# Parametric Optimization Study of Novel Winglets for Transonic Aircraft Wings
###### Abstract  
This paper deals with the topic of reducing drag force acting on aircraft wings by incorporating novel winglet designs, such as multi-tip, bird-type, and twisted. The high-speed NASA common research model (CRM) was selected as the baseline model, and winglet designs were retrofitted while keeping the projected wingspan constant. Computational analysis was performed using RANS coupled with the Spalart-Allmaras turbulence model to determine aerodynamic coefficients, such as \(\mathrm{C_{L}}\) and \(\mathrm{C_{D}}\). It was observed that the multi-tip and bird-type designs performed exceptionally well at a low angle of attack (\(0^{\circ}\)). A parametric study was conducted on multi-tip winglets by tweaking the parameters such as sweep angle (\(\Lambda\)), tip twist (\(\mathrm{\copyright}\)), taper ratio (\(\lambda\)), and cant angle (\(\Phi\)). The best combination of parameters for optimal aerodynamic performance while maintaining the wing root bending moment was determined using both the Taguchi method and Taguchi-based grey relational analysis (T-GRA) coupled with principal component analysis (PCA). Also, the percentage contribution of each parameter was determined by using the analysis of variance (ANOVA) method. Winglets for Transonic Aircraft Wingsings 20  
and flight tests were performed [2]. [PERSON] discovered that winglets could improve efficiency by more than 7% in a full-size aircraft [3]. This equates to millions of dollars in fuel expenditures for airlines. This influenced several researchers and engineers to work on novel winglet designs for different aircraft types. [PERSON] et al. [4] used multi-objective shape optimization to create the best winglet design. The above technique used two objective functions: low drag and structural weight. According to the analysis, fuel weight was lowered by 3.8%, equivalent to 29 million dollars in 15 years for Boeing 747 aircraft. [PERSON] et al. [5] investigated the aerodynamic properties of a wing with winglets at 0\({}^{\circ}\) and 60\({}^{\circ}\) and no winglets. The C\({}_{\rm L}\) and C\({}_{\rm D}\) were predicted using a fuzzy expert system model, with a relative mean error of 6.52% and 4.74%, respectively. C\({}_{\rm L}\) and C\({}_{\rm D}\) were found to be higher in wings with winglets at a 60-degree angle. [PERSON] et al. [6] analyzed a Cessna wing with a winglet to determine C\({}_{\rm D}\) and C\({}_{\rm L}\) at different cant angles of 0\({}^{\circ}\), 30\({}^{\circ}\), and 45\({}^{\circ}\). From analyses, wings with winglets increased the lift by 12% and decreased the drag by 4%. Moreover, an 11% improvement in C\({}_{\rm L}\)/C\({}_{\rm D}\) was witnessed. [PERSON] et al. [7] studied the winglet dihedral effect on the tip vortex. Winglets with dihedral angles showed reduced vorticity compared to the baseline wing model. Also, the lift-induced drag was reduced after installing a winglet with the dihedral angle to the baseline wing model. [PERSON] et al. [8] modelled the wing of Hydra Technologies' Unmanned Aerial System UAS-S45 Baalam and examined its aerodynamics and baseline performance. CFD software was used to calculate the flow field around the Hydra S45 Baalam wing. Appending winglets to the wing changed the moment coefficient dramatically. Many other researchers have also performed comparative studies on different types of winglet shapes. A comparative analysis was performed by [PERSON] et al. [9] between split and blended winglets, using the k-\(\epsilon\) model in Ansys-Fluent. The results showed that blended winglets have better aerodynamic characteristics, high C\({}_{\rm L}\)/C\({}_{\rm D}\), high C\({}_{\rm L}\), and low C\({}_{\rm D}\) at \(\alpha\) = 10\({}^{\circ}\) and 15\({}^{\circ}\). The aerodynamic characteristics of blended and naked winglets were analyzed by [PERSON] et al. [10] at different cant angles and compared with a wing-alone model. A blended winglet at a 60\({}^{\circ}\) cant angle was observed to have a high C\({}_{\rm L}\)/C\({}_{\rm D}\). [PERSON] et al.