To propel a bike at a constant speed, power needs to be developed at the rear hub to overcome the forces of friction, wind and gravity. Adding these forces, multiplying by the bike speed, and allowing for the mechanical efficiency of the drive-train forwards to the pedals, the power developed at the crankshaft can be computed from well-known equations (see, for example: https://support.strava.com/hc/en-us/articles/216917107-How-Strava-Calculates-Power).
In a pedal-assist bike, the question arises: how much of this power is supplied by the rider?
The following graphs give examples for two different masses (rider+bike+gear) and two different gradients. In the legend, Crr is the coefficient of rolling resistance for a properly inflated 700x45 tire, and CdA is the combined value of the air-drag coefficient and the frontal area for a rider in an upright position. The bike is taken to be a Specialized Como, for which the motor support in the ECO, SPORT and TURBO modes is quoted to be 35, 75 and 100%, respectively. To get the rider’s contribution to the total power developed at the crankshaft, pick a speed, then go up to the particular power mode of interest, and then read across to the power.
For example, in the 200-lb case at 24 km/h in ECO mode on the flat, the rider is putting out 120 W. With the motor OFF, the rider would need to develop 162 W.
Another example: in the260-lb case at 20 km/h in TURBO mode on a 5% hill, the rider is putting out 214 W. With the motor OFF, the rider would need to develop 428 W.
In a pedal-assist bike, the question arises: how much of this power is supplied by the rider?
The following graphs give examples for two different masses (rider+bike+gear) and two different gradients. In the legend, Crr is the coefficient of rolling resistance for a properly inflated 700x45 tire, and CdA is the combined value of the air-drag coefficient and the frontal area for a rider in an upright position. The bike is taken to be a Specialized Como, for which the motor support in the ECO, SPORT and TURBO modes is quoted to be 35, 75 and 100%, respectively. To get the rider’s contribution to the total power developed at the crankshaft, pick a speed, then go up to the particular power mode of interest, and then read across to the power.
For example, in the 200-lb case at 24 km/h in ECO mode on the flat, the rider is putting out 120 W. With the motor OFF, the rider would need to develop 162 W.
Another example: in the260-lb case at 20 km/h in TURBO mode on a 5% hill, the rider is putting out 214 W. With the motor OFF, the rider would need to develop 428 W.