TIDE ENGINE
This is a working model of a tide-predicting machine , the mechanical computers that produced the world's tide tables from 1876 until the 1960s. Lord Kelvin built the first with 10 constituents; NOAA's "Old Brass Brains" (Tide-Predicting Machine No. 2, 1912) carried 37 and ran the US tables until 1965. Everything on this page is computed the way those machines computed it, and drawn the way their patents were: in ink, on paper.
How it works
The tide at a place is a sum of cosines: h(t) = Σ f·A·cos(V(t) + u − κ). Each term is a constituent : a fixed astronomical frequency (the Moon's semidiurnal tide M2, the Sun's S2, the lunar-declination tide K1…) with an amplitude A and phase lag κ measured at the station. The main shaft turns once per mean solar day. Each station's gear train turns a crank at its constituent's speed (tooth counts chosen so (a/b)·(c/d)·(e/f) lands within about a millionth of the true ratio). The crank pin drives a scotch yoke , so the pulley rises and falls as a pure sinusoid whose amplitude is the crank throw. One wire runs over every pulley and under a fixed idler between each pair: lift any pulley and the wire takes up twice the lift. The free end carries the pen , so the pen's height is the sum of every pulley's height — a mechanical Fourier synthesizer. The paper is driven from the same shaft.
Before a run the operator "sets" the machine: each crank's throw is f·A and its phase is V(t₀)+u−κ for the starting date. Here that happens automatically at each New Year (nodal factors f, u for the 18.6-year lunar-node cycle are taken at mid-year, as NOAA did) or when you press Re-set cranks . After that only the gears keep time, so the machine drifts by its gear errors — hover a station to see them.
What's real
Harmonic constants are NOAA CO-OPS accepted values (epoch 1983–2001), public domain, via the Neaps tide database . Equilibrium arguments use Meeus' mean longitudes; nodal corrections use Schureman's exact formulas. The wire is solved as tangent lines and arcs of contact, and the pen sits where the wire's length puts it; the trace on the paper is that pen, not a formula. The machine agrees with a direct digital evaluation to a few millimeters over a year, and the digital evaluation agrees with an independent predictor to about 2 mm.
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Any CO-OPS station with published harmonics. Needs the NOAA API to be reachable from your browser.
Not for navigation. Predictions ignore weather, surge and the fact that it is not 1912. Check the official tables before attempting a bar crossing.
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