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Quantifying Cadence/Force/Power relationship
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All,

Anyone who has ridden with a power meter has discovered that you can generate more watts with less peak force by pedaling at a higher cadence. At low cadence, you have to really stomp on the pedals to get the same wattage. I'm trying to demonstrate that lesson to new triathletes & cyclists, to emphasize the importance of developing the skill of getting your legs around faster. I'm also arguing that its easier to develop a high cadence than it is to develop stronger legs.

I'd like to put some numbers behind that assertion that will really drive the lesson home. Does anyone have a formula, or maybe some empirical results, that relate the maximum force on the pedals vs cadence resulting in watts? For example, I'd love to say that to generate 200 watts at 80 RPMs requires you to exert a peak force of 30 lbs, but to generate 200 watts at 100 rpm only requires a peak force of 20 lbs. (I just pulled those numbers out of thin air but that's the kind of statement I'd like to be able to make.)

I'm also personally curious to hear different opinions on where the extra power comes from. I have two theories: One is that at higher cadences force is applied more smoothly, so the total work done by one pedalstroke is higher or the same even though the peak force is lower, because you exert force throughout the pedalstroke. That's the biomechanical factor. The other is that the work per pedalstroke is lower but you make it up by more pedalstrokes per minute, or less time per pedalstroke. That's the physics phactor -- same work in less time means more power. Both factors have to play a role, but I don't know if one dominates or if there's some other effect that I'm not thinking of.

I'm sure this has been studied extensively and there's a paper I can read, but I don't know where to find it.

Thanks for any references, pointers, or answers.

Lee Silverman
JackRabbit Sports
New York City
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Re: Quantifying Cadence/Force/Power relationship [lsilverman] [ In reply to ]
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[reply]All,

Anyone who has ridden with a power meter has discovered that you can generate more watts with less peak force by pedaling at a higher cadence. At low cadence, you have to really stomp on the pedals to get the same wattage. I'm trying to demonstrate that lesson to new triathletes & cyclists, to emphasize the importance of developing the skill of getting your legs around faster. I'm also arguing that its easier to develop a high cadence than it is to develop stronger legs.

I'd like to put some numbers behind that assertion that will really drive the lesson home. Does anyone have a formula, or maybe some empirical results, that relate the maximum force on the pedals vs cadence resulting in watts? For example, I'd love to say that to generate 200 watts at 80 RPMs requires you to exert a peak force of 30 lbs, but to generate 200 watts at 100 rpm only requires a peak force of 20 lbs. (I just pulled those numbers out of thin air but that's the kind of statement I'd like to be able to make.)

I'm also personally curious to hear different opinions on where the extra power comes from. I have two theories: One is that at higher cadences force is applied more smoothly, so the total work done by one pedalstroke is higher or the same even though the peak force is lower, because you exert force throughout the pedalstroke. That's the biomechanical factor. The other is that the work per pedalstroke is lower but you make it up by more pedalstrokes per minute, or less time per pedalstroke. That's the physics phactor -- same work in less time means more power. Both factors have to play a role, but I don't know if one dominates or if there's some other effect that I'm not thinking of.

I'm sure this has been studied extensively and there's a paper I can read, but I don't know where to find it.

Thanks for any references, pointers, or answers.

Lee Silverman
JackRabbit Sports
New York City[/reply]

The problem with your hypothesis is the energy required to make the pedals go around varies with the cube of the cadence. So, while it may take less force on the pedals to generate the same power, it takes more energy overall if one is above the most efficient cadence, which will vary depending upon how much power the rider is generating. The most efficient cadence is probably around 60 or so for grandmothers riding to the store for a loaf of bread, 70-85 for most competitive athletes, and 90-100 for the pros putting out 350-400 watts. If it were as simple as how much force was on the pedals indicated how "easy" it is to generate power we would all be riding at cadences or 200 or more but I challenge you to try.

--------------
Frank,
An original Ironman and the Inventor of PowerCranks
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Re: Quantifying Cadence/Force/Power relationship [lsilverman] [ In reply to ]
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It would be nice if you could quantify and rate it like cars, with horsepower and torque. They're similar but different and peak at different RPM (cadence). I would guess that in a cyclist, higher torque would help at lower cadence like climbing, and horsepower better for high rpm sprinting. I assume torque would be influenced a lot by the length of a rider's legs, and more specifically by the length of the femur and tibia(is that the lower one?). Pretty soon we'll be able to list a whole pile of trivial stats about ourselves and be just like baseball players!

Greg.
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Re: Quantifying Cadence/Force/Power relationship [lsilverman] [ In reply to ]
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In Reply To:
All,

Anyone who has ridden with a power meter has discovered that you can generate more watts with less peak force by pedaling at a higher cadence. At low cadence, you have to really stomp on the pedals to get the same wattage. I'm trying to demonstrate that lesson to new triathletes & cyclists, to emphasize the importance of developing the skill of getting your legs around faster. I'm also arguing that its easier to develop a high cadence than it is to develop stronger legs.


I disagree with this. At least for me, it's way easier to maintain 200w at a cadence of 70 than at 95.

I'd be careful with the use of "strong" here, too. I think some will object.

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