# Automation of Winglet Wings Geometry Generation for Its Application in TORNADO
AVL [6], Surfaces [7], XFLR5 [4] and VSPAERO [8] are also vortex lattice-based and can give good results for preliminary studies. Some articles show the significant evolution and application capacity of these methods, for example, using non-linear VLM [9; 10], unsteady VLM (UVLM) [5] or even adapting VLM to supersonic aircraft [11]. From this point on, the focus will be on TORNADO, which was the tool chosen to develop the code due to the simplicity of adapting the program. The wing is supposed to be divided into trapezoidal panels (see Figure 1), each of them with an associated horseshoe vortex. The turbilonary field generated by the vortices is divided in two regions: the free vortices, which cause the induced velocity, and the bound vortices, which are related to the airfoil lift effect. The panels have two important points, the control point in 3/4 of the wing chord (c) and the head of the vortex in 1/4c. Each vortex has a circulation distribution (associated with the induced velocity and the interaction between vortices), which allows to calculate the lift distribution. With that distribution and the angle of attack, the lift and induced drag coefficient can be obtained. The VLM method is one of the most extended methods to calculate aerodynamics properties based on potential features of the flow, that is, lift force, moment and induced drag. The computational effort is extraordinarily low due to the linearized nature of the equations, as well as the final result of solving linear systems of equations (even of large dimensions). According to this, the VLM method haslimitations, as it can be applied when low angles of attack are considered (to avoid effects of stall conditions) to ignore the compressibility effects, and it is a method by which any type of drag dependent on viscosity cannot be calculated [12]. The wings to be studied in this article are those that introduce wingtip devices. Winglets are becoming increasingly important elements in aircraft design, as operating costs and environmental concerns are on the rise. Therefore, from an aerodynamic point of view, wingtip devices are able to reduce induced drag [13] and increase aerodynamic efficiency. Figure 2 presents different configurations that have been used or are in development. Figure 1: VLM scheme. In the figure it can be seen the dotted black line \(1/4\)c, and the control points and horseshoes in red. The horseshoes start in line \(1/4\)c and continue downstream. Figure 2: Winglet configurations that have been used or are in development. [PERSON] was the first person to mention the possibility of creating a vertical surface (end-plate), in the belief that it would reduce drag by controlling wing tip vortices [14]. Later, it was [PERSON] who developed the first winglet, with the inspiration of bird wings [15]. One of the conclusions was that the winglets' presence helped at a Mach number of 0.78, and keeping the lift coefficient from the state without winglets decreased the induced drag about 20% and increased the aerodynamic efficiency about 9% [15]. Another important contribution was made by [PERSON], who realized a study about the effects that winglets have in low elongation configurations. He concluded that the reduction in the induced drag depends solely on the ratio of the winglet length to the wingspan [16]. Figure 3 shows some winglet examples that are designed with the developed algorithm, such as the blended winglet [17], the spiroid winglet [18; 19; 20; 21; 22; 23] and a first approximation of the wing grid [24; 25; 26; 27]. They were selected due to the previous investigations conducted in the past years. It is worth noting that companies have already implemented the blended winglet and the grid wing. The blended winglet is the main design adopted by the aeronautical industry for commercial airplanes. Top companies, such as Airbus and Boeing, have implemented those designs for new aircraft models, with satisfactory results in terms of efficiency and fuel consumption [28].