SUBSIM Radio Room Forums - View Single Post - Holy horology Batman, I think I found my next watch

Platapus · 03-10-19, 11:41 AM

Thank you for pointing out that in my long bombastic post I neglected to drone on about the third factor that can affect what is considered accuracy in a watch -- Loss/gain. Yikes, that's a pretty important thing to leave out. So let me repair with an even longer and more bombastic post. That' will learn ya!

Accuracy is an absolute instantaneous comparison to an external source. That source can be anything which is why whenever the term accuracy is used, it needs to be followed up with either to what extent or to what. With watches is is ass-umed to be accurate when compared to an atomic time signal, but that is not always a safe assumption. Nothing can be accurate with regard to itself. That concept is called variance which I will cover next.

Accuracy is an instantaneous absolute value. For example: At this instant, my watch is -4 seconds from the NIST time signal. The next time I check, my watch may be +3 seconds from the NIST time signal. Like any set of absolute values, I can take a Mean, Median, and Mode to create all sorts of statistics. But it is incorrect to use the commonly used phrase "My watch is accurate to +/- 5 seconds." A lot of people do it including watch people, but it is not actually the correct way to express it. I can, however report that my watch is on the average (mean) +3 seconds from the NIST time signal. I can say that my watch's median (center) is -2 seconds and that the mode (majority) may be 0 seconds. I can even calculate standard deviations of this data if I want to ensure of never being invited out to parties.

Variance, on the other hand is an internal measurement. It is a measurement of how repeatable is the precision of the watch movement. Mechanical watches are often measured in Beats per Hour. An hour was chosen many years ago as a good period of representation. A specific watch's balance wheel may operate at 28,800 BPH. This is actually a common BPH. This translates down to 8 beats per second or 4 hertz.

So a 28,800 BPH watch "ticks" at 4 ticks per second. You can see this if you can look carefully or better yet record the movement and slow it down. You should see four tiny jumps between each second mark.

Generally speaking higher BPH CAN result in some variance being "averaged out". However, a well made 2.5 hz watch will be better than a poorly made 5 hz watch. How does this relate to variance?

No watch beats at exactly 28,800 beats per hour every hour. But they get close. Sometimes it beats at less than 28.8k and sometimes it beats more than 28.8k and sometimes it beats exactly 28.8k. This being a mechanical watch full of mechanical stuff, position, movement, and gravity are only three of about a million things that can affect the precision of a watch movement.

The range of these values is called variance. This has nothing directly to do with accuracy. This is just how predictable does the watch movement .. well.. move.

Variance is reported out as a range. This range may be centered over zero as in this watch has a variance of +/- 5 seconds a day (aka the range of between -5 and + 5 seconds). But it can also be centered over another number. For example some METAS certified watches have a variance of -0/+5. (centered over 2.5) But just to keep the math easy, let's just consider a watch that has a variance of -5/+5 seconds a day.

Let's take this watch and sync it to the NIST time signal or some other other recognized "correct time" reference. After 10 days what will the accuracy of this watch? (show your work)

Pencils down

It will be somewhere between -50 seconds and + 50 seconds from the time reference. -5 seconds per day times 10 days is pretty close to -50.

Assuming no other factors, it will be a Gaussian distribution around the reference zero. This is why it is important to know what the center reference is and it is mostly but not always zero.

Unfortunately, with anything mechanical, the phrase "assuming no other factors" is a fantasy as there are always external factors. But watch engineers work very hard to mitigate these factors. But let's continue in our fantasy world of no external factors to keep the numbers easy. That's the great thing about math -- you can create fantasy worlds where numbers work easy. Engineers have to deal with reality.

This means that there is a tiny chance this watch will be -50 seconds and an equally tiny chance that this watch will be +50 seconds and a much larger chance it will be closer to zero difference. Now a watch with a smaller variance will have a greater chance of being close to zero than a watch with a wider variance. But at any one instant, a watch with a narrow variance may be less accurate than a watch with a larger variance!

But the odds are better with a smaller variance. Which is why watches with small variances are more difficult to make and are often more expensive. Adjusting the variance on a watch is a complicated process and often requires the disassembly of the mechanism.

Then there is the item I neglected to write about in my previous post.

Loss/gain. A loss/gain is a cumulative change in the accuracy of a watch over a period of observation. It is in one direction. A watch either gains or loses time. If a watch both loses and gains time, that is variance. The cumulative change in the accuracy is affected by the variance of the watch. The variance is not affected by the loss/gain.

HUH?

Here is an example I had with my watch.

