# The Physics of Power on a Bicycle

jbriggs444
Homework Helper
My question is about what happens to power output when you stand and apply that greater downward force WITHOUT changing gearing/resistance - i.e., - when you increase downward force without a increasing the opposing force?
That cannot be done. Newton's third law applies. The force of the rider's foot on the pedals is always exactly equal to the force of the pedals on the rider's foot.

However... For a fixed gearing, as the force exerted on the pedal increases, the speed of the pedal will increase. As the speed of the pedal increases, the cadence increases. The amount of force that a rider can apply may drop as a result.

Like throwing a feather, will be dissipating effort moving your hand instead of moving the feather.

A.T.
The observation I'm talking about is actually what appears as a brief drop in power (as reported on the power meter) when the rider stands. It usually comes back up (at least to some degree) after a few pedal strokes,
A transient effect like that is most likely due to something physiological, like the body adapting to the new mode of movement.

billy_joule
sophiecentaur
Gold Member
2020 Award
Now you have TWO sources of force (and power) - the force of the rider physically pushing on the pedals and gravitational force.
I know it's tiresome for a non-Physicist to be told to use the right terminology but it is really critical in the understanding of these things. You can't afford to confuse Force with Power.
You can alter the forces involved on the bike frame, pedals and the rider but there is only one source of Power / Energy and that is the rider's muscles. Gravity doesn't give you power, You can use gravity to store energy, temporarily, in order to be more effective in some operations. For instance, you can lift an axe up high, storing gravitational potential energy, and then bring it down with a bash - expending all the input energy in a fraction of a second as the axe splits the wood. No extra energy is available - it's just redistributed in time. With a bike, the situation is not like using an axe because you don't require short bursts of high power during each turn of the pedals. In fact, it would be better, in many ways, to have a steady source of energy - as with a motor. Unfortunately, our bodies don't work that way and the way cyclists use the pedals is a sort of work around to get the best overall result (hence the selection of the best gear for each situation). 'Good' cyclists tend to have learned different styles from your average guy on a bike, who can be very inefficient in the way they pedal, just because they are knackered and clutching at straws. I always know I'm on the way out when I start standing on the pedals rather than just dropping a gear.

That cannot be done. Newton's third law applies. The force of the rider's foot on the pedals is always exactly equal to the force of the pedals on the rider's foot.

However... For a fixed gearing, as the force exerted on the pedal increases, the speed of the pedal will increase. As the speed of the pedal increases, the cadence increases. The amount of force that a rider can apply may drop as a result.

Like throwing a feather, will be dissipating effort moving your hand instead of moving the feather.

See - THAT'S what I'm getting at. That "dissipating effort" when you stomp on the pedal WITHOUT adding resistance.

A.T.
See - THAT'S what I'm getting at. That "dissipating effort" when you stomp on the pedal WITHOUT adding resistance.
Speaking of resistance, how is it generated exactly, and what dependency on speed and changes in speed does it have? How does the resistance generated by the machine compare to the resistance on an actual bike?

I know it's tiresome for a non-Physicist to be told to use the right terminology but it is really critical in the understanding of these things. You can't afford to confuse Force with Power.

But isn't "FORCE" part of the power equation?

You can alter the forces involved on the bike frame, pedals and the rider but there is only one source of Power / Energy and that is the rider's muscles. Gravity doesn't give you power, You can use gravity to store energy, temporarily, in order to be more effective in some operations. For instance, you can lift an axe up high, storing gravitational potential energy, and then bring it down with a bash - expending all the input energy in a fraction of a second as the axe splits the wood. No extra energy is available - it's just redistributed in time.

In some ways - standing, shifting your weight over the pedal, and pressing down hard is a little like that axe falling. The input energy is expended in a shorter time.

In your example - if you could measure the torque of the axe falling - would it be higher or lower than if you took an axe of the same weight and pressed it down against some type of reciprocating force - like a see-saw, for example?

With a bike, the situation is not like using an axe because you don't require short bursts of high power during each turn of the pedals. In fact, it would be better, in many ways, to have a steady source of energy - as with a motor. Unfortunately, our bodies don't work that way and the way cyclists use the pedals is a sort of work around to get the best overall result (hence the selection of the best gear for each situation). 'Good' cyclists tend to have learned different styles from your average guy on a bike, who can be very inefficient in the way they pedal, just because they are knackered and clutching at straws. I always know I'm on the way out when I start standing on the pedals rather than just dropping a gear.

Again, I know that steady power output is more efficient for cyclists. I know about gear selection for terrain and riding style (seated vs standing). That's not my question. My question is more academic than performance related.

