Are you asking whether there is something fundamental about the nature of moving a plane by twirling a propeller that makes it impossible to move faster than sound?

This is just a gut feeling, but I think that if the motor's air was fed to it in a regulated way, or was some high-tech electric motor, and that the plane itself could withstand the pressures, there is nothing fundamental preventing it. That is, given enough horsepower and torque.

On the other hand newer technologies make the engineering challenge seem not worth while, and probably not energy efficient.

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Forming opinions as we speak