The problem of optimal driving techniques during fuel economy competition is considered. The kinetic model of the record wheeled vehicle is proposed. It is regarded as a particle moving on a trace with variable slope angle. Engine characteristics are taken into account. The fuel consumption is minimized as the vehicle goes over a given distance. The problem is formulated in optimal control. The direct pseudospectral Chebyshev’s method is employed. The motion of student’s vehicle representing the Faculty of Power and Aeronautical Engineering during Shell Eco-marathon in Nogaro, France, in 2006, is used as an example.

The minimum-time problem for a glider flying in the vertical plane is considered. The glider is regarded as a particle moving in the atmosphere in given thermal conditions. The problem is formulated in optimal control and solved using direct pseudospectral Chebysev's method. The data are taken for the Word Class Glider PW-5 "Smyk". Computed optimum results are compared with glider's trajectories from the Second Domestic Glider Championship 2006, Suwałki, Poland.