Rotor blade thrust - torque and angular velocity

[ChromeBit]

Imagine a motor, spinning a rotor blade around and around and around and around and around...

How does the angular velocity of the rotor blade, and the torque affect the thrust produced?

 

[russ_watters]

Rotational speed is linearly related to airflow and airflow velocity, thrust is a square function of rotation rate.

Torque is also a square function of rotation rate because torque comes from aerodynamic drag.

 

[CWatters]

If this were a prop attached to a plane...

Angular velocity * Torque = Power_prop

That's the power required to turn the propeller. The power available to move the plane is somewhat less due to the efficiency of the prop..

Power_plane = Power_prop * Eff_prop

A well designed propeller might achieve 80% efficiency (with lots of caveats) but it will only achieve that under certain flight conditions.

The power required to move the plane (non accelerating flight) is roughly..

Power_plane = Thrust * Velocity_plane

So with some substitutions...

Thrust = Angular velocity * Torque * Eff_prop/Velocity_plane

The problem is not all are independent variables. For example prop efficiency will change with plane velocity.

PS: This equation is no use for testing a model plane prop on a bench (the plane velocity in that case would be zero, among other problems).