# Power considerations

The total change in energy per unit mass (*E) along the streamtube is given by:

*E = 2(VC + vi )vi

As power can be defined as massflow multiplied by change in energy: P = m*E = pA(VC + vi) x 2(VC + vi)vi

P = T(VC + vi) = TVC + Tvi (2.2)

So the power required to drive a climbing rotor can be seen to come from two sources: the power required to generate the rate of climb (the useful power = TVC) and the power required to generate the thrust (the induced power = Tvi). The power calculated using Equation (2.2) represents an ideal minimum value because this simple theory neglects all forms of losses.

It has been seen that power estimations require a knowledge of thrust, rate of climb and induced velocity. Whilst the thrust can be related to the weight of the helicopter

and the rate of climb is an easily specified variable the induced velocity is more difficult to determine. However, Equation (2.1) can be re-written as:

v2 + v;vc-^-7 = 0 2pA

Only the positive root of this quadratic has any meaning in this case, so: Vc Vc2 T

V = 2 + J 4 + 2pA

Note that Equation (2.3) can be used to predict the induced velocity in the hover (Vc = 0):  (2.4)