Each combustion chamber of the Fourier engine is open to multiple cylinders, which have pistons connected to crankshafts that rotate at different rates. The displacements of the individual cylinders and the relative phases of the pistons are selected according to a Fourier approximation of a prescribed time dependence of the volume of the combustion chamber. The parameters are selected so that the duration of the intake and ignition strokes is greater than the duration of the compression and exhaust strokes. As the speed of an engine increases, the power curve initially climbs approximately linearly, but it levels off as intake and ignition become less efficient at high rpm. By increasing the duration of these strokes relative to the duration of the other strokes, it may be possible to allow the power curve to climb higher before leveling off.