Resistance of friction in cycling

For a cyclist, the friction (non-aerodynamic) **Rm** is the sum of two different resistances, the first comes from the contact of wheels on the ground and the second from mechanical pieces.

Contact of the wheels on the ground

The contact requires a sufficient grip to prevent falls but generates in return a rolling resistance **Rr** which is important. This resistance is proportionate to the total weight through a coefficient **Cr** and depends on the slope **Pt** (slope calculation). The total weight depends on the total mass **Mt** (cyclist plus equipment) and the acceleration of gravity **g**.

The coefficient defines the rolling efficiency of wheels. It depends on the nature of the ground (asphalt, cement, etc.) and the type of tires (constitution, form, size, inflation pressure, etc.).

For standard wheels (700x23C), we can consider:Cr = 0.010 for a bad asphalt roadCr = 0.008 for a good asphalt roadCr = 0.006 for a very smooth asphalt roadCr = 0.004 for a velodrome track |

Friction of mechanical pieces

The friction depends on the moving pieces, ie the wheels, crank, chain, sprocket, gears. Among all these things, the wheels generate the most important friction resistance **Rf**. It is is proportionate to the square of the speed relatively to the air **Va** through a coefficient **Cf**.

The coefficient defines the friction efficiency of wheels. It depends on the design (hub, spokes, rim). For example, there are wheels with profiled spokes, disc wheels.

For standard wheels (700x23C), we can consider:Cf = 0.0030 for low-end wheelsCf = 0.0027 for good quality wheelsCf = 0.0024 for high-end wheels |

**N.B.** The friction resistance is very low compared to others. The use of special wheels is justified only in extreme situations.

Calculation formula

In summary, the mathematic formula allowing calculation is:

**Rm = Mt g Cr Cos(Arctan(Pt)) + Cf Va²**

Calculation of the cycling power

J.L