The suspension of a Formula One racing car is modelled using kinematic analysis. A set of non-linear equations are derived and then solved and fitted to a multivariate polynomial. This meta-model maps the normal tyre forces and heave spring stiffness to the roll and ride heights of the car. Numerical optimal control is used to calculate the minimum lap time trajectory for a vehicle model which includes the suspension system characteristics. A parametric study is then conducted to determine the optimum suspension set-up.