From thin airfoil theory to finite wings: consistent implementation of Lifting Line-based models

Lifting Line (LL) models are widely used in engineering aerodynamic analysis and design loops for conventional and airborne wind energy applications. However, different implementations can predict different results when the assumptions of high aspect ratio and straight wings are violated. Although rigorous formulations of LL theory exist, they are often expressed in forms that are difficult to translate into unambiguous implementation choices for engineering LL codes. This work provides implementation-oriented guidance by formulating LL as a coupled system consisting of an outer 3D vortex system and an inner 2D airfoil model. We provide practical coupling rules that are consistent with the Crossflow Principle and 2D unsteady thin airfoil theory (UTAT). Specifically, the inner model is driven by the span-perpendicular component of the relative velocity, excluding the section’s own 2D disturbance; force magnitudes are determined from the flow at the three-quarter-chord point, while force directions are determined from the flow direction at the quarter-chord point. In addition, we introduce an explicit force contribution from the chordwise bound vortex segments, termed the attached trailed vortex, which becomes particularly relevant for swept wings and is absent in existing LL models known to the authors. The proposed implementation is compared with representative alternatives from the literature and with a Vortex Lattice Method (VLM) reference using inviscid airfoil polars, covering straight rectangular and elliptic wings, curved wings and simple steady roll maneuvers. Although the validation is carried out on finite-wing cases, because they provide a simpler and more transparent testbed, the proposed implementation is general and applies equally to rotating rotor configurations, including wind turbine rotors. Across the test cases, the proposed implementation closely matches VLM predictions for both lift and induced drag, whereas other implementations exhibit large errors for wings with low aspect ratio and/or curved planforms.