Question

What is the relation between the induced velocity in far wake region (w) and that at the rotor disk (v) for hovering condition?

(a) w=v

(b) w=v^2

(c) w=2v

(d) w=v/2

I had been asked this question during an interview.

My query is from Momentum Theory in section Helicopter Dynamics of Aerodynamics

Answer 1

The correct choice is (c) w=2v

To explain: The momentum equation for the rotor is given by:

T=\(\dot {m}\)w

Which can be rearranged as:

\(\frac {T}{\dot {m}}\)=w (equation 1)

And the energy equation is given by:

Tv=\(\frac {1}{2}\dot {m}\)

Which is rearranges as:

\(\frac {T}{\dot {m}}=\frac {1}{2}\)vw^2 (equation 2)

On equating equation 1 and 2 we get w=2v

Thus, the induced velocity in the wake region is twice that of the velocity at the rotor disk.