The question is - When a rider stands, shifts their weight over the pedals, and expends force quickly without providing additional reciprocating force to push against (shifting gears) - what happens to torque and/or power?

A.T.
The input energy is expended in a shorter time.
Okay.
and expends force quickly
There you go again, confusing force and energy.
without providing additional reciprocating force to push against
What?

Speaking of resistance, how is it generated exactly, and what dependency on speed and changes in speed does it have? How does the resistance generated by the machine compare to the resistance on an actual bike?

I'm not exactly sure I'm answering the question you're asking - but on a bike, "resistance" is changed by shifting gears. To maintain the same cadence when you add "more resistance" (shift to a bigger gear), you need to apply more force to the pedal (apologies if I'm using the wrong terminology - but I think you get the idea). The result is an increase in speed (assuming all other factors - aerodynamic drag, etc., are equal) because as the gearing increases, each revolution of the pedals translates to further rotation of the wheels.

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A.T.
To maintain the same cadence when you add "more resistance" (shift to a bigger gear), you need to apply more force to the pedal
On an real bike, If you shift to a bigger gear, the cadence doesn't stay the same but inevitably drops intially. To bring cadence to the old value you have to accelerate the bike.

Is this also the case for the simulated resistance on the bike machine? Is there a flywheel or something?

Yes - there's a fly wheel and a resistance unit - either a brake pad or magnetic resistance unit.

It occurs to me that perhaps the question I should have been asking all along is what happens to torque & angular velocity, since that's what the power meter is measuring.

sophiecentaur
Gold Member
2020 Award
The flywheel is modelling the mass of the rider plus bike and the brake is modelling friction and the energy used in going uphill. Once the flywheel has reached its speed then it takes no more energy.

I'm going to rephrase the question to clarify what I'm asking.

When a cyclist pedals a bicycle in seated position, they apply pressure to the pedal to create torque at a relatively constant rate around the full circumference of the pedal stroke. The resistance - or gearing - of the bicycle provides an opposing force for the rider to press against when pedaling. As resistance (or gearing) is increased, the rider needs to apply more pressure (increased torque) to maintain the same revolutions per minute. When resistance or gearing is decreased, the opposite occurs.

When the rider shifts to standing position, they shift their body mass over one pedal and apply a sharp downward force assisted by their own body weight resulting in a more piston-like motion as opposed to the smoother, more circular pattern of force application when seated. If gearing and revolutions per minute remain constant - would this difference in the way force is applied to the pedal alter torque - and if so - how?

I'm going to rephrase the question to clarify what I'm asking.

We've already answered your question, but you're not comprehending. I explicitly wrote this out for you on the previous page.

When a cyclist pedals a bicycle in seated position, they apply pressure to the pedal to create torque at a relatively constant rate around the full circumference of the pedal stroke. The resistance - or gearing - of the bicycle provides an opposing force for the rider to press against when pedaling. As resistance (or gearing) is increased, the rider needs to apply more pressure (increased torque) to maintain the same revolutions per minute. When resistance or gearing is decreased, the opposite occurs.

No. Gearing is not resistance. The resistance comes from all the friction and drag that opposes your motion. It has nothing to do with gearing or torque. If you change gears to increase the torque it will lower your cadence. This is because the power source (i.e., human body) is still the same. And no matter how you position your body the cranks always turn the same way. The torque may change and the RPM may change, but their product is always the power the cyclist is generating.

When the rider shifts to standing position, they shift their body mass over one pedal and apply a sharp downward force assisted by their own body weight resulting in a more piston-like motion as opposed to the smoother, more circular pattern of force application when seated. If gearing and revolutions per minute remain constant - would this difference in the way force is applied to the pedal alter torque - and if so - how?

For RPM to remain the same while increasing torque, the power would have to increase. Where's that extra power coming from?

We've already answered your question, but you're not comprehending. I explicitly wrote this out for you on the previous page.

No. Gearing is not resistance. The resistance comes from all the friction and drag that opposes your motion. It has nothing to do with gearing or torque. If you change gears to increase the torque it will lower your cadence. This is because the power source (i.e., human body) is still the same. And no matter how you position your body the cranks always turn the same way. The torque may change and the RPM may change, but their product is always the power the cyclist is generating.

And I still think you're not quite understanding my question...

Maybe resistance isn't the correct term. Maybe you can enlighten me as to what the right term should be. But when you shift into a larger gear - you have to press harder to turn the pedals at the same rate. Maybe there is a temporary reduction in cadence, but often very brief. Bigger gears at the same cadence produce more power. Perhaps reciprocating force or reciprocating torque are the terms I'm looking for. But the bottom line is that bigger gearing requires more force to turn - smaller gearing provides less force.

