How to Calculate Airfoil Thickness Distribution Along the Chord

The distribution, not the maximum

Two sections can share a 12% maximum thickness and still be different airfoils. One can carry that thickness forward, with a large leading-edge radius and a thin trailing edge. Another can carry it aft, with a finer nose and more depth near the flap hinge. The function you want is t/c versus x/c. Maximum thickness is only the peak of that curve.

From a named NACA 4-digit equation

For the classical 4-digit thickness family, with x as fraction of chord and τ as the maximum thickness fraction (0.12 for a 12% section):

yt(x) = 5 τ (0.2969 √x − 0.1260 x − 0.3516 x² + 0.2843 x³ − 0.1015 x⁴)

Here yt is the half-thickness measured perpendicular to the camber line. The full thickness is 2 yt. The coefficient 0.1015 leaves a very small trailing-edge thickness; 0.1036 closes it. The √x term is why the leading-edge radius is finite: the slope is infinite at x = 0 in the coordinate sense, but the radius is

rle / c ≈ 1.1019 τ²

For τ = 0.12 that radius is about 1.6% of chord. This formula is the thickness distribution of the NACA 4-digit family only. A 6-series section, a supercritical section or a CST shape has a different t(x) even at the same maximum.

From an arbitrary coordinate file

1. Normalize to unit chord and put the chord on the x-axis.
2. Split the polyline into upper and lower surfaces at the leading edge.
3. Choose stations in x. Cluster them near the nose, because that is where t(x) rises fastest. Cosine spacing, x = (1 − cos φ) / 2, does this without a special case.
4. Interpolate yu(x) and yl(x). If the points are not monotone in x, fix the order before you interpolate. Linear interpolation is enough for a check. A spline will invent a wiggle if the points are noisy.
5. Build the mean line yc = (yu + yl) / 2 and its slope. The perpendicular thickness is the distance between the surfaces along the normal to that line. The vertical gap yu − yl is the approximation for mild camber.
6. Plot t/c against x/c. Read the maximum and its location. Also read t/c at the spar line you actually have, which is rarely the maximum.

What the plot is for

• A spike or a negative value is a broken file, not a radical design.
• A flat spot in t(x) can be a real geometric feature or a digitizing plateau. Check the curvature.
• Structural depth is t at the spar, minus the skin, not t max if the spar sits elsewhere.
• After you scale to a physical chord, the same curve in millimetres is what the loft and the mold see.

Keep the distribution next to the polar. A change in drag that you cannot see in t(x) or in the camber line is a change you should be able to see in the pressure plot instead. One of those three pictures has to explain it.

---

Where this sits in the series

In simple words: what this page is for

Maximum thickness is one number. The thickness distribution is the whole function t(x), and it is what the spar, the stall and the panel code actually see.

This lesson exists because section decisions fail when geometry, method labels and selection reasons are scattered. How to Calculate Airfoil Thickness Distribution Along the Chord 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 Airfoil Thickness Distribution Along the Chord 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 Airfoil Thickness Distribution Along the Chord 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: Maximum camber vs maximum thickness
• Next: Leading-edge radius and trailing-edge geometry
• 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.