How tide predicting, analog computers won World War II

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.


  1. I love learning about the technical backstory about events like D-Day because you gain a greater appreciation of the sheer complexity involved. In addition to the analog computers detailed here, there’s the man and computer power involved in intelligence gathering, the logistics, planning and engineering of the ships and supplies  used and countless of other factors all towards one event. It’s mind-blowingly complex and awesome.

  2. More fun with analog computers! If you like this, be sure to check out these Navy training films from 1953 on real-time mechanical computers used for firing guns on ships. 

    (part 1)

  3. There were other anolog computers at use in WW2. Onboard battleships, spotters at the prow and stern would use instruments to sight on an enemy ship, and thay had split-filed lenses that allowed them to determine distance by keeping the shot in focus. All this data was transmitted back to the fire-control center, which also tracked the vessel’s own motion through the sea. The analog system made minute changes in elevation of the big guns so that when they fired the ballistic arc would end up on the enemy vessel.

  4. @Eduardo Balsa:

    You do know that the 2nd of May in 1945 is not “a few days before” the 6th of June in 1944, right? It’s a whole eleven months after.

    In any case, no one is saying that the war ended with D-Day. But it’s highly improbable that the war could have been won without the success of D-Day.

    1. I mixed up the dates with the liberation of Leningrad [ 27 January 1944 ] where the tide (sic) changed.
      D-Day was not a victory against the nazis but a way to avoid the soviet union from taking over all of europe.

      1. Sorry…I can’t tell if you’re serious or I’m just not getting the joke.

        D-Day as an operation against the Soviets? Our allies during WWII? That’s a new theory. And what’s up with the “sic” for your own misplacement of “tied” where the word “tide” is called for? Why not just use the right word in the first place.

        I have a feeling someone’s yanking my chain.

  5. Not against the soviets, but to prevent them marching through Germany, and in to the rest of Europe.

    [btw … Sorry if my mother tongue is not English… we can speak in Portuguese if it’s easier for you to understand…]

    1. Your English is pretty good, but you may have missed that the headline was intentionally absurd.

      also, I understand your confusion re:Lenningrad.

  6. This guy Eduardo is trolling pretty hard. Stalin was NOT happy about having to fight for Stalingrad without any help, but he was able to pull it off at the cost of many Russian lives. The Allies’ effort in Italy, North Africa, and the Pacific were crucial to defeating the Axis powers. Theoretically, Russia *might* have been able to conquer all of Europe if the Allies wanted to throw up their hands and give everything away. It would have been more bloody and prolonged and uncertain. No one wanted that, including Stalin. The goal was to defeat Hitler’s Germany as quickly as possible so that people could rebuild and get back to normal life.

    Stalin even met with the other Ally leaders at the Tehran conference in 1943 to discuss how they would work together in a 2-front war and the future of postwar Europe.

    Stalin was still a “bad guy” and wanted to conquer and invade, but that didn’t make him any less of an ally. Given the likelihood of the Allies giving up basically all of Europe without any effort (which is to say, none), the only real offensive choice was to regain their own territory and get ready for the upcoming cold war. Even prior to Hitler invading Russia, their sites for conquest were on countries next to them like Finland, Poland, Austria, etc. Taking France and Spain would have been an incompetent decision even by Hitler’s standards (which is saying a lot).

    “Without American production the United Nations could never have won the war.” – Stalin

  7. In many ways, the secret weapons of the Axis were just better versions of existing stuff (even the V2 was just a super version of Artillery), but with the exception of the atomic bomb (and making a bomb more than 1000x as powerful as what had gone before is more than just better) Allied secret weapons were mostly informational and radical, from code breaking to microwave radar (which also made proximity fuses, without which the Japanese Kamakazis would have been much more effective), and these are just further examples, even night vision gear was used by Allied troops in WWII (P-61 night fighters had it in the Pacific).

    The only “super” weapon our troops had was the M1 Garand rifle (first semi auto service rifle in widespread use).

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