Resistance of the air in cycling

For a cyclist, the resistance of the air increases with the speed.
This resistance does not depend on the cyclist weight but depends on several parameters not always well perceived.

Cyclist's speed

The resistance of the air Ra is proportional to the square of the speed relative to the air Va.
Therefore, going twice as fast requires eight more power (cube of the speed), then eight more force on the pedals .
Furthermore, the speed relative to the air means that with front wind, it is necessary to do an effort identical to the one consisting to go without wind in a speed equal to the cyclist's speed plus the wind speed.

Weather conditions

The resistance of the air is proportional to the air density ρ which depends on the weather conditions.
It is lower when the air is warm or when the atmospheric pressure is low (bad weather, high altitude).

Aerodynamic profile

The resistance of the air is proportional to the frontal area of the cyclist S and the coefficient of aerodynamic shape Cx.
The frontal area depends on the morphology (size, shoulder width, etc.), but essentially the position of the cyclist.
The coefficient of aerodynamic shape is proper to the air flow (bike, helmet, clothes, etc.).
The product of these two elements defines the penetration coefficient SCx.

For a road cyclist, we can consider:
SCx = 0.40 for a traditional cyclist with tense arms
SCx = 0.35 for a traditional cyclist with bent arms
SCx = 0.30 for a traditional cyclist with hands at the bottom of the handlebar
SCx = 0.25 for a cyclist "against time" or triathlete
Profile

Calculation formula

In summary, the mathematic formula allowing calculation is:
Ra = ½ ρ SCx Va²

Calculation of the cycling power

J.L