A propulsion system for an aircraft is provided having a propulsion engine configured to be mounted to the aircraft. The propulsion engine includes an electric machine defining an electric machine tip speed during operation. The propulsion system additionally includes a fan rotatable about a central axis of the electric propulsion engine with the electric machine. The fan defines a fan pressure ratio, RFP, and includes a plurality of fan blades, each fan blade defining a fan blade tip speed. The electric propulsion engine defines a ratio of the fan blade tip speed to electric machine tip speed that is within twenty percent of the equation, 1.68×RFP−0.518, such that the propulsion engine may operate at a desired efficiency.