Journal of Aircraft
American Institute of Aeronautics and Astronautics, Inc.
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 
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 . In steady level flight, L is equal to the weight, W, and the induced drag can be written as 
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.
Taylor, J. D., and Hunsaker, D. F., “Minimum Induced Drag for Tapered Wings Including Structural Constraints,” Journal of Aircraft, Vol. 57, No. 4, July-August 2020, pp. 782-786. doi:10.2514/1.C035757