Inclined Road Forces

Gradient Resistance (GR)

The gradient resistance (climbing resistance, inclined road force) depends on the angle of the

road inclination and the weight of the car.

          GR = w sine = mg sin θ

where :

     w= the car weight (N) = mg

     θ = the angle of road inclination

Road inclination (gradient):

The road gradient can be described as 1 in N, this description can be either:

The description (b) is not suitable incase of level road the gradient will be l in ∞, especially when using the computer. So, the description of the gradient will be as in (a), and the gradient will be (G = sin θ). The gradient can be written in as a percentage (G = sine θ = S%).

* For small angle (θ (radians) ≈ sin θ ≈ tan θ)

* The road gradient in the highway usually does not exceed 4% and on the local roads it could reach 10%-12%.

* The steepest gradient the vehicle is expected to climb (this may normally be taken as 20%, that is 1 in 5)

The gradient effect on the car:

Uphill:

     1- Increase the car motion resistance; F_G = w sin θ (against the direction of motion)

     2- Increase the load on rear axle and decrease the load on the front one.

     3- Decrease the stopping distance when using the brakes (4% is equal to 0.04 g)

Downhill:

     1- Increase the tractive effort; F_G = w sin θ  (in the direction of motion)

     2- Increase the load on front axle and decrease the load on the rear one.

     3- Increase the stopping distance when using the brakes (40% is equal to 0.04 g)