point 1 to point 2, the mixture is ignited and burns instantaneously and the pressure in the combustion chamber increases at point 2 to a pressure at point 3. The high- pressure combustion gas depresses a piston in the expansion stroke from point 3 to point 4 to deliver engine output. An exhaust valve is opened at point 4, exhaust pressure drops instantaneously in a time from point 4 to point 5, and the gas is discharged from the combustion chamber in a time from point 5 to point 6. Occurrence of knocking will be explained with reference to FIG. 18. Knocking, i.e., the generation of unpleasant sound and vibrations, occurs when boost pressure is excessively high, the temperature of the compressed mixture, i.e., the temperature at point 2, is excessively high, and detonation other than normal flame propagation starts in a portion of the unburned mixture. A conventional knocking evasion method sets the engine at a low compression ratio. However, in the conventional engine in which valve opening timing and valve closing timing are fixed, expansion ratio is decreased if the compression ratio is decreased, and the efficiency of the conversion of thermal energy generated in the combustion chamber into engine output is reduced. In FIG. 18, a compression ratio 6 and an expansion ratio 6' are expressed by: