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ABACUS · HARMONIC TRIPOD

Three parameters. One analytic surface.

Slenderness, curvature amplitude, and section area ratio tune the complete geometry. The three intake arches stay forced by the fan-area requirement and never become an aesthetic dial.

Descended parameters

Slenderness λ = H / Wb

The complete axial proportion. Footprint scale remains fixed to the component package.

Curvature wave ε

The sole triaxial curvature mode. ε = 0 is the circle; baseline ε = 0.20.

Section area ratio A₁/A₀

Top cross-sectional area over bottom. The mean-width ratio W₁/W₀ is solved from it against the real section polygons, not assumed.

Package

Physical scale and component choices, not shape dials. Base width scales the whole appliance at fixed proportions; fan diameter forces the arch rise through the intake law.

Base mean width W₀

Intake fan Ø

Arch rise is solved so filtered intake equals fan swept area — bigger fan means taller arches, roughly as Ø².

Board tilt

The board is inverted — CPU, memory and M.2 all face down into the fan stream. Tilt swings the whole assembly, heat sink included.

Packing verdict: —
Fan frame clearance: —

Forced intake boundary

z₀(q) = hₐ · [1 − cos(6πq)] / 2

The phase comes from the same curvature field. The rise hₐ is solved so the filtered opening equals one 140 mm fan swept disk.

Derived arch rise: —
Rise / height: —
Total geometric intake: —
Each arch: —
Effective intake / fan: —

Fixed basis: 275 mm bottom mean width, 180 mm top mean width, 4 mm wall, 140 mm fan, 80% filter free area.

View

component envelopes intake-area curtain surface wire overlay transparent shell zebra curvature analysis perspective projection

Zebra makes the shell a perfect mirror against a striped environment. Straight, evenly spaced bands mean fair curvature; kinks or pinches in the bands localise curvature defects. Uncheck perspective for orthographic, which removes foreshortening when judging the bands.

Derived geometry

Bottom mean width: —
Top mean width: —
Height: —
Curvature ratio: —
Top / base area (measured): —
Solved width ratio W₁/W₀: —
Top mean width: —
Outer volume: —
Iron mass estimate: —
Minimum draw: —
Maximum draw: —

Component stack

Arch apex (sight line): —
Plate underside: —
Board plane: —
Board corner clearance: —
Stack top (PSU): —
Headroom under rim: —

The plate underside clears the arch apex, so nothing internal is visible along a horizontal sight line through an arch. Negative headroom means the PSU no longer fits under the top rim at these parameters.