Acceleration Performance

The acceleration of a vehicle is defined by its acceleration time and distance covered from zero speed to a certain high speed on a level ground. The acceleration of the vehicle can be expressed as

     (36)

where δ is the rotational inertia factor taking into account the equivalent mass increase due to the angular moments of the rotating components. This mass factor can be written as

                                              (37)

To determine the value of δ, it is necessary to determine the values of the mass moments of inertia of all the rotating parts. In case the mass moments of inertia are not available then, the rotational factor ( δ) can be approximated as:

                                                                                                          (38)

The acceleration rate along with vehicle speed for a petrol engine powered vehicle with a four gear transmission and an electric motor powered vehicle with a single gear transmission are shown in Figure 10 and Figure 11 respectively.

 

Figure 10: Acceleration rate of a petrol engine powered vehicle with four gears

 

Figure 11: Acceleration rate of an electric machine powered vehicle with a single gear

From Equation 36 , the acceleration time t_a and distance S_a from a lower speed V₁ to a higher speed V₂ can be expressed as

                                    (39)

and

                                     (40)

The power plant torque T_p in equation 39 and equation 40 is a function of speed of the power plant. The speed of the power plant is in turn a function of the vehicle speed and gear ratio of the transmission. Hence, analytical solution of equation 39 and equation 40 is not possible. Numerical methods are usually used to solve these equations.

Suggested Reading

[1] I. Husain, Electric and Hybrid Electric Vehicles , CRC Press, 2003

[2] G. Lechner and H. Naunheimer, Automotive Transmissions: Fundamentals, Selection, Design and

Application , Springer, 1999