I have a cyclette with 8 resistance levels set magnetically using a knob (a magnet is moved near the rotating disk thereby increasing its rotating resistance). The distance from the pedal to the center is 0.165 m. At resistance level 4, if I put a weight greater than or equals to 0.75 kg on the pedal (such that the direction of the force is normal to the ground and tangent to the circle generated by the rotating pedal, that is when the pedal is at "hour 9 position"), then the system rotates. The system does not rotate if I use a lower weight. If I pedal at 65 rpm I should generate the following power in watts:

P = 0.75 x 9.81 x 0.165 x 2 x Pi x 65 / 60 = 8.26 W

Is the above calculation correct? It assumes the force applied by the legs is constant for the whole round (which is not actually the case but I hope it's a good approximation).

Are there other assumptions I didn't consider? The reason I'm skeptical is that 8 W seems a very low number, considering that I'm using a resistance of 4 of 8.

Even if I were pedaling at 120 rpm and level 8, the power (using the above formula) would only be 18.71 W.

What am I missing?



Your estimate is much too low.
I assume that you are possibly incapable of generating the 700 W generated by this cyclist I would imagine you can do much better than 8 W.
A trained cyclist can generate a power of 400 W over an hour and if you are reasonably fit you should easily manage 50 - 100 W over an hour.

The error in your calculation is to assume that the force that you apply on the pedal stays constant at 7.5 N.
In your device the resistive force is produced because you have a conductor (rotating disc) moving in a magnetic field.
It is a homoplanar generator which generates an emf which in turn drives a current round an electrical circuit.
Lenz's law states that the induced current is in such a direction as to try and oppose the motion producing it which in this case is you pedalling.
The faster the disc rotates the larger is the emf, the larger the current, the larger the force opposing you pedalling and hence the larger the force that you have to exert to keep the disc rotating at constant speed.
So that force of 7.5 N that you found to move the pedal and start the disc rotating is an underestimate of the force that you are exerting when pedalling at 65 rpm.
That force of 7.5 N is possibly overcoming the frictional forces which exists within you device.

Bringing the magnets closer to the disc means that the disc finds itself in a larger magnetic field and so for a given speed of revolution produces a larger emf, a larger current and hence you have to work harder to keep the disc spinning.

As you have noted if you apply a constant force on the pedals the torque varies as the crank wheel goes around so you would have to average it the torque over a complete revolution.

  • $\begingroup$ I'm accepting the answer. $\endgroup$ – user2068022 Jul 4 '17 at 7:07

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