**7. Conclusions**

The objective of the present work has been to develop a series of 2D foil sections with partly parallel sides. Such sections are found on many dinghy centerboards. Starting from 7 design variables, 200 sections and 1200 cases are systematically investigated. Trends are found between different solutions, and the exceptions are explained. Six tables with the best shapes are created to help the designers to choose the optimal profile for a specific application. These tables are found in Appendix B.

The general conclusions from the study may be summarized as follows: Zero angle of attack:


Lift coefficient 0.4:


• A rather small (but not too small) leading edge radius is the best for the thin sections. The same is true for the thick sections. There is however an exception at high Reynolds number and short leading edge.

The thin parallel-sided sections at the smallest Reynolds number are in fact better than the NACA sections by about 10%. For the intermediate and high Reynolds number, they are about equal. The thick sections have on average 35% higher drag than the NACA sections.

Optimizing wing sections using CFD is a difficult task, since it relies on the accurate prediction of two important physical phenomena: transition and separation. The latter depends strongly on the accuracy of the turbulence model. In the text above, we have tried to give motivations for the use of the models adopted, which have been validated in the literature for a very large number of cases, and are recommended by the developers of the software used. A formal validation of the present computations is unfortunately not possible, due to the lack of information about experimental accuracy. Estimates are however made of the numerical uncertainty, which is low, due to the very high grid density.

**Author Contributions:** The four authors of the paper, A.S., A.P., L.L. and A.M. contributed as follows. Conceptualization, L.L. and A.P.; methodology, L.L., A.P. and A.S.; software, A.P. and A.S.; validation, A.S., L.L. and A.P.; formal analysis, A.S., A.P., L.L. and A.M.; investigation, A.S.; resources, L.L.; data curation, A.S.; writing—original draft preparation, A.S.; writing—review and editing, L.L., A.P. and A.M.; visualization, A.S.; supervision, L.L. and A.M.; project administration, A.S., L.L. and A.M.; funding acquisition, L.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study received funding from the Chalmers University of Technology Foundation for the Strategic Research project Hydro- and Aerodynamics. It was also partly funded by Hugo Hammar's fund for international research in shipping, project number HHS280. The computations were performed on resources at Chalmers Centre for Computational Science and Engineering (C3SE) provided by the Swedish National Infrastructure for Computing (SNIC).

**Acknowledgments:** The first author gratefully acknowledges the invitation by Chalmers University of Technology and SSPA and the help and contributions by the staff duringhis six months' visiting period as a PhD student of the University of Palermo.

**Conflicts of Interest:** The authors declare no conflict of interest.
