# Elliptical wing

> Why is the elliptical wing considered ideal?

- Category: Aircraft design › Wing planforms
- Kind: Standard part
- Basis: Design rules and figures from the cited sources; example geometry by Xem Studio
- Page: https://xemstudio.com/objects/elliptical-wing/ · JSON: https://xemstudio.com/api/geometry?object=elliptical-wing · Plain text: https://xemstudio.com/objects/elliptical-wing/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); files Xem Studio Design License (free to use and sell from, not to redistribute as files: https://xemstudio.com/license/)
- Use in every chat: add https://xemstudio.com/mcp as a connector (https://xemstudio.com/use-with-ai/)

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

## 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.

## Sizes

| parameter | value or range | source |
|---|---|---|
| Span efficiency, elliptical loading | e = 1 (minimum induced drag) | TU Delft AE1101 |
| Induced drag | CDi = CL^2 / (pi AR e) | TU Delft AE1101 |
| Spitfire root chord / span | 100 in / 445 in | ERAU (Leishman) |
| Spitfire AR / area | 5.67 / 242.71 ft^2 | ERAU (Leishman) |
| Reference build | span 1000 mm, root 225 mm (Spitfire proportions scaled) | computed |

## Where the files are

- TU Delft OpenCourseWare: [AE1101 Introduction to Aerospace Engineering, Aerodynamics 6](https://ocw.tudelft.nl/wp-content/uploads/AE1101-Aero-6.pdf) — web — Publisher's page; dimensions are facts
- Embry-Riddle (Leishman), Introduction to Aerospace Flight Vehicles: [Wing Shapes and Nomenclature](https://eaglepubs.erau.edu/introductiontoaerospaceflightvehicles/chapter/wing-shapes-and-nomenclature/) — web — Publisher's page; dimensions are facts
- Kitplanes (B. Wainfan): [Design Process: Planform Effects on Span Loading and Drag (2020)](https://www.kitplanes.com/design-process-planform-effects-on-span-loading-and-drag/) — web — Publisher'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 UAV](https://arxiv.org/pdf/1801.02938) — web — Publisher's page; dimensions are facts

## Free STEP/STL (1 parts, Xem Studio Design License, Xem Studio)

Index: https://xemstudio.com/files/hardware/elliptical-wing/index.json · license: https://xemstudio.com/files/hardware/elliptical-wing/LICENSE.md

- elliptical-wing-wing: [STEP](https://xemstudio.com/files/hardware/elliptical-wing/elliptical-wing-wing.step) · [STL](https://xemstudio.com/files/hardware/elliptical-wing/elliptical-wing-wing.stl) — elliptical planform: span 1000, root 225, tip 0 mm, LE sweep 0°, dihedral 3°, NACA 2412

## 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).

## Fits with

- [Rectangular (constant-chord) wing](https://xemstudio.com/objects/rectangular-wing/)
- [Tapered wing (taper ratio for minimum induced drag)](https://xemstudio.com/objects/tapered-wing/)
- [Swept-back wing](https://xemstudio.com/objects/swept-wing/)
- [Forward-swept wing](https://xemstudio.com/objects/forward-swept-wing/)
- [Delta wing](https://xemstudio.com/objects/delta-wing/)
- [Cranked arrow / double delta wing](https://xemstudio.com/objects/cranked-double-delta-wing/)