Power required for helicopter to hover.

[Fruh2theline]

Homework Statement

A helicopter can hover when the output of its engines is P. A second helicopter, an exact copy of the first one, but its linear dimensions are half of those of the original. What power output is needed to enable this second helicopter to fly?

Homework Equations

The teacher describes this problem as being "maximum physics and minimum maths" so I am modeling the helicopter as a sphere for simplicity and working from there.

The Attempt at a Solution

If the helicopter is a sphere then decreasing the radius of the sphere by a half will decrease the volume by an eighth (V is proportional to radius cubed).
If the volume is decreased by an eighth then the mass is decreased by an eighth.

The lift of the blades if proportional to area of the circle they sweep out so decreasing their length by a half will decrease the area of the circle by a quarter (area is proportional to r squared).

So if the weight is decreased by an eighth and the lift from the blades is decreased by a quarter then half of the power of the original helicopter will suffice for this one to hover.

Am I missing anything?
Is this solution plausible?
Thanks for the help.

 

[Quinzio]

Honestly I think you went further.
The power needed is just one eight of the bigger helicopter.

 

[Borek]

It is all about scaling. Power scales with mass (you better try to prove it).

Rotor diameter doesn't matter, as amount of air moved depend not only on rotor diameter, but also on the rotation speed - and it doesn't have to be constant.