*5.2. Pair Motor/Propeller Optimization*

The optimization method is applied to the database used for validation. For each example, the optimal propeller parameters allowing the motor/propeller efficiency maximization are located using the SA algorithm. Figure 10 gives an example of an optimized pair motor/propeller, in which the motor/propeller efficiency with the corresponding propeller parameters is presented. However, a filtering condition is required in order to select the appropriate combinations that satisfy constraints, such as the GTOW, imposed by the drone. This condition is based on the computing of the relative error *ε<sup>r</sup>* between the maximum thrust *TMPmax* (*N*) generated by the optimized pair motor/propeller and the thrust imposed by the drone weight (GTOW) *TMax*(*N*). The maximum thrust generated by the optimized pair motor/propeller is deduced from the constraints imposed on the propeller velocity and output torque given in Equation (32):

$$T\_{MP\_{max}} = \left(M\_{max}^{-4} \cdot \frac{\mathbf{C}\_T^{-5}}{\mathbf{C}\_M^{-4}} \cdot \left(\frac{N\_{max}}{60}\right)^2\right)^{\frac{1}{5}}.\tag{35}$$

The thrust imposed by the drone weight *GTOW* is deduced from the acceleration *ac* required during the flight by

*TMax* <sup>=</sup> *GTOW* · (*<sup>g</sup>* <sup>+</sup> *ac*) *Np* , (36)

where *g* and *Np* are, respectively, the gravity acceleration and propulsion chain number. Thus, the relative error is given by

$$
\varepsilon\_r = \left| \frac{T\_{MP\_{\text{max}}} - T\_{\text{Max}}}{T\_{\text{max}}} \right|. \tag{37}
$$

An error reference value *εref* = 5% is fixed as the threshold value in order to make the filtering process.

**Figure 10.** Motor/propeller optimization example with the objective function *ηMP* and propeller parameters *Dp*, *ϕp*.

The motor/propeller combinations, which are able to generate the thrust imposed by the specifications, are given in Table 1:

**Table 1.** Sizing process methodology outcome.


It is remarkable that the two combinations, in terms of the specific efficiency *ηMP*, remain equivalent, which makes the choice between them very similar. Combination 1 is used in the multirotor drone considered for validation.
