Presets
Playback
Apparatus
Time acceleration only changes how fast the clock runs: a real run takes about a minute.
Wiring
Model checks
The science
What is modelled
Two streams of drops fall from grounded nozzles. Each stream passes through a metal ring connected to the bucket of the other stream. A ring at potential V induces charge of opposite sign on the forming drop, which then falls into its bucket. Because the rings are cross-connected, every bucket charges the ring of its neighbour: a tiny seed voltage grows exponentially until a spark equalises the buckets.
Equations
- Charge induced per drop
q = -k Ci Vring / (1 + |V|/Vs), bucket voltage stepΔV = q / Cb. - For small voltages the antisymmetric mode grows as
eλtwithλ = g r e-λ T - 1/τ,g = k Ci/Cb, drop rate r, fall time T. - Humidity leakage
τ = 230 exp(-0.041 (RH - 20))s (heuristic). - Spark when the gap field reaches the breakdown value; energy
E = ½ Ceq ΔV².
Checks run in the page
- Simulated growth rate against the linear-theory root of the equation above (15 %).
- Leakage decay with the water off against
exp(-t/τ). - First spark at or just above the threshold with the right energy.
Honest simplifications
Drops are charge packets with a fixed fall time, the induction capacitance is a single lumped number and the saturation term is empirical. Real droppers depend on drop break-up, stray fields and surface conduction; the humidity law is a heuristic, not a calibration.
What to try
- Watch the log graph: the straight line is exponential growth, its slope matches the dashed theory.
- Switch to Straight wiring: the voltages stay near zero because feedback becomes negative.
- Choose Humid day: leakage beats the charging and nothing builds up.