Tide prediction machines at the Liverpool Tidal Institute

Abstract

Abstract. The 100th anniversary of the Liverpool Tidal Institute (LTI) was celebrated during 2019. One aspect of tidal science for which the LTI acquired a worldwide reputation was the development and use of tide prediction machines (TPMs). The TPM was invented in the late 19th century, but most of them were made in the first half of the 20th century, up until the time that the advent of digital computers consigned them to museums. This paper describes the basic principles of a TPM, reviews how many were constructed around the world and discusses the method devised by Arthur Doodson at the LTI for the determination of harmonic tidal constants from tide gauge data. These constants were required in order to set up the TPMs for predicting the heights and times of the tides. Although only 3 of the 30-odd TPMs constructed were employed in operational tidal prediction at the LTI, Doodson was responsible for the design and oversight of the manufacture of several others. The paper demonstrates how the UK, and the LTI and Doodson in particular, played a central role in this area of tidal science.

How the Liverpool Tidal Institute was established: industry, navy and academia

“…This worked on both semidiurnal and diurnal tides and required fewer data from tidal gauges. This was further developed by George Howard Darwin (1845Darwin ( -1912 in the 1880s, again with BAAS support (Hughes, 2005;Cartwright, 1999;Woodworth, 2020). BAAS support of tidal research appears to have been important though intermittent.…”

“…The synthetic method, devised by John William Lubbock (1803-1865) (e.g. Lubbock, 1835) and developed with support from BAAS in the 1820s and 1830s, was still in use in the twentieth century despite recognised limitations for areas with particular types of tides -it works better in areas with semidiurnal (twice daily) tides than those with diurnal (once daily) tides (Reidy, 2008;Hughes, 2005;Woodworth, 2020). During the 1860s, William Thomson (Lord Kelvin, 1824-1907, working as part of a BAAS committee, and the American William Ferrel (1817-1891), independently developed the harmonic method of tidal analysis and prediction.…”

“…TI acquired its first tidal predictor in 1924, with an additional machine purchased in 1929 (Woodworth, 2020). The tidal predictors were used alongside general purpose calculating machines.…”

“…Doodson's work on the practices and technologies of calculation involved in tidal predictions meant he could manage a larger number of calculations than had been possible for Thomson, Darwin, and other earlier tidal analysts (Doodson, 1922, p. 218), as explained by Woodworth (2020;see also Carlsson-Hyslop, 2015). These practices and technologies were used to rework the earlier version of the harmonic theory, using mathematical analysis techniques learnt from former Cambridge students during his studies at Liverpool University, combined with computational analysis of tidal data (Doodson, 1924), using techniques developed in mathematical laboratories in London during the war.…”

Preface: Developments in the science and history of tides

“…These included presentations on tides at the EGU General Assembly in Vienna in April 2019 and the IUGG General Assembly in Montreal in July 2019. Events were also held locally to mark the LTI anniversary, including a large meeting for the public at the Merseyside Maritime Museum in May 2019 (Woodworth, 2020b) and in talks to Liverpool history groups.…”