NACA456(1)

naca456 creates right, left, or paired wing geometry in a BRL-CAD .g database using NACA airfoil section definitions. Each wing is a semi-span model and may be output as a closed Bag of Triangles (BoT) mesh or a boundary representation (BREP). A single wing is written as a solid plus a region comb; a pair also receives a top-level combination containing both wing regions.

The implemented section math covers classic 4-digit NACA airfoils, 5-digit mean-line sections, 5-digit reflex mean-line sections, and the NACA 6/6A families covered by the public-domain NACA456 reference implementation from Public Domain Aeronautical Software:

The --airfoil and --tip-airfoil options accept these NACA designations:

The parser ignores whitespace and hyphens and accepts an optional NACA prefix. For example, NACA 63-215, 63-215, and 63215 are equivalent.

For 5-digit sections the first digit sets design lift coefficient, the second digit sets the camber-position family, the third digit selects normal (0) or reflex (1) mean-line behavior, and the last two digits set thickness percent. The supported camber-position families are those tabulated by the NACA456 reference equations: 5, 10, 15, 20, and 25 percent chord for normal 5-digit sections, and 10, 15, 20, and 25 percent chord for reflex sections.

For 6-series sections the first two characters select the profile family, the next digit is design lift coefficient in tenths, and the final two digits are thickness percent. The --six-a option controls the loading parameter a for ordinary 6-series mean lines. 6A sections use the modified 6-series mean line behavior from NACA456, where a is fixed at 0.8.

The --tip-specification file uses a strict JSON object schema. Unknown keys are errors, the version field is required, and version 1 is the only version currently accepted. Length values are model-space values in the same units as the other command-line dimensions.

The rounded schema exposes the default rounded closure parameters:

The closure_length field is optional; when omitted, naca456 derives a conservative value from the tip chord and semi-span. terminal_scale is the final cap scale relative to the nominal tip section, center_chord_fraction sets the normalized chord location about which the section shrinks, and segments controls closure refinement.

The raked schema adds a spanwise extension inside the requested semi-span:

For raked, the nominal tip section is placed at the start of the extension and the terminal section is placed at the semi-span. rake_offset is the additional leading-edge X offset accumulated across the extension. terminal_chord, terminal_airfoil, and twist_delta define the outer section. The initial raked implementation supports cap_style value flat.

The hoerner schema creates a clipped, drooped rounded closure:

closure_length, terminal_scale, and segments control the same closure refinement concepts used by rounded. tip_cut_angle shears the shrinking sections in planform to approximate the Hoerner cut, and droop lowers the outer closure in model Z.

The winglet schema creates an upright tip extension from the nominal tip section:

height is the winglet rise, cant_angle controls how strongly the winglet rotates upward from the wing plane, toe_angle yaws the section, and sweep_offset shifts the outer winglet leading edge in X. chord, taper, optional airfoil, and optional twist_delta define the outer winglet section. side is up or down. The current winglet cap support is cap_style value flat.

The blended_winglet schema adds a root blend ahead of the upright winglet:

root_blend_length reserves inboard span for the transition from the main wing to the winglet. transition_segments refines that transition, and curvature_profile is cosine or linear.

For each requested airfoil, naca456 creates cosine-spaced chordwise sample locations. This concentrates points near the leading edge, where the curvature is highest. It computes mean-line ordinate and slope, computes half-thickness, and offsets the section normal to form upper and lower surface points.

Four-digit thickness uses the conventional polynomial form, with either the standard finite trailing-edge coefficient or the sharp trailing-edge coefficient selected by --sharp-te. Four-digit camber uses the usual two-piece parabolic mean line.

Five-digit normal and reflex mean lines use the tabulated r, k1, and k2/k1 relationships from the NACA456 implementation. Five-digit thickness uses the same polynomial thickness form as the four-digit family.

Six-series and 6A-series thickness is generated from the epsilon/psi conformal mapping data embedded from NACA456. The implementation evaluates the tabulated epsilon and psi functions, scales them for the requested thickness ratio, maps the circle to airfoil coordinates, and interpolates the resulting half-thickness curve at the requested chordwise samples. Ordinary 6-series mean lines use the NACA456 MeanLine6 equations. 6A-series mean lines use the NACA456 modified six-series mean line.

The planform transform is then applied station by station. Chord length, leading-edge sweep offset, dihedral, and twist are linearly interpolated from root to the nominal tip section. Twist is applied around the local quarter chord. The model-space translation options are applied after the local section transform.

The default --tip-style rounded adds an elliptical closure beyond the nominal tip section. The closure progressively scales the tip airfoil outline around mid-chord, giving the planform a rounded wing-tip outline while preserving closed, explicit BoT/BREP topology. Both output modes add refined closure stations and close with a small terminal cap, avoiding the broad planar fan used by a simple pole closure. BREP represents the rounded closure with the same NURBS side-surface mode selected by --brep-surface; BoT writes per-face-vertex normals for smoother display while preserving the refined mesh geometry. The fallback --tip-style flat places the final section at the semi-span location and closes it with a planar triangulated cap.

