# The cycling power equation

These calculators are based on the equation in the paper detailed below. Aerocoach Australia thanks the authors for their contribution to our understanding of cycling power models.

Validation of a Mathematical Model for Road Cycling Power

Authors: James C. Martin, Douglas L. Milliken, John E. Cobb, Kevin L. McFadden, Andrew R. Coggan
Journal of Applied Biomechanics Volume: 14 Issue: 3 Pages: 276-291

## Ptotal = [ Pat + Pke + Prr + Pwb + Ppe ] / Ec

Ptotal - Total power demand (W)
Pat - Power required to overcome aero drag (W)
Pke - Power from changes in kinetic energy (W)
Prr - Power required to overcome rolling resistance (W)
Pwb - Power required to overcome wheel bearing drag (W)
Ppe - Power from changes in gravitational potential energy (W)
Ec - Efficiency of drivetrain (unitless)

Pat = ½ ρ.Va2.Vg . (CdA + Fw)
Pke = ½ (m+(I/r2)) . (Vgf2-Vgi2) / (Tf-Ti)
Prr = Vg.Crr.m.g.Cos(i)
Pwb = 0.0087 Vg2 + 0.091 Vg
Ppe = Vg.m.g.Sin(i)

ρ - air density (kg.m-3)
Va - air velocity relative to direction of travel (m.s-1)
Vg - ground velocity (m.s-1)
CdA - coefficient of drag x frontal area (m2)
Fw - wheel rotation factor, expressed as incremental frontal area (m2)
m - total mass of bike + rider (kg)
l - wheel moment of inertia (kg.m2)
r - outside radius of tyre (m)
Vgf - final ground velocity (m.s-1)
Vgi - initial ground velocity (m.s-1)
Tf - final time (secs)
Ti - initial time (secs)
Crr - coefficient of rolling resistance (unitless)
g - acceleration due to gravity (m.s-2)