This is starting to hurt!
The wind accelerates you as you turn downwind - but only with reference to the ground.
The wind does not accelerate you as you turn downwind - with reference to the wind.
Now no-one has mentioned coriolis force/effect yet where the turning helicopter would be deflected to the right in the Northern Hemisphere, or the red or blue doppler shift as you accelerate or decelerate relative to an observer at the edge of the universe (is he coming towarsd you or going away)?