Module 2: Dynamics of Electric and Hybrid vehicles

Lecture 3 : Motion and dynamic equations for vehicles

The typical values of the rolling resistance coefficient (fr) are given in Table 1 .

The values given in table 1 do not take into account the variation of fr with speed. Based on experimental results, many empirical formulas have been proposed for calculating the rolling resistance on a hard surface. For example, the rolling resistance coefficient of a passenger car on a concrete road may be calculated as:


In vehicle performance calculation, it is sufficient to consider the rolling resistance coefficient as a linear function of speed. For most common range of inflation pressure, the following equation can be used for a passenger car on a concrete road


The Equation 7 can predict the values of fr with acceptable accuracy for speed upto 128km/h.

Aerodynamic drag

A vehicle traveling at a particular speed in air encounters a force resisting its motion. This force is known as aerodynamic drag. The main causes of aerodynamic drag are:

The shape drag is due to the shape of the vehicle. The forward motion of the vehicle pushes the air in front of it. However, the air cannot instantaneously move out of the way and its pressure is thus increased. This results in high air pressure in the front of the vehicle. The air behind the vehicle cannot instantaneously fill the space left by the forward motion of the vehicle. This creates a zone of low air pressure. Hence, the motion of the vehicle creates two zones of pressure. The high pressure zone in the front of the vehicle opposes its movement by pushing. On the other hand, the low pressure zone developed at the rear of the vehicle opposes its motion by pulling it backwards.

The air close to the skin of the vehicle moves almost at the speed of the vehicle while the air away from the vehicle remains still. Between these two layers (the air layer moving at the vehicle speed and the static layer) the molecules move at a wide range of speeds. The difference in speed between two air molecules produces friction. This friction results in the second component of aerodynamic drag and it is known as skin effect.

The aerodynamic drag is expressed as