Calculate the power generated by a rotating rod turning a generator

[Jim Ruxton]

I want to know how much electrical power I could potentially generate by putting a generator at the pivot point of a rotating arm. I figured I can calculate the Kinetic Energy of the arm by:
E=(Iw**2)/2 where I is moment of Inertia and w is angular velocity.
I = (mL**2)/3 for a uniform rod
in my case I am using L=.25 metre , m= .09 Kg and w =2Pi rad/sec
This gives me approx. .04 J . Assuming this is rotating at a constant velocity how do I know what the instantaneous output power of the generator could be assuming 100% efficiency. I know Power is just Energy/Time but what do I use for time in this case? I am used to calculating electrical power as voltage*amps but never figured out how to convert from the mechanical equivalent. Ultimately I want to figure out if I can power an LED using a small generator. Thanks

 

[berkeman]

Welcome to the PF.

What is turning the rod? That will determine the power output you can get from the setup. Or do you want to calculate how long the generator will keep turning until it slows down with no mechanical energy input?

 

[Jim Ruxton]

For now I just wanted to assume it is spinning at a constant rate of 1 rad/sec. In reality it will be spun by hand. Really I am just trying to get a baseline to try and determine feasibility.
Thanks

 

[russ_watters]

If turning at constant rpm, the kinetic energy is not changing, so there is no power output from it. You need to use the power input to find the power output: power input is torque times angular velocity.

 

[Vanadium 50]

For now I just wanted to assume it is spinning at a constant rate of 1 rad/sec.

Then the answer is zero. You need to either slow it down, or provide power to keep it from slowing down. In the latter case, we're right back to berkeman's question.

 

[Jim Ruxton]

What if I assume someone is holding onto the rod to provide power and spinning it at a constant rate to keep it from slowing down?

 

[russ_watters]

What if I assume someone is holding onto the rod to provide power and spinning it at a constant rate to keep it from slowing down?

How much torque can he apply?

[Edit:] Trying to move this along, I see that single hand crank generators seem to max out at about 60w, for a double. But you have to be a beast to run one:

http://www.ebay.com/bhp/hand-crank-generator

 

[Vanadium 50]

What if I assume someone is holding onto the rod to provide power

Then that's how much power you can get from the generator.

 

[Jim Ruxton]

Thanks @Vanadium and @russ_waters. And how would I calculate that power in watts based on a given torque applied to the rod? I thought the power would be somewhat related to the KInetic Energy I calculated at the beginning of this thread.

 

[CWatters]

Power = Torque * angular velocity

KE doesn't figure in the equation.

 

[russ_watters]

Thanks I thought the power would be somewhat related to the KInetic Energy I calculated at the beginning of this thread.

Since KE doesn't change, you aren't harnessing it.

 

[CWatters]

Just to add to what Russ said above. There papers that can tell you how much power a human is capable of generating by just about any means imaginable (rowing, cycling, hand cranking with one or two arms etc). Example..

https://www.researchgate.net/publication/228883044_Human_power_comfortable_one-hand_cranking

Human power; comfortable one-hand cranking

Abstract: Research into ergonomics is one of the aspects in the research for human-powered energy systems. In this specific field, data on maximum force exertion and endurance can be found in a large number of publications, mainly originating from sport or military related research. Data on comfortable or sustainable force exertion however prove not to be available. In this research project we attempted to measure comfortable/sustainable force exertion. We mapped one specific movement (one-handed cranking) using the Critical Power test. This test is based on the assumed linear relation between maximal work and time to exhaustion (Morton's 3-parameter critical power model). The experimental set-up consisted of an altered cycle-ergometer which was adjustable in height. We measured the subjects' (eight young males) maximum power output and the time to exhaustion at different power levels. The research showed a sustained power output from cranking to be: 54 ± 14 Watt (mean ± SD). In the paper we will present the research project and its results and link them to literature in the field of comfort.

 

[Jim Ruxton]

Thanks @CWatters this will be very useful information.