# ABACUS R8 Tripod Intake — FreeCAD Package

This package updates the ABACUS R8 minimum-action harmonic-curvature shell with the analytically forced three-foot intake boundary.

## Primary geometry controls

Only two values are primary shape degrees of freedom:

1. `LAMBDA = H / Wb` — overall slenderness.
2. `EPSILON0` — amplitude of the first triaxial curvature mode.

Edit these at the top of `ABACUS_R8_Tripod_FreeCAD.FCMacro`, then run the macro in FreeCAD.

The lower tripod is not a third shape control. Its phase and waveform are inherited from the same triaxial curvature field, and its rise is solved from the fan intake requirement.

## Canonical laws

Cross-sectional curvature:

```text
k(q,u) = 2/W(u) · [1 + ε(u) cos(6πq)]
```

Tripod lower boundary:

```text
z₀(q) = hₐ · [1 − cos(6πq)] / 2
```

The shell is the same analytic surface restricted to:

```text
u₀(q) ≤ u ≤ 1,   u₀(q)=z₀(q)/H
```

The derived rise `hₐ` is numerically solved so:

```text
filter free area × geometric intake curtain area
    = swept disk area of the 140 mm fan
```

## Run in FreeCAD

1. Open FreeCAD.
2. Choose **Macro → Macros… → Create** or open the supplied `.FCMacro`.
3. Run `ABACUS_R8_Tripod_FreeCAD.FCMacro`.
4. The macro creates:
   - the exact triangulated shell mesh;
   - a faceted BRep conversion when supported;
   - a translucent intake-area curtain;
   - Mini-ITX, fan, heat-sink, PSU, fan-deck, and support-pad studies;
   - an `.FCStd` document;
   - STL and attempted STEP exports.

The canonical geometry is the mathematical law. The mesh/BRep is its numerical CAD representation.

## Validated baseline

- bottom mean width: 275 mm
- height: 285 mm
- top mean width: 180 mm
- curvature amplitude: 0.20
- wall: 4 mm
- derived arch rise: 44.8017 mm
- geometric intake: 192.4226 cm²
- filtered effective intake: 153.9380 cm²
- 140 mm fan swept area: 153.9380 cm²
- effective intake / fan: 1.000000
- shell mesh: watertight
- estimated gray-iron shell mass: 5.216 kg

## Included files

- `ABACUS_R8_Tripod_FreeCAD.FCMacro` — FreeCAD generator.
- `abacus_r8_tripod_generate.py` — independent Python validation/export generator.
- `ABACUS_R8_tripod_parameters.json` — canonical parameters and derived values.
- `ABACUS_R8_harmonic_tripod_shell.stl/.obj/.glb` — immediately viewable geometry.
- `ABACUS_R8_harmonic_tripod_preview.png` — exterior/intake preview.
- `ABACUS_R8_harmonic_tripod_rim_law.png` — lower-edge law.
- `TRIPOD_GEOMETRY_REPORT.md` and `TRIPOD_GEOMETRY_METRICS.json` — validation results.
- `MATHEMATICAL_DESCENT.md` and `TRIPOD_GEOMETRY.md` — mathematical authority.

## Current limitation

FreeCAD is not installed in the generation environment, so the macro was syntax-checked but the `.FCStd` and STEP files were not executed here. The Python generator was executed; the supplied STL/OBJ/GLB shell is watertight.