Changing positions does change the way that force is applied. Vector power meters produce some really nice force diagrams that clearly display the difference - but any rider can tell you that there is a difference in the way force is applied to pedals in seated vs. standing position.

I understand that as torque and RPMs change, the power generation changes - again - that's not the question I'm asking. You're answering a different question than the one I'm trying to ask -which is why I attempted to rephrase it - but apparently I'm still not getting through.

For RPM to remain the same while increasing torque, the power would have to increase. Where's that extra power coming from?

I know that. Still not my question... Oh well. I give up....

Torque and pedal velocity aren't constant in practice, and none of the power meters have a fast sampling rate. If you have a power meter you (like the rest of us using them) must have seen the numbers jumping all over the place. They all require smoothing via averaging over period - longer than 1sec for most of them on the market. So I doubt your measurements are even valid. Anyway, there is plenty of discussion on various cycling forums about this.

A.T.
Vector power meters produce some really nice force diagrams that clearly display the difference

This post is mainly about pedaling a recumbent bicycle, but srcoll most of the way down to the section titled "Pedaling Standing"

Here's another discussing the same graphs, plus another interesting graph showing an undulating pattern of pedal force when force for each leg is measured separately. I think this probably actually explains what I've observed as well as anything, since I'm talking about a power meter that measures power at the crank on one side and doubles it.

Let me try this from another angle - work output.

On a stationary bike, the mechanical or magnetic resistance brake provides a resistance force (I'm removing reference to gearing & a rolling bicycle to remove that variable from the discussion). When the rider stands, they are able to produce a greater EFFORT FORCE on the pedals. For the WORK OUTPUT to remain constant would require an equal increase in the RESISTANCE FORCE. Without increasing resistance force to counter the increased effort force, work output decreases.

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sophiecentaur
Gold Member
2020 Award
Maybe resistance isn't the correct term. Maybe you can enlighten me as to what the right term should be.
The force is a Reaction force - same as when you push directly against a frictionless mass. You have to overcome both reaction (to accelerate) and resistance (to keep going).
"For the WORK OUTPUT to remain constant would require an equal increase in the RESISTANCE FORCE." This is the purpose of the flywheel in simulators. But how can the work input be the same as at steady speed if you are actually accelerating? If the Energy per cycle is the same then there can be variation on Power over the cycle. (This, again, is where using the right terms is essential if you want to make progress with this question.)

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A.T.
This post is mainly about pedaling a recumbent bicycle, but srcoll most of the way down to the section titled "Pedaling Standing"
Okay, this covers what already has been said here: Standing can create high peak forces with less work of the leg muscles at the time of that peak.

When the rider stands, they are able to produce a greater EFFORT FORCE on the pedals.
Right, but the relevant quantity here is torque. A vertical force on a pedal at it's lowest point doesn't do any work.

For the WORK OUTPUT to remain constant would require an equal increase in the RESISTANCE FORCE.
That doesn't make any sense. The reaction force always equals the applied force. If the average torque over a cycle increases, then the work done over a cycle must also increase. It cannot stay constant.

work = torque * angle_moved

This thread is getting repetitive. I want to reiterate what Sophie said. These terms are not just semantic choices. They are well defined, and you're doing yourself a disservice not to look them up and understand them. You seem confused about force, torque, pedal velocity and work. Alex Simmons has just recently written an excellent article addressing this topic on his blog - probably in response to your common confusion which fills cycling forums for years back, and has gotten worse with the ubiquity of power meters (and their miscalibration) in recent years: http://alex-cycle.blogspot.com/2015/01/the-sin-of-crank-velocity.html

This thread is getting repetitive. I want to reiterate what Sophie said. These terms are not just semantic choices. They are well defined, and you're doing yourself a disservice not to look them up and understand them. You seem confused about force, torque, pedal velocity and work. Alex Simmons has just recently written an excellent article addressing this topic on his blog - probably in response to your common confusion which fills cycling forums for years back, and has gotten worse with the ubiquity of power meters (and their miscalibration) in recent years: http://alex-cycle.blogspot.com/2015/01/the-sin-of-crank-velocity.html

Thanks for the link - interesting stuff!

In this animated gif you can make out the subtle reaction forces oscillating the bike back and forth on the rollers where this guy is putting well over 1500 Watts into the cranks:

ooof! 1500 watts...

It's actually that variation/oscillation in force & power that I've been trying to get at all along - I just don't think I explained it very well...

I guess I was looking more for the "how" and "why" that variation takes place, why those variations appear to be larger in standing vs seated position, - and trying (and failing, I think!) to understand the physics behind it all... But I think I've taken up enough of your time on this topic! :) I appreciate your patience with me, I've enjoyed the discussion.