Helicopter Lift Equation

I have a further question regarding the earlier answer on the lift formula. You use the same equation for an airplane and a helicopter, but what if the helicopter is in hover? The velocity in hover is zero, so the lift must also be zero according to this equation.
- question from Tieo Jing Jin
You are indeed a sharp cookie and noticed an inconsistency in our answer. In order to simplify that previous discussion, we only explained the lift equation used for forward flight. For a helicopter in hover, you are correct in noting that the forward velocity is zero, and therfore the lift calculated using this formula is zero. Since a hovering helicopter does produce lift (otherwise it wouldn't remain airborne), this equation is obviously no longer valid under these conditions.

Unfortunately, there is no simple equation to compute the lift generated by a helicopter rotor in hover like there is for forward flight. Instead, we must rely on substantially more complicated methods like the Blade Element Momentum Theory or the Actuator Disk Vortex Theory. Both approaches involve complex jargon and even more complex mathematics that would require far more explanation than we have the time or space to discuss here (to emphasize the point, I have a 1,000 page book on the subject of helicopter theory!). In either case, we are not concerned with computing the lift so much as we are the power required to maintain hover and the thrust force generated by the rotor.

Air being accelerated through a hovering rotor

In order to generate this thrust, the rotor pulls air down through it, as illustrated above, acting just like an airplane propeller that has been turned 90°. The spinning rotor accelerates the air as it goes through the rotor disk creating a force that acts in the opposite direction. This upward force is the rotor thrust. If you think about it, since this "thrust" points straight up and is the only force counteracting the weight of the helicopter, this force is the lift.
- answer by Jeff Scott, 29 July 2001