Γ

Method & Assumptions

Classical Fourier collocation solution
⌄

Circulation

Odd Fourier modes represent the symmetric spanwise circulation.

Γ(θ)=2bV∞ Σ Aₙ sin(nθ)

Lift

The first coefficient controls total finite-wing lift.

CL=π AR A₁

Induced drag

Higher modes capture non-elliptical loading.

CDi=π AR Σ nAₙ²

Efficiency

Elliptical loading approaches e=1.

e=CL²/(π AR CDi)
Applicability

Steady, incompressible, inviscid, attached flow; straight unswept wing, linear taper/twist and linear section lift curve. No profile drag or stall.

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Wing Definition

Planform and operating point

Geometry

Aerodynamics

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Results

Finite-wing coefficients and loading
CL
–
CDi
–
Span efficiency e
–
Aspect ratio AR
–

Wing & Vortex System

Top view · circulation & trailing wake

Cyan curve represents Γ(y); trailing filaments visualize the shed wake.

Spanwise Loading

Section lift coefficient cl(y)

Wing Properties

Wing area S–
Mean aerodynamic chord–
Tip chord–
Induced drag factor δ–