The summary of the vertical loads acting on a vehicle in a gradient are indicated in the table.
The static ratio of axle loads on the front axle can be determined by a moment balance around the rear tire contact point. The static ratio of axle load on the rear axle can be similarly determined from a moment balance around the front tire contact point. In this case, aerodynamic and dynamic shares are neglected. In a gradient, the additional shift of the axle load dependent on the angle of the gradient has to be considered in the calculation of statistic axle loads.
The aerodynamic component produced by the air flow around the moving vehicle has an effect on the vertical loads in the form of lift. Similar to the force of air resistance, lift is also calculated using a coefficient of lift cA. Lift can either be positive (lift) or negative (negative lift).
Acceleration or deceleration generates a dynamic axle load ratio as a result of inertia forces and moments.
The force of inertia acting at the centre of gravity of the vehicle is produced by the translational acceleration of the vehicle mass, while the moment MTquer, by the rotational acceleration of the masses. In order to calculate the axle load, the mass inertia forces of these parts (wheels, drive shafts, also engine and transmission in a transversally installed engine) are reduced to the driven axle.
If only the forces of inertia acting on the accelerated vehicle are considered, the moment balance around the front tire tread point results in:
Eq. 3-38
With and for the dynamic component at the rear axle:
Eq. 3-39
From the vertical force balance, the dynamic axle load ratios are found to be equal and opposite:
