# How to relate energy consumption to force?

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Hi, I'm working on a bicycling simulation and I have some basic physics questions. I want to relate the energy a bicyclist uses to the speed he/she achieves. First of all I'm confused with the term "power". I know Power = Force * Speed Does this mean that when for example a weightlifter keeps a weight above its head the power is 0 when the speed is 0? How should I calculate in this case the energy per time unit that is needed for the weightlifter to keep the weight above its head? Does this involve something other than "power"? http://www.analyticcycling.com/Glossary_Disc.html gives a formula that mentions the term "pedaling force". It is defined by Power/speed. How can I calculate the pedaling force If I know the amount of energy that the rider outputs? What about the pedaling force if the speed of the bikers is 0? (e.g. biker climbs a hill and outputs just enough energy so he doesn't roll back down the hill) I think I should go from the energy that a biker outputs to a force on the pedals. Once I have this force I can calculate the net force on the rider (taking into account rolling resistance, wind resistance, etc) and with that the acceleration. Using integration I could than calculate speed and position. Is this the proper way to do it? If this is so my main question is: how do I relate the energy a biker spends (per time unit) to a force on the pedals? I really hope some of you can help me out. Thanks I advance. [Edited by - crocomire on June 13, 2005 5:53:10 AM]

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It's actually biological question, not physical. If you hold weight, obviously your muscles "consume" energy (convert chemical energy to heat), and in case of too much force(anaerobic metabolism) produce lactic acid. In result, you can't hold weight for long. Yet, work done is zero, even unpowered weight-holding frame could do it.

Getting back to rider, force=power/speed (while true) seems completely useless there. That's because you compute your power from force anyway, using power=force*speed, and substituting you get force=(force*speed)/speed .
It's like entry in dictionary, "stone: see boulder", "boulder: see stone"

You already have your drag forces acting on rider (assuming you implemented rest of simulation), and you don't already have any power. Take these forces, and then you can compute forces on pedals using simple mechanical laws.

Let force on bike wheel is f (wind, drag, slope, acceleration etc), radius of wheel is r1 and radius of pedal is r2. Let transmission ratio is n (wheel rotates n times faster than pedals)
Then, torque on wheel is
f*r1
and torque on pedal is
f*r1*n
and force on pedal is
f*n*r1/r2

In summary, how I would do it:
compute speed of pedals as
o=velocity_of_bike*r2/(r1*n)
In case biker is pedaling, have ["average"]force defined as function of rotationspeed (like with any other engune) and some value for tiredness.
Get ["average"]force on pedals, f using this function
Compute force on wheel = (f/n) * r2/r1
use this force together with all other forces in simulation to find acceleration of rider.

It's pretty much like how car simulation works.

[Edited by - Dmytry on June 13, 2005 7:26:02 AM]

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Quote:
 Original post by DmytryIt's actually biological question, not physical. If you hold weight, obviously your muscles consume energy, and produce lactic acid. Yet, work done is zero, even unpowered weight-holding frame could do it.Getting back to rider, force=power/speed (while true) seems completely useless there. That's because you compute your power from force anyway, using power=force*speed, and substituting you get force=(force*speed)/speed .It's like entry in dictionary, "stone: see boulder", "boulder: see stone"You already have your drag forces acting on rider (assuming you implemented rest of simulation), and you don't already have any power. Take these forces, and then you can compute forces on pedals using simple mechanical laws.Let force on bike wheel is f (wind, drag, slope, acceleration etc), radius of wheel is r1 and radius of pedal is r2. Let transmission ratio is n (wheel rotates n times faster than pedals)Then, torque on wheel isf*r1and torque on pedal isf*r1*nand force on pedal isf*n*r1/r2

I want to start from the energy a rider spends and from there calculate the speed. Something like that is done here I think: http://www.analyticcycling.com/ForcesSpeed_Page.html
But I'm still confused about the term "power". This has little relation to the amount of energy a rider spends?

