RotorcraftMixing

This page describe how to compute "mixing" for an arbitrary multirotors configuration.

Let us consider a vehicle comprising a set of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} identical power trains $R_{i},i\in [1:N]$ located at coordinates Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (X_i,Y_i), i\in[1:N]} and spinning in the same plane in the direction Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D_i, i\in[1:N], D_i\in[-1;1]} at a rotational speed Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \omega_i, i\in[1:N]} .

Assuming a quasi hovering regime, the force produced by each rotor can be considered normal to the rotor plane and proportional to the square of its rotational speed. Under the same assumption, the torque produced by each rotor can also be assumed to be in the same direction and proportional to the square of the rotational speed.