Torque (in $Nm$) of a cyclist We're discussing bicycles with a friend, and it came to safety, speed and power. Now the question we have is: how much torque do my legs provide to the bicycle?
I'm no expert in physics sadly, and the results we came up seem a little on the high side... Here are the calculations:
Based on the formula given on another stack exchange (https://bicycles.stackexchange.com/q/18199/), the formula for torque is
t = r * F
where t = torque in Newton-meters
      r = radius in meters
      F = force in Newton

and

F = w * g
where F = force in Newton
      w = weight
      g = gravity

Assuming the following:
My weight is 65kg
Gravity is still 9.81 m/s²
My bicycle cranks (the pedal levers) are 170mm long

Then, assuming I'm standing on one pedal, I end up with the following:
t = 0.17 * (65 * 9.81)
  = 108.40

108.40Nm seems like a very large value, especially assuming that my big bad motorcycle develops "only" 63Nm. So is that all correct, or is there something wrong somewhere?
And if that's correct, how come I can't go faster than my motorcycle?
 A: Suppose you pedal at about 100 rpm (I don't know what a typical rate of pedalling is, but this seems a plausible order of magnitude).
To make a fair comparison with your motorbike you need to gear the moorbike engine down from 7,000 rpm to the same 100 rpm that you pedal at, i.e. a factor of 70, and this will multiply the torque by a factor of 70. So at 100 rpm your motorbike engine would be producing a torque of 4,410 Nm or about a factor of 40 greater than the torque you can produce.
That's why the motorbike can accelerate faster than your bicycle can.
A: You're using a vector formula with cross product.  Let's switch to this:
t = r * F * sin theta, where theta is the angle between your leg and the lever on the sprocket wheel.  Theta will change depending on where you are in the cycle of pedaling your bike.  Greatest value for sin theta will be when the sprocket crank is horizontal and your leg is perpendicular to it.
For force, use your mass rather than your weight in the formula:
F = m * g
Plugging in your numbers:
F = 65 * 9.81 = 637
t = .17 * 637 * 1 = 108 newtons
You got the correct torque.  But your motorcycle has a flywheel which stores energy and rotates at a much faster rate than the sprocket wheel on your bicycle.  The flywheel inertia is much greater than your sprocket wheel, and the motorcycle engine can keep pumping much faster and much longer than you can.  You can't match your motorcycle's RPM.  That's why your motorcycle has more power than your bicycle.
Your bicycle is higher torque with lower speed, and your motorcycle is lower torque with higher speed.
