Tuesday, October 23, 2007

The Equation of Time

This is really about the different ways of representing "the equation", but first a little preamble. (or you could Google "equation of time" and view all 94,700 results :wink:)

Watches are, of course, mainly instruments to measure the passage of "time". However, "time" in that context is a man-made concept and is dependent on the machinations of atomic clocks and such-like. Furthermore, the division of the planet into time zones, although good for commerce and the punctuality of trains, has also helped to divorce us even further from the reality of the time by which humanity once lived i.e. solar time; for example - when it is noon at Greenwich (by "noon" I mean when the Sun is at it's highest, not 12 o/clock), the Sun over Rockall Island still has yet to climb quite a bit, even though it's in the same time zone. This also explains why using your watch to find North can send you wandering up to 15 degs off, and that's not including the 6 deg penalty for forgetting to correct for Summer Time (who, me?).

Anyway, the "equation of time" represents the imperfect motion of our planet around the Sun. The equation itself is horrendous, don't even bother to look at it. Generally, we tend to use the term to mean it's result for any given day of the year. Lindbergh used such a result on his epic flight to Paris. The equation of time is also of significance to garden gnomes, strangely enough. "What's the time, Grumpy?" - "Bloody 'ell have I got to climb up the sundial again??". You see, if you set a sundial to your watch on Feb 14th to please SWMBO, I guarantee it will be a half-hour fast when you next look at it on Nov 5 between fireworks.

So, without further ado, here are several ways from worst to best to represent this "equation of time" . . . ta daaa . . !!

The most seriously boring way is a table:

Part of a Sun Data table . . .
Col. 1: Date
Col. 2: Equation of Time. Number of minutes and seconds the Sun is off compared with an accurate clock which shows local mean time.
Col. 3: fast or slow (Sun).
Col. 4: Declination of the Sun in degrees and minutes. When negative, the Sun is south of the celestial equator; when positive, north. Values are averaged over the 4 year leap year cycle.


A little better - a graph

I prefer, at the very least, a visual approach. Here's the equation plotted out on bog-roll. You'll notice that clocks do agree with the Sun four times a year but it's not really obvious why in this graph form.

equation of time in graph form

Better yet

If the graph is plotted against the angle of the Sun instead of against the time of year, the effect of our wobbly orbit, etc becomes immediately apparent.

The figure below is called an "analemma" (no jokes, please).

graphic figure of eqn of time

and there's an even prettier one on our family globe, I didn't even know what it was until yesterday:

However it does look like the folks below knew all about it. It's a Jaeger-LeCoultre Gyrotourbillon (photo by Ron DeCorte, taken from Timezone.com). The cam rotates just once per year, as you should expect by now ;-) - if anyone knows what the months cam does, please leave a comment to this post.

jeager le coultre eqn of time cam

However I like this one the best. Straight from nature - a time-lapsed sequence of the Sun at 8:30 AM for a year, by Dennis di Cicco

time lapse of Sun at 8:80 am for one year

Here's quite a good site on the subject analemma.com.

Monday, October 22, 2007

An Accidental Sparkle!

As I recall, you can buy a special filter to get the sunburst effect - but the tiny sparkle below, just above the balance jewel, was completely accidental and no filter was used!

gruen movement

My setup uses three lamps, hence the six-pointer. You'll notice that the angles between the points and the point intensities are not equal because of my unequal lamp placements and distances.

So, how did the sparkle appear? The light from each lamp hits the curved bevel on the regulator and is reflected up into the camera's field of view. Even though the lamps have diffusers on them, the single curvature concentrates the reflected light and gives a fan shaped reflection beam rather than a spot beam. The "accident" occurred due to the exposure setting used. It was enough to saturate the image at the center of the sparkle but to have less and less saturated area going outwards along each reflection beam.



Thursday, October 18, 2007

The risk of getting humidity in a watch

People tend to fear that all kinds of nasty stuff will rush into their watches the moment the slightest opening appears, such as when setting the time.  Rest easy - it just ain't so.  Stuff only gets in if air flows in.  Air only flows if there is a pressure difference to cause it to do so.  Usually there is no difference in pressure between the inside and outside of your watch - even sealed ones! No pressure difference = no flow.  Therefore, that horribly humid air will stay outside of your horological masterpiece for the short period during which you'll be setting the time.

But if you leave the crown pulled out and it is unsealed (unlikely) another process takes place.  The humidity (by this I mean absolute humidity, not the kind given in weather forecasts) inside and out will equalize by a process called diffusion.  This is less good.   Picture the following:

In hot and humid Bahrain, due to an interruption, you leave your watch on the Hotel balcony for a week with it's unsealed crown pulled out.  Just before leaving your room to check out, you spot the watch, throw it in your bag & rush off to the airport.  I guarantee that there will be liquid water inside your watch before you get through your first Jack Daniels!

It's the drop in temperature that does it.  Have a look at the psychrometric chart here  (Opens in a new tab, click on the chart there to enlarge it).  Let's say it's 36 deg C and 80% relative humidity (RH) inside your watch.  Find that point on the curve for 80% RH.  Now move to the left until you reach the 100% curve - this is the so-called dew-point temperature for a water content of 0.030 as shown by the scale on the right.  The distance you moved is only 4 deg C.  Any cooling after that causes condensation inside your watch and, as you know, water+oxygen+steel=rust  ;-(

best regards,