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# Power/Watts: Independent of Pedal Speed?

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Road Cycling “It is by riding a bicycle that you learn the contours of a country best, since you have to sweat up the hills and coast down them. Thus you remember them as they actually are, while in a motor car only a high hill impresses you, and you have no such accurate remembrance of country you have driven through as you gain by riding a bicycle.” -- Ernest Hemingway

# Power/Watts: Independent of Pedal Speed?

10-12-17, 08:34 PM
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Power/Watts: Independent of Pedal Speed?

Probably a basic physics question. Is wattage affected by cadence? If, say, two identical riders on identical bikes are riding together, same speed; one is in a large gear pedaling at ~70rpm, while the other is spinning at 110+rpm. Is one producing more watts than the other?
10-12-17, 08:37 PM
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It depends on how exact “exact” means. The slower cadence will produce less drag. Slightly. From a meaningful standpoint though, power produces speed, and it doesn’t matter how you get that power.
10-12-17, 08:49 PM
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HP = Torque x RPM ÷ 5252

Power and Torque: Understanding the Relationship Between the Two, by EPI Inc.
10-12-17, 08:54 PM
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Originally Posted by patrickgm60
If, say, two identical riders on identical bikes are riding together, same speed; one is in a large gear pedaling at ~70rpm, while the other is spinning at 110+rpm. Is one producing more watts than the other?
No. Same power if they're going the same speed and everything else (position, tire etc) are equal.
10-12-17, 08:58 PM
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^ Which is to say, slower rpm means more torque is needed with each pedal stroke. A faster rpm means you need to apply less torque with each stroke but as you have to do more strokes per minute it all balances out in the end so your power is theoretically the same regardless of what rpm you do.

I say theoretically because in practical terms there will be slight gains and losses due to friction in the drivetrain. Plus, I've always wondered about the aero effects of higher rpm. Does spinning your feet about faster mean more drag? If only I had a wind tunnel...
10-12-17, 09:15 PM
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Originally Posted by smarkinson
^ Which is to say, slower rpm means more torque is needed with each pedal stroke. A faster rpm means you need to apply less torque with each stroke but as you have to do more strokes per minute it all balances out in the end so your power is theoretically the same regardless of what rpm you do.

I say theoretically because in practical terms there will be slight gains and losses due to friction in the drivetrain. Plus, I've always wondered about the aero effects of higher rpm. Does spinning your feet about faster mean more drag? If only I had a wind tunnel...
Yes. Triathletes have done the testing. It’s also more efficient metabolically.

10-12-17, 10:12 PM
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Originally Posted by patrickgm60
Probably a basic physics question. Is wattage affected by cadence? If, say, two identical riders on identical bikes are riding together, same speed; one is in a large gear pedaling at ~70rpm, while the other is spinning at 110+rpm. Is one producing more watts than the other?
If you neglect the friction in the rider/the movement of the legs, and any aero churn, then from the physics standpoint bike alone - your example - no.
If the force on the pedal is the same the 110rpm will be <110/70 more powerful due to transmission drag.

But since this is a human, max power over longer time events is closer to 93ave rpm for most racer types. Short range power/sprint is closer to 110/120 rpm.

Power is measured as force times distance per unit time (second).
So to be equal power the 70rpm needs to push harder.

Last edited by Doge; 10-12-17 at 10:18 PM.
10-12-17, 11:33 PM
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Same wattage.
10-13-17, 03:17 AM
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Originally Posted by Bah Humbug
It depends on how exact “exact” means. The slower cadence will produce less drag. Slightly. From a meaningful standpoint though, power produces speed, and it doesn’t matter how you get that power.
And as far as exactitude goes, it's important the riders be identical in physiology and metabolism, and that we're talking about watts measured at the bike, not total watts. Not just because a heavier rider has more resistance to overcome to move the bike, but he has to work harder just to move his own legs. And if one rider is able to sit still above the waist and the other has to dance all over the place, total watts would differ even at the same cadence and speed, but of course watts through the pedals would be the same. I think this is why fit is so important. It's not just about positional comfort, it's about efficiency in movement, too.
10-13-17, 04:44 AM
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wattage = power = work.

if 2 riders are overcoming the same quantity of resistance (mechanically, aerodynamically), and still riding at the same speed... then theyre doing identical work.

