Tides of War, Part One

The best-known story about environmental science and D-Day has to be that of the last-minute forecast that let the invasion go ahead. That prediction, though, was only one of many contributions by Allied environmental scientists to the success of the invasion. Another was the secretive preparation of mundane but vital preparations for the assault: calculating the tides for D-Day.

The theoretical basis for tide prediction was the work of Newton, Daniel Bernoulli, and Pierre Simon Laplace, the third of whom was the first to outline the equations that describe the rise and fall of the tides. Laplace’s equations were too complex to use in practice, but in the mid-nineteenth century the British scientist William Thomson (later ennobled as Lord Kelvin) demonstrated that, given enough tidal measurements, one could use harmonic analysis to divide the tide-generating forces for a particular shoreline into a series of waves of known frequencies and amplitudes (the tidal constituents). That same process, carried out in reverse, would let one predict the tides along that shore. Unfortunately, making those calculations was was time-consuming the point of impracticality. However, Thomson also demonstrated that it was possible to construct an analog machine that would do the necessary work automatically.

Thomson’s machine drew a curve representing the height of the tide with a pen that was attached to the end of a long wire. The wire ran over top of a series of pulleys, which were raised and lowered by gears which reflected the the frequency and amplitude of the tidal constituents. As each pulley rose or fell, it affected the length of the wire’s path and thus the position of the pen. Altogether, they reflected the combined effect of the tidal constituents being simulated.

Thomson's design sketch for the third tide-predicting machine, 1879. Image courtesy Wikimedia.

Thomson’s design sketch for the third tide-predicting machine, 1879. Image courtesy Wikimedia.

The first machine, built in 1872, had gears for only ten constituents, but later machines could represent many more. Machines of his design, many of them built in Great Britain, were also used in other countries to create the necessary tide tables for their ports. In the United States, a different mechanical approach developed by William Ferrel was used to build similar machines. Altogether, though, tide-predicting were specialized, expensive, and rare. According to a modern inventory, only thirty-three were ever built – twenty-five of them in London, Glasgow, or Liverpool.

During the Second World War, the Admiralty Hydrographic Office relied on two tide-predicting machines operated by Arthur Thomas Doodson at the Liverpool Tidal Institute to do all their tidal calculations. One was Thomson’s original machine, refitted to handle twenty-six constituents. The other was a machine designed by Edward Roberts in 1906 and equipped for forty constituents.

Both Doodson and the Tidal Institute had their own unique histories of military collaboration. Doodson, despite being a conscientious objector, had worked on anti-aircraft ballistics for the Ministry of Munitions during the First World War. The Institute, established in 1919 with corporate and philanthropic support, had an important connection with the Admiralty’s own Hydrographic Department. Though the Hydrographic Department did not provide any direct funding until 1923, after that it made the Institute the Admiralty’s exclusive supplier of tide calculations. At the same time, the Hydrographic Department began appointing a representative to the Institute’s governing board.

Though they were the basis for only some of the Institute’s Admiralty work during the war, the tide-predicting machines in Liverpool were busy creating tide tables for Allied ports. According to historian Anna Carlsson-Hyslop’s research, the number of tidal predictions being performed doubled from 77 for 1938, the last pre-war year, to 154 for 1945. (Carlsson-Hyslop’s research is focused on areas of the Institute’s work other than the creation of tide tables, but much of it sheds light on its relationship with the Royal Navy and state patronage.)

In 1943 the Admiralty Hydrographic Office requested calculations to create tide tables for the invasion beaches to be used on D-Day in Normandy. Since the landing zone remained top secret, Commander William Ian Farquharson was responsible for establishing the constituents and providing them (anonymized under the codename “Point Z”) to Doodson in Liverpool. Unfortunately, there were no existing calculations for the area of the beaches. Nor, because tidal constituents were sensitive to local conditions, could he just extrapolate from the data for the ports to the east and west at Le Havre and Cherbourg. Instead, Farquharson combined fragmentary data from some local measurement points near the beaches, clandestine on-the-spot measurements made by Allied beach reconnaissance teams, and guesswork to come up with eleven tidal constituents. Oceanographer Bruce Parker suspects that he began with the Le Havre constituents and then adjusted them to approximate the data he had. The calculations, despite the roughness of the information on which they were based, proved sufficiently accurate for the invasion planner.

In the Pacific, tide tables for amphibious operations were generated by the US Coast and Geodetic Survey’s Tide Predicting Machine No. 2. In both theaters, as well as the Mediterranean, oceanographers supplemented the tide tables for beaches with wind, wave, and surf forecasts. The story of wave forecasting is, if anything, even more cloak and dagger than that of the D-Day tide forecasts, since one of the scientists involved was actively suspected (incorrectly) of being a Nazi sympathizer.

Dr. E. Lester Jones, Chief, U.S. Coast and Geodetic Survey, with the Tide Predicting Machine he built. Harris & Ewing, photographer, 1915. Retrieved from the Library of Congress, https://www.loc.gov/item/hec2008004303/

A US tide predicting machine, probably No.2. The caption from the Library of Congress attributes the machine’s construction to E. Lester Jones, Chief of the Coast and Geodetic Survey. Harris & Ewing, photographer, 1915. Retrieved from the Library of Congress, https://www.loc.gov/item/hec2008004303/

Beyond their civilian and military wartime work, tide-predicting machines had an oblique impact on Second World War cryptanalysis. Those developments would eventually put the machines out of work after the war, but not before the machines would have their final strategic significance.

Forward to Part Two, including Source Notes

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