My watch is a COSC certified chronometer that has a design variance of -4/+6 seconds per day. That's 10 seconds not centered at zero! Note that it is a design variance. Whether my watch actually has a variance of -4/+6 will have to be determined.

My watch had a loss of about 11 seconds a day. This loss was cumulative. One day after syncing, it was 11 seconds slow. The next day it was 22 seconds slow, the third day 33 seconds slow. Since this was a cumulative loss over a period of time, it is often called a Gain Rate or Loss Rate.

This being a loss and not a variance, there was no countering "+". This meant that my watch was experiencing a loss as opposed to an undesired variance.

True to Swiss precision, my watch was almost exactly 11 seconds slow. The actual variance values were between -2 and +4 according to my spreadsheet.

What? You don't keep a spreadsheet of the variances of YOUR watches???

This was actually good news as the variance was supposed to be -4/+6 but was actually -2/+4. This meant that my watch was very precisely inaccurate. If you are going to be wrong, at least be precisely wrong.

Let's say for a counter example that my watch's accuracy varied thusly:

Day 1: -11 seconds
Day 2: -4 seconds
Day 3: +1 seconds
Day 4: +20 seconds

This would not be an indication of gain/loss but an indicator of the variance being out of specs. That would be an expensive fix

But my watch was, with great precision losing about 11 seconds a day. This meant that the repair consisted of demagnetizing the movement and performing what is called a regulation which is often (and in my case was) a simple physical adjustment of the watch. Omega did it for free (yea) but took three weeks to do it (boo). If it was a problem in variance, it would have taken about $600.00 MINIMUM and about 12 weeks to fix.

So we have three separate, but often commonly confused concepts that affect what is called accuracy.

Accuracy - Instantaneous absolute comparison to an external reference
Variance - Continuous changes, over a period of observation, of the repeated precision of the movement
Gain/loss - Cumulative change over a period of time of the accuracy.

Of course, in the real world, your watch is affected by all of these at the same time. Actually all clocks are affected by this.

Even the venerated Cesium clocks have variance. Very very tiny variances that have mostly insignificant impacts on reality, but they are there. This is why UTC is actually a group effort involving multiple atomic clocks from all around the world or across the flat world depending on your beliefs. It is actually a Time that is Universally Coordinated.

My rant about the misuse of the term UTC will have to wait for another bombastic post.

