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ashfordeOU (@ashfordeou) published this skill. Their other Agent Skills are listed on their SkillMD profile.

Airfoil Geometry by ashfordeou — Agent Skill

Name: Airfoil Geometry
Author: ashfordeOU

Airfoil Geometry

Use when you must work with classic NACA airfoil geometry: decode NACA 4-digit, 5-digit, and 6-series designations into camber, camber position, and thickness; compute the 4-digit thickness distribution, mean camber line ordinates and slope; and derive leading-edge radius and section area from the public-domain NACA formulas. Produces the geometry parameters that feed section selection, structural depth checks, and coordinate generation for panel or CFD analysis. Trigger: naca airfoil, camber, thickness distribution, mean line, leading edge radius, section area, airfoil coordinates.

ashfordeOU 3f949b4 3 files · 17.6 KB Updated Sep 17, 2026

File contents

NACA Airfoil Geometry (aerodynamics/airfoil/airfoil-geometry)

Use when the task is classic NACA airfoil geometry: designation decode, thickness and camber formula computation, and derived geometric properties.

Domain quick reference

NACA 4-digit MPXX: M = max camber in percent chord (m = M / 100), P = camber position in tenths chord (p = P / 10), XX = max thickness in percent chord (t = XX / 100).
Thickness half-ordinate (NACA Report 460; public domain): y_t = (t / 0.2) * (0.29690 * sqrt(x) - 0.12600 * x - 0.35160 * x^2
- 0.28430 * x^3 - 0.10150 * x^4). Max half-thickness t / 2 at x = 0.3; the polynomial leaves a small trailing-edge thickness (0.0105 * t) that is faired to a sharp edge in practice.
Mean camber line: for x <= p, y_c = (m / p^2) * (2 * p * x - x^2); for x >= p, y_c = (m / (1 - p)^2) * (1 - 2 * p + 2 * p * x - x^2). Slope dy_c / dx = (2 * m / p^2) * (p - x) for x <= p, and (2 * m / (1 - p)^2) * (p - x) for x >= p; zero at x = p.
Upper surface = y_c + y_t, lower surface = y_c - y_t.
Leading-edge radius: r_le = 1.1019 * t^2 (fraction of chord).
Enclosed section area per unit span: A = 2 * integral(y_t dx) = 0.68508 * t (chord^2); independent of camber.
NACA 5-digit: design cl = first digit * 0.15 (23012 -> 0.3), camber position = second digit * 5 percent chord (23012 -> 15 percent), thickness = last two digits percent. Mean line 230: m = 0.15, k1 = 15.957. Third digit 1 marks a reflexed mean line.
NACA 6-series: 65-218 = 6-series, min pressure at 0.5 chord (digit 5 in tenths), design cl 0.2 (digit 2 in tenths), thickness 18 percent. A parenthetical digit (65(3)-218) marks a modified mean line; the decoder rejects it rather than guess the variant.
Practical data sources: NACA Report 824 ordinate tables, Abbott and von Doenhoff "Theory of Wing Sections", and the UIUC airfoil coordinate database.

Workflow

Decode the designation with decode_4digit, decode_5digit, or decode_6series.
Compute thickness half-ordinates with thickness_ord at the mesh stations.
Compute camber ordinates and slope with camber_ord and camber_slope; form surfaces with surface_ords.
Derive leading_edge_radius and section_area for structural and geometric checks.
Cross-check ordinates against published tables when available.

Pitfalls

Reading the 5-digit second digit as percent chord instead of digit times 5.
Applying the 4-digit thickness formula to 5-digit or 6-series sections; each family has its own ordinate tables.
Treating y_t as a surface ordinate; the upper surface is y_c + y_t and the lower is y_c - y_t.
Quoting the polynomial's trailing-edge thickness as a design value.
Confusing the 5-digit design cl with the cl at a flight condition.
Assuming the decoder handles modified 6-series or A-series thickness variants; it does not.

Behavior contract (gate 3)

The decode and geometry logic is exercised by the gate 3 contract test: scripts/test_airfoil_geometry.py against scripts/airfoil_geometry_logic.py (stdlib unittest, offline). Run: python3 scripts/test_airfoil_geometry.py

Compliance

NACA Report 824 is US government work (public domain); formulas and summary values only, per standards-map.yaml.
compliance: STANDARDS-REF, gated: false.

