# estimation of the drag coefficient

The vehicle speed at one moment is the balance beetween the driving resistance forces and the drive forces supplied from the engine. The driving restance force is the sum of the
• air resistance force
• rolling resistance force
• tilt-resistance force
• and the slip-resistance force
• It is usual to draw the sum of the driving resistance force and the drive force on whell over the vehicle speed. Such a traction diagram of a vehicle in standard design is shown below.

Here can be seen, that the rolling resistance force has a very small amount at higher speeds. At higher driving speed (above 120 km/h), the last three points can be neglect. This leads to the equation (1.1)

$F_A = F_L$ (1.1)

The air drag force is given by the equation:

$F_L = \frac{1}{2} \cdot c_W \cdot A_{ref} \cdot \rho \cdot v^2$ (1.2)

$P_L = \frac{1}{2} \cdot c_W \cdot A_{ref} \cdot \rho \cdot v^3\\ \rightarrow c_W = \dfrac{2\cdot P_{L}}{A_{ref} \cdot \rho \cdot v^3}$ (1.1)

The unknown values in equation (1.1) are the cross sectional area and the air restance performance.