# What is the relationship between speed, torque and pitch in a helicopter?

Can someone clarify the relationship between aircraft speed, torque, prop length and pitch and how this applies to a helicopter.

In addition I want to know if the amount of lift a helicopter generates changes dependant on pitch, how much does the pitch change?

• Aircraft pitch or rotor pitch? – Sanchises Mar 21 '18 at 8:52
• Rotor pitch Sanchises – Chris James Mar 21 '18 at 9:04

## 1 Answer

I'm afraid that a thorough answer requires the contents of chapters 2 and 3 of Leishman, but here is an outline. The relationship between power and true airspeed from this answer:

Power equals torque times angular velocity of the rotor: $$P = Q * \Omega$$. Most helicopters have constant speed rotors, so the relationship between torque and speed would be similar to the power curves.

Rotor blade length and pitch appear as follows. Power P and torque Q equations for momentum theory in the hover:

$$P = C_P \cdot ½ \rho A (\Omega R)^3$$

$$Q = C_Q \cdot ½ \rho A (\Omega R)^2 R$$

At forward speed the momentum based power becomes less due to lower induced power requirements. An inflow equation relates forward velocity of the helicopter with blade tip speed - too much scope for an answer here.

Blade length appears in the rotor disk area A. Torque and power are functions of the rotor solidity $$\sigma$$, defined as (total blade area)/(disk area). Note that $$C_P$$ is always the same value as $$C_Q$$

From Leishman:

..if the amount of lift a helicopter generates changes dependant on pitch, how much does the pitch change..

Thrust T of the rotor Again from Leishman: