Scaling laws and similarity models for the preliminary design of multirotor drones

Efficient sizing and optimization of multirotor drones based on scaling laws and similarity models

“…Step 1: Define a system of algebraic equations S based on estimation models and simulation models subject to inequality constraints Analytical models, Scaling laws, Datasheet regression [24,34,14] Step 2: Reduce (when possible) the number of inequality constraints First Monotonicity Principle (MP1) Section 3.2.1, [35] Step 3: Build undirected bipartite graph/design graph from S, identify Strongly Connected Components (SCC) and solve them by implementing the NVH formulation Design graphs, Symbolic computation, Graph algorithms Section 3.3, Section 3.4, [36,37,34,28] Step 4: Perform a matching and ordering of the modified system and generate the sizing procedure Graph algorithms, Symbolic computation [36,37,34] the efficiency of the ordering and is useful to visualize the models involved and the shared variables. Once the required thrust for every mission is estimated from an initial guess of the total drone mass, propeller torque and speed characteristics are estimated.…”

“…Most of the design methodologies, despite the wide variety of implementations [20][21][22], are based on analytical expressions or catalog data regressions and benefit, as most continuous problems, of numerical optimization capabilities and high convergence performance. The paper [14] has shown how dimensional analysis and the Buckingham theorem can be used to estimate analytically the main characteristics of the components of a drone. A component characteristic y can be expressed as an algebraic function f of geometrical dimensions and physical/material properties:…”

“…Otherwise, when data is available, regression models [25,26] are used such as for modeling the propeller performance or landing gear structural analysis. A detailed description of the hypotheses and methods associated with these sizing models of drone components can be found in [14]. [15]; (motors, battery and ESC) [16,17]; (frame) [18,19].…”

“…It is here, where the criteria of "degradation" or design drivers will be manifested, conditioning the optimal performance of the system. These criteria have been selected by carrying out an intensive study of the existing technology, in which regression models and scaling laws are involved and where more information can be found in the article of Budinger, Reysset et al [14]. With the purpose of not exceeding the scope of this research, we have simply detailed them in Appendix A and Fig.…”

“…• To formulate a reusable optimization code valid for a wide range of MRAVs based on scaling laws and surrogate models extracted from the dimensional analysis or the study of physical laws, as proposed in [14].…”