Minimum Induced Drag for Tapered Wings Including Structural Constraints

Authors

Jeffrey D. Taylor, Utah State UniversityFollow
Douglas F. Hunsaker, Utah State UniversityFollow

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 B_nsin(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 B_n 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]

D_i = (2(W/b)²/πρV_∞²)[1+ Σ^∞_n-2 B_n²] (2)

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

Recommended Citation

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