<< Now from momentum considerations you can show that the tip speed should
be equal to the exhaust velocity- in this case ~200 m/s >>
I may be missing part of this scenario, but there seems no reason for rotor
tip speed to equal exhaust velocity. I would think rotor tip speed would
increase until the torque of the overall drag forces on the rotor equaled the
torque produced by the engines. IF this "terminal velocity" HAPPENS to equal the
exhaust velocity of rocket, then additional energy from the rocket propellant
would go mainly into the kinetic energy of the air moved by the rotor
(downwash, shock waves, etc.), less an allowance for inefficiencies.
In ordinary rockets, the classic rocket equation does link exhaust velocity
to final vehicle velocity through total propellant mass. For instance, the
burnout velocity of an ideal, free space, single stage is equal to its exhaust
velocity when the propellant mass is "e-1" (1.718..) times the mass of everything
else. But I would think a rotor would reach its drag-limited "terminal
velocity" long before fuel consumption becomes an issue.
--Best, Gerald
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