# Velocity of bicycle pedals

1. Feb 13, 2010

### tsrgb

1. The problem statement, all variables and given/known data
A bicyclist travels in a light head wind on a level, horizontal road. The bicyclist keeps a constant speed of v = 20 km per hour. He pedals evenly. The back wheel has a radius of r = 0.33 m. The back cog wheel has a radius of r = 0.035 m. The front cog wheel has a radius of r[f] = 0.085 m. Each pedal arm has the length L = 0.16 m, measured from the center of the front cog wheel.

Find an expression for the maximum and minimum value of the pedal velocity based on the given radii, L and the velocity v.

2. Relevant equations
v=r*omega

3. The attempt at a solution
I have assumed that the angular velocity of the front and back wheel must be the same.
I have assumed that the angular velocity of the pedals must be the same as the front cog wheel.

Hence:
omega[front cog wheel & pedals] = v/radius of wheel * radius of rear cog wheel/radius of front cog wheel
omega[front cog wheel & pedals] = ((20 km/hr) / (0.33 m)) * ((0.035 m) / (0.0085 m)) = app. 24.96 km/hr*m

v[pedal] = (0.16 m) * (24.96 km/hr*m) = app. 3.99 km/h

Does anyone have an explanation for why the pedal velocity should have a maximum and minimum value and not just be constant?

Any help is much appreciated.

Sincerely,
tsrgb
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 13, 2010

### Spinnor

You wrote,

Does anyone have an explanation for why the pedal velocity should have a maximum and minimum value and not just be constant?

I think they want the velocity of the pedal with respect to the ground. When the pedal is at the top it moves forward with greatest velocity, a sum of two motions.

3. Feb 16, 2010

### tsrgb

Thank you.
I'll try that.

Sincerely,
tsrgb