A rotary internal combustion engine includes an arcuate compression chamber, an arcuate expansion chamber, an output shaft, and a piston coupled to the output shaft for movement through the arcuate compression chamber and the arcuate expansion chamber. The piston has a leading end, a trailing end, an inlet valve that is located at the leading end of the piston for receiving a compressible fluid from the compression chamber and an outlet valve that is located at the trailing end of the piston for expelling a combustion gas into the arcuate expansion chamber.