Resistive sheet (Teledeltos) Laplace solver

Realizes: solutions to Laplace's equation ∇²φ = 0 (electrostatics, heat, groundwater flow)

A sheet of Teledeltos — carbon-coated resistive paper with ~6 kΩ/square resistivity — conducts current that obeys the same Laplace equation as electrostatic potential, steady-state heat conduction, inviscid fluid flow, and Darcy groundwater seepage. Boundary conditions are imposed by painting silver-loaded conductive ink in the shape of conductors or flow boundaries; a voltage is applied across them. A probe voltmeter scanned over the sheet reads the potential field directly. Complex 2D geometries that would require days of PDE numerics can be mapped in hours. Widely used from the 1930s through the 1970s in capacitor design, transformer core analysis, dam seepage studies, and aircraft aerodynamics before finite-element codes displaced it. Speed: hours for full field map (manual probe scanning); boundary setup in minutes. Capacity: 2D scalar field on arbitrary domain geometry; ~1-2% accuracy.

Examples

Teledeltos — Wikipedia

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What's All This Teledeltos Stuff, Anyway? — Electronic Design

Practical history of Teledeltos paper as an analog field plotter for electrostatics, heat flow, and fluid mechanics problems

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