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    Re: How Many Chronometers?
    From: Greg R_
    Date: 2009 Sep 16, 13:14 -0700

    LOL - this is why our spouses/significant others/etc. think we're half-crazy a 
    lot of the time. Or maybe they're on to something...  ;-)
    
    Thanks for a good read, Gary.  :-)
    
    --
    GregR
    
    
    
    --- On Wed, 9/16/09, Gary LaPook  wrote:
    
    > From: Gary LaPook 
    > Subject: [NavList 9766] Re: How Many Chronometers?
    > To: navlist@fer3.com
    > Date: Wednesday, September 16, 2009, 10:37 AM
    > 
    > 
    > 
    >   
    >   
    > 
    >  
    > As usual, George is right again (mostly.)� I will keep
    > the watches is
    > the freezer for a while longer but even the� short
    > time period so far
    > has shown a considerable change in the rates of the
    > watches. The
    > temperature in the freezer has been in the range of 1�
    > F to - 10�F, say
    > an average of about -5� about 80�F (45� C)
    > lower than before. In the
    > 10.3 hours that they have been in the freezer so far they
    > have lost
    > 1.5, 1.5 and 1.0 seconds corresponding to daily rates of
    > -3.5, -3.5 and
    > -2.3 seconds per day. Based on their performance in the
    > past they
    > should have each gained some small amount but that is lost
    > in the
    > imprecision of my reading of the watches compared to the
    > WWV time
    > signals, about one half second resolution. George predicted
    > a change of
    > rate of 7 or 8 seconds per day with this change in average
    > temperature
    > but the observed change in the short period so far is only
    > about half
    > of that but this might be masked by the imprecision of the
    > readings
    > also.
    > 
    > 
    > 
    > Apache Runner provided a formula for the change in
    > frequency of the
    > watch crystal as:
    > 
    > 
    > 
    > "Quartz crystals have the great advantage that they
    > have very little
    > temperature dependence.�� Typically, they're
    > fabricated to have a
    > minimum sensitivity to temperature around 25 degrees C.
    > 
    > 
    > 
    > As I
    > recall, the dependence is roughly a quadratic, and goes
    > like the square
    > of the difference in temperatures - departures from 25
    > degrees C.�� The
    > coefficient is something like 0.04 ppm/(degrees C)**2
    > 
    > 
    > 
    > So, at freezing, one might expect 25 ppm shift, which is 2
    > seconds
    > per day - pretty significant, if I consider that my typical
    > systematic
    > drift is 0.1 seconds per day at standard temp's."
    > 
    > 
    > 
    > Using this formula would also predict a change of rate of 7
    > seconds per
    > day which hasn't happened so for but we will follow it
    > for a while
    > longer. Assuming that this formula is approximately
    > correct, a change
    > of average temperature of 5�C would predict a change
    > of rate of .09
    > seconds per day and a change of 10�C would cause a
    > change of .35
    > seconds per day. 
    > 
    > 
    > 
    > So I disagree with George to the extent that if the watches
    > are kept in
    > an insulated box, to limit the effect of diurnal changes in
    > cabin
    > temperatures, then the change in rate will only happen
    > based on long
    > term changes in ambient temperature, say on a cruise from
    > the Caribbean
    > to England. But, if the cabin is kept in a range of
    > temperatures which
    > are habitable for humans then the change of rates can be
    > kept to a
    > small number. 
    > 
    > 
    > 
    > And my advice for anyone wanting to use these watches for
    > celestial
    > navigation on an expedition across Antarctica is to duct
    > tape them to
    > your stomach under all of your clothes which will turn you
    > into a
    > temperature stabilizing "oven" for the crystals.
    > Off course, prior to
    > your expedition, you must determine their rates by wearing
    > them taped
    > to your stomach for some reasonable period of time.
    > 
    > 
    > 
    > gl
    > 
    > 
    > 
    > George Huxtable wrote:
    > 
    >   Gary wrote-
    > 
    > "So I have decided to extend my experiment. I have
    > just placed all thee 
    > watches in my freezer which is at -7� right now (along
    > with the recording 
    > thermometer) and will see what the rates are after three
    > weeks and I will 
    > report back then."
    > 
    > Let me predict that Gary will then see all three watches
    > losing about 7 or 8 
    > seconds a day (if he's talking about temperatures
    > measured in Fahrenheit 
    > degrees).
    > 
    > Quartz crystal frequencies do change with temperature, but
    > not necessarily 
    > in a linear way. By choosing the way that the crystal is
    > cut, it's possible 
    > to make its resonant frequency change parabolically with
    > temperature, such 
    > that it's a maximum at a convenient ambient temperature
    > (such as 25� C) and 
    > falls away either side, at temperatures that are higher or
    > lower. This means 
    > that it's most constant over the range of ambient
    > temperatures that a watch 
    > has to live in. (I understand that in some circumstances
    > crystal oscillators 
    > can be made to give a point-of-inflection rather that a
    > maximum frequency at 
    > that temperature, which can extend the useful temperature
    > range somewhat 
    > further.)
    > 
    > But, as with any such parabolic variaition, once you get
    > away from the 
