I’m kind of reluctant to add much more explanation to the title, honestly. Anyone who’d be able to answer would probably understand it immediately. 
But, to be thorough—a question inspired by a few time travel/alternate history stories I’ve read, over the years…which would be the better, even superior Marine Chronometer; Harrison’s “H4” from 1761, or a $10 Casio wristwatch bought at a drugstore today? We’ll assume the Casio has fresh batteries, for the record.
Eh?
My feeling is that the 250-year-old chronometer would still be up to 10x better than a cheap-shit quartz wristwatch; have you tried measuing your Casio for a few months to determine its accuracy in at least one case?
I would be leery of using some random uncalibrated device as a master chronometer.
If we take an upper bound on H4’s worst performance as 1/2-second per day, that is still a little better than the Casio, though not an order of magnitude better. It’s actually comparable. Maybe if you calibrated a batch of Casios in advance, then took the 3 best ones with you, you could trust to them an ocean voyage.
Does anyone know what chronometers (and sextants) were used by the winners of the recent Golden Globe Race?
A temperature-compensated Real Time Clock chip like the DS3231 is guaranteed accurate to ±2ppm over normal environmental temperature.
That translates to ±16 seconds/year or ±1.3 seconds/month.
And these chips are about $6 ea.
So, “cheap” isn’t the issue…
The manual for your Casio says: “Accuracy at normal temperature: +/- 30 seconds a month.” But that’s the guaranteed accuracy, so the actual accuracy is likely to be much better. Also, some of the error will be systematic (i.e. losing/gaining the same amount every day), so you should be able to apply manual corrections to obtain a much better accuracy.
The Harrison H4 was found to have a systematic error of 2.6 seconds per day, but after correcting for that, it was accurate to a few seconds over many weeks. Hard to say if that’s better than the Casio, but seems to be comparable.
Note that the biggest source of inaccuracy in a Quartz watch is due to temperature variations. Wearing it 24/7 will increase it’s accuracy substantially.
I’d watched the movie Longitude and read a little about Harrison but still found some new intriguing facts in the Wiki article: Two of the earliest clocks include one for James Cook’s famous voyages; another ended up on Pitcairn Island with Fletcher Christian. “Initially [the clocks cost] roughly 30% of a ship’s cost” — a date would be nice there: did this cost apply to the clocks of Cook’s Resolution and the Bligh-Fletcher Bounty ?
BTW, I think pendulum clocks are also extremely accurate (better than H4?) but couldn’t be used for the Admiralty prize since they must be stationary to be accurate.
[From the historical trivia desk:] The slightly different speeds of a pendulum in England compared with the tropics (where gravity is weaker) were key to the 18th-century prediction and measurement of the (slightly non-spherical) shape of the Earth!
Finally [in which septimus reveals his utter ignorance] can anyone explain how a clock like H4 even keeps time? :smack: I understand that a pendulum clock works because gravity’s force is constant. But things like springs don’t have constant force. Even if H4 ultimately works because of gravity, wouldn’t flaws or frictions in the escapements be troublesome?
Springs don’t have a constant force, but if the amplitude of the oscillation is kept constant, the system will have a constant period. Managing that is the crucial bit of the design. Note that the same is also true of a pendulum. It doesn’t have a constant period if the amplitude varies. But that is generally easier to manage.
So yes, friction in the system can cause all manner of problems, one of which is a change in the amplitude of the oscillation and hence period.
In any escapement the trick is to impart the precise amount of energy needed to keep the system oscillating in the face of losses in the oscillator, whilst not impeding the motion of the oscillation, and at the same time having the period of those transfers of energy act to regulate rate of the rest of the mechanism - and thus have it tell the time.
Crystal oscillators are the same thing. Just an electromechanical version. They suffer from all the same ills. But which are easier to manage are different. A neat version of a crystal time piece uses two crystals cut for different frequencies. The change in period with temperature is different for the two, and by comparing how the two oscillators vary with respect to one another you can derive the temperature and the needed compensation. A few Swiss watches used it, I remember one from Longines. It was good for a second or two a month. It was so wildly better than the Chronometer certified mechanical watches that it was absurd.
From Wikipedia:
AFAIK they carried two clocks so double the cost.
Quartz watches are almost always more accurate than mechanical watches, even insanely well-manufactured ones. Even a junk Casio is likely going to lose/gain less than 10 seconds a month and the amount they lose/gain is nearly always going to be exactingly consistent and will largely lose almost exactly the same amount of time every month. As mentioned before, the H4 lost 3 seconds a day and even after correction still lost a second or so a month that couldn’t be corrected. Quartz watches don’t have that problem. As said above, their biggest issue is temperature change and a wristwatch that is worn daily in roughly human ideal environments doesn’t experience the kind of temperature change to really throw it off. If all you care about is the correct time, your 10 dollar casio is a pretty amazing machine. I’ve used quartz, automatics and winders and some fairly nice ones at that and cheapo quartzes beat even the best mechanicals by a long shot.
To put this into comparison, COSC standards for mechanical watches are -4/+6 seconds a day to achieve ‘chronometer’ ranking (Only 3% of Swiss watches make the cut.) For Quartz watches, it’s +/- .07 seconds a day. COSC actually had to alter their requirements after Quartz watches emerged simply because random junk was smoking the mechanical standards and COSC was always considered an ‘elite’ ranking and they didn’t want to hand it out to junk. The only thing that will really beat quartzes is the ‘radio watches’ that reset themselves according to the atomic clock radio signal every day (And can also be picked up for a song-entry levels are under 50 bucks) If you put them in a Faraday cage so they don’t get their signal, they typically perform like other quartz watches since that’s what they are.
Bottom line is that your quartz Timex from Walmart will keep much better time than a 2500 dollar Rolex and keeps better time than an H4. Of course, the primary purpose of a Rolex is not really to keep time since very few of us have any need of truly accurate timekeeping, its purpose is to convey status and wealth and that is something that a Timex or Casio is very poor at doing.
Actually, for a pendulum or spring, variations in amplitude mostly don’t matter. For a pendulum, as long as the amplitude is small (less than 10º is usually good enough), it matters almost not at all precisely how small it is. And for an ideal spring (i.e., one which obeys Hooke’s Law), amplitude matters not at all, so for a real one, all that matters is how nonideal it is.
Oh, also, I have sitting on my desk a cheap Casio wristwatch (I think it cost $10) that I haven’t made any attempt to correct for something like 15 years. Aside from being on DST, it’s currently 28 minutes ahead of the correct time. And that’s even with a battery that’s at two and a half times its design lifetime: Back when it was new, it drifted even less. And I could improve it further by calibration and correction for systematic error.
The only reason it’s sitting on my desk, incidentally, instead of on my wrist, is that Casio makes poor-quality bands, which wear out quickly.