# Converting Impulse to power

Hello everyone,
I am currently working on a project where I am trying to find power by being able to measure the force as a function of time within a chain system, similar to a bicycle. If I know the force in the chain and how it varies with time I would be able to determine the impulse the chain sees. I need a way of converting this impulse into a power measurement. Simply measuring the velocity of the chain is not a possibility.
I was thinking along the lines that if I know the mass of the system, ie the bicycle and rider, and the force, I would be able to calculate the acceleration and then the product of acceleration and impulse would give me power, but the problem with this is as the speed of the object is increased the forces would increase as well at an unknown rate, just like a bicycle, i guess it is very similar to a person riding a bicycle and trying to figure out the power generated by the person by knowing the time variant force in the chain.

I could also take the derivative of the F(t) which would give me the units |Kg*m/s^3| Im not sure what this is, if anyone knows please tell me. But I would still need another distance term.

Any help or info would be appreciated.
Thanks!

It's true, impulse is a change in momentum, and momentum and energy can have a correlation. However, you'd need to be careful because the force in a chain may not be the same as the total force on the bicycle. First, just because there is tension in a chain doesn't mean its actually doing anything (think about pushing your hands against each other without moving anywhere). Also, you would have to take into account gearing ratios because the force in the chain won't be the same as force from wheel to road. Without knowing how much the chain is displaced it's hard to put a hard number on energy.

That is where I am having difficulty. Let me know if you think this idea is valid...
If I know the length of the chain and how the tension force in the chain varies with time, then I should be able to calculate the...?Average?...power done for each cycle of the chain revolution. And then by know where the peak forces occurred I could use this data to plot a decent Power vs. Time graph, regardless of what gear I am in. I am assuming that the peak power would coincide with peak force. This is not taking into consideration frictional losses.
Is this line of thinking correct? I am ultimately trying to get a Power vs. Time chart.

You would still have to know how fast the chain is going, either instantaneously, or an average rpm, to make a connection to your force-time data.

Force or impulse is not enough to calculate power.

 F·dx is work or energy where dx is displacement

 F·dx/dt = F·v is power. (where v = velocity).

 An impulse is ∫F(t) dt

 The average force is Fav = ∫F(t) dt/∫dt = ∫F(t) dt/Δt

 The average power is Pav = ∫F(t)·v(t) dt/∫dt = ∫F(t)·v(t) dt/Δt

So you can not have power output unless the chain force is combined with the chain velocity in .

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Correct, but since the velocity of the chain is due to the input force, shouldn't the peaks in the Power vs. Time plot coincide with the peaks in the force input? What this would mean is that the Power vs. Time would look identical to the Force vs. Time plot except it would be shifted vertically?

Ultimately, am I able to acquire a power vs time plot knowing F(t), the length of the chain, and how long it takes for the chain to make one complete rotation? I know I will be able to calculate the average power but could I somehow determine how the power varries between each chain rotation, or how it varies with time.

Maximum power need not occur at maximum force or torque. For example say the bike is driven by an electric motor. Maximum torque occurs at zero velocity (start-up) for a DC motor and maximum power peaks later as the torque decreases but the speed increases.

Are you looking for raw power input (torque times angular speed at the crank pedals) or power of forward motion (force times velocity at the rolling axles)? Is this a measurement effort or a calculation/simulation effort?

I am looking to measure raw power input, but I have no way of measuring instantaneous velocity, only average velocity for each rotation of the chain, which is not a good enough resolution since the power will vary significantly within one rotation of the chain.

Right. To get instantaneous power you would sample crank speed and torque sensors at least a few times per second. If you have a good model of mass and rotational interta, and do an acceleration run on a flat surface to sample the crank speed data, it would be possible to estimate the power via numerical methods.