# Automation of Winglet Wings Geometry Generation for Its Application in TORNADO
## 2 Methods
### Definition of the Wingtip Devices
#### 2.2.2 Open and Closed Spiroid Winglet
The algorithm implementation achieved the aim of the article: to make an algorithm that can create complex geometry in TORNADO using a basic data entry mechanism and to obtain the optimal geometry with very low computational cost before using CFD. Moreover, \begin{table}
\begin{tabular}{c c c c c} \hline
**Aerodynamic** & **Reference Wing** & **Closed Spiroid** & **Closed Spiroid** & **Experimental** \\
**Coefficient** & **TORNADO** & **Winglet TORNADO** & **Winglet Ansys-Fluent** & **Reference Wing** \\ \hline \(C_{L}\) & 0.21 & 0.27 & 0.22 & 0.21 \\ \hline \(C_{D}\) & 0.0156 & 0.0187 & 0.048 & 0.067 \\ \hline \(E\) & 13 & 14.55 & 4.51 & 3.05 \\ \hline \end{tabular}
\end{table} 
Table 1: Aerodynamic coefficients (lift coefficient, \(C_{L}\); drag coeffient, \(C_{D}\)) and efficiency, \(E\); calculated for the reference wing without winglets and the closed spiroid winglet for TORNADO, Ansys-Fluent and experimental. Figure 14: Details of the vortex and wake structure for the types of winglets studied. (**a**) No winglet. (**b**) Blended winglet. (**c**) Open spiroid winglet. (**d**) Closed spiroid winglet. the algorithm allows the automation of the winglet generation process selecting basic wing characteristics, such as the root and tip chord, the airfoil, tape, dihedral, the winglet type, panel distribution, number of joints, and the according radius, among others. In addition, in order to complete the drag reduction study, TORNADO has the capability to calculate the lift and induced drag coefficients. This may lead to the development of a new algorithm (e.g., genetic algorithm) to determine the optimal winglet during the initial design. The final winglet design could then be subject to CFD and experimental analysis for validation. Therefore, this article provides a solid basis for the subsequent phases of winglet development. Conceptualization, A.A.R.-S., R.B.-M., A.L.-C.-A. and D.A.-M.; Methodology, A.A.R.-S., A.L.-C.-A. and D.A.-M.; Software, A.L.-C.-A., D.A.-M., J.C.M.-G., E.B.-B. and J.F.-A. ; Validation, A.A.R.-S., R.B.-M., A.L.-C.-A., D.A.-M., J.C.M.-G., E.B.-B. and J.F.-A. ; Formal Analysis, A.A.R.-S. and R.B.-M.; Investigation, A.A.R.-S., R.B.-M., A.L.-C.-A., D.A.-M., J.C.M.-G., E.B.-B. and J.F.-A. ; Resources, R.B.-M. and D.A.-M.; Data Curation, R.B.-M.; Writing--Original Draft Preparation, A.A.R.-S. and A.L.-C.-A. ; Writing--Review and Editing, A.A.R.-S., R.B.-M., A.L.-C.-A., D.A.-M., J.C.M.-G., E.B.-B. and J.F.-A. ; Visualization, D.A.-M.; Supervision, A.A.R.-S. and R.B.-M.; Project Administration, A.A.R.-S. and R.B.-M. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors declare no conflict of interest. The following abbreviations are used in this manuscript:

CFD Computational fluid dynamics

\(n_{wing}\) Number of wings

\(n_{part}\) Number of parts

VLM Vortex Lattice Method

LD Linear dichroism

\(n_{x}\) Number of panels in chord

\(n_{y}\) Number of panels in semi-span

\(b\) Wingspan

\(c_{r}\) Root chord

\(\lambda\) Wing taper

\(\Lambda\) Wing sweep

\(\Gamma\) Wing dihedral

\(TOT\) Total

\(w\) Wing

\(comp\) Component

\(\Delta\) Increment

\(r_{p}\) Radius according

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