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Quote:
Original post by crocomire
Quote:
 Original post by DmytryIt's actually biological question, not physical. If you hold weight, obviously your muscles consume energy, and produce lactic acid. Yet, work done is zero, even unpowered weight-holding frame could do it.Getting back to rider, force=power/speed (while true) seems completely useless there. That's because you compute your power from force anyway, using power=force*speed, and substituting you get force=(force*speed)/speed .It's like entry in dictionary, "stone: see boulder", "boulder: see stone"You already have your drag forces acting on rider (assuming you implemented rest of simulation), and you don't already have any power. Take these forces, and then you can compute forces on pedals using simple mechanical laws.Let force on bike wheel is f (wind, drag, slope, acceleration etc), radius of wheel is r1 and radius of pedal is r2. Let transmission ratio is n (wheel rotates n times faster than pedals)Then, torque on wheel isf*r1and torque on pedal isf*r1*nand force on pedal isf*n*r1/r2

I want to start from the energy a rider spends and from there calculate the speed. Something like that is done here I think: http://www.analyticcycling.com/ForcesSpeed_Page.html
But I'm still confused about the term "power". This has little relation to the amount of enery a rider spends?

Exactly. Humans aren't efficient. Also, it matters not how much chemical energy has been released in rider, but how much rider is tired.
Also, take into account changing ratio of transmission.

In either case, even if you compute speed of rider, it is very likely that all empirical data you used had been computed from speed of rider anyway.

I edited post above and added how I would do it for game.

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My first idea was the following: each rider has some sort of energy budget. A good rider perhaps has more total energy and/or a higher rate in which stored energy can be released. The stored energy comes from food that is eaten.
During a race each rider should determine how and when to spend his energy. These are tactical decisions. Therefore I had the idea of calculating speed from the amount of enery a rider decides to spend. But you suggest I should work the other way around? Start from speed and calculate needed pedaling force. But how do I relate the pedaling force to energy spend? Would you suggest I shouldn't use the concept of an energy budget?

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from http://www.analyticcycling.com/ForcesSpeed_Page.html:
"Speed is estimated based on rider power and the forces acting on a rider from wind resistance, rolling resistance, and gravity."

What is meant by this "rider power"? How can they use Power as an input variable if Power is computed from Force?

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Don't confuse power, energy and work. Actually you cannot compute anything from just knowing the rider's available energy. The term power relates to the maximum (overall!) force the rider can apply to the bike in order to push the pedals, keep it stable, change the direction and so on.
While applying this force, the rider performs physical work, which in turn “consumes” (or more physically correct - transforms) energy.

So you essentially need to provide an amount of energy the rider is able to spend and his/her maximum power. The former defines how long the rider can apply a force, while the latter tells you how much force can be applied.

Energy can be represented in Wh (Watt-hours) and the power in Watts determines the maximum amount of Watts that are used at a time. So say the rider has 1,000Wh of energy and applies an average power of 200W, (s)he can ride for 5 hours before the energy runs out.

A final note on Power = Force * Speed is that this formula only applies if and only if force and speed are constant, which surely doesn't apply. Otherwise power is ΔWork / ΔTime, which fits nicely into a physics simulation (since you have a Δt).

HTH,
Pat

PS: Corrections welcome, been a while since I dealt with mechanics [smile]

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Quote:
 Original post by darookieDon't confuse power, energy and work. Actually you cannot compute anything from just knowing the rider's available energy. The term power relates to the maximum (overall!) force the rider can apply to the bike in order to push the pedals, keep it stable, change the direction and so on.

How do I find this maximal force? Is it just F = P/v? So, this maximum force is dependant on the speed?

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Quote:
 Original post by darookieA final note on Power = Force * Speed is that this formula only applies if and only if force and speed are constant, which surely doesn't apply.

Wrong. The power at time t is the force at time t times (dot product) the velocity at time t. Nothing needs to be constant.

Quote:
 Original post by darookieOtherwise power is ΔWork / ΔTime, which fits nicely into a physics simulation (since you have a Δt).

ΔW / Δt = ΔW/Δs * Δs/Δt = force*velocity

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Quote:
 Original post by crocomirefrom http://www.analyticcycling.com/ForcesSpeed_Page.html:"Speed is estimated based on rider power and the forces acting on a rider from wind resistance, rolling resistance, and gravity."What is meant by this "rider power"? How can they use Power as an input variable if Power is computed from Force?

The "rider power" is the power the rider puts into the pedals, ie at what rate he is doing work (as seen from the outside - what goes on inside his muscles is another story). From the power and a bunch of other parameters you can calculate the riders steady state velocity, just like in the page you are refering to. That way you don't have to worry about pedal forces and gears and transmission and so on, but it all comes down to how detailed a model you want to use.

The rider power is typically measured on a cycle ergometer. The power, together with the riders weight and size says quite a lot on what level of performance you can expect from him, so I think it is a good starting point for what you're trying to do.

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