In this presentation, the use of orthogonal collocation methods in the solution of optimal control problems relating to Formula One racing is analysed. These methods can be used to optimise driver controls such as the steering, brakes, and throttle and to optimise vehicle setup parameters such as the aerodynamic down force distributions and the engine maps. Of particular interest is the optimal usage of on-board energy recovery systems. The talk focuses on the control of the hybrid kinetic-thermal energy recovery systems known as ERS-K and ERS-H that have been introduced into Formula One racing for the 2014 season. It is demonstrated that these systems, when properly controlled, can produce contemporary lap time using approximately two-thirds of the fuel required by last year’s vehicles.