Midshaft rating for turbomachine engines

A turbomachine engine comprising:

• an engine core including a high-pressure compressor including eight stages, nine stages, ten stages, or eleven stages, a high-pressure turbine including one stage or two stages, 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;
• a low-pressure shaft coupled to the power turbine and characterized by a midshaft rating (MSR) from one hundred fifty (ft/sec)1/2 to three hundred thirty (ft/sec)1/2, wherein low-pressure shaft has a redline speed between fifty and two hundred fifty feet per second (ft/sec), and 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;
• and
• a high-pressure shaft coupled to the high-pressure compressor and the high-pressure turbine, the high-pressure shaft characterized by a high-speed shaft rating (HSR) from 1.5 to 6.2, wherein the high-pressure shaft is further characterized by an inlet area high-speed shaft rating (HSP_AIN) from 1,038 in2 to 5,017 in2, wherein HSR is given by:
• HSR
• =
• 1
• k
• *
• N
• ⁢
• 2
• R
• L
• *
• D
• CORE
• *
• (
• L
• CORE
• D
• CORE
• )
• 2
• ,
• where N2R/L is a redline speed of the high-pressure shaft, LCORE is a length of the engine core, DCORE is a diameter of the engine core, and k is a constant with a value of 106 inch-RPM, and
• HSP_AIN is given by:
• (
• L
• CORE
• D
• CORE
• )
• 2
• *
• A
• IN
• R
• HUB
• ,
• IN
• R
• TIP
• ,
• IN
• *
• R
• TIP
• ,
• EX
• R
• TIP
• ,
• IN
• ,
• where RHUB,IN/RTIP,IN is an inlet radius ratio of the high-pressure compressor, RTIP,EX/RTIP,IN is a high-pressure compressor tip radius ratio, and AIN is an area at an inlet of the high-pressure compressor.