How Does Pedal Rotation Relate to Bicycle Efficiency in Physics Labs?

[Tektriax]

Hello, while my question is not from a textbook, it still has to do with a lab I'm creating. My lab was to view the efficiency of rotational KE of a bike's pedals to the KE of the bike itself. Using 1/2*I*ω^2 and 1/2*m*v^2 to find KE, I seemed to have run into a problem. The KE of the bike was around 30 J, but the rotation KE of my pedals was around .4 J. I'm not the best at physics, but how could the bike "create" energy? I would assume I'm wrong in some form. I'm sparing you the details, for I simply just need to know what about the value I'm getting is wrong. Thanks for your help!

 

[CWatters]

My lab was to view the efficiency of rotational KE of a bike's pedals to the KE of the bike itself.

They aren't related. Consider..

1) The pedals do not provide energy to power the bike, the rider does.

2) A bike can have KE even the pedals aren't rotating (eg you are coasting).

3) If you keep the velocity (and hence the KE of the bike) constant but change gear the pedals will turn at a different rate. The pedals would have a different KE. That would happen even if the gears were 100% efficient.

I think you need to look at power instead of energy. You could measure the input power supplied by the rider (perhaps by measuring the torque and rpm at the pedals) and compare that with the output power (perhaps by measuring the torque and rpm at the wheel).

 

[rcgldr]

The pedals aren't the source of the energy. The person applying a toque to the pedals generates the power required to accelerate and maintain speed (against losses like drag and inernal friction). Once at speed, the pedals and crank have a portion of the total KE. Note that part of the bike's KE is angular energy in the wheels.

 

[haruspex]

You seem to have a basic misunderstanding about energy transfer in a chainset.
The cyclist does not give KE to the pedals (in some kind of neutral gear), then lift the feet off and let that KE be transferred to forward motion of the bicycle. The mass of the pedals is irrelevant, likewise the wheels. Forces transfer the mechanical energy from the legs all the way through to forward motion of the bicycle.
(You might argue that in going from rest to cruising speed some of the KE is accumulated in the rotation of pedals and wheels, but it is not lost. If the cyclist stops pedalling that small amount of KE can be used to maintain speed.)
For the purposes of mechanical efficiency, you could compare energy input to energy output (for which you'd need some energy source of known value, rather than human legs), or compare the torque ratio (when moving) to the rotational ratio.

 

[Tektriax]

Ok thank this cleared things up a bit, let me give more details about the lab. I planned to use the gears of a bike (really just the main 3) to show the relationship between the diameter of the gear and the distance traveled by the bike (using constant velocity and exactly 2 revolutions of the pedals). I do like the idea of using power as CWatters suggested; however, I don't see how I could measure the torque of the pedals and the wheel. Regardless, any suggestions would be great. In my lab, we are required to use energy, power, or momentum to explain an efficiency.

 

[haruspex]

I do like the idea of using power as CWatters suggested; however, I don't see how I could measure the torque of the pedals and the wheel.

As CWatters wrote, measuring torque while rotating is pretty much the same as measuring power.
Here's a specific suggestion:
turn the bike upside down;
attach a smallish drum to each of crankshaft and wheel hub;
wrap a length of string around each drum, suspending a heavy weight (much heavier for the crankshaft).
The drums need to be small and the weights heavy so that the bike doesn't need to be tens of metres above the ground.
Adjust the hub weight so that the system just about turns. Repeat with increasing hub weights, each time allowing the system to reach a steady rotation (if the bike's high enough). Measure the time taken for each descent. Plot up the results.

 

[CWatters]

I planned to use the gears of a bike (really just the main 3) to show the relationship between the diameter of the gear and the distance traveled by the bike (using constant velocity and exactly 2 revolutions of the pedals).

If that's all you want to do it's easy. However it doesn't tell you anything about the bikes efficiency.

In my lab, we are required to use energy, power, or momentum to explain an efficiency.

Efficiency is usually either Energy out/Energy in or Power out/Power In, so you need to work out ways to measure those. Haruspex has suggested one way.

There might be a way to estimate it..

You might estimate the input power (or energy) by removing the saddle so the rider has to ride by "standing on the pedals". Think about what he has to do... For each turn of the pedals he is effectively climbing 2 steps that depend on the length of the pedal cranks. So count the number of turns/steps and use an equation derived from E=mgh or P=mgh/t.

Then for the output power... Measure the rate of KE gain by the bike as it accelerates from a standing start (eg measure the velocity after say 10 seconds). This would ignore losses due to air resistance and rolling resistance but at low speed perhaps air resistance can be ignored?