    > optimum temperature, the dependence on temperature becomes
    > more severe.
    > 
    > In the freezer, Gary will be operating his watches at about
    > 47�C below their 
    > optimum temperature of 25�C. Similarly, I would expect
    > that if he operated 
    > them at 47�C, above it, at 72�C, if they will
    > stand that (he may be 
    > understandably reluctant to try), then I would expect them
    > to run similarly 
    > slow, 7 or 8 seconds a day.
    > 
    > Wearing a watch on the wrist well help to keep its
    > temperature up in the 
    > daytime, but won't help much if it's taken off at
    > night, in many 
    > environments (such as small craft) that don't expect
    > central heating. Nor 
    > will "wrapping the watch in blankets"; an
    > inanimate object will derive 
    > little benefit from such attentions, much less than  Gary
    > or I would. They 
    > will only delay changes in ambient temperature reaching the
    > watch; but they 
    > will get to it in the end.
    > 
    > Gary refers to the use of a "crystal oven", to
    > compensate for changes in 
    > ambient temperature. Indeed, that's a viable
    > technology, that I was using 
    > for precise time measurement, 40 years ago. The crystal is
    > put into a little 
    > insulated housing containing a heating element and a
    > temperature sensor, 
    > with feedback to keep the crystal's temperature
    > constant. It's done that 
    > way, because it's so much easier to heat things above
    > ambient temperature 
    > than to cool them below it. An operating  temperature is
    > chosen that's 
    > higher than the environment is ever expected to reach
    > (40�C, say) and a 
    > crystal is chosen which has its optimum temperature to
    > correspond. Such an 
    > oscillator has its own "warm-up" period, after
    > switch-on, until the oven 
    > stabilises. This technique is seldom used for anything
    > portable, unless 
    > unavoidable, because of the power consumption by the oven.
    > 
    > George.
    > 
    > contact George Huxtable, at  george@hux.me.uk
    > or at +44 1865 820222 (from UK, 01865 820222)
    > or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    > 
    > 
    > =====================
    > 
    > ----- Original Message ----- 
    > From: "Gary LaPook" 
    > To: 
    > Sent: Wednesday, September 16, 2009 1:34 AM
    > Subject: [NavList 9757] Re: How Many Chronometers?
    > 
    > 
    > I remember when I first got involved with radios back in
    > the '60s that I 
    > coveted a high end radio that had an "oven" to
    > keep the oscillator crystal 
    > at a constant temperature to keep the radio frequency from
    > drifting as the 
    > crystal changed temperature. I now think, however, that
    > that was mainly "a 
    > self inflicted wound" due to the tubes (valves) in the
    > radios having 
    > "heaters" to "boil off" electrons from
    > the cathodes in order to make the 
    > tubes function which caused the radios to change
    > temperature a lot and to 
    > run quite hot. The young guys won't remember waiting
    > for a radio to "warm 
    > up" before it would start working but us old timers
    > will remember the orange 
    > glow coming out of the back of the radio from the glow of
    > the "heaters" in 
    > each tube. I clearly remember warming my hands on cold
    > nights over the hot 
    > radio.
    > 
    > I now wonder if the much less extreme swings of temperature
    > that would be 
    > expected in a wrist watch, or by a watch kept in an
    > insulated box below 
    > decks, would make a large change in the watch crystals'
    > resonant frequency 
    > affecting their rates in any significant way.
    > 
    > So I have decided to extend my experiment. I have just
    > placed all thee 
    > watches in my freezer which is at -7� right now (along
    > with the recording 
    > thermometer) and will see what the rates are after three
    > weeks and I will 
    > report back then.
    > 
    > gl
    > 
    > --- On Tue, 9/15/09, Werner Luehmann 
    > wrote:
    > 
    > From: Werner Luehmann 
    > Subject: [NavList 9737] Re: How Many Chronometers?
    > To: navlist@fer3.com
    > Date: Tuesday, September 15, 2009, 10:21 AM
    > 
    > 
    > Sorry Gary, wrong conclusion. The problem with quartz
    > watches (or any quartz
    > driven oscillator) is their temperature dependance. Only
    > under a constant
    > temperature you would get constant "rates". For
    > example, in high class
    > radios the quartz is kept at a constant temperature higher
    > than the ambient
    > temperature in order to ensure frequency stabilty. In wrist
    > watches
    > compensating electronic devices can be used. But this is
    > expensive and not
    > found in 17 Dollars pieces, if at all.
    > So unfortunately this cheap solution doesn't work for
    > us.
    > B.T.W.: I have some nice digital (and not too cheap)
    > stopwatches (made by 
    > the
    > German manufacturer "Hanhart") that elected to
    > adjust their rates according
    > to the year's season ;-)
    > 
    > Werner
    > 
    >  Am Dienstag, 15. September 2009 11:22:33 schrieb Gary
    > LaPook:
    >   
    >   
    >     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
    > 
    > 
    >     
    >   
    >   
    > 
    > 
    > 
    > 
    > 
    > 
    > 
    > 
    >   
    > 
    > 
    > 
    > 
    > 
    > > 
    >  
    > 
    > 
    > 
    > 
    
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