Modern Implementation and Evaluation of Lifting-Line Theory for Complex Geometries

Abstract

A numerical lifting-line method (implemented in an open-source software package) is presented that can accurately estimate the aerodynamics of wings with arbitrary sweep, dihedral, and twist. Previous numerical lifting-line methods have suffered from grid convergence challenges and limitations in accurately modeling the effects of sweep, or have relied on empirical relations for swept-wing parameters and have been limited in their application to typical wing geometries. This work presents novel improvements in accuracy, flexibility, and speed for complex geometries over previous methods. In the current work, thin-airfoil theory is used to correct section lift coefficients for sweep, providing a more general closure to the lifting-line problem. A linearized solution is presented, which can be used as a rapid approximation for the full solution, or as an initial guess for the nonlinear system of equations to speed convergence. Sensitivities to model parameters are investigated, and appropriate recommendations for these parameters are given. Agreement with Prandtl’s classical lifting-line method is excellent in the case of straight wings. Comparison with experimental data shows that this method can reasonably predict lift, drag, and lift distribution for a range of wing configurations. The speed and accuracy of this method make it well-suited for preliminary design and optimization.