[kingstnap]

Not for moving sideways at a constant altitude.

If you think about what a plane does to keep itself up, it sweeps through a curtain of air which ends up blowing downwards.

In a second it must blow down a large volume of air with enough speed to equal the impulse created by gravity in a second.

Basically m_air × v_down = m_plane × gravity × time

The energy you need to do this is the same quadratic, 1/2 m_air × v_down^2

A larger volume of air with a smaller v_down (a huge curtain of air of a fast plane with very wide wings) is more efficient then the smaller disk of air with high velocity of a helicopter.

But if the plane isn't moving forward the curtain has no volume and the plane stalls and falls. But helicopters have no trouble lifting off vertically.