# Tapered wing (taper ratio for minimum induced drag)

> What taper ratio gives the lowest induced drag?

- 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/tapered-wing/ · JSON: https://xemstudio.com/api/geometry?object=tapered-wing · Plain text: https://xemstudio.com/objects/tapered-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

- Taper ratio is tip chord divided by root chord (Leishman, ERAU). Tapering moves the span loading toward elliptical, raising span efficiency and lowering induced drag (Kitplanes, Wainfan).
- Torenbeek's guidance, quoted in a UAV design paper, picks a taper ratio of 0.45 'because it gives fairly elliptic lift distribution and good stall characteristics' (arXiv 1801.02938). Leishman notes linear taper is a good compromise between weight and structural efficiency.
- Strong taper loads the tips more, so tapered wings need washout to keep the stall inboard (Boldmethod; R/C Soaring Digest).
- 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 |
|---|---|---|
| Taper ratio definition | lambda = c_tip / c_root | ERAU (Leishman) |
| Recommended taper (unswept) | 0.45 | arXiv 1801.02938 citing Torenbeek (1976) |
| 2:1 taper example | lambda = 0.5 | ERAU; Kitplanes |
| Span loading example plotted | lambda = 0.4 closer to elliptical than constant chord | Kitplanes (Wainfan) |
| Model dihedral correction for taper | EVD factor F = 0.8 + 0.2 (Ct/Cr) | McCombs, Model Aviation 1994 |
| Reference build | span 1000, root 220, tip 99 (lambda 0.45) | computed |

## Where the files are

- 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
- 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
- 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
- Model Aviation (AMA), W.F. McCombs: [Wing and Tail Dihedral for Models (Dec 1994)](https://library.modelaviation.com/article/wing-and-tail-dihedral-models) — web — Publisher's page; dimensions are facts
- Boldmethod (pilot training): [How Stall Strips Keep Your Plane Under Control](https://www.boldmethod.com/learn-to-fly/aerodynamics/how-stall-strips-keep-your-plane-under-control/) — web — Publisher's page; dimensions are facts
- R/C Soaring Digest: [Twist Distributions for Swept Wings, Part 2 (June 2002)](https://new.rcsoaringdigest.com/2002/06/twist-distributions-for-swept-wings/[pdf].pdf) — web — Publisher's page; dimensions are facts

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

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

- tapered-wing-wing: [STEP](https://xemstudio.com/files/hardware/tapered-wing/tapered-wing-wing.step) · [STL](https://xemstudio.com/files/hardware/tapered-wing/tapered-wing-wing.stl) — tapered planform: span 1000, root 220, tip 99 mm, LE sweep 0°, dihedral 3°, NACA 2412

## Questions

**What taper ratio should I use?**

Torenbeek's 0.45 is a well-cited choice for unswept wings (via arXiv 1801.02938).

## Fits with

- [Rectangular (constant-chord) wing](https://xemstudio.com/objects/rectangular-wing/)
- [Elliptical wing](https://xemstudio.com/objects/elliptical-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/)