In BoT mode, adjacent station outlines are triangulated into a closed mesh. The root cap and flat tip caps are triangulated as constrained polygons rather than centroid fans, avoiding poor triangles on concave or sharply cusped airfoil outlines. Rounded tips use the same side triangulation and close to a small terminal cap. The generated mesh is checked for finite coordinates, valid indices, manifoldness, orientation, closure, self-intersection, and triangle quality before it is written as a solid BoT. BoT output includes surface normals for smoother rounded-tip display; root and terminal cap normals are kept flat.

In BREP mode, every outline vertex is represented explicitly. Chordwise outline edges and spanwise edges are shared by adjacent faces. The side skin is represented as local bilinear ruled NURBS patches between neighboring spanwise stations and chordwise outline edges. Local patches avoid the span-curve overshoot that can occur when a single interpolated strip crosses a sharp wing-tip transition.

Root caps and flat tip caps are represented by triangulated planar faces; rounded tips use additional NURBS side/closure bands down to a small terminal triangulated cap. The BREP is standardized, compacted, and checked with OpenNURBS IsValid() and IsSolid(), plus additional libbrep quality checks for duplicate vertices, zero-length edges and trims, edge trim pairing, face aspect ratio, and conservative self-intersection risk, before it is written.

With --brep-surface smooth, the side skin uses bicubic Hermite NURBS patches for each station-to-station, chord-to-chord cell. Tangents are estimated from neighboring spanwise and chordwise samples, then limited against each local edge direction and length to avoid overshoot at sharp tip transitions. The patch boundary curves are shared as explicit BREP edges. This produces smoother local side-surface geometry while preserving explicit loop and trim topology.

When either the root or tip section has a collapsed trailing edge, the lower trailing-edge duplicate is omitted for all interpolated stations. This keeps the spanwise topology stable and avoids zero-length BREP edges in mixed root/tip cases.

Each generated solid and region receives naca456:: attributes recording the inputs used to create it. These include generator name, metadata version, algorithm source, geometry mode, wing side, BREP surface mode, root and tip airfoil designations, tip style, semi-span, full span, root and tip chord, sweep offset, sweep angle, dihedral, tip twist, 6-series loading parameter, station/sample counts, trailing-edge mode, and model-space offsets. When a JSON tip specification is used, the compact JSON payload is recorded; when it comes from --tip-specification, the filename is recorded as well.

For paired output, the top-level combination records the pair configuration, the left and right region names, and the semi-span and full-span values. Its two solids and regions each record their own left or right wing side.

For example:

The attributes are intended to make generated models auditable. They are not a parametric regeneration contract; future versions may add metadata fields or change BREP construction details.

naca456 is a geometric airfoil and wing-shape generator. It does not perform aerodynamic analysis, structural analysis, aeroelastic analysis, certification checks, or optimization.

Each generated wing is a semi-span solid. A pair is two independently capped solids that meet at the center plane; it is not a fused solid or a wing-body blend. The tool does not currently generate control surfaces, flaps, slats, spars, ribs, skins with physical thickness, fuel volumes, fasteners, or manufacturing features.

The simple --tip-style option intentionally exposes only the default rounded closure and flat fallback. More parameterized tips are available through --tip-specification. The Hoerner and winglet styles are geometric approximations intended for procedural model generation; they are not a substitute for aerodynamic design, load analysis, or manufacturer-specific tip-device geometry.

The BREP output is checked with OpenNURBS IsValid() and IsSolid(), but it is not a general CAD healing pipeline. Downstream Boolean operations may still be sensitive to extreme parameter combinations, very thin sections, aggressive twist, or highly tapered planforms.

The airfoil definitions are mathematical NACA sections produced from the referenced NACA456 equations and tables. They are not guaranteed to match any particular manufactured, wind-tunnel, or proprietary derivative airfoil.

All length inputs are BRL-CAD model-space values. They are intentionally unitless at the command line: a value of 1000 means 1000 database model units, whatever unit system the receiving .g database is interpreted to use. The generated shape uses a semi-span per wing; use --semi-span to specify that length directly, or --full-span when starting from a full aircraft span. Sweep is available either as --sweep-angle for an aerodynamic planform description or as --sweep-offset for exact model-space placement.

The section mathematics are implemented from the public-domain NACA456 program by Ralph Carmichael, distributed by Public Domain Aeronautical Software (PDAS):

The BRL-CAD implementation references the NACA456 source files nacax.f90, epspsi.f90, and splprocs.f90. In particular, it uses the NACA456 MeanLine3, MeanLine3Reflex, MeanLine6, MeanLine6M, ScaleFactor, and six-series epsilon/psi table logic as the basis for the local C++ implementation.

The NACA456 source package and PDAS reference page identify these principal references for the underlying airfoil coordinate algorithms and data:

The broader PDAS bibliography is maintained at:

naca456 exits with a nonzero status if option parsing fails, if the requested NACA code is unsupported, if the output database cannot be opened, if appending would overwrite an existing object name, if BoT mesh validation fails, or if BREP validation or solid classification fails.

brlcad(1), mged(1), rt(1), libwdb(3)

BRL-CAD Team

This software is Copyright (c) 1989-2026 by the United States Government as represented by U.S. Army Research Laboratory.

Reports of bugs or problems should be submitted via electronic mail to devs@brlcad.org