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Why does a helicopter that uses the Coandă effect instead of a tail rotor need a direct jet thruster as well. Why couldn't they just vary the pitch of the ducted fan used for the Coandă effect?

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The responses to changes in the Coandă effect are too slow to be useful as a precise anti-torque input control operated from the pedals. Remember that the sideways lift is coming from the main rotor downwash. CE is only allowing a tubular boom to make substantial side ways lift from the downwash, not producing any sideways thrust itself from the fan flow.

Hughes found that it only worked if you used CE induced lateral lift from the downwash as a baseline anti-torque force, and used the thruster to fine tune the total force for yaw control.

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