## Class

Article

## College

College of Engineering

## Presentation Type

Oral Presentation

## Abstract

Implementations of lifting-line theory model the flow over a finite wing using a sheet of semi-infinite vortices extending from a vortex filament placed along the locus of aerodynamic centers of the wing. Prandtl's classical implementation is restricted to straight wings in flows without sideslip. In this work, it is shown that these limitations can be overcome if, at the control points where induced velocity is calculated, the second derivative of the locus of aerodynamic centers is zero and the trailing vortices are perpendicular to the locus. Therefore, a general implementation of lifting-line theory is presented that conditionally forces the second derivative of the locus of aerodynamic centers to zero at each control point, and joints each trailing vortex such that there is a finite segment of the trailing vortex perpendicular to the locus of aerodynamic centers. Consideration is given to modeling the locus of aerodynamic centers of non-straight wings and the section aerodynamic properties of such wings. The resulting general formulation is analyzed to determine sensitivity, accuracy, and numerical convergence. The general implementation demonstrates second-order convergence when the control points are clustered at the root and tips of the wing, and produces results that closely match those of a high-order panel method and experimental data.

## Start Date

4-8-2020 12:00 PM

## End Date

4-8-2020 1:00 PM

A General Approach to Lifting-Line Theory, Applied to Wings with Sweep

Implementations of lifting-line theory model the flow over a finite wing using a sheet of semi-infinite vortices extending from a vortex filament placed along the locus of aerodynamic centers of the wing. Prandtl's classical implementation is restricted to straight wings in flows without sideslip. In this work, it is shown that these limitations can be overcome if, at the control points where induced velocity is calculated, the second derivative of the locus of aerodynamic centers is zero and the trailing vortices are perpendicular to the locus. Therefore, a general implementation of lifting-line theory is presented that conditionally forces the second derivative of the locus of aerodynamic centers to zero at each control point, and joints each trailing vortex such that there is a finite segment of the trailing vortex perpendicular to the locus of aerodynamic centers. Consideration is given to modeling the locus of aerodynamic centers of non-straight wings and the section aerodynamic properties of such wings. The resulting general formulation is analyzed to determine sensitivity, accuracy, and numerical convergence. The general implementation demonstrates second-order convergence when the control points are clustered at the root and tips of the wing, and produces results that closely match those of a high-order panel method and experimental data.