Pickup Construction

A tone target must fit in a bobbin

ArcoAura connects electrical goals to physical construction. A requested DC resistance and inductance imply a number of turns, a wire gauge, a mean turn length, layer count, winding depth, and total wire length. A design that sounds plausible but does not fit is reported as a design problem.

The solver evaluates available American Wire Gauge sizes, derives turns from target resistance, refines mean circumference as the winding grows, estimates inductance from turns, geometry, and effective magnetic permeability, then scores electrical error and physical fit together.

The calculation chain

Coated wire diameter determines turns per layer
Target resistance and resistance per metre estimate turn count
Layer count determines winding depth
Winding depth changes the mean circumference of later turns
Mean circumference refines wire length and achieved resistance
Inductance scales approximately with the square of turns and a geometry factor
Overflow, resistance error, and inductance error become explicit warnings

Readable winding geometry

This ArcoBASIC example shows the core geometry without pretending that a target number alone creates a buildable pickup. Every intermediate value has a physical meaning and a real unit.

ArcoBASICArcoBASIC communication example: derive coil layers and winding depth

' Derive whether a winding plan fits its physical bobbin.
FUNCTION CoilGeometry(turns, channelMm, coatedWireMm, bobbinDepthMm)
    turnsPerLayer = MAX(1, FLOOR(channelMm / coatedWireMm))
    layers = CEIL(turns / turnsPerLayer)
    windingDepth = layers * coatedWireMm

    RETURN {
        "TurnsPerLayer": turnsPerLayer,
        "Layers": layers,
        "WindingDepthMm": windingDepth,
        "Fits": windingDepth <= bobbinDepthMm,
        "HeadroomMm": bobbinDepthMm - windingDepth
    }
END FUNCTION

solution = CoilGeometry(8000, 56, 0.063, 10)
PRINT solution.Fits
PRINT solution.WindingDepthMm

Construction remains editable

The pickup specification retains bobbin dimensions, pole geometry, rail geometry, magnet material, cover and shielding choices, wax potting, coil taps, conductors, per-voice turns, and active electronics. Presets can seed a design but do not replace the underlying model.

Measured pickup profiles can later refine empirical magnetic and inductance factors without changing the language of the construction specification.

When a spec has to survive contact with a bobbin

American Wire Gauge tables and turns-to-inductance math are specific to winding a coil. Almost no other project will solve exactly this equation. What is worth taking is how a target got checked against physical reality before being accepted as a design.

The same discipline governs any solver that has to respect a physical or structural constraint: a bin-packing algorithm that has to report when items do not fit rather than truncating silently, a build system that has to fail loudly when a dependency graph does not resolve instead of guessing. A calculation that cannot fail honestly is not actually checking anything.

Treat "does it fit" as a first-class output, not an afterthought. CoilGeometry returns Fits and HeadroomMm alongside the numbers a designer wanted, so a plan that does not physically work is caught by the function itself.
Let later geometry feed back into earlier estimates. Winding depth changes the mean circumference of later turns, which changes wire length and achieved resistance, so the solver refines its own inputs instead of computing everything in one static pass.
Surface disagreement as an explicit warning, resistance error, inductance error, overflow, rather than silently returning the nearest available answer and letting a builder discover the mismatch on the bench.
Keep every intermediate value physically meaningful and unit-carrying, turns per layer, winding depth in millimetres, so a design problem traces to the exact step that caused it instead of just "the final number looks wrong."

LEARNING LAYER

Key terms, in plain language

You do not need a systems background to follow the work. These are the specialized terms used on this page.

AWGAmerican Wire Gauge: A standard for wire diameter. Pickup winding wire gauge affects resistance per unit length, turns per layer, total fit, and construction choices.
DCRDirect Current Resistance: The resistance of a pickup coil measured with steady current. It reflects wire length and gauge, but it does not describe the pickup’s complete frequency response.
Inductance: An electrical property of a coil that opposes changes in current. Together with capacitance and resistance, it helps determine a pickup’s resonant character.
Capacitance: The ability to store electrical charge. Pickup winding capacitance, cable capacitance, and the connected load all affect high-frequency response.