The Physics of Cycling
Formulas
Definitions:
Cad - Cadence (in RPM)
Ct - Nr. of teeth in the front chainring
Rt - Nr. of teeth in the rear sprocket
D - Tire's diameter (in mm)
S - Slope (5% = 0.05, 10% = 0.1, etc.)
m - Total mass of the set: cyclist+bicycle+cargo [Kg]
Gear ratio in Gear inches:
G = (D/25.4) x Ct/Rt
Bicycle's linear speed:
V [Km/h] = Cad [rpm] x G x 0.0048
V[mph] = Cad [rpm] x G x 0.0029826
Power to overcome gravity:
Pg [Watts] = m [Kg] x Cad [rpm] x G x Sqrt (S^2/(1+S^2)) x 0.013
Note: These and other formulas are present in the downloadable Excel sheet on the left.