go back and look at some IM videos from the early 90s..... Allen, Welch etc are spinning away at cadences of 90+."

i think the best gauge of one's cadence throughout a race is to just look at what the computer or power meter says at the end of the race. in kona, you have a lot of tailwinds and shallow descents that call for riding at a faster cadence than you'll sustain over an average.

nevertheless, you might be right, that these were their average cadences. i don't know, because, while i was there every year, i don't have their bike computers' data.


Dan Empfield
aka Slowman
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Re: cadence [Frank Day] [ In reply to ]
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The numbers you give above seem pretty nonsensical to me since I just posted a link to a study that showed muscle contractile efficiency on the knee extensor varied between 26 and 28% depending upon frequency.

You are overlooking the fact that, when using Anderson's single leg knee extensor model, there is considerable non-contracting but nonetheless O2-consuming muscle in the leg being studied. As a result, the measured muscle (limb, really) efficiency is lower than observed during one- or two-legged cycling.
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Re: cadence [pedaller] [ In reply to ]
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Frank,


"But, once in motion the energy variation of the thighs must be absorbed somewhere in the system or it must be lost to the system because the total energy of the system can never go up once external forces are removed. It cannot be transferred to the speed of the bike because the different masses and speeds cannot be made equal because the gearing is fixed."

No one said the energy of the system in free motion had to go up. Why do you think the different masses and speeds need to be made equal? There will be a proportionality based on crank position, but so what? The rate of change of bike+rider speed is influenced by its inertia when viewed as a single mass combined with the inertia of the thighs. The rate of change of the thighs is influenced by their own inertia combined with the linear inertia of bike+rider. That inertia of bike+rider is a relatively large reservoir of kinetic energy which is added to or taken from, as appropriate. I think you must be thinking of the thighs and the bike+rider mass partly as independent systems, but they aren't. (Maybe you've spent too long thinking about independent cranks?)

Would it help to conceive of the MMF as a single-legged rider? Then gravitational potential energy enters the issue, but surely you can see that the rate of fall of the leg will be limited by the need to accelerate the bike+rider, and the leg will rise again by taking kinetic energy out of the system. Actually, in the first half of the descent, the rate of fall will not only be limited by the bike+rider acceleration, but also by the acceleration of the thigh; the rate in the second half of the descent will be limited by the bike+rider acceleration, but assisted by the deceleration of the thigh; and so on. Does that help?

I think it also might help you to make a simple Excel model and for small delta-angle of the crank work out pedal force, effect on bike speed and thigh speed over the related time interval, and work your way around the crank circle. Keep track of the sum of kinetic energy of the thighs and kinetic energy of the bike+rider. At some point the light will go on, surely. The 'work done' (component of pedal force tangential to the circle times the distance covered over the iteration cycle) is what adds to the kinetic energy of bike+rider and subtracts from the kinetic energy of the thighs. The same number is used as a basis for both.


"A perfectly rigid material cannot absorb the energy because it would fracture."

Well, if you are talking about mechanical deformation, then it would be undefined. That is obviously what was being excluded. There is still the possibility of thermal, gravitational potential, kinetic, and chemical potential energy (maybe I've missed some other types as well).


"As far as I know, that material does not exist."

Obviously. The point is to isolate different things to enhance discussion and understanding.


"So, where is the energy lost to? Energy must be lost through materials distortion and hysterisis losses (heat), the only place it can go in a frictionless system."

So the implication is that an ideal MMF could not move? The pieces would just shatter?
What your ideal MMF proposes is a perpetual motion machine. At least I know I have one supporter on my side in this debate, the US Patent office.

Simply show me a mechanism by which the energy of the different parts of the bicycle, when totaled up, remain constant while this bicycle is "coasting" along such that it would continue to coast forever. I will allow you to have frictionless bearings, joints, and chains. But, everything else must be real material with mass.

The difference between this problem and the "double pendulum" problem someone else presented is the double pendulum was simply converting potential energy into kinetic energy. In the MMF case there is a need to convert kinetic energy into kinetic energy through a fixed mechanism to keep the total energy constant. Good luck.

--------------
Frank,
An original Ironman and the Inventor of PowerCranks
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Re: cadence [Nicko] [ In reply to ]
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In Reply To:
"I know what it means. It is impossible using everyday masses of the various
parts of the system over the range of speeds normally encountered. (edit: if I
am wrong someone should be able to do the math and prove that I am wrong)"

Frank, if your theory were true -- that the metal biker on the fixie must lose energy because of the fixed gearing -- then it should not matter to you that the members of the metal biker are made of an ideal material. So please provide a mechanism whereby accelerating the thigh link in the metal-man-fixie scenario will actually cause energy loss in the thigh in the form of heat. (You may want math, but that is putting the cart before the horse. No calculations can be done on something that is unspecified.)

Put another way, what are you trying to say? Are you trying to say that if the man-metal-fixie (MMF) is positioned at standstill with the thighs at top and bottom, that giving the bike a push will not cause the thighs to move? (Ie, that energy cannot be transferred from the bike to the thighs?) Are you trying to say that if the MMF is in motion and the thighs are next to each other, that as they begin to slow (by application of a drive force to the pedals) that the bike will not accelerate? (Ie, that energy cannot be transferred from the thighs to the bike?) As you answer, bear in mind that forces normal to the pedalling circle do not result in lost energy. If energy is being lost, where is it going, and how is it getting there?

