# Parametric Optimization Study of Novel Winglets for Transonic Aircraft Wings
###### Abstract
Due to the nature of the up-flow at the wingtip, it was determined that a negative geometric twist with negative root incidence must be used in addition to dihedral to ensure that the winglet is working at optimal conditions. The leading winglet provides lift by having a moderate positive angle of attack with respect to the effective flow velocity at the wingtip. [PERSON] et al. [22] investigated the effects of adding numerous active winglets to an existing UAV to improve cruising and maneuvering performance. When comparing a wing with multiple winglets to a baseline wing with the same aspect ratio, it was proven that a wing with multiple winglets can boost range and endurance by up to 40%. [PERSON] et al. [23] describe a multidisciplinary design exploration technique for a commercial jet aircraft winglet design that included high-fidelity analysis. From the Pareto front generated in this analysis, the winglet's large cant angle was favourable for both block fuel and maximum take-off weight. [PERSON] et al. [24] developed a winglet design for a solar aircraft using a multi-constrained optimization method. Moreover, the effect of winglets was compared for wings with different aspect ratios. It was concluded that winglets incorporated into wings with an aspect ratio of 29 have detrimental effects on wings. It was also observed that wings with an aspect ratio greater than 15 require winglets with small cant angles and larger cant angles for an aspect ratio less than 10 for optimal performance. Most of the above-cited works showed comparative studies carried out on winglets such as blended, elliptical, raked, and split [5; 6; 8; 9; 10; 13; 19] types, which are generally used in the aviation industry. Some worked on unconventional winglet designs, such as multi-tip, morphing winglet, and C-wing [12; 14; 16; 20; 21; 22], and they claim that their performance is superior to existing winglet designs. However, there is not enough comparison between these unconventional designs. Moreover, the influence of design parameters on aerodynamic efficiency has also not been much discussed. Although there is much research work on winglet designs, comparing the studies with each other has not been possible due to the use of different wing baseline wing models with different dimensions and configurations like tapered wings, rectangular wings, etc. [5; 6; 10; 13]. Furthermore, many authors [3; 5; 7; 10; 12; 20] analyzed their designs in the subsonic regime; however, commercial aviation requires design analysis in the transonic regime. Many researchers purely focused on the aerodynamics of the winglet design [6; 7; 9; 10; 12; 13; 16]. However, they did not consider offsetting factors such as wing root bending moment and net weight increment of the model. This study's objective is to tackle the induced drag issue on commercial aviation aircraft. A transport transonic wing model, NASA's common research model, was selected as the baseline wing model, which cruises at 0.85 M [25; 26] and a Re of 40 million. In the first stage of this work, unconventional winglet designs such as twisted, bird-type, and multi-tip winglets were designed and analyzed on ANSYS Fluent V2020. The optimal one was determined by comparing their aerodynamic coefficients such as C\({}_{\text{L}}\) and C\({}_{\text{D}}\) for varying angles of attacks. In the second stage, the influence of design parameters such as cant, sweep, tip twist angle, and taper ratio on multi-tip winglets was also determined to understand the relative importance of each parameter. The best combination of parameters for optimal performance was determined using the Taguchi method. Moreover, the significance of each parameter was determined by the analysis of variance (ANOVA) method [27].