03-10-19, 11:41 AM	#12
Platapus Fleet Admiral Join Date: Oct 2006 Posts: 19,405 Downloads: 63 Uploads: 0	Thank you for pointing out that in my long bombastic post I neglected to drone on about the third factor that can affect what is considered accuracy in a watch -- Loss/gain. Yikes, that's a pretty important thing to leave out. So let me repair with an even longer and more bombastic post. That' will learn ya! Accuracy is an absolute instantaneous comparison to an external source. That source can be anything which is why whenever the term accuracy is used, it needs to be followed up with either to what extent or to what. With watches is is ass-umed to be accurate when compared to an atomic time signal, but that is not always a safe assumption. Nothing can be accurate with regard to itself. That concept is called variance which I will cover next. Accuracy is an instantaneous absolute value. For example: At this instant, my watch is -4 seconds from the NIST time signal. The next time I check, my watch may be +3 seconds from the NIST time signal. Like any set of absolute values, I can take a Mean, Median, and Mode to create all sorts of statistics. But it is incorrect to use the commonly used phrase "My watch is accurate to +/- 5 seconds." A lot of people do it including watch people, but it is not actually the correct way to express it. I can, however report that my watch is on the average (mean) +3 seconds from the NIST time signal. I can say that my watch's median (center) is -2 seconds and that the mode (majority) may be 0 seconds. I can even calculate standard deviations of this data if I want to ensure of never being invited out to parties. Variance, on the other hand is an internal measurement. It is a measurement of how repeatable is the precision of the watch movement. Mechanical watches are often measured in Beats per Hour. An hour was chosen many years ago as a good period of representation. A specific watch's balance wheel may operate at 28,800 BPH. This is actually a common BPH. This translates down to 8 beats per second or 4 hertz. So a 28,800 BPH watch "ticks" at 4 ticks per second. You can see this if you can look carefully or better yet record the movement and slow it down. You should see four tiny jumps between each second mark. Generally speaking higher BPH CAN result in some variance being "averaged out". However, a well made 2.5 hz watch will be better than a poorly made 5 hz watch. How does this relate to variance? No watch beats at exactly 28,800 beats per hour every hour. But they get close. Sometimes it beats at less than 28.8k and sometimes it beats more than 28.8k and sometimes it beats exactly 28.8k. This being a mechanical watch full of mechanical stuff, position, movement, and gravity are only three of about a million things that can affect the precision of a watch movement. The range of these values is called variance. This has nothing directly to do with accuracy. This is just how predictable does the watch movement .. well.. move. Variance is reported out as a range. This range may be centered over zero as in this watch has a variance of +/- 5 seconds a day (aka the range of between -5 and + 5 seconds). But it can also be centered over another number. For example some METAS certified watches have a variance of -0/+5. (centered over 2.5) But just to keep the math easy, let's just consider a watch that has a variance of -5/+5 seconds a day. Let's take this watch and sync it to the NIST time signal or some other other recognized "correct time" reference. After 10 days what will the accuracy of this watch? (show your work) Pencils down It will be somewhere between -50 seconds and + 50 seconds from the time reference. -5 seconds per day times 10 days is pretty close to -50. Assuming no other factors, it will be a Gaussian distribution around the reference zero. This is why it is important to know what the center reference is and it is mostly but not always zero. Unfortunately, with anything mechanical, the phrase "assuming no other factors" is a fantasy as there are always external factors. But watch engineers work very hard to mitigate these factors. But let's continue in our fantasy world of no external factors to keep the numbers easy. That's the great thing about math -- you can create fantasy worlds where numbers work easy. Engineers have to deal with reality. This means that there is a tiny chance this watch will be -50 seconds and an equally tiny chance that this watch will be +50 seconds and a much larger chance it will be closer to zero difference. Now a watch with a smaller variance will have a greater chance of being close to zero than a watch with a wider variance. But at any one instant, a watch with a narrow variance may be less accurate than a watch with a larger variance! But the odds are better with a smaller variance. Which is why watches with small variances are more difficult to make and are often more expensive. Adjusting the variance on a watch is a complicated process and often requires the disassembly of the mechanism. Then there is the item I neglected to write about in my previous post. Loss/gain. A loss/gain is a cumulative change in the accuracy of a watch over a period of observation. It is in one direction. A watch either gains or loses time. If a watch both loses and gains time, that is variance. The cumulative change in the accuracy is affected by the variance of the watch. The variance is not affected by the loss/gain. HUH? Here is an example I had with my watch. My watch is a COSC certified chronometer that has a design variance of -4/+6 seconds per day. That's 10 seconds not centered at zero! Note that it is a design variance. Whether my watch actually has a variance of -4/+6 will have to be determined. My watch had a loss of about 11 seconds a day. This loss was cumulative. One day after syncing, it was 11 seconds slow. The next day it was 22 seconds slow, the third day 33 seconds slow. Since this was a cumulative loss over a period of time, it is often called a Gain Rate or Loss Rate. This being a loss and not a variance, there was no countering "+". This meant that my watch was experiencing a loss as opposed to an undesired variance. True to Swiss precision, my watch was almost exactly 11 seconds slow. The actual variance values were between -2 and +4 according to my spreadsheet. What? You don't keep a spreadsheet of the variances of YOUR watches??? This was actually good news as the variance was supposed to be -4/+6 but was actually -2/+4. This meant that my watch was very precisely inaccurate. If you are going to be wrong, at least be precisely wrong. Let's say for a counter example that my watch's accuracy varied thusly: Day 1: -11 seconds Day 2: -4 seconds Day 3: +1 seconds Day 4: +20 seconds This would not be an indication of gain/loss but an indicator of the variance being out of specs. That would be an expensive fix But my watch was, with great precision losing about 11 seconds a day. This meant that the repair consisted of demagnetizing the movement and performing what is called a regulation which is often (and in my case was) a simple physical adjustment of the watch. Omega did it for free (yea) but took three weeks to do it (boo). If it was a problem in variance, it would have taken about $600.00 MINIMUM and about 12 weeks to fix. So we have three separate, but often commonly confused concepts that affect what is called accuracy. Accuracy - Instantaneous absolute comparison to an external reference Variance - Continuous changes, over a period of observation, of the repeated precision of the movement Gain/loss - Cumulative change over a period of time of the accuracy. Of course, in the real world, your watch is affected by all of these at the same time. Actually all clocks are affected by this. Even the venerated Cesium clocks have variance. Very very tiny variances that have mostly insignificant impacts on reality, but they are there. This is why UTC is actually a group effort involving multiple atomic clocks from all around the world or across the flat world depending on your beliefs. It is actually a Time that is Universally Coordinated. My rant about the misuse of the term UTC will have to wait for another bombastic post. __________________ abusus non tollit usum - A right should NOT be withheld from people on the basis that some tend to abuse that right.