Resistance to vehicular motion

A moving vehicle experiences several resistances that the engine must overcome. Their sum is the tractive resistance, and the driving force (tractive effort) must be at least equal to it.

Types of resistance

1. Air (wind) resistance $R_a$: from the drag of the air on the front, sides and rear of the vehicle. It is proportional to the square of the relative speed: $$R_a = \tfrac12\rho\,C_d\,A\,v^2$$
2. Rolling resistance $R_r$: caused by tyre deformation and road surface roughness; $R_r = f_r W$ with $f_r \approx 0.01$-$0.02$ for good paved surfaces, higher for gravel and earth.
3. Gradient resistance $R_g$: the component of weight along the slope, $R_g = W\sin\theta \approx W\,G$ ($G$ is the gradient).
4. Curve resistance $R_c$: extra resistance on horizontal curves from lateral slip and steering; allowed for in design by grade compensation.
5. Inertia (acceleration) resistance $R_i$: the force needed to accelerate the vehicle mass, $= \gamma\,\dfrac{W}{g}a$.
6. Internal (transmission) resistance: friction in the engine and the transmission; usually allowed for by an efficiency factor.

$$R_{total} = R_a + R_r + R_g + R_c + R_i$$

The total determines the engine power required, the speed on a grade and the gradients adopted in design.