# Cajón Family — Parametric Design Sheet **Owner:** Tony Koop · Heifer Zephyr Instruments **Family:** Box drum, six-sided closed box, single thin front plate (tapa), back-port Helmholtz, optional internal snare **Members:** Compact (CJ-C), Standard (CJ-S, prototype), Bass (CJ-B) — coordinated three-size family **Manufacturing variants:** four end-to-end paths (V1 finger-joint / V2 dovetail / V3 rabbet / V4 miter+spline) — each with a snare/no-snare option **Status:** Design v1 — workbook formulas parametric; family tuning predictions populated; first prototype is Standard with finger-joint shell + guitar-string snare; tuning calibration pending first measurement. --- ## Authority boundary This packet is a pre-build V5 build-packet candidate. The design table, OpenSCAD master, jig templates, and reviewed SVG sheets are the current planning authority. They are not a substitute for measured panel stock, CNC test cuts, seat-load tests, strike-response captures, or snare-onset measurements. Generated previews, site imagery, visual-BOM layouts, and future concept images are support artifacts only. The packet records visual and CAD authority in `visual-output-register.csv`; no image or preview should be used to infer panel thickness, snare contact geometry, screw positions, joinery tolerances, or CNC toolpaths. ## 1. Intent Document the cajón as a portfolio-grade parametric instrument, not as one box. The same design sheet drives three sizes (Compact / Standard / Bass) with a single shared geometric law, and the same shell can be realized through four joinery paths and either lineage of snare: | Lineage | Snare | Character | |-----------|--------------------------------|---------------------------------------------| | Peruvian | None (or finger-mute pad) | Dry, woody, deep "thump"; tonal pitch reads cleanly | | Flamenco | Guitar strings (adjustable) | Bright, snappy slap on edges; modern default | A fifth artifact — the existing CNC inlay workflow (Broinwood-derived) — is the visual signature: walnut body with maple/yellowheart inlay panels, with the inlay routed before assembly so the pockets are clamped flat. The cajón's "secret" is that two simultaneous resonators tune together: the Helmholtz cavity (`f_H`) sits within a few semitones of the tapa (1,1) plate mode, and the player perceives the *coupled* note as the bass voice. Designing the family is therefore a matter of co-tuning those two systems while keeping snare-buzz, slap-zone geometry, and seat-height ergonomics inside their own envelopes. --- ## 2. Family scaling law The cajón family is a *closed-box, single-thin-plate, back-ported Helmholtz* drum. Two governing modes are co-dominant in the bass voice: the front-plate (1,1) bending mode and the cavity Helmholtz mode. Both must be modeled; the perceived bass pitch is the lower of the two if they are well separated, or a coupled hybrid if they are within ~6 semitones. ### 2.1 Tapa front plate — clamped rectangular plate, (1,1) mode For an orthotropic plywood plate clamped on all four edges (the cajón seats the tapa under screws every ~3″ around the perimeter; the central span is the active region), the (1,1) bending-mode fundamental is approximated by the isotropic clamped-plate expression: ``` f_plate_(1,1) ≈ (π / 2) · (1/a² + 1/b²) · √( D / (ρ · h) ) ``` where `a, b` are the clear span (in metres), `h` is plate thickness, `ρ` is panel density, and `D = E·h³ / (12·(1−ν²))` is flexural rigidity. For a 3 mm Baltic-birch tapa (`E ≈ 8 GPa`, `ρ ≈ 680 kg/m³`, `ν ≈ 0.30`), this places the (1,1) mode in the 60–110 Hz band over the family — which is exactly where you want it for "thump on the centre, snap on the edge." ### 2.2 Cavity — Helmholtz back-port For the box cavity coupled to a circular back-port: ``` f_H = (c / 2π) · √( A / (V · L_eff) ) L_eff = t_back + 1.7 · (d_hole / 2) ``` where `V` is internal volume, `A = π·(d/2)²` is the port area, `t_back` is back-panel thickness, and `1.7·r` is the standard end-correction for a thin-wall flush orifice (both sides counted). The original spreadsheet (`cajon-design-table.xlsx`) used `L_eff = t_back` only. That under-predicts L by ~5–10× for typical cajón dimensions and over-predicts `f_H` by a factor of ~3. The corrected formula is what the workbook uses now; the historical predictions are flagged in `risks.md` as **A4**. ### 2.3 Family scaling Volume scales roughly with H·W·D, so `f_H ∝ 1/√V` for a constant port. To keep `f_H` proportional to a target pitch span across the family, the port diameter is also scaled — larger box ⇒ larger port to push `f_H` back up; smaller box ⇒ smaller port. The catalog defaults below split the family into a P1 / P2 / P3 voice each separated by ~3–4 semitones. | Member | H (in) | W (in) | D (in) | Body t (in) | Back t (in) | Port d (in) | Tapa t (mm) | Predicted f_H (Hz) | Predicted