Estimate power required to keep 3,000 kg helicopter with rotor diameter 10 m hovering?

Answer 1

A helicopter's rotor generates lift by forcing air downward, (according to Newton's third law). This is analogous to how a rocket motor works, and, in fact the same kind of equation can be used to describe it's lift or thrust:

F = ve∙(dm/dt);

where ve is the exhaust velocity, and dm/dt is the rate at which propellant mass leaves the nozzle. If the helicopter is hovering, I can set:

F = mh∙g

where mh is the mass of the helicopter, and g is the acceleration of gravity. But how do I go about finding ve, and dm/dt? If I assume the density of air to be constant (ρ), then intuitively:

dm/dt = ρ∙(dV/dt) (the rate of downward airflow)

= ρ∙A∙ve

= ρ∙πr²∙ve.

This changes the thrust equation to:

mh∙g = ρ∙π∙r² ∙ve².

So, solving for the unknown downward flow velocity:

ve = √[ (mh∙g) / (ρ∙π∙r²) ].

Now, the power generated by a rocket can be written:

P = F∙ve.

(As a side note, this leads to the observation that, a rocket motor with a better specific impulse, will typically generate much less thrust, than a less efficient motor of the same size....) As I have already stated, since the helicopter is hovering.......

F = mh∙g.

This means that, the formula for power becomes

P = mh∙g∙√[ (mh∙g) / (ρ∙π∙r²) ].

= √[ (mh∙g)³ / (ρ∙π∙r²) ]!

Now, I need only plug in the numbers. At standard ambient temperature and pressure (25 °C and 1 atm), dry air has a density of ρ = 1.168 kg/m³. I already know the mass of the helicopter, mh = 3,000 kg; and off the top of my head, g = 9.81 m/s²..........



P ≈ 263.6 kW

Hope that's instructive....
~W.O.M.B.A.T.

Answer 2

nicely, i comprehend no longer some thing about helicopters, so i theory the pilot is a smoker, and that he has devised a kinda of air flow duct :) i like Michel Verheughe's answer (between others). astounding shot, BTW.

Answer 3

A = pi(r^2) = 78.5m^2 = 845 ft^2

Power loading = Power(hp) / Area(ft^2)

Torque loading(lbs/hp) = 8.6859 x Power loading^(-0.3107)

Lift(lbs) =Torque Loading(lbs/hp) x Power(hp) = 6,600 pounds

~720 Horsepower


Add 10-15% for tail rotor:

[ ~810 Horsepower ]