what horse power is required to balance a unit weight in air? eg a helicopter hovering.+?

Question

what HP is required to accelerate a unit weight at 32.2 ft/sec continuously?

Answer 1

This is a tricky question, because air behaves in a tricky way.

If the object were sitting on the ground, it would take no power at all to remain there. However, an object in the air must constantly exert a force on the air. The air continuously gives way under this force in a turbulent and unpredictable way.

The amount of lift that a helicopter rotor is able to generate is:
L = Cl*(q*A)
where L is the lift force, Cl is the lift coefficient (which is different for every rotor at every angle of attack and every speed), q is the dynamic pressure, and A is the surface area of the blades.

The amount of power you need is a function of the drag force on the propeller times its velocity.
D = 1/2*rho*Cd*A*v^2
where D is the drag force, rho is the density of air, Cd is the drag coefficient (which is again different for every setup), A is the surface area of the blades, and v is their velocity. This is further complicated by the fact that the outer tips of the blades are moving faster than the inner parts.

The power dissipated is, roughly speaking:
P = D * v
P = 1/2*rho*Cd*A*v^2 * v
P = 1/2*rho*Cd*A*v^3

So, the higher the lift coefficient, the less power you need. The lower the drag coefficient, the less power you need. In fact, the measure of the efficiency of a wing or propeller is the lift coefficient divided by the drag coefficient. The higher this ratio, the more efficient the wing or propeller is.

In practice, a problem like this would be done with computational fluid dynamics software. It's essentially impossible to do it by hand.

Answer 2

No power is required to balance a force.
Power if force dot velocity and here velocity is zero.

The power is required to work the blade. An equivalent power measure is torque dot rotational velocity.

What hp is required to accelerate 1 g continously?
f = Mg
v = v0 +.5*g*t^2: let v0 be zero
f dot v = .5* M * g^2 * t^2 would be a function of t.

of course if the helicopter lifted at a constant velocity Vo:
f = Mg, v=v0
Hp = MgV0

However, it would take a lot more engine HP to provide this lift HP.