Finding optimum Ackermann geometry for a car undergoing steady state cornering using tire data

Abstract

For a car to have minimum lap times across a track it should be able to produce the maximum cornering force or side force in order to complete the corner at the maximum velocity possible. The grip level of a particular tire limits the maximum side/lateral force it can produce. To find the best steering geometry for a car one should know the grip limit of the tire and at which slip angle it is being produced. This paper provides a simple methodology to find the appropriate Ackermann steering geometry, which can produce the maximum lateral tire grip going through different high speed constant radius corners. Hence, reducing the time spent on-track while testing to find out the suitable steering setup and improving the overall cornering ability of the car. The raw tire data from tire testing runs of the tire: Hoosier 18.0 X 6.0 – 10 R25b is used to fit curves to the raw data using two tire models based on the Magic Formula and Data Non-dimensionalization methods respectively. The results from both of the methods are compared. These tire models are then used to find the ideal steer angles of the front tires at various constant radius steady-state turns and thus the Ackermann geometry of a Formula Student car producing the maximum possible grip.