Geometry parameters
How to Calculate the Leading-Edge Radius of an Airfoil from Coordinate Data
HENDOI · 26 October 2026
The leading-edge radius is the circle that fits the nose. On a coordinate file it is a local fit, and a coarse or faceted nose makes that fit a guess. A NACA four-digit section also has a closed-form estimate.
Radius is curvature at the nose
The aerodynamic consequences of a blunt or sharp nose are in the leading-edge radius lesson. This lesson is how to get the number from a file. Normalize first: leading edge at the origin, chord along x, trailing edge at x = 1, upper surface positive. A radius computed in millimeters and then quoted as a fraction of the wrong chord is a different airfoil.
For a smooth nose the radius is the reciprocal of curvature at the leading edge. On a polyline you do not have a derivative, so you fit a circle. Three points A, B and C near the nose have a circumradius
R = |AB| · |BC| · |CA| / (4K)
where K is the area of triangle ABC. That triplet is a local estimate. A least-squares circle through the points on a short arc, a few percent of chord either side of the nose, is more stable. Report the arc you used and the point count. A three-point fit on a nose that was sampled every 5% of chord is not a radius. It is the corner of the polygon.
When a formula is allowed
| Section | How to get the radius |
|---|---|
| NACA four-digit, generated from the thickness equation | As a fraction of chord, about 1.1019 τ², where τ is the maximum thickness ratio. This matches the family. It does not describe a file that was later edited. |
| Any other coordinate list | Fit the circle. Do not paste the four-digit formula onto a 6-series, an Eppler section, or a digitized plot. |
| A spline or a CST shape | Use the curvature of the spline at the nose, then refit after you sample it. Sampling can shrink the radius if the nose points are too sparse. |
Compare two files only after both have been normalized and fitted the same way. A “sharper” nose that is really a missing point will change stall in the solver and will not match the hardware. Recompute the radius after every repair, resample, or trailing-edge edit. Record it next to the geometry hash.
Where this sits in the series
In simple words: what this page is for
The leading-edge radius is the circle that fits the nose. On a coordinate file it is a local fit, and a coarse or faceted nose makes that fit a guess. A NACA four-digit section also has a closed-form estimate.
This lesson exists because section decisions fail when geometry, method labels and selection reasons are scattered. How to Calculate the Leading-Edge Radius of an Airfoil from Coordinate Data helps you keep a clean trail from shape to polar to choice.
Why the topic matters
Engineers lose time when a title sounds clear but the page only sketches the idea. This article expands How to Calculate the Leading-Edge Radius of an Airfoil from Coordinate Data so you can answer three questions without jargon: what is the idea, when do you use it, and how do you check it in a HENDOI product.
Read the sections above for the core definitions. Use the steps below to move from reading into a real project trail you can share with a teammate.
How to apply this in HENDOI
In practice: create a HENDOI account or log in, open HENFOIL, bring a section in (create, import DAT, or digitize), pass the geometry gate, climb the analysis ladder only as far as the decision needs, then compare and archive. Every calculated number should keep its method label.
When the section choice is ready for the aircraft, continue in HENSYNTH for mission, compliance and trades. Same account. Same plans.
What this page will not claim: a teaching polar or geometry note is not a flight-Re certificate. HENFOIL labels methods so you know what you bought. Tunnel data and professional judgement still sit outside any single software run.
Checklist before you leave this page
- Can you state the idea of How to Calculate the Leading-Edge Radius of an Airfoil from Coordinate Data in one sentence?
- Do you know which product owns the next action — HENFOIL or HENSYNTH?
- Will every number you keep carry a method label or a stored-run source?
- If you are new here, have you opened Register or Login?
Related reading on this site
- What Is Airfoil Stall? Comparing Leading-Edge and Trailing-Edge Stall
- Leading-Edge Radius and Trailing-Edge Geometry: Effects on Airfoil Performance
- How Leading-Edge Slats Delay Airfoil Stall and Increase Maximum Lift
- Airfoil Leading-Edge Suction: Physical Principles and Aerodynamic Significance
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- HENSYNTH product page
- Pricing — Student, Professional & Team
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- Previous: An automated airfoil analysis workflow
- Next: Thickness-to-chord ratio
- Index: all HENFOIL airfoil lessons
These pages teach the ideas. They are not wind-tunnel data and not a certification analysis. When a number matters, compute it at a stated Reynolds number, Mach number and transition setting, and keep the method label on the result. In HENFOIL that production polar is a VIC polar — see the analysis ladder and the polar field guide.
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Use this lesson in the HENDOI workspace
This page sits in Geometry parameters. HENFOIL and HENSYNTH are both live on one account. These articles are screening lessons — not certification reports.
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Turn this lesson into a section you can draw, check, analyse and compare. Run the polar at the Reynolds number of the vehicle. The method name stays on the result.
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