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Low Speed Aerodynamics, Notes 8: Prandtl's Lifting Line Method and the Glauert Solution

Prandtl's model for the high aspect ratio wing uses a "lifting line" vortex placed along the quarter-chord line of the wing, with its strength varying along the span. The variation in strength of this "bound vortex" is matched by streamers of vorticity from the wing, forming a "trailing vortex sheet". At each outer edge of this sheet is a tip vortex, stretching back to where the wing started, leaving behind a Starting Vortex, whose strength is equal and opposite to that of the Lifting Line. This steady-flight model is amenable to unsteady phenomena as well, when a starting vortex is added every time the strength of the lifting line changes due to changes in angle of attack or other maneuvers.

Glauert's Fourier series solution to the lifting line problem is described, leading to expressions for the lift and induced drag of high aspect ratio straight wings with twist and taper. Please download the notes in pdf here.



Introduction to Aerodynamics: Some results to provide physical intuition.

Laws of Physics and Fluid Dynamics.
Conservation Equations in Integral Form.
Specializing the Conservation Equations for aerodynamics.
The Potential Flow Method
Vortex Interactions, and Thin Airfoil Theory.
Finite Wings.
Prandtl's Lifting Line Method
Viscous Flow
Practical Methods and Data Sources