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Elliptical wing

Why is the elliptical wing considered ideal? · Standard part · basis: Design rules and figures from the cited sources; example geometry by Xem Studio

Also called: elliptical planform, spitfire wing, elliptical lift distribution, elliptical wing rc, why elliptical wing, oswald efficiency, elliptical wing template, span efficiency factor

Exact dimensions. True size, with no printing tolerance added.

sizes
5 in table

Notes

  • An elliptical span loading gives span efficiency e = 1, the minimum induced drag for a given span; non-elliptical loading has e < 1 and more induced drag (TU Delft AE1101; Kitplanes).
  • The Spitfire is the textbook elliptical wing: root chord 100 in, span 445 in, AR 5.67 and S = 242.71 ft^2 (Leishman, ERAU).
  • Curved edges are harder to build than a straight taper, which is why a 0.45 taper is often used to approximate elliptical loading (arXiv 1801.02938 citing Torenbeek).
  • Used on: Supermarine Spitfire.
  • The file is a reference example built by Xem Studio from the numbers above. Sizes the sources do not fix are illustrative; scale the example to your own vehicle.

Elliptical wing size chart

parametervalue or rangesource
Span efficiency, elliptical loadinge = 1 (minimum induced drag)TU Delft AE1101
Induced dragCDi = CL^2 / (pi AR e)TU Delft AE1101
Spitfire root chord / span100 in / 445 inERAU (Leishman)
Spitfire AR / area5.67 / 242.71 ft^2ERAU (Leishman)
Reference buildspan 1000 mm, root 225 mm (Spitfire proportions scaled)computed

Where the files are

Other publishers' files are linked, not hosted. "verify" = check the license at the link before commercial use.

TU Delft OpenCourseWareAE1101 Introduction to Aerospace Engineering, Aerodynamics 6webPublisher's page; dimensions are facts
Embry-Riddle (Leishman), Introduction to Aerospace Flight VehiclesWing Shapes and NomenclaturewebPublisher's page; dimensions are facts
Kitplanes (B. Wainfan)Design Process: Planform Effects on Span Loading and Drag (2020)webPublisher's page; dimensions are facts
arXiv 1801.02938 (citing Torenbeek, Synthesis of Subsonic Airplane Design, 1976)Systematic design methodology for a variable pitch quadrotor biplane VTOL UAVwebPublisher's page; dimensions are facts

Free files

★ Free files 1 parts. Xem Studio design: free to use, print and sell things from; not to be republished as files. Xem Studio Design License. index.json

elliptical-wing-wingelliptical planform: span 1000, root 225, tip 0 mm, LE sweep 0°, dihedral 3°, NACA 2412STEP · STL
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Plain text: sheet.txt · JSON: /api/geometry?object=elliptical-wing

Elliptical wing, isometric render of a generated part
Render of elliptical-wing-wing from the free STEP; not to scale.

Fits with

Rectangular (constant-chord) wing, isometric render of a generated part
Rectangular (constant-chord) wing6 sizes★ 1 file
Tapered wing (taper ratio for minimum induced drag), isometric render of a generated part
Tapered wing (taper ratio for minimum induced drag)6 sizes★ 1 file
Swept-back wing, isometric render of a generated part
Swept-back wing4 sizes★ 1 file
Forward-swept wing, isometric render of a generated part
Forward-swept wing4 sizes★ 1 file
Delta wing, isometric render of a generated part
Delta wing5 sizes★ 1 file
Cranked arrow / double delta wing, isometric render of a generated part
Cranked arrow / double delta wing4 sizes★ 1 file

Questions

Is an elliptical planform needed for elliptical lift?

No; taper (about 0.45) or twist can approach it (Torenbeek via arXiv 1801.02938; Kitplanes).