A turbomachine engine including an engine core including a high-pressure compressor, which has an exit stage having an exit stage diameter (DCORE), a high-pressure turbine, and a combustion chamber in flow communication with the high-pressure compressor and the high-pressure turbine, a power turbine in flow communication with the high-pressure turbine, and a low-pressure shaft coupled to the power turbine and characterized by a midshaft rating (MSR) between two hundred (ft/sec)1/2 and three hundred (ft/sec)1/2. The low-pressure shaft has a redline speed between fifty and two hundred fifty feet per second (ft/sec). The turbomachine engine is configured to operate up to the redline speed without passing through a critical speed associated with a first-order bending mode of the low-pressure shaft. The low-pressure shaft has a length (LMSR) defined by an engine core length (LCORE) given by: LCORE=[m(20+m)*n(10+n)](1/100)*DCORE+CIS.