A pulse detonation cluster includes a cluster housing and a plurality of pulse detonation engines mounted within the housing. Each pulse detonation engine has an inner tubular housing rigidly and concentrically mounted within a cylindrical bore of an outer tubular housing. The inner housing has a plurality of inner housing ports, and the outer housing has a plurality of outer housing ports. A detonation chamber is formed in the annulus between the inner housing and the outer housing. An outer valve sleeve is rotatably mounted to the outer housing for selectively allowing air to enter the detonation chamber through the outer housing ports. A fuel delivery member is aligned with each inner housing port to deliver fuel to the detonation chamber through the inner housing ports. An inner sleeve is mounted to the inner housing to protect the fuel delivery members during detonation. The air and fuel mixture is detonated by several igniters located in the detonation chamber. The detonation creates a detonation wave that travels through an open downstream end of the detonation chamber, thereby creating thrust for the engine. When combined in the cluster housing, outer valve sleeves of the pulse detonation engines are rotated by a common gear, which allows the engines to be easily timed to share inlet air entering the cluster housing. A pulse detonation bank is a combination of two or more pulse detonation clusters within a bank housing having a bank inlet. All of the pulse detonation engines within the bank share the bank inlet and are timed to maximize consumption of inlet air.