how they complete that work - by spinning fast or spinning slow - doesnt matter.
10-13-17, 04:54 AM
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Same wattage OP...but...rider with the slower cadence is applying more force on the pedals.
Because P = T X RPM, for maximum power, riders will opt for higher RPM because for the same force to the pedals, this will translate to more power. This for example is part of the reason that higher cadence riders like Lance and Froome were successful...because they put out more power for the amount of force they applied to the pedals for each pedal stroke.
10-13-17, 07:17 AM
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Every pedal stroke we have to pull our legs up, which takes energy, so from the perspective of physics the slow cadence is more efficient and will deliver more of your power to moving the bike. However, the slow cadence using more fast-twitch muscles and with more forceful strokes tend to utilize our glycogen energy stores, leading to muscle exhaustion. The fast cadence burns more fat, slow more carbohydrates. Because of that, we consider the fast cadence to be more economical.

But, considering the above more closely you have to consider not only the pedal speed but also the bike speed, because the muscle fiber recruitment depends also on the amount of force applied. In other words foot speed and bike speed.
10-13-17, 08:15 AM
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Believe it depends on definition of 'economical'. What is your definition?

Quite sure...will speak for myself...the reason why higher cadence is used on a sustained basis is endurance. At lower cadence...call it mashing...my legs will lactate and I will slow down. So I can sustain higher speed at an optimal cadence.

And higher cadence isn't just about endurance, it is about speed. The top sprinters in the world near the finish of a race spin the cranks at 120-130 RPM to achieve maximum power.
10-13-17, 08:25 AM
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Originally Posted by redfooj
wattage = power = work.

if 2 riders are overcoming the same quantity of resistance (mechanically, aerodynamically), and still riding at the same speed... then theyre doing identical work.

how they complete that work - by spinning fast or spinning slow - doesnt matter.
Not exactly. Wattage equals power, but that does not equal work. Work is independent of time. There's a certain amount of work required to, say, lift a piano up 50 flights of stairs, that is based on the gravity, and the weight of the piano. The EXACT same amount of work will be performed whether it is done in an hour, or 10 years. Power will be much higher the faster it is done though.

Wattage = power. Watts are the unit for power.

Power = work/time

work = force x distance

On the bike, you can use each revolution of the pedals as a measure of distance. Time for this equation is pedaling cadence. Double cadence, you're halving the amount of time it takes to bring the pedals around 1 revolution. The force is the force exerted on the pedal. If you double the force, you double the power. If you double the cadence, you double the power.

So yes, if one person is pedaling at 50rpm, while exerting 100lbs of force on the pedal, while another person pedaling at 100rpm while exerting 50 pounds of force on the pedal, power output (watts), will be exactly the same.

As others pointed out, there are other things to consider, but yes power is the same.
10-13-17, 08:40 AM
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And you touched upon why I don't put out more power since power is a function of work. I hate work.
10-13-17, 08:43 AM
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Originally Posted by Campag4life
And you touched upon why I don't put out more power since power is a function of work. I hate work.
Well, there's always the other option for moar watts....

10-13-17, 08:51 AM
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Originally Posted by Campag4life
Believe it depends on definition of 'economical'. What is your definition?
We, as in road cyclists, consider higher cadence to be more "economical" as in the most effective use of our limited reserves of power. Even though the "convention wisdom" is wrong that the power is the same, higher cadence is preferred for several reasons and I lump them together as "more economical". I'm just answering OP's question literally.

Originally Posted by Campag4life
Quite sure...will speak for myself...the reason why higher cadence is used on a sustained basis is endurance. At lower cadence...call it mashing...my legs will lactate and I will slow down. So I can sustain higher speed at an optimal cadence.

And higher cadence isn't just about endurance, it is about speed. The top sprinters in the world near the finish of a race spin the cranks at 120-130 RPM to achieve maximum power.
At extreme levels of power, the extra investment of energy for higher cadence is such a small fraction that it would be a non-factor.
10-13-17, 08:55 AM
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Originally Posted by wphamilton
We, as in road cyclists, consider higher cadence to be more "economical" as in the most effective use of our limited reserves of power. Even though the "convention wisdom" is wrong that the power is the same, higher cadence is preferred for several reasons and I lump them together as "more economical". I'm just answering OP's question literally.

