Optimization of an open rotor propulsion system comprising an unducted fan and a ducted fan

An open rotor propulsion system comprising:

• a fan section including an unducted rotating element comprising a first array of fan airfoil blades and a non-rotating stationary element;
• an forward frame housing an inlet duct including an inlet located between the unducted rotating element and the non-rotating stationary element;
• a ducted fan positioned aft the unducted rotating element within the inlet duct, wherein the ducted fan comprises a second array of fan airfoil blades;
• a fan duct and a core duct extending aft the ducted fan;
• an engine positioned within the core duct and comprising a low-pressure compressor, a high-pressure compressor, an intermediate case located between the low-pressure compressor and the high-pressure compressor, a fan drive turbine and a shaft connected to the fan drive turbine and configured to drive the ducted fan;
• and
• four bearings configured to support the shaft with respect to an engine case,
• wherein the four bearings comprise:
• a first bearing connected to one of the forward frame and the intermediate case;
• and
• a second bearing aft of the first bearing and comprising a gravity center axially positioned between a first plane that comprises a gravity center of the low-pressure compressor and a second plane that comprises a gravity center of the intermediate case.