Aerodynamics of Rotor Blades for Quadrotors

TL;DR

This paper develops aerodynamic models for quadrotor rotor blades using momentum and blade element theories, enabling better understanding and control of thrust, horizontal forces, and power consumption for various blade geometries.

Contribution

It introduces a combined theoretical framework for modeling quadrotor aerodynamics, including the effects of blade geometry and aerodynamic properties, with practical applications in robotics.

Findings

Optimal hovering rotor identified as most efficient design.

Geometric variations influence thrust and horizontal force ratios.

Lumped parameter models facilitate robotic control applications.

Abstract

In this report, we present the theory on aerodynamics of quadrotors using the well established momentum and blade element theories. From a robotics perspective, the theoretical development of the models for thrust and horizontal forces and torque (therefore power) are carried out in the body fixed frame of the quadrotor. Using momentum theory, we propose and model the existence of a horizontal force along with its associated power. Given the limitations associated with momentum theory and the inadequacy of the theory to account for the different powers represented in a proposed bond graph lead to the use of blade element theory. Using this theory, models are then developed for the different quadrotor rotor geometries and aerodynamic properties including the optimum hovering rotor used on the majority of quadrotors. Though this rotor is proven to be the most optimum rotor, we show that geometric variations are necessary for manufacturing of the blades. The geometric variations are also dictated by a desired thrust to horizontal force ratio which is based on the available motor torque (hence power) and desired flight envelope of the vehicle. The detailed aerodynamic models obtained using blade element theory for different geometric configurations and aerodynamic properties of the aerofoil sections are then converted to lumped parameter models that can be used for robotic applications. These applications include but not limited to body fixed frame velocity estimation and individual rotor thrust regulation [1, 2].