Maximum Acceleration

Maximum Acceleration The approach used to model vehicle maximum acceleration in SwashSim is based on the vehicle performance theory and equations given in Principles of Highway Engineering and Traffic Analysis (Mannering and Washburn, 2016). An overview of this approach is given here.

The approach at its most basic level determines acceleration through the fundamental equation relating tractive force to resistance forces, as follows.

$$ F = ma + {R_a} + {R_{rl}} + {R_g}\ $$

The tractive force, F, referred to here as available tractive effort, is taken as the lesser of maximum tractive effort and engine-generated tractive effort. Maximum tractive effort is a function of several of the vehicle’s physical characteristics (such as wheelbase, center of gravity, and weight) and the roadway coefficient of road adhesion. Maximum tractive effort represents the amount of longitudinal force that can be accommodated by the tire-pavement interface. Engine-generated tractive effort is a function of engine torque, transmission and differential gearing, and drive wheel radius. For vehicles with low power-to-weight ratios, such as commercial trucks, maximum tractive effort is very rarely the governing condition. Thus, the acceleration calculations for trucks in SwashSim are based on engine-generated tractive effort.

The major resistance forces are aerodynamic, rolling, and grade. The equation for determining aerodynamic resistance is

$${R_a} = \frac{\rho }{2}{C_D}{A_f}{V^2}$$

$$ {f_{rl}} =  0.01\left( {1  +  \frac{V}} \right)\ $$

$$ {R_{rl}} =  {f_{rl}} W\ $$

$$ {R_g} =  W \sin {\theta _g}\ $$

$$ {R_g} \cong  W \tan {\theta _g}  =  WG\ $$

$$ V =  \frac\ $$

$$ {\rm{h}}{{\rm{p}}_e} =  \frac\ $$

$$ {\rm{h}}{{\rm{p}}_e} =  \frac\ $$

$$ {F_e} = \frac{r}\ $$

$$ a = \frac\ $$

$$ {\gamma _m} =  1.04 + 0.0025\varepsilon _0^2\ $$