Rotor blade thrust - torque and angular velocity

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SUMMARY

The discussion focuses on the relationship between angular velocity, torque, and thrust in rotor blades. It establishes that thrust is a square function of rotation rate, while torque also follows a square function due to aerodynamic drag. The equation linking these variables is defined as Thrust = Angular velocity * Torque * Effprop / Velocityplane. It emphasizes that propeller efficiency varies with plane velocity, impacting the overall power required for flight.

PREREQUISITES
  • Understanding of angular velocity in rotational dynamics
  • Knowledge of torque and its relationship to aerodynamic drag
  • Familiarity with propeller efficiency and its impact on flight
  • Basic grasp of power equations in aerodynamics
NEXT STEPS
  • Research the principles of angular momentum and its application in rotor dynamics
  • Explore the effects of aerodynamic drag on torque in propeller design
  • Learn about propeller efficiency metrics and their significance in aviation
  • Investigate the relationship between thrust and velocity in various flight conditions
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Aerospace engineers, mechanical engineers, and aviation enthusiasts interested in understanding the dynamics of rotor blades and propeller performance.

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

Angular velocity * Torque = Powerprop

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..

Powerplane = Powerprop * Effprop

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..

Powerplane = Thrust * Velocityplane

So with some substitutions...

Thrust = Angular velocity * Torque * Effprop/Velocityplane

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).
 

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