# Parametric Optimization Study of Novel Winglets for Transonic Aircraft Wings
## 6 Conclusions  
This present numerical study was focused on reducing induced drag acting on a commercial transport NASA CRM wing model. A typical industrial retrofitting approach was carried out throughout our design process; i.e., winglets were attached at the end of the wing while maintaining the span constant. Unconventional winglet designs such as twisted, multi-tip, and bird-type winglets were analyzed to understand their flow behaviour and determine their aerodynamic performance. Furthermore, a parametric study was carried out on a multi-tip winglet design. Four important design parameters, cant angle, sweep angle, tip twist angle, and taper ratio, were investigated to understand their relative importance and optimize their design using the Taguchi method and Taguchi-based grey relational analysis coupled with principal component analysis. Moreover, the percentage of the contribution of each parameter to dependent parameters was determined through ANOVA analysis.  
This study found the \(\mathrm{C_{M}}\) for the wing's root at the quarter chord location. In this study, an optimal winglet design was developed by maximizing \((\mathrm{C_{L}}/\mathrm{C_{D}})/\left|\mathrm{C_{M}}\right|\), and an optimal aerodynamic design was developed while considering the wing root bending moment. Some of this study's important findings are listed below.  
* A multi-tip winglet performs better than other winglet designs.
* \(\mathrm{\Phi}\) is the most important parameter and contributes around 45-60% to aerodynamic coefficients \(\mathrm{C_{L}}\), \(\mathrm{C_{D}}\), and \(\mathrm{C_{M}}\).
* The proposed optimum method for the selected design parameters in this work improves the \(\mathrm{C_{L}}/\mathrm{C_{D}}\), \(\mathrm{C_{M}}\), and \((\mathrm{C_{L}}/\mathrm{C_{D}})/\left|\mathrm{C_{M}}\right|\) of a transonic wing.
* In the Taguchi technique, the optimised multi-tip winglet based on \((\mathrm{C_{L}}/\mathrm{C_{D}})/\left|\mathrm{C_{M}}\right|\) improved by 18.291%, and in T-GRA combined with the PCA approach, it improved by 20.771%. Furthermore, it exceeded the blended winglet by 8% and the baseline wing by 6%, respectively.
* The optimized design has cant angle first-tip = 75\({}^{\circ}\), taper ratio = 0.4, sweep angle = 25\({}^{\circ}\) and tip twist = \(-\)6\({}^{\circ}\).  
Figure 17: (**a**) Front view and (**b**) top view of the optimized winglet.  
* The relative importance of parameters for high \(\mathrm{C_{L}/C_{D}}\) is cant angle (\(\Phi\)) > sweep angle (\(\Lambda\)) > tip twist (\(\mathrm{\bar{C}}\)) > taper ratio (\(\lambda\)), and for high \(\mathrm{C_{L}/C_{D}/\left|\mathrm{C_{M}}\right|}\), it is \(\Phi>\Lambda>\lambda>\mathrm{E}\).  
Conceptualization, P.P. and A.S.; methodology, numerical analysis, and validation, S.A., P.P. and A.S., P.R.K. and N.R.D.; writing--original draft, P.P., A.S., S.A., K.P., P.R.K. and N.R.D.; supervision P.R.K., P.P. and J.T.; writing--review and editing, P.P., A.S., S.A., K.P., P.R.K., N.R.D., D.T. and T.S.; formal analysis, T.S., A.S., P.P. and P.R.K.; data curation, B.W. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.