---name: airfoil-geometrydescription: Use when you must work with classic NACA airfoil geometry: decode NACA 4-digit, 5-digit, and 6-series designations into camber, camber position, and thickness; compute the 4-digit thickness distribution, mean camber line ordinates and slope; and derive leading-edge radius and section area from the public-domain NACA formulas. Produces the geometry parameters that feed section selection, structural depth checks, and coordinate generation for panel or CFD analysis. Trigger: naca airfoil, camber, thickness distribution, mean line, leading edge radius, section area, airfoil coordinates.license: Apache-2.0---# NACA Airfoil Geometry (aerodynamics/airfoil/airfoil-geometry)Use when the task is classic NACA airfoil geometry: designationdecode, thickness and camber formula computation, and derivedgeometric properties.## Domain quick reference- NACA 4-digit MPXX: M = max camber in percent chord (m = M / 100), P = camber position in tenths chord (p = P / 10), XX = max thickness in percent chord (t = XX / 100).- Thickness half-ordinate (NACA Report 460; public domain): y_t = (t / 0.2) * (0.29690 * sqrt(x) - 0.12600 * x - 0.35160 * x^2 + 0.28430 * x^3 - 0.10150 * x^4). Max half-thickness t / 2 at x = 0.3; the polynomial leaves a small trailing-edge thickness (0.0105 * t) that is faired to a sharp edge in practice.- Mean camber line: for x <= p, y_c = (m / p^2) * (2 * p * x - x^2); for x >= p, y_c = (m / (1 - p)^2) * (1 - 2 * p + 2 * p * x - x^2). Slope dy_c / dx = (2 * m / p^2) * (p - x) for x <= p, and (2 * m / (1 - p)^2) * (p - x) for x >= p; zero at x = p.- Upper surface = y_c + y_t, lower surface = y_c - y_t.- Leading-edge radius: r_le = 1.1019 * t^2 (fraction of chord).- Enclosed section area per unit span: A = 2 * integral(y_t dx) = 0.68508 * t (chord^2); independent of camber.- NACA 5-digit: design cl = first digit * 0.15 (23012 -> 0.3), camber position = second digit * 5 percent chord (23012 -> 15 percent), thickness = last two digits percent. Mean line 230: m = 0.15, k1 = 15.957. Third digit 1 marks a reflexed mean line.- NACA 6-series: 65-218 = 6-series, min pressure at 0.5 chord (digit 5 in tenths), design cl 0.2 (digit 2 in tenths), thickness 18 percent. A parenthetical digit (65(3)-218) marks a modified mean line; the decoder rejects it rather than guess the variant.- Practical data sources: NACA Report 824 ordinate tables, Abbott and von Doenhoff "Theory of Wing Sections", and the UIUC airfoil coordinate database.## Workflow1. Decode the designation with decode_4digit, decode_5digit, or decode_6series.2. Compute thickness half-ordinates with thickness_ord at the mesh stations.3. Compute camber ordinates and slope with camber_ord and camber_slope; form surfaces with surface_ords.4. Derive leading_edge_radius and section_area for structural and geometric checks.5. Cross-check ordinates against published tables when available.## Pitfalls- Reading the 5-digit second digit as percent chord instead of digit times 5.- Applying the 4-digit thickness formula to 5-digit or 6-series sections; each family has its own ordinate tables.- Treating y_t as a surface ordinate; the upper surface is y_c + y_t and the lower is y_c - y_t.- Quoting the polynomial's trailing-edge thickness as a design value.- Confusing the 5-digit design cl with the cl at a flight condition.- Assuming the decoder handles modified 6-series or A-series thickness variants; it does not.## Behavior contract (gate 3)The decode and geometry logic is exercised by the gate 3 contracttest: scripts/test_airfoil_geometry.py againstscripts/airfoil_geometry_logic.py (stdlib unittest, offline). Run:python3 scripts/test_airfoil_geometry.py## Compliance- NACA Report 824 is US government work (public domain); formulas and summary values only, per standards-map.yaml.- compliance: STANDARDS-REF, gated: false.

Frequently asked questions