Document Type

Article

Journal/Book Title/Conference

Journal of Aircraft

Volume

57

Issue

4

Publisher

American Institute of Aeronautics and Astronautics, Inc.

Publication Date

8-2020

First Page

1

Last Page

13

Abstract

LIFTING-LINE theory [1,2] is the foundation for much of our understanding of finite-wing aerodynamics. Solutions based on lifting-line theory are widely accepted and have been shown to be in good agreement with CFD [3-10]. From Prandtl’s analytic solution to the classical lifting-line equation [1,2], the wing section-lift distribution can be expressed as a Fourier series of the form [11]

bL~ (θ)/L = (4/π)[sin(θ) + Σ∞n-2 Bnsin(nθ)]; θ = cos-1(-2z/b) (1)

where b is the wingspan, L~ is the local wing section lift, L is the total wing lift, z is the spanwise coordinate, and Bn are the Fourier coefficients. For any given planform, the twist distribution required to produce this lift distribution can also be obtained using Prandtl’s lifting-line equation [12]. In steady level flight, L is equal to the weight, W, and the induced drag can be written as [11]

Di = (2(W/b)2/πρV∞2)[1+ Σ∞n-2 Bn2] (2)

where ρ is the air density and V∞ is the freestream airspeed.

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