Critical Speed Control of a Solar Car

The World Solar Challenge is a 3000 km race for solar powered cars across the Australian continent from Darwin to Adelaide. Each car is powered by a panel of photovoltaic cells which convert sunlight into electrical power. The power can be used directly to drive the car or stored in a battery for later use. Previous papers (P. Howlett, P. Pudney, T. Tarnopolskaya, and D. Gates, IMA Journal of Mathematics Applied in Business and Industry vol. 8, pp. 59-81, 1997; P. G. Howlett and P.J. Pudney, Dynamics of Continuous, Discrete and Impulsive Systems vol. 4, pp. 553-567, 1998) using a simplified model of the battery, have shown that the optimal strategy is essentially a speedholding strategy. In this paper, with a more realistic model of the battery, we show that the optimal driving strategy is a critical speed strategy. For an optimal journey with no beginning and no ending the solar car must always travel at the critical speed. For an optimal journey of finite length the speed must be close to the critical speed for most of the journey. The critical speed depends on the solar power and will normally vary slowly with time.