Sweet LORAN

Country Joe & The Fish "Not So Sweet Martha Lorraine"
The story about Eddie Rickenbacker ditching in the Pacific Ocean during WW2 got me to thinking: just how did those guys navigate back then? My dad was a gunner on a B-24 bomber during WW2 in the Pacific. Raids in the Pacific were very different than the ones in Europe. The ranges were much farther and navigation was much more critical. In Europe you head vaguely southeast from England for a hundred miles and you were over enemy territory. Drop your bombs and turn around, head northwest and in short order you will be over England which was littered with airfields. In the Pacific, if you screw up one number 3 places to the right of decimal point when plotting your return flight and you could easily miss your destination completely and end up like Eddie, floating around in the Pacific hoping someone comes looking for you.


History of the LORAN System
Excerpted from a 1947 Coast Guard film
They started with the same tools mariners had used for the last couple hundred years: a sextant, a compass and a chronometer. In Europe they soon got LORAN which was another one of those super-top secret projects, like the Norden bombsight, the proximity fuse, the atomic bomb and the code breakers at Bletchley Park. The original LORAN was only good for about 750 miles. It was superseded by LORAN-C and now by eLORAN. From the map shown at the end of the video, I surmise that they didn't get LORAN in the Pacific until very late in the war, and even then it didn't cover much of the area.


Lines plotted from difference in distance to points A and B.
LORAN is kind of weird. You need at least three base stations in order to get a good fix. The base stations all send out a periodic pulse, and they all do it simultaneously. You measure the difference in time between when you receive the pulse from two different stations, and that will place you on a line. Do that for a different pair of stations and you get a different line. Plot the two lines on a chart and their intersection is your location. Since radio waves travel at the speed of light, your timing needs to be critical. Light travels about one foot in one nanosecond (one billionth of second), so in a microsecond, it travels about one thousand feet. So if you can measure the arrival time of the pulses to the nearest microsecond, you can determine your location within a thousand feet, which for navigating across the ocean is fine.


MathLapse: Constructions by pin-and-string: conics | Construções de fio esticado: cónicas
Hyperbola starts at 1:45
LORAN is often called a "hyperbolic navigation system", but all that means is that the lines you plot on the charts are hyperbolas.

You can see about 200 miles from a B-24 flying at 25,000 feet.

P.S. Thinking about LORAN must have triggered my memory of Sweet Loraine. There is another version of the song sung by several people, but the one by Country Joe is the one I remember. I don't know where they got Martha from.