Multi-Objective Airfoil Shape Optimization
NSGA-II AND CST PARAMETERIZATION FOR LOW REYNOLDS UAV AIRFOILS
Overview
This is a poster project presented at the LOCUS Research Symposium 2026, part of the 22nd National Technological Festival at Pulchowk Campus. We wrote a Python framework that designs airfoils automatically. It starts from three low-Reynolds parent airfoils (S1223, SD7062 and E387), describes them with CST (Class-Shape Transformation) parameters, and uses the NSGA-II genetic algorithm to evolve new shapes while XFOIL scores each one at Re = 4×105.
Because the search is multi-objective, the result is a set of 15 Pareto-optimal airfoils that trade cruise efficiency against maximum lift. The best airfoil improves peak L/D by 33.8% over the best parent, and the whole run was repeated as two independent runs to check that it converges.
Introduction
Small unmanned aerial vehicles and fixed-wing drones operate in a difficult aerodynamic regime, around Re = 400,000, where the transition from laminar to turbulent flow has a large effect on performance. Traditional gradient-based methods often struggle with the non-linear, multi-modal nature of the aerodynamic objective functions in this range.
Our work combines NSGA-II with CST parameterization, starting from three different parent airfoils. That gives a much richer 2D design space and lets the genetic algorithm find new, efficient geometries that lie outside the convex hull of the parent designs.
Objectives
- Maximize the lift-to-drag ratio (L/D) at cruise, α = 6 degrees and Re = 4×105
- Maximize the peak lift coefficient (Clmax) over the full polar sweep, α = 0 to 10 degrees
- Generate a Pareto-optimal set of airfoils that captures the whole L/D versus Clmax trade-off
- Keep the designs structurally feasible with a minimum thickness-to-chord ratio of t/c ≥ 0.09
Methodology
The framework is a loop. First the parent airfoil files (.dat) are read and CST parameters are fitted to their upper and lower surfaces. An initial population is generated by blending the parents and adding some noise. Then the NSGA-II loop runs from generation 1 to N: each candidate is checked against the thickness constraint (t/c ≥ 0.09), and the ones that pass go to XFOIL, which runs a polar sweep. From each sweep we extract two objectives, L/D at the target angle and Clmax. The population is then sorted by non-dominated sorting, and the loop repeats until the maximum number of generations is reached. The final Pareto front is then validated with several independent runs. XFOIL is used for the aerodynamic evaluation and the evolutionary loop is built on the DEAP library.
Results
The peak L/D improved by 33.8% over the best-performing parent airfoil (E387), and the design produced 15 Pareto-optimal solutions. The convergence was validated over two independent runs. The optimized airfoil has a higher camber than any of the three parents and performs better than all of them at the design condition of α = 6 degrees and Re = 4×105, while still holding up across the operating range.
The Pareto front makes the trade-off visible. One end has the airfoils with the highest L/D, which suit long-endurance UAVs. The other end has the airfoils with the highest peak lift, which suit STOL aircraft, and a group in the middle is closer to general aviation needs. This allows an airfoil to be selected straight away for a given UAV mission.
Conclusion and Future Work
NSGA-II coupled with CST parameterization gives an automated and effective framework for multi-objective airfoil design. Mapping the Pareto front lets us choose an airfoil for a specific mission, whether that means cruise efficiency or maximum lift, and it removes the need for trial and error in the design process.
The next steps are to extend the framework to 3D wing planform optimization with induced drag and lifting-line theory, and to check the 2D results with high-fidelity RANS CFD in OpenFOAM.
References
- M. Drela, “XFOIL: An analysis and design system for low Reynolds number airfoils,” in Conference on Low Reynolds Number Airfoil Aerodynamics, University of Notre Dame, 1989.
- F.-A. Fortin, F.-M. De Rainville, M.-A. Gardner, M. Parizeau and C. Gagné, “DEAP: Evolutionary Algorithms Made Easy,” Journal of Machine Learning Research, vol. 13, pp. 2171–2175, 2012.
- B. M. Kulfan, “Universal parametric geometry representation method,” Journal of Aircraft, vol. 45, no. 1, pp. 142–158, 2008.
- K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182–197, 2002. ieeexplore.ieee.org/document/996017
- M. S. Selig, J. J. Guglielmo, A. P. Broeren and P. Giguère, Summary of Low-Speed Airfoil Data, Vol. 1. SoarTech Publications, 1995.
- UIUC Low-Speed Airfoil Tests and Airfoil Coordinates Database. m-selig.ae.illinois.edu