# Calculating work done by a bicycle

1. Jul 27, 2010

### Xyius

I run a lot and recently started cycling. I want to calculate the work done by a bicycle and compare it to the work done by running. My problem is I am having trouble calculating the work done by a bicycle. Would it simply be a matter of calculating it using the formula..

$$\frac{1}{2}I\omega^2$$

And I would need to calculate the moment of inertia off the bicycle wheel with the center turning radius taken into account, since that is the only part of the bicycle the user moves by peddling.

Does anyone agree with this analysis? What are your opinions?

2. Jul 27, 2010

### Staff: Mentor

3. Jul 27, 2010

### Xyius

To calculate the torque I need the moment of inertia. If I write the torque as T=Fr, then what would be F?

Here is something interesting.
W=$$\tau \theta = Fr\frac{x}{r} = Fx$$
This is the formula for translational work. So would that suggest that it takes the same work to run and bike? That isn't true though because I get way more tired when running. :\

Unless F in the rotational sense has a different value than the translational sense.

Last edited: Jul 27, 2010
4. Jul 28, 2010

### Staff: Mentor

No, torque is not dependent on moment of inertia unless the wheels are continuously accelerating.

Torque (and power) is primarily dependent on wind and rolling resistance (unless you are going uphill!).
F is the force your feet apply to the pedals or the force the wheels apply to the road, depending on from which you want to calculate the work.
The reason you get more tired running has much more to do with biology. Bicycle pedals and gears are optimized for you to efficiently apply power to them. In running a huge fraction of the power is lost just in making your legs move.

5. Jul 28, 2010

### IMK

Also remember when you are running you are also going up and down and it is the lift that needs also to be concidered