Question

What is the formula for induced velocity for a helicopter while it hovers?

(a) vh=\(\frac {T}{2\rho A}\)

(b) vh=\(\sqrt {\frac {T}{2\rho A}}\)

(c) vh=\(\frac {T^2}{\rho A}\)

(d) vh=2ρAT

I got this question in homework.

My question comes from Momentum Theory topic in division Helicopter Dynamics of Aerodynamics

Answer 1

Right answer is (b) vh=\(\sqrt {\frac {T}{2\rho A}}\)

Best explanation: Momentum equation helps in giving us a relation between the thrust of the rotor and the induced velocity. It is given by:

T=2ρAvh^2

Which is rearranged to obtain the induced velocity:

vh=\(\sqrt {\frac {T}{2\rho A}}\)

Where, T is the total thrust

A is area of actuator disk

vh is induced velocity at rotor disk.