plate (1,1) (Hz) | Tonal voice | |---------------|--------|--------|--------|-------------|-------------|-------------|-------------|--------------------|-----------------------------|-------------| | Compact (CJ-C)| 15 | 11 | 11 | 0.625 | 0.50 | 4.0 | 3 | 107 | 107 | bright A2/G♯2 | | **Standard (CJ-S) ⭐** | 18 | 12 | 12 | 0.75 | 0.50 | 4.5 | 3 | **96** | **84** | balanced G2 | | Bass (CJ-B) | 22 | 14 | 14 | 0.75 | 0.50 | 5.0 | 3 | 77 | 60 | deep D♯2/E2 | All values from the parametric design sheet; the workbook is the source of truth for any update. The Compact accidentally lands with `f_H ≈ f_plate` — that's the "tightly coupled" regime and produces the punchiest, most pitch-distinct bass in the family. The Bass deliberately separates them by ~5 semitones so the cavity rumble dominates; the plate then acts mainly as the slap voice. --- ## 3. Snare strategy The cajón has three valid snare paths. The workbook supports all three; the first prototype runs **option B**: | ID | Snare | Mechanism | Use | |----|------------------------------|-------------------------------------------------------------------------------------------------|----------------------------------| | A | None (Peruvian) | bare cavity; finger pad or palm mute on outside if a softer, more melodic voice is wanted | trad / world percussion | | B | Guitar-string snare ⭐ | 3–4 wound or plain steel guitar strings clamped on an angled internal block; tension adjustable via guitar tuners | flamenco / modern default | | C | Snare-drum wires | a section of standard snare-drum wires mounted on a tension lever; thicker buzz, less articulate | studio / loud genres | Snare wires sit *behind* the tapa, lightly contacting the inside face. The contact force is the tunable: too light = no buzz; too heavy = chokes the slap and overhangs the bass. --- ## 4. Joinery / construction variants The shell is a six-sided box. Five of the six faces (top, bottom, two sides, back) are 3/4″ Black Walnut by default; the sixth face is the 3 mm Baltic birch tapa. The four major joinery paths each ship as a manufacturable option: | ID | Joint | Method | Strength | Visual | Difficulty | Notes | |----|------------------------|-------------------------------------|----------|---------------------------------------|------------|-------| | V1 | Finger / box joint ⭐ | table saw + jig OR CNC parametric | ★★★ | ★★★ — contrasting maple fingers possible | medium | First-prototype default; CNC route enables variable-width fingers | | V2 | Half-blind dovetail | CNC | ★★★ | ★★★ — heirloom | hard | Showpiece path; needs jig fixtures + dust collection | | V3 | Rabbet | table saw or router | ★★ | ★ — hidden | easy | Commercial baseline; quickest to build | | V4 | Miter + spline | table saw + spline jig | ★★★ | ★★★ — contrasting splines visible | medium | Clean show-up corners; spline inlay ties to the inlay aesthetic | V1 (finger joint) is the recommended first prototype: it tolerates ±0.005″ panel error gracefully, the jig is reusable, and the visible joint complements the inlay. The tolerance claim is a design target, not a measured result. Validate it with scrap finger-joint samples and the square assembly jig before cutting show stock. --- ## 5. CNC inlay strategy The cajón's six flat faces are a perfect canvas for the Broinwood-style ball-nose inlay technique. Critical rule: **route inlay before assembly.** Once the box is glued, you cannot clamp panels flat for routing. The workflow ships in detail on `cajon-design-table.xlsx` § "CNC Inlay Workflow". Summary: 1. Two paired toolpaths per inlay element: a *pocket* (negative) cut into the body panel and an *insert* (positive) cut from contrasting wood. Both use the same TBN 12.4° tapered-ball-nose bit. 2. Pocket depth 0.080–0.100″; feed 30 IPM at 18,000 RPM in walnut. Test-cut on scrap to dial allowance. 3. The inlay-allowance setting in VCarve Pro controls press-fit. Too tight cracks the insert; too loose leaves a visible gap line. 4. Glue with Titebond III, clamp flat with wax-paper underlay, cure 24 hours, then drum-sand the panel flush before joinery. Visual layout default for the prototype: - **Side panels (2):** geometric mandala or Celtic-knot pattern, ~70% of panel area - **Back panel:** rosette around the sound hole only - **Top (seat):** subtle border inlay; nothing raised (you sit on it) - **Tapa:** no inlay (active surface, you hit it; preserve plate uniformity) --- ## 6. Critical dimensions (Standard, V1 finger-joint, snare option B) These are the numbers that drive cut-list, drawings, and CNC. Anything not here is either derived in the workbook or a non-critical aesthetic choice. | Feature | Dimension | Tolerance | Source | |----------------------------------|--------------------|----------------|--------------------------------| | Outer height | 18.000″ | ±0.020″ | family table | | Outer width | 12.000″ | ±0.020″ | family table | | Outer depth | 12.000″ | ±0.020″ | family table | | Body panel thickness | 0.750″ | ±0.005″ | stock spec | | Tapa thickness | 0.118″ (3 mm) | +0/−0.005″ | Baltic birch ply spec | | Back panel thickness | 0.500″ | ±0.005″ | stock spec | | Sound-hole diameter | 4.500″ | ±0.020″ | family table | | Sound-hole position | centred L–R, 1/3 H from top on back panel | ±0.10″ | trad practice | | Tapa screw spacing | every 3″ | ±0.10″ | trad practice | | Slap-zone unscrewed margin | top 4–5″ of tapa, both upper corners | as drawn | trad practice | | Internal corner glue blocks | 8× ¾″ triangle, full panel height | hand-fit | rigidity / overtone control | | Snare angle (option B) | 8–12° off vertical, contact 1″ below top | ±2° | trad practice | | Rubber-foot height | 0.50″ | ±0.05″ | airflow + bass projection | Datums for drawings: bottom outside face = primary horizontal datum (Z = 0); back outside face = secondary; centerline of tapa width = vertical reference. --- ## 7. What's parametric vs. what's measured **Parametric (formula-driven, edit the workbook to change):** - Helmholtz frequency `f_H` per member - Plate (1,1) mode estimate per member - Internal cavity volume - Sound-hole area and effective neck length - Family table member dimensions - Joint / bit / feed parameter recommendations **Measured (TBD on first prototype, will populate `validation.csv`):** - Actual `f_H` of the assembled cavity (tap-and-record, expect ±10 Hz from prediction) - Actual plate (1,1) of the mounted tapa (varies with screw torque and tapa moisture) - Slap-zone vs centre-strike spectrum delta (`risks.md` E1 acceptance test) - Snare-buzz onset velocity (subjective; recorded per snare option) - Sustain T60 of the bass voice - Actual panel thickness after milling, tapa thickness after finish, and any local thinning from CNC inlay pockets - Finger-joint fit, glue-line closure, diagonal squareness, and seat-load behavior A second-pass design sheet revision happens after the first prototype is measured. The empirical correction (`f_H_predicted` vs `f_H_measured`) gets logged in `validation.csv`, and any cents-error >50 cents triggers a family-table revisit. --- ## 8. Open assumptions These are explicit so the reviewer knows what is *concept* vs *manufacturable*: 1. **Tapa material is treated as isotropic.** Real Baltic birch ply is mildly orthotropic; the (1,1) prediction is a coarse estimate — expect ±20% from the simple formula. A measured tapa will be the source of truth. 2. **Snare contact pressure is not yet a parameter** in the workbook. It is dialed by ear on the first prototype. 3. **Glue-block contribution to plate clamping is unmodeled.** The 8 internal glue blocks effectively change the plate boundary condition near the corners; we treat the full panel as clamped, which over-stiffens the model slightly. 4. **CNC inlay pocket depth has not been verified to leave structural panel above the pocket.** 0.080″ pocket in 0.625″ stock leaves 0.545″ — comfortably safe — but is recorded as a check in `risks.md` (S2). 5. **Panel material defaulted to Black Walnut** for the visual contrast story; the workbook supports any species but the BOM and cost numbers assume walnut. --- ## 9. First-prototype recommendation Build the **Standard (CJ-S), V1 finger-joint, snare option B** as the first instrument. Reasons: - Standard is the family's tonal centre; if its measured tuning lands on prediction, the Compact and Bass scale by simple geometry from there. - V1 finger-joint is forgiving on stock-prep error and uses the same CNC fixture as future variants. - Snare option B (guitar strings) is the modern default; the snare can be removed or detensioned to demo "Peruvian style" without rebuilding the box. Total estimated material cost for prototype: ~$200 (see `bom.csv`). Estimated build time, in-shop, with CNC for joinery and inlay: ~30 hours over 4 days (acclimate / mill / inlay / joinery / glue-up / sand / finish / mount / tune). --- ## 10. References - `cajon-design-table.xlsx` — workbook source of truth (all formulas live) - `bom.csv` — bill of materials, all variants - `sourcing.csv` — suppliers, lead times, price-volatility flags - `cut-list.csv` — operation-by-operation lumber and stock cuts - `validation.csv` — predicted vs measured tuning + acceptance bands - `assembly-manual.md` — phase-by-phase build procedure - `risks.md` — red-team acoustic / structural / ergonomic / supply / fit-finish failure modes - `wolfram-starter.wl` — Wolfram package: plate, Helmholtz, two-zone synthesis - `drawing-brief.md` — list of required drawings + conventions - `drawings/*.svg` — dimensioned drawings - `cad/` — SolidWorks placeholders (master layout to follow) - `cnc/` — CNC inlay and finger-joint cut strategy notes - `site/index.html` — public build-log site