A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: How Many Chronometers?
From: Gary LaPook
Date: 2009 Sep 15, 10:24 -0700
From: Gary LaPook
Date: 2009 Sep 15, 10:24 -0700
It wouldn't seem that motion would affect their rates. They have spent the last 110 days next to each other in a cabinet where the temperature is pretty constant. According to the recording thermometer in the room, the temperature stayed in the range of 66� to 82� F. But since I didn't think ahead, I didn't reset the memories in the thermometer when I started the experiment so the recorded temperature range actually covers a longer period of time than the 110 days so the temperature swings experienced by the watches might have been somewhat less but I have no way of knowing. To deal with the temperature issue, place the three watches in a small box with some kind of insulation (or wrapped in a blanket) to smooth out temperature swings and keep it below decks which is where chronometers were traditional kept. gl On Sep 15, 9:09�am, Lu Abel
wrote: > Gary: > > A fascinating experiment and experimental confirmation of my long-held > belief that even the cheapest digital watch makes a superb chronometer. > > Now a challenge for anyone wanting to repeat the experiment or extend > the results: > > 1. � Take the "watch board" and simulate motion. � Okay, maybe we can't > take it to sea but maybe drive it around town with us? > > 2. � Vary the temperature. � Maybe put the board outside in direct > sunlight (and rain and maybe even snow). > > Remember, Harrison's biggest challenge was not making an accurate > chronometer (that had been done already) but rather making one that > remained accurate despite the motion and temperature changes experienced > at sea. > > Whoops, as I write this I'm looking at my digital watch on my wrist and > watching it bounce around. � Maybe experiment #1 isn't required. � In > fact, the very nature of digital watches should make them > motion-insensitive (excluding relativistic effects :-P ). > > Lu Abel > > Gary LaPook wrote: > > Based on our discussion, I became curious about the accuracy of digital > > watches and their suitability for use as chronometers so I went to my > > local TARGET store and purchased three identical watches for $17.00 > > each, the cheapest that they had. I set them and let them run for a few > > days and, as I expected, they each had different rates. Based on this I > > labeled them "A", "B", and "C" in the order of their rates starting with > > the slowest. I then reset them to UTC at 0121 Z on May 28, 2009. I > > checked them against UTC from WWV eleven days later on June 8th and > > found that they were all running fast by 2, 4 and 7 seconds respectively > > and I worked out their daily rates as .1818, .3636, and .6363 seconds > > per day, respectively. > > > On July 11th, 44 days after starting the test, the watches were fast by � > > 9, 17 and 28 seconds. Using the rates determined in the first 11 days > > the predicted errors would have been 8, 16 and 28 amounting to errors in > > prediction of 1, 1, and 0 seconds. If using these three watches for a > > chronometer we could average the three errors and end up with only a .66 > > second error in the UTC determined by applying the daily rates to the > > three displayed times after 33 days from the last check against WWV > > which took place on June 8th. > > > I determined new rates now based on the longer 44 day period of .2045, > > .3864 and .6363 seconds per day, respectively. > > > On September 15th at 0800 Z (per WWV), 110 days after starting the > > test, �I took a photo of the watches which I have attached. The photo > > shows the watches fast by 21, 41 and 69 seconds but by carefully > > comparing them individually with the ticks from WWV the estimated actual > > errors are 21.5, 41.8 and 69.0 seconds. Using the 44 day rates, the > > predicted errors are 22.5, 42.5, and 70 seconds giving the errors in the > > predictions of 1.0, 0.7 and 1.0 seconds which, if averaged, would have > > caused a 0.9 second error in the computed UTC after 66 days from the > > last check against WWV on July 11th. > > > If, instead, I used the 11 day rates then the predicted errors would > > have been 20.0, 40.0, and 70.0 seconds which would result in errors of > > prediction of -1.5, -1.8, and 1.0 which, if averaged, would cause and > > error in the computed UTC of -0.6 seconds after 99 days from the last > > check against WWV which would have been on June 8th in this example. > > > �From this experiment it appears that fifty one dollars worth of cheap > > watches would give you a perfectly adequate chronometer. > > > gl > > > ------------------------------------------------------------------------ > > --~--~---------~--~----~------------~-------~--~----~ NavList message boards: www.fer3.com/arc Or post by email to: NavList@fer3.com To unsubscribe, email NavListemail@example.com -~----------~----~----~----~------~----~------~--~---