Closed-form solutions for vehicle traction problems
Conventional approaches to vehicle traction and propulsion analysis have used spread-sheets or numerical integrations owing to the difficulty in deriving closed-form solutions. This is inconvenient if a parameter is to be varied, and it is even more difficult when multiple parameters of a complex model are evaluated at the design phase. In this paper, it is intended to formulate two non-linear differential equations representing road load and power consumption. By expanding inertia force, air drag, rolling resistance, gravitational force and tyre tractive force, the equations can be simplified as functions of velocity v, i.e. s 1 v = s 2-s 3 v2 and m v = (-r 1 v3 - r 2 v + r 3)/v respectively. With these two equations, engineers can use either numerical or analytical methods to study key parameters at the design phase. To demonstrate the effectiveness of these equations, Wright State's electric car model is used. The results for front-wheel drive, rear-wheel drive and four-wheel drive cases are presented.