Tide prediction and D-Day

The September issue of Physics Today has an excellent article on the use of analog (i.e., physical as opposed to electronic) computers to predict tides during World War II, and in particular during the planning of D-Day:

Farquharson became responsible for finding a way to provide Doodson with the harmonic constants—or the data to calculate them—he would need for making accurate tide predictions for the landing beaches. But because of extremely tight security, Farquharson could not tell Doodson the biggest secret of the war—that the landings were to take place in Normandy. So he labeled the coastal location to which a particular set of harmonic constants or tidal data belonged with a code name. And he, in Bath, and Doodson, in Liverpool 200 km away, used those code names in their exchange of letters and telegrams.

To produce accurate tide predictions for the Normandy beaches, Doodson ideally needed accurate harmonic constants calculated from tide data measured at or very near each landing beach. But the British had no such data. The only harmonic constants they had were for the two French ports that bracketed the beaches: Le Havre to the east and Cherbourg to the west. Simple interpolation would not work, because shallow-water conditions varied from place to place. Shallow-water distortion of the tide can speed up the rise from low to high water, giving demolition teams less time to do their work. Very accurate shallow-water tidal data from the beaches themselves were therefore essential.

The 1943 Admiralty Tide Tables did include three locations near the Normandy beaches. But all three were secondary stations, and the tables contained warnings about the probable inaccuracy of predictions for those locations. Now Farquharson desperately needed tide data direct from the invasion beaches. So British teams in small boats and midget submarines carried out several secret midnight reconnaissance missions on the enemy beaches. Those dangerous missions did yield a few tide and current measurements, but much less than is normally required for tidal analysis.

On 9 October 1943, Farquharson sent Doodson a three-page handwritten letter marked “MOST URGENT” (see figure 3). It included 11 pairs of harmonic constants for the location code-named “Position Z.” He asked Doodson to produce hourly height predictions for four months commencing 1 April 1944. “The place is nameless and the constants inferred,” he wrote. “There is in fact very little data for it. I am gambling on the inferred shallow-water constants giving something like the right answer.”

The next time I'm stressing out about slow computation / missing data / coding difficulties, I'm going to stop, breathe, and say "well, at least I'm not trying to figure out how to land 160,000 soldiers on a beach at a specific point in the tidal cycle at a specific time of day so that we can defeat the Nazis."

hat tip: Maggie Koerth-Baker of boingboing