Playback
Presets
Parameters
Model checks
The science
What is modelled
Current in the coils pulls the armature lever toward the magnet cores; a return spring lifts it again when the key opens. The lever hits a lower stop (a click) when the key closes and an upper stop (a second click) when it opens, so the operator hears the rhythm of the message.
Equations
J θ̈ = −k(θ − θ_open) − c θ̇ − F(I, gap)·ℓ with F = C·I²/(gap + 4 mm)² and gap = 3 mm + ℓ·θ. Morse timing: a dit lasts 1200/WPM ms, a dah 3 dits, gaps 1, 3 and 7 dits, so PARIS takes exactly 50 units.
Honest simplifications
A lumped rigid-lever model with a simplified magnetic force law (no coil inductance, saturation or eddy currents) and inelastic stops; the angle is drawn exaggerated. The mechanism is a historically informed composite, not a specific museum object.
Built-in checks
Pull-in against the spring at the closed position, the spring release time against a damped-oscillator quarter period, and the Morse timing standard.