The position of a watch influences accuracy (2020)

These days I've got watches ranging from the low-end Casio Terrorist Watch to mid-range Rolexes, and a lot in between, and they typically come in boxes or cases without a stand of any kind.

And, of course, clock accuracy is even more critical now in the age of GPS.

Specifically:

> One degree of latitude equals approximately 364,000 feet (69 miles), one minute equals 6,068 feet (1.15 miles), and one-second equals 101 feet. One-degree of longitude equals 288,200 feet (54.6 miles), one minute equals 4,800 feet (0.91 mile), and one second equals 80 feet.

* https://www.usgs.gov/faqs/how-much-distance-does-a-degree-mi...

> One minute of latitude covers about 1.8 kilometers (1.1 miles) and one second of latitude covers about 32 meters (105 feet).

* https://education.nationalgeographic.org/resource/latitude/

When using a sextant:

> Sextants measure the angle between the sea horizon and a celestial body. These angles are measured in degrees and minutes of arc (1/60th of a degee). Measuring this angle to an accuracy of 1 minute of arc (1') will result in a positional accuracy of 1 nautical mile. Accurate sextants can measure this angle to an accuracy of 0.2'. This means that theoretically one can determine their position to 1/5 of a mile [~320m]. Additionally, a good clock is required to accurately compute the GP of the celestial body. An error of 1 second in the clock will create a positional error of up to 1/4 of a mile [~400m].

* http://www.cse.yorku.ca/~amana/personal/navigation/

Airplanes also used to use sextants for trans-oceanic flights (when beyond radio beacon range). Part 63 of FAA regulations has a section on Flight Navigators:

* https://www.ecfr.gov/current/title-14/chapter-I/subchapter-D...

Doing a search for FAA-H-8083-18 will lead you to The FAA Flight Navigator Handbook.

1. Set up a big transmitter in some major city that fires off a big noisy pulse at every day at solar-noon.

2. Equip your long-distance ships with mediocre clock and a radio-receiver that is just good enough to detect the pulse if a crewmember is waiting and listening for it.

3. Using the low-accuracy clock, measure the difference between (A) solar noon where the ship is and (B) when the radio-pulse is received. Every 4 minutes is 1 degree of longitude.

P.S.: The pulse-listener will have to shift their listening-window as the ship travels, but it shouldn't be too tough since they already have a so-so clock and know their latitude. Sailing 200km/day along the equator means the pulse-listener would have to adjust their listening-window by ~8 minutes/day to keep "centered" on the pulse moment.

I wonder if that fact inspired the mysterious and bizarre Guild Navigators in Dune.

At the end of the day, he would check if the watch had gained or lost time during the day (compared to the broadcast bell chimes radio stations used to broadcast on the hour).

Based on the observation he would set the watch on its right side or left for the night, causing the spring in the self winding mechanism to be slightly more or less tensioned, leading to a slight gain or loss of time by morning to tune the watch to the precise broadcast signal.

The most accurate quartz movements drift by around 5 secs a year. Chip scale atomic clocks are accurate to around 37ms a year.

Current chip scale atomic clocks are still a little too big for watches, but some applied creativity might change that.

Personally I don't care about clockwork, but I think having an atomic clock on your wrist would be quite cool.

It's said that George Daniels could make mechanical watches that were more accurate than the quartz watches of his day[1], 0.4 seconds per year.

Of course that doesn't really matter if the thing is a priceless work of art that no one can afford to wear day to day but it's still really interesting to know how he did it.

Quartz watches' real advantage is just their accuracy but that they are accurate and cheap to make. There's something rather wonderful about a practically disposable Casio like a Bic Biro.

1. https://www.sothebys.com/en/articles/george-daniels-the-worl...

2. https://www.danielslondon.com/daniels-watches/the-space-trav...

'Luxury Software' hasn't become a thing (beyond ludicrously priced free-to-play whalebait)