# Parametric Optimization Study of Novel Winglets for Transonic Aircraft Wings
###### Abstract
[11] examined a wing made with the NACA 4412 airfoil, with and without the blended winglet design, using analytical, modelling, and CFD analysis. The results showed that a wing with a winglet can increase the lift-to-drag (L/D) ratio by approximately 6% to 15%. A split winglet was modelled by [PERSON] et al. [12] to improve the aerodynamic characteristics of a wing. It was observed that a split winglet diffused the vortex core more effectively than a simply blended winglet, and aerodynamic performance improved when using a split winglet compared to using a wing without a winglet. [PERSON] et al. [13] numerically investigated the aerodynamic performance of the wing with single- (blended winglet) and double-winglet (split winglet) designs. The large eddy simulation (LES) method was used for numerical computations since it accurately predicts the transitional flows. The analysis showed that double-winglet configurations performed aerodynamically better than a wing with a single winglet. [PERSON] et al. [14] created a C-type winglet using numerical optimization methods while considering C\({}_{\rm L}\), C\({}_{\rm M}\), V\({}_{\rm stall}\), and weight. This wing is useful for tailless aircrafts. Their results showed that the drag was reduced by 15% without considering the structural dynamics. They also analyzed the problems of tip extension with winglets using non-linear optimization. Several additional researchers investigated various winglet arrangements. [PERSON] et al. [15] performed winglet optimization using numerical methods. Induced drag was obtained using the Trefftz plane method, and a model for profile drag was incorporated with the induced drag optimization method to obtain total drag. Analysis was performed on VSAERO. The geometry was parameterized based on design variables such as root incidence, tip incidence, and the twist of the winglet. [PERSON] et al. [16] conducted a comparative study between fixed winglets and morphing winglets. In the morphing winglet, camber variation was achieved by changing the angle of the leading and trailing edge. It was found that the camber morphing winglet showed less fuel consumption compared to the fixed winglet. [PERSON] et al. [17] developed a procedure to design and analyze winglets. Winglet parameters such as chord-wise location, length, taper ratio, area, sweep, and cant angle were studied on a KC-135 wing. For a winglet with a length of 0.135 times the wing's semi-span, a cant angle of 20\({}^{\circ}\) reduced the induced drag by 17%, increasing WRBM by 6%. Winglets reduced the overall drag of the KC-135 wing by 6.2%. [PERSON] et al. [18] conducted computational analysis on a medium-altitude long-endurance (MALE) unmanned aerial vehicle (UAV) with winglets. The study was performed using the Spalart-Allmaras turbulence model. The flow around the wing-winglet was analyzed at first, followed by an investigation of the entire aircraft. Based on different aerodynamic parameters and root bending moments, the winglet design was optimized for height, sweep angle, cant angle, toe angle, etc. Better aerodynamic performance was found after optimizing the initial winglet design, which increased the total flight time by approximately 10%. A blended winglet was designed with design variables such as cant, sweep angle, and height by [PERSON] et al. [19]. After thorough analysis, a winglet with a cant angle of 45\({}^{\circ}\) and a height of 15% of the wing's semi-span was considered the best design. At its design condition, a net drag reduction of 4.8% was observed at Mach 0.7 and 2.5% at Mach 0.8. [PERSON] et al. [20] examined multi-tip winglets with three tip-tail winglets without a sweep angle. Analysis was performed at different cant angles and angles of attack combinations. The result showed that those winglets at cant angle +45\({}^{\circ}\), +15\({}^{\circ}\), and \(-15^{\circ}\) showed better aerodynamic performances than other configurations. [PERSON] et al. [21] conducted an experimental study on multi-winglets.