Cyclist produced power is used to overcome the following types of resistances:

-aerodynamic resistance.

-rolling resistance

-gravity resistance

-Inertia

-friction among mechanical elements.

Apart from the last one, all the other components can be evaluated mathematically.

Power necessary to overcome aerodynamic resistance can be evaluated as: Being,

ρ: air density (kg/m3).

Vg: cyclist speed (m/s).

Va: air speed incising in the cyclist, or speed relative to the air (Vg+ Vair frontal )(m/s)

Cd: aerodynamic coefficient.

A: Area that the cyclist exposes to the air. (m2)

1. Rolling Resistance

Prolling =Crr x M x  Vg; Eq. 2

being,

Crr: Rolling Coefficient

M: mass (bicycle +cyclist) (kg)

Vg: cyclist speed(m/s)

2. Power to overcome Gravity

Pg= M x g x Vg x sin (α); Eq. 3 sin α= sin (arctan(Δh/ Δd)); Eq. 4

For small angles, sin(α ) ≅ tan (α ), so :

sin α= Δh/ Δd =slope ; Eq. 5

3. Power to accelerate:

P = 0,5 x (M + I/r2)x (Vf2- Vi2)/(tf-ti); Eq. 6

being,

M: mass (bicycle +cyclist)  (kg)

I: Wheels Inertia. (kgm2)

r: Wheel external radius (m)

Vf: final speed after acceleration   (m/s).

Vf: initial speed before acceleration (m/s).

From all of them, quantitatively, aerodynamic resistance is the most important, but also the one that can be modified more easily.

For instance, if a cyclist rides with constant speed, in a plain road, without wind, and we consider  the mechanical the friction  as negligible:

with Crod de 0,0025, for a mass of 85kg, a speed 35 km/h, and a CdA of 0.41 the rolling resistance will be only 24,3w. That means, only a 9% of the total required power: 253w. As consequence, the 91% of the power is used to overcome the air resistance. 