Ways To Measure And Evaluate Accuracy

Watch Accuracy

Re:the length of a piece of string.

Posted by Watchbore on February 05, 1998 at 1:07:22:

In Reply to: My input on the most accurate for the money… posted by Roy Scott on February 04, 1998 at 11:55:13:

:Watches can never be accurate enough. They can have the distance to their goal and never reach it. Accuracy depends not only on the daily departure from true time, but also the consistency of that departure, the positional differences in rate, the effects of temperature, secondary errors and rate resumption.

In the old days observatories used to rate watches against true time determined by astronomical observations, awarding points to the best timekeepers, in keenly fought contests. The Grand Prix of horology.

The toughest test ever was the British craftsmanship test. From 1951 to 1978 only 12 watches (most Ulysse Nardin) reached the minimum standard, and only one (a Patek Philippe) reached the highest grade.These are probably the most accurate mechanical watches ever made.

Today, time-of-day watches are rated by COSC. It is comparitavely easy. Nearly 900,000 watches are awarded chronometer status each year and the pass rate is 97%.

Watch companies and watchmakers are reluctant to make any claims as to the timekeeping performance of their mechanical watches. They are terrified of smartasses armed with graphs and charts and lawyers demanding compensation. A good mechanical time-of-day watch can be expected to accumulate one or two minutes of departure from true time every month.

Another yawn from Watchbore

Excellent! Let me add 1 more item: RMS short-term error…

Posted by Walt A. on February 05, 1998 at 2:33:37:

In Reply to: Re:the length of a piece of string. posted by Watchbore on February 05, 1998 at 1:07:22:

Hi, Watchbore and Guys,

You have put your finger on the heart of the matter: There are all sorts of ways to measure and evaluate accuracy. And we accept only a very specific measurement type: The error at the moment the second hand stops on a second mark. That is because we are not too concerned about the brief 1/8 second in between these instants. In actuality, the best we can do with a mechanical watch is set it so that it is 1/16 second fast at the moment the hand stops on the second mark and over the next 1/8 second, until just before the hand jumps to the next second, the error will build up in the negative direction, until the indication will be 1/16 second SLOW. All this applies to a 28800 bph escapement.

OK, no problem so far. Now how about the quartz watch, which advances only once per second? Here the error is more pronounced. The best we can do is set the watch so it is 1/2 second fast at the moment the hand lands on the second mark, and then gradually, the error will creep downwards, past zero, and finally be minus 1/2 second just before the hand jumps to the next second mark.

Do you accept that much error? Then how about the quartz dress watch without the second hand, which advances once every 20 seconds and jumps 1/3 minute on the dial each time? Most owners don’t mind. Yet the error of this watch reaches 10 SECONDS 3 times every minute!

Well, then, if that’s OK, why not a watch that advances only every 12 HOURS? It will be absolutely accurate by the same criterion as the three examples above, but you can get this accuracy by merely painting the hands on the dial!

Not to try to make the whole argument sound ridiculous, let me summarize by saying that our criterion for accuracy is actually a little vague. Quite a few months ago I sent in a post that described a watch’s accuracy in terms of RMS ERROR, which takes into account the moment by moment error of a ‘perfectly accurate’ watch. To those who still remember that description, my apologies for subjecting you to it again.

The RMS (Root Mean Square) error is a mathematical quantity well known to all engineers and scientists and is conceptually a parameter independent of direction or frequency. It is conceptually a measure of the ‘energy’ dissipated by the error, i.e., the amount of heat you could get from it if you hooked up a coil to a system generating the error. It is also the most likely error you would be reading off the watch’s dial if you consulted it at a totally random moment.

I won’t go into the actual detail of how you calculate the RMS error, but the RMS error of a 1 bps quartz watch keeping ‘perfect time’ is 0.2887 seconds. That is, if you consult your ‘perfect’ quartz chronometer, this is the most likely error you will be seeing.

On a ‘perfectly adjusted’ 28800 bps mechanical watch, the RMS error is only .0194 seconds, suggesting that the mechanical watch is about 15 times as accurate as the 1 bps quartz watch!

Of course, the only watch with a zero RMS error would be one with a synchronous motor phaselocked to a quartz oscillator. I don’t believe any such watch exists today or is likely to come along in the foreseeable future. The energy consumption would probably require a hockey-puck sized battery.