How can you be sure that the 'impossible' doesn't happen all the time? What does a flywheel do, anyway?
Yes, you can push the bike and start the wheels and the thighs in motion. At that point the sysem contains x amount of total energy. But, once in motion the energy variation of the thighs must be absorbed somewhere in the system or it must be lost to the system because the total energy of the system can never go up once external forces are removed. It cannot be transferred to the speed of the bike because the different masses and speeds cannot be made equal because the gearing is fixed. A perfectly rigid material cannot absorb the energy because it would fracture. It would take a perfect spring in the leg or crank or somewher to absorb the energy as potential energy and then return it without any loss. As far as I know, that material does not exist. Hence, even if this device could be made frictionless, it would not be a perpetual motion machine.

So, where is the energy lost to? Energy must be lost through materials distortion and hysterisis losses (heat), the only place it can go in a frictionless system.
Frank, prove this and there is a Nobel prize with your name on it at the horizon. Seriously.

Your bragging rights would finally equal your panache and you wouldn't have to be the Don Quijote of ST :-)


Hint: This guy Newton thought about these things some 350 years ago. He even made a little 3-step "rule-book" to stick to when in doubt. He has since been called the most influential man of science ever. Maybe you can replace him?
My proof? Simply the US Patent office has declared perpetual motion machines to be impossible so it will never grant a patent for one regardless of how persuasive someone's "proof" is. This would be a perpetual motion machine. So, no Nobel prize for me I am afraid.

I am not the one proposing a perpetual motion machine. It is up to you guys to show your perpetual motion machine will work, not for me to show that it won't. I have attempted to show you why it won't work (even using some of newton's principles) but you folks simply refuse to believe.

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Frank,
An original Ironman and the Inventor of PowerCranks
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Re: cadence [Andrew Coggan] [ In reply to ]
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The numbers you give above seem pretty nonsensical to me since I just posted a link to a study that showed muscle contractile efficiency on the knee extensor varied between 26 and 28% depending upon frequency.

You are overlooking the fact that, when using Anderson's single leg knee extensor model, there is considerable non-contracting but nonetheless O2-consuming muscle in the leg being studied. As a result, the measured muscle (limb, really) efficiency is lower than observed during one- or two-legged cycling.
???. Where does all this "non-contracting but nonetheless O2-consuming" muscle go when one gets on the bicycle?

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Frank,
An original Ironman and the Inventor of PowerCranks
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Re: cadence [Frank Day] [ In reply to ]
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What your ideal MMF proposes is a perpetual motion machine. At least I know I have one supporter on my side in this debate, the US Patent office.

Simply show me a mechanism by which the energy of the different parts of the bicycle, when totaled up, remain constant while this bicycle is "coasting" along such that it would continue to coast forever. I will allow you to have frictionless bearings, joints, and chains. But, everything else must be real material with mass.

The difference between this problem and the "double pendulum" problem someone else presented is the double pendulum was simply converting potential energy into kinetic energy. In the MMF case there is a need to convert kinetic energy into kinetic energy through a fixed mechanism to keep the total energy constant. Good luck.

There are only two reasons why such a "perpetual motion cyclist" could not exist in reality are:

1) friction, and

2) the fact the ankle joint is flexible, not fixed.

You've already stated that you are willing to allow for a completely frictionless (i.e., lossless) environment - if you are willing to fix the ankle then badabing, badaboom! problem solved.
Last edited by: Andrew Coggan: Oct 22, 09 10:18
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Re: cadence [Frank Day] [ In reply to ]
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The numbers you give above seem pretty nonsensical to me since I just posted a link to a study that showed muscle contractile efficiency on the knee extensor varied between 26 and 28% depending upon frequency.

You are overlooking the fact that, when using Anderson's single leg knee extensor model, there is considerable non-contracting but nonetheless O2-consuming muscle in the leg being studied. As a result, the measured muscle (limb, really) efficiency is lower than observed during one- or two-legged cycling.
???. Where does all this "non-contracting but nonetheless O2-consuming" muscle go when one gets on the bicycle?
Nowhere. It (e.g., the hamstrings) does, however, start contracting, such that overall efficiency increases (since resting muscle consumes O2, but does not generate any power, dragging down the overall average efficiency that is calculated).
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Re: cadence [Andrew Coggan] [ In reply to ]
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Here is a link to a study looking at contractile efficiency in human muscle at different frequency. From this data it is clear that gross efficiency can drop as cadence goes up simply because of the contractile velocity. While I knew this I didn't expect it to be so large in this narrow range. This loss would be in addition to any losses we are discussing above.

Such losses are not in "addition to", they are the primary "energy sink". Once the limbs are actually set in motion by muscle contraction, there is very little additional loss (cf. Jim Martin's studies using inverse dynamics).
LOL.

First, they are "in addition" to what we have been talking about here. We can discuss the relative size of these losses if you want but it seems to me that this particular loss is all one needs to throw out to those who say that pedaling style doesn't matter, just ride your bike and do what comes naturally. Cadence is part of pedaling style so pedaling style does matter.

Second, Martin is crazy if he is talking about cycling (not so if he is talking about walking or running). In cycling the limbs (both the thigh and lower leg) are constantly either accelerating or decelerating and usually doing so against substantial resistance. I look forward to hearing about at which point of the pedal stroke the muscles are allowed to "rest" because they "have been put in motion".

The oxygen cost to contracting muscle has to do with how much external work they do. Isometric contraction doesn't involve a lot of oxygen cost. Unloaded contraction doesn't involve a lot of oxygen cost. However, loaded contraction does. That is what most cycling involves, loaded contraction of these prime mover muscles. Isn't that your mantra, "just push harder".

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Frank,
An original Ironman and the Inventor of PowerCranks
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