Without Lord Kelvin, there would have been no D-Day.
There's some very cool science history in the September issue of Physics Today, centering around a collection of analog computers, developed in the 19th century to predict tides. This was a job that human mathematicians could do, but the computing machines did the job faster and were less prone to small errors that had big, real-world implications. David Kaplan, an assistant professor in the University of Wisconsin-Milwaukee physics department, sent the links over. He says that these machines ended up being crucial and are a big, in-your-face reminder of the complications of living in a world without calculators:
"... it was particularly important during WWII in order to properly plan beach landings, but even without the war part I found it fascinating. We take this so for granted now, that we can crank out sin() and cos() values instantly, but that was not always the case."
We're talking about predictions a bit more precise than simply saying, "the water is low" or "the water is high." Physics Today explains why the behavior of tides was so important at D-Day and why the tide calculators were so important to Allied success.
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.
You can read more about tide predicting machines on Wikipedia, and try out a Java simulation of Lord Kelvin's tide predicting machine at the American Mathematical Society website.