How do you land 140,000 allied troops on an 5-mile long stretch of beach under heavy German bombardment? Very carefully. And to ensure the deployment of forces without stranding landing craft—while juking Field Marshal Rommel out of his sneakers—the Allies employed these machines to predict the height of the tides on D-Day.
These purpose-built analog calculators were first developed in the late 19th and early 20th century. Their primary, well, only purpose was to mechanically replicate the tedious, laborious, and often error-prone task of calculating the tides—much like the early precursors to Excel eliminated the massive workload that analog spreadsheets required. These machines could predict the time and height of the tides hours, days, months, or more in advance.
Tidal prediction stems from Newton's Principia—published in 1687—that applied gravitational theory to estimate the effects of the Sun and Moon tugging on the Earth's oceans. By the 1770s, mathematician Pierre-Simon Laplace expanded Newton's work by integrating tidal motion into the equation. This was a significant step forward, but was still really just an approximation of the tidal positions rather than a proper prediction.
In the 1860's, William Thomson (aka the 1st Baron of Kelvin) applied Fourier analysis to tidal motion equations. This extrapolation was then expanded by George Darwin, who applied recently revised Lunar theory. By the late 19th century, mathematician AT Doodson updated the theory with even more recent advances in lunar theory by E W Brown. The theory has changed little since then.
The essential function of a tidal prediction machine is to convert rotary motion into sinusoidal motion—which the tides operate on. Think of high and low tides as roughly equivalent to the peaks and troughs of a Sin graph.
To create this effect in real life, a drive wheel is employed with an off-center peg that fits into a vertical slot on the machine you see above. As the wheel rotates, the peg moves up and down as it travels around the drive wheel's axis—creating a sinusoidal motion. Essentially, the time that a tide would hit a certain height (i.e. the peg's height in the vertical slot) could be determined by measuring how far the drive wheel has been cranked.
These ingenious machines were being used for official tidal predictions and navigation well before WWI. They proved their mettle during the first Great War and were subsequently deemed so valuable that during the second that the US classified their very existence. They were most famously used to predict the tides along Omaha beach, a 5-mile strip of French beach with a tidal difference (the height variation from high and low tide) of nearly six meters. That's a big difference when you're slogging up an extra 14 feet of sand with German pill boxes raining leaden death from the overhead bluffs. As Physics Today describes,
As an Allied cross-channel invasion loomed in 1944, Rommel, convinced that it would come at high tide, installed millions of steel, cement, and wooden obstacles on the possible invasion beaches, positioned so they would be under water by midtide.
The Allies would certainly have liked to land at high tide, as Rommel expected, so their troops would have less beach to cross under fire. But the underwater obstacles changed that. The Allied planners now decided that initial landings must be soon after low tide so that demolition teams could blow up enough obstacles to open corridors through which the following landing craft could navigate to the beach. The tide also had to be rising, because the landing craft had to unload troops and then depart without danger of being stranded by a receding tide.
There were also nontidal constraints. For secrecy, Allied forces had to cross the English Channel in darkness. But naval artillery needed about an hour of daylight to bombard the coast before the landings. Therefore, low tide had to coincide with first light, with the landings to begin one hour after. Airborne drops had to take place the night before, because the paratroopers had to land in darkness. But they also needed to see their targets, so there had to be a late-rising Moon. Only three days in June 1944 met all those requirements for "D-Day," the invasion date: 5, 6, and 7 June.
All of these constraints were taken into account during the planning of the Invasion of Normady. And only through the careful coordination of military might and natural rhythm was the assault a success.
But the military's interest didn't stop there. Mechanical tide predicting machines remained in vogue until they were dethroned by the advent of digital computers—even then, they remained in active service until the early 1970's.
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