# How do you roll a bike

## Friction and locomotion

#### Air resistance

As you surely know from experience, the drag force F increasesL. with the velocity v to. How big it is, however, also depends on how "slippery" the cyclist and bike are. This is what is known as cw-Value (pure number) taken into account. In addition, the density \ (\ rho \) of the air that has to be pushed away and the frontal area \ (A \) of the driver including the bike play a role.

The following applies:

 \ ({F_L} = \ frac {1} {2} \ cdot {c_w} \ cdot \ rho \ cdot A \ cdot {v ^ 2} \)

Very clever students will be able to understand the derivation of this formula after the chapter on energy.
The table below shows the cwValues ​​and the frontal areas for different types of bicycles.

 bicycle cw-Value Frontal area A in m2 City bike 1,1 0,45 Racing bike 0,90 0,33 Recumbent 0,77 0,35

The following graphic shows quite impressively how the drag force \ (F _ {\ rm {L}} \) increases with the speed \ (v \). The drag force of our model cyclist Richard of \ (F _ {\ rm {Rad}} = 4 \, \ rm {N} \) is also entered in this drawing. If our cyclist rides on the plane at a constant speed (i.e. acceleration resistance and incline resistance are zero), the following applies:

Total resistance = wheel resistance + air resistance

The dependence of the total drag force on the speed is marked in red. You can see from the graphic that from a speed of approx. 18 km / h the air resistance is greater than the wheel resistance.
At high speeds - such as those driven in bike races - air resistance dominates. It is therefore understandable that the drivers first try to save energy in the slipstream of the competition.