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Coordinates and numerics
Airfoil Coordinate Interpolation: Linear, Spline and Shape-Preserving Methods
HENDOI · 26 October 2026
Interpolating an airfoil is how you add points or build a CAD curve. Linear interpolation facets the nose. An unconstrained spline can loop. A shape-preserving fit stays between the points.
Do not treat the whole outline as y(x)
Upper and lower surfaces share x values near the nose only in a special construction. On a general file the outline is a curve in the plane, best parameterized by arc length or by a surface index, not by a single function y of x through the leading edge. If you force y(x) across the nose, the slope is infinite or the interpolant folds. Split the surfaces. Give the nose its own treatment, ideally a local radius or a dense cluster of points, and interpolate each surface on its own parameter.
Three interpolants
| Method | What you get | Where it hurts an airfoil |
|---|---|---|
| Linear, point to point | The polyline you already had. No overshoot. Areas and closure stay honest. | The nose becomes a polygon. Curvature is zero on each facet and infinite at each corner. A coarse file will stall like a faceted shape. |
| Cubic spline | A smooth curve and a continuous slope, which CAD and panel codes prefer. | Splines overshoot. Near a sharp trailing edge or a noisy digitizer point they can loop, cross, or invent a wavy camber that was not in the data. |
| Shape-preserving, such as a monotone piecewise cubic on a well-chosen parameter | Smooth enough for panels, and unwilling to invent a hill between two neighbouring points. | It will not recover a true circular nose from three bad points. Preservation is not the same as knowing the design radius. |
A practical rule
- If the source is a generator (NACA, CST), do not interpolate the output. Ask the generator for the points you need. Interpolation is for measured or legacy files.
- If you spline a measured section, plot curvature versus arc length. A smooth outline can still have a curvature that changes sign every few points. That sign chatter is waviness.
- Compare thickness distribution and leading-edge radius before and after the fit. If either moved more than your measurement uncertainty, the interpolant redesigned the section.
- Close the trailing edge the way the original file closed it. A spline that pulls an open edge shut has changed the base thickness.
The next lesson uses one of these interpolants to place a new point set. Pick the interpolant here, with the failure mode in view, before you resample.
Where this sits in the series
In simple words: what this page is for
Interpolating an airfoil is how you add points or build a CAD curve. Linear interpolation facets the nose. An unconstrained spline can loop. A shape-preserving fit stays between the points.
This lesson exists because section decisions fail when geometry, method labels and selection reasons are scattered. Airfoil Coordinate Interpolation: Linear, Spline and Shape-Preserving Methods 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 Airfoil Coordinate Interpolation: Linear, Spline and Shape-Preserving Methods 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 Airfoil Coordinate Interpolation: Linear, Spline and Shape-Preserving Methods 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
- Active Flow Control on Airfoils: Suction, Blowing and Synthetic Jets
- What Is the Aerodynamic Center of an Airfoil? Location, Meaning and Applications
- How to Identify Numerical Convergence Problems in Airfoil Analysis
- How to Build an Airfoil Analysis Database with Consistent Simulation Conditions
- All HENDOI blog articles
- HENFOIL product page
- HENSYNTH product page
- Pricing — Student, Professional & Team
- FAQ
- Login · Register now
- Previous: Detect duplicate and invalid coordinate points
- Next: Resample airfoil coordinates
- 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.
Both products live
Use this lesson in the HENDOI workspace
This page sits in Coordinates and numerics. HENFOIL and HENSYNTH are both live on one account. These articles are screening lessons — not certification reports.
Live · section
HENFOIL
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.
To Know MoreLive · aircraft
HENSYNTH
After the section is chosen, set geometry and mission requirements, run screening, read compliance, synthesize candidates and download or mail the report.
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Related articles
- How to Detect Duplicate and Invalid Points in Airfoil Coordinate Files
A zero-length panel, a repeated trailing edge, a crossed surface or a point that jumps backward will quietly ruin a panel solution. Detect them before the solver runs.
- How to Resample Airfoil Coordinates Without Distorting the Profile
Resampling places a new point set on the same curve. Cosine clustering protects the nose. Uniform spacing in x does not. Always compare thickness and leading-edge radius afterward.
- Panel Methods for Airfoil Analysis: How Discretization Affects Accuracy
A panel method replaces the airfoil with panels carrying source or vorticity. Lift can be accurate with a modest set. The nose, the trailing edge and the pressure peak show the discretization first.