Hold the right quantity
Changing aspect ratio at fixed angle also changes lift. Use the CL–CDi plot to compare induced drag at equal lift coefficient.
02 / EXTEND · Aerodynamics
Finite Wings & Induced Drag
Lift & dragBrowser calculation
Stretch an elliptical wing at fixed area. Connect span loading, downwash and the drag created by lift.
SPAN CHANGES THE PRICE OF LIFTLIVE B
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An elliptical planform and elliptical loading, with e = 1. The planform uses one geometric scale. Arrows above it are a normalised span-loading graph, not force directions in the plan view. Wake ribbons are explanatory, not a calculated vortex field.
Locate the lost incidence
Induced angle subtracts from geometric incidence. The section sees αeff = α − αi.
Keep drag separate
Only induced drag is calculated. Profile drag, viscous separation, compressibility and stall are excluded.
CALCULATED FROM THE SAME MODEL
Read the parameter study
B · solid turquoise A · dashed amber
Dots mark the selected settings; curves sweep one variable
Compare the evidence
| Quantity | A · saved | B · live | Unit |
|---|
A remains fixed until you save again. Export includes settings, selected outputs and curve data.
Equations, assumptions and topic connections
Physical model
Low-speed, small-incidence lifting-line approximation for an untwisted elliptical wing. Section lift slope a₀ = 2π rad⁻¹, zero-lift angle 0°, e = 1, density 1.225 kg/m³. Aspect ratio 6–18; incidence ±6°. Geometry, loads and downwash all use the same span and area.
b = √(AR S); a = a₀/(1 + a₀/(π AR)); CL = aα; αi = CL/(π AR); CDi = CL²/(π AR). L′(y) = 4L/(πb) √[1 − (2y/b)²]. Downwash at the lifting line w ≈ Vαi.
Topic connections
S05 · Incompressible Flow over Wings: PDF pp. 4–12, 27–38. Candidate diagrams: pp. 4, 8, 11–12; not reproduced. Bridges drag-polar work.
Original schematic diagrams. No manufacturer performance, certification or maintenance-authorisation claim. Numerical verification checks the declared model; it is not experimental validation. Model version: course-foundations-v1.