At extreme levels of power, the extra investment of energy for higher cadence is such a small fraction that it would be a non-factor.
non factor for what?...lol and conventional wisdom isn't wrong.
10-13-17, 09:05 AM
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Originally Posted by Campag4life
non factor for what?...lol.
A non-factor in having any discernible adverse effect on the top sprinters in the world in their final sprint.

Or most likely, any sprinter. It would be stupid to worry about a tiny difference in energy efficiency when you're laying out as much power as possible, when that difference is swamped by other factors.

As I mentioned, it's not *just* the pedal speed that determines this. It's the amount of force on the pedals, to recruit more fast-twitch muscles, which will produce more short-term power.

Originally Posted by Campag4life
... lol and conventional wisdom isn't wrong.
It's dead wrong, but as I've explained it's not really significant.
10-13-17, 09:19 AM
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Originally Posted by wphamilton
A non-factor in having any discernible adverse effect on the top sprinters in the world in their final sprint.

Or most likely, any sprinter. It would be stupid to worry about a tiny difference in energy efficiency when you're laying out as much power as possible, when that difference is swamped by other factors.

As I mentioned, it's not *just* the pedal speed that determines this. It's the amount of force on the pedals, to recruit more fast-twitch muscles, which will produce more short-term power.

It's dead wrong, but as I've explained it's not really significant.
Sorry, but what you write is simply ridiculous. This is proven every day in any pro sprint. Timing the sprint is everything. Pedaling at maximum RPM with max pedal force is a fleeting window of energy expenditure. It is only for a few seconds that a top pro can spin the cranks at max RPM and max pedal force. It has everything to do with energy expenditure..this window. The exact opposite of what you write.
10-13-17, 09:22 AM
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Originally Posted by Campag4life
Sorry, but what you write is simply ridiculous. This is proven every day in any pro sprint. Timing the sprint is everything. Pedaling at maximum RPM with max pedal force is a fleeting window of energy expenditure. The exact opposite of what you write.
I think that you have misunderstood the posts, since that is consistent with what I wrote.

Any questions, I'll be glad to elaborate, but I'm not going to argue on the level of "what you write is simply ridiculous".
10-13-17, 09:30 AM
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Originally Posted by wphamilton
I think that you have misunderstood the posts, since that is consistent with what I wrote.

Any questions, I'll be glad to elaborate, but I'm not going to argue on the level of "what you write is simply ridiculous".
I believe what you just did is punt...lol. Its ok. We all write silly things from time to time.
10-13-17, 09:56 AM
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Thanks for the helpful replies. So, the answer is No, there is no difference in the two riders' wattage/power, except for minor inefficiencies caused by faster spinning. But, when you factor in our limitations, as humans, there are cadences that are "better" than others.

Haven't read the torque vs. horsepower article, yet, although I have some understanding, based on my motorcycling experience - Harley (torque) vs. crotch rocket (hp.)
10-13-17, 10:13 AM
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Originally Posted by patrickgm60
Thanks for the helpful replies. So, the answer is No, there is no difference in the two riders' wattage/power, except for minor inefficiencies caused by faster spinning. But, when you factor in our limitations, as humans, there are cadences that are "better" than others.

Haven't read the torque vs. horsepower article, yet, although I have some understanding, based on my motorcycling experience - Harley (torque) vs. crotch rocket (hp.)
Well, keep in mind that power put into the bike is EXACTLY the same. These inefficiencies derive from the effort required to move your own body; this will manifest itself in increased heart rate.

And, just to elaborate on these human limitations...an easy analogy is to consider weight lifting.

Imagine a bench press. Let's say an average person can bench press a 1 time max of 100lbs. They lift it once, bring it back down, can't get it up a second time. The exact same person will likely be able to lift a 10lb weight 10 times with ease, and then continue on indefinitely. Lifting the 10lb weight 10 times performs the same work as lifting the 100lb weight once. This is why it makes sense to pedal at a higher cadence...your muscles are generally the limiting factor before your heart rate.

Last edited by Abe_Froman; 10-13-17 at 10:18 AM.
10-13-17, 10:25 AM
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