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Could a wing be added to the rear of a helicopter to catch the vortex from a helicopter for more lift? How would that affect transitional lift while in forward flight?

enter image description here Source: https://www.danubewings.com/translational-lift/

How do modern helicopters tackle Vortex Ring State?

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Yes, in forward flight only and with questionable effectiveness, since the rotor would need to compensate for the pitch down moment. Note some helicopters have a small horizontal stabilizer on the tail boom, that is mostly used to pitch up and keep the airframe level in forward flight as seen here (look at the camber of the stabilizer):

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In all other flight regimes the wing would be a liability as it would interfere with the airflow downstream of the rotor.

It would also require significant structural reinforcement of the tail boom to transfer the bending moment of the wing, likely large enough to compromise the VTOL capabilities.

In summary, yes, but it would make no sense, there are better places to place a wing on a helicopter.

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