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Harmonic Tide Synthesizer

This is what a tide-predicting machine does — with the brass removed. Set each constituent's amplitude and phase below, exactly as an operator set crank pins with a spanner (see the 1910 setup ritual), and the viewports draw what the machine's wire-and-pulley adder would have summed (how the adder works). The mathematics behind it is explained in Harmonic Analysis: Kelvin to Doodson.

1 · Set the constituents

Amplitude in metres, phase in degrees. Periods are locked — the moon refuses round numbers, as the gear primer explains.

2 · Watch the waves add

Top viewport — each constituent waves alone at its own locked period.

Bottom viewport — the sum: your predicted tide. The gold line marks the travelling present moment.

Span:

3 · Run the machine

The virtual pen plotter: press run and a brass pen draws your synthesis onto a rolling paper strip, hour ticks and all — the way real prediction rolls were made.

Press run to start the machine.

4 · Take it with you

Free for schoolwork and papers with a link back.

Try this

Make a spring tide: set M2 and S2 phases equal. Watch the range swell — the mechanism from springs vs. neaps.
Make a neap tide: set S2 phase 180° away from M2. The sea goes slack.
Make a Gulf-of-Mexico day: zero M2 and S2, raise K1. One tide a day — see Why 37? for why.

Workshop questions

Is this how the real machines computed?
Yes in mathematics, no in medium. The machines added continuous shaft motions through floating pulleys; this page adds the same cosines digitally. Same sums, different century.

Why only four constituents?
Four waves teach 90% of the physics and keep the bench readable. Real machines carried up to 37 — the full cast is named in Why 37?.

Can I use the exported figure in a paper?
Yes, with attribution and a link to this page, under the Terms of Use.