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Dr. Kolbe

Sorry for the delayed response. I had been working on a response, saving
it as a draft, and editing it a day at a time. My e-mail client
(Thunderbird) has an undocumented feature. Open a draft and start typing
without clicking “Edit” first and it vanishes into a bit
bucket--location unknown.

I have long considered you one of the more informed members of Navlist.
Having compiled and published a "perpetual" almanac, I surmised you must
already know the answers to the questions you asked me, so I was stymied
as to why you would ask. Was it a pop quiz? Did I lee bow a warlock on
the weather leg of a race? 

I initially asked Gary if he had factored leap seconds into his
computations, and the fun began. I could have been clearer had I used
“projections” rather than “computations.” Nonetheless, I believe it was
a reasonable question.

I also later responded to your post, “Navigation or not, he has to
compare the watch's time to some standard.” This was sloppy on my part.
I did not differentiate between “rating” and “using for cel nav.”

Apologies for my contributions to any ambiguities.

I believe the issues, simply stated, are:

*Should one use a uniform or non-uniform time scale to *rate* a chronometer?

*Should one use a uniform or non-uniform time scale for cel nav?

*Which of the many time standards are appropriate in each case?

Given: A chronometer is precise but not necessarily accurate. It may not
keep perfect time, but its rate of change is *uniform* and therefore
predictable. It follows we would want to use a uniform time scale to
rate the chronometer. Atomic Time (TAI) would be suitable. Using a
non-uniform scale like UTC would be similar to measuring a distance
repeatedly with an elastic tape measure, the other end being held by a
pit bull believing it is a tug-of-war game.

If I understand Gary's methodology, he was essentially tracking TAI when
rating his digital "chronometer" array. He knew UTC, DUT1, and UT1 when
he started. There were no leap seconds during the rating period, but he
did monitor DUT1 and adjust for it yielding a uniform time scale. In a
nutshell, TAI plus a constant. He could now attempt to predict any drift
on a daily basis.

In practical use for cel nav he would want to use a non-uniform time
scale that takes into account the fact that through part of history
Earth's rotation has slowed down, speeded up, and then slowed down
again. True, the exact change at any given instant can only be nailed
down through observation, but UTC does try to keep civil time within 0.9
seconds of "Earth" time via leap seconds, and UT1 within 0.1 seconds via
leap seconds and DUT1.

As you pointed out, "UTC (broadcast time, which is derived from atomic
clocks) is currently forced to keep pace with this 'Earth Time'..."
Clearly they are now joined at the hip, like it or not, so the TAI
techno marvel so useful to astronomers and other scientists who require
a uniform time scale becomes a tail wagging the Earth-time dog.

Point being, Gary had a UT1 starting point after a uniform-time-scale
rating and therefore needs to track leap seconds and DUT1 to adjust his
predictions to current Earth time before entering the Nautical Almanac.

I would argue that we were in agreement on most issