Torque and Force

I'm an avid cyclist and in order to better my performance, I'm learning newtonian mechanics to have a better understanding of what's going on exactly when my legs push down hard on the pedals. As far as I know, a force is what changes an object speed and direction. Cyclists are very concerned about air drag and with good reasons as air drag is proportional to the square of the speed. Therefore there's a lot of info available on google on this matter. As I understand, your top speed on a perfectly flat terrain is reached when the propulsive force is equal to the total drag on your bicycle (air drag an rolling friction) because since these 2 cancel out each other, propulsion cannot accelerate your bicycle anymore as it is 100% used to overcome drag thus fixing your top speed. Now here comes my question. The force that moves you foward is a propulsive force (in newtons) while the force you put into the pedals is converted into torque (in newton meters) by the crankshaft; they aren't the same. How do I convert my torque (which I can measure) into propulsion (which I don't know)? I cannot find anything on this on google which is astounding. Thank you for taking the time to answer my question.
- Anonymous

Let's say that your pedals were connected to the rear wheel by a simple chain between same-size gears. Then the torque on the rear wheel would be the torque you measure. The torque exerted by the ground on the wheel is just the tangential (propulsive) force between the tire and the ground times the wheel radius. So the force is just the torque divided by the wheel radius. 

When you  use other gear ratios, you have to multiply the torque by the gear ratio. That might sound like you should just increase the gear ratio to get more propulsion, but that requires you to pedal faster, so you couldn't actually keep up and supply your maximum torque.

Mike W.

(published on 10/06/2017)