This article has been adapted from Chapters 1 and 3 of my research project entitled ‘An historic analysis of tide prediction machines using an adapted prosopographic approach and digital humanities tools’, which I wrote during the first year of my Master’s degree. A copy of the full text can be found at: http://doi.org/10.5281/zenodo.3265011.

What are tide prediction machines?

Tide Prediction Machines are analogue computers that were used to predict the times of high and low tides worldwide from the end of the 1800s up to the digital age. The first tide prediction machine was designed by William Thomson (1824–1907), and was built in London in 1873. It was developed as a response to increasing pressure from commercial shipping lines towards the middle of the nineteenth century who wanted a greater number of more accurate tidal predictions more quickly than could be calculated by hand. As well as helping shipping lines and navies to safely navigate the seas and the shores, tide prediction machines became crucial to the building of ports and effective flood defences. A total of 25 of the 33 tide prediction machines ever built were constructed in the UK but were then shipped to other countries who wanted to do their own calculations.

How do you calculate tidal predictions?

Tidal observation refers to the act of continuously measuring the height of a body of water at any one location, usually using a tide gauge, to produce a set of tidal observations. Such sets of tidal observations are key to calculating predictions of future (or past!) tides using the harmonic method of tidal analysis.

The harmonic method of tidal analysis uses a set of tidal observations for any given location to isolate and identify every factor, known as a constituent, that contributes to the tides there (Pouvreau 2008, p. 37). Each constituent is related to a different lunar or solar frequency with a known period T. The harmonic analysis allows for each constituent to be broken down into harmonic constants: an amplitude A and a phase φ, which are dependent on the chosen location. Inversely, harmonic tidal prediction involves summing each individual constituent that contributes to the tides at a chosen location and therefore requires the harmonic constants for that location to have already been calculated. The more constituents taken into account in the calculation, the more accurate the prediction will be. Tide prediction machines use the harmonic method of prediction to calculate the times and heights of high and low tides at any moment in time and at any location in the world, provided the corresponding harmonic constants are known.

The equation above shows the equation that tide prediction machines were designed to calculate (Bell 1962, p. 1; Woodworth 2016, p. 6). It sums over a finite number N of constituents i as a function of time t, where A_i is the amplitude of the constituent i, ω_i = 2π ∕ T_i is the angular speed of the constituent i for which T_i is the period of the corresponding lunar or solar frequency, and φ_i is the phase of the constituent i. The equation gives as an output H(t), which is the height of the water above (H(t) > 0) or below (H(t) < 0) the mean water level at time t. The times t at which the maxima and minima of H(t) occur are the times of high and low tide respectively. The height of the water at any time is given by H(t) + H₀, where H₀ is the mean water level.

How do tide prediction machines work?

Tide prediction machines are made up of a system of pulleys, shown the photograph below, each representing a different constituent. The pulleys simultaneously oscillate vertically and rotate. The period of each constituent is pre-programmed into the corresponding pulley, and the amplitude and phase of each pulley is set by the machine operator according to the harmonic constituents for the chosen location. A wire wound around the pulleys allows for the movement of the pulleys to be added, giving the output of the total rise or fall of the tide above the mean water level as a function of time for the programmed place. Not all tide machines were built the same but most operated on this principle and gave the outputs in the form of graphs, on dials or in displays.

Bibliography
Bell, W. H. (1962). Tide Predicting with TIDAC. en. Tech. rep. 130. Nanaimo: Pacific Oceanographic Group, Fisheries Research Board of Canada, p. 18.
Pouvreau, Nicolas (2008). ‘Trois cents ans de mesures marégraphiques en France : outils, méthodes et tendances des composantes du niveau de la mer au port de Brest’. fr. Doctor of Philosophy. La Rochelle: Université de La Rochelle.
Woodworth, Philip L. (2016). An inventory of tide prediction machines. en. URL: http://nora.nerc.ac.uk/id/eprint/513660 (visited on 10/10/2018).

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