This is a simulator of Kelvin’s tide predicting mechanism, highlighting the way in which the various tidal constituents contribute to the total water level. Nine constituents are summed here: M2, S2, N2, K1, O1, P1, K2, M4, and M6.

Select the amplitudes for a given port from the drop-down menu, then click run/pause to start and stop the animation; clicking step when paused advances the plot by ten minutes (slow) or half an hour (fast).

Horizontal lines on the chart are spaced one metre apart; the vertical lines are at 24-hour intervals.

In the simulations all the constituents start in phase – upper pulleys set to zero, and lower ones set to 180°. The typical character of a port’s tidal record will not be apparent until a plot of a week or longer is produced.

The semi-diurnal constituents (occurring twice a day, and denoted by the ‘2’ subscript) are: M2 principal lunar, S2 principal solar, N2 larger elliptical lunar, and K2 declinational lunar. Diurnal constituents are: K1 principal lunar and solar, O1 principal lunar, and P1 principal solar. M4 (four times a day) and M6 (six times a day) are shallow-water constituents.

Liverpool (and nearby Hilbre Island) has large semi-diurnal tides with a tidal range that can exceed 10m at spring tides. Tides at Southampton, while smaller, have prominent double high waters during certain stages of the neap to spring cycle.

The simulator is adapted from a Feature Column on ocean tides of the American Mathematical Society with software originally by Bill Casselman, University of British Columbia. Modifications for this presentation: units, constituents, locations, direction of time.

The following constituent amplitudes (in metres) are available in the simulator: