Model of thrust/Load-Torque in terms of geometric parameters of the blade for design and simulation of small scale propellers used in miniature UAVs

Abstract

Autonomous flight of miniature UAVs demands high performance actuators satisfying the requirements of modern control algorithms. Specially for quadrotors, where lift and control forces are the result of a synchronized action of the four BLDC/propeller actuators, the form of their propellers are fundamental to attain a fast and reliable dynamic response. In this paper, we present a mathematical model of the thrust and the Load-Torque produced by a small scale propeller used in miniature quadrotors in terms of the geometric properties of the blade assuming an operation in hover mode. This model is intended to provide a useful expression for simulation analysis with design purposes. The model is based on the Blade Element Theory and the Euler equation for fluids, and describes the Lift on a thin and curved airfoil with a known angle of attack, as the normal acceleration between the deflected streamlines of an incompressible fluid. This allows the calculation of the thrust and the Load-Torque of a turning propeller in terms of the geometric parameters of its blades, i.e. radial and cross section length, curvature and angle of attack, but preserving the conventional results relating the thrust to a square function of the rotational speed of the propeller. As a reference, we include the conventional model based on experimental coefficients of Lift and Drag before introducing our approach, and then, we illustrate the advantage of our approach with an example based on a propeller with blades of fixed and constant pitch angle and constant width, and finally, we briefly discuss about the evidence, based on experimental and simulation data obtained in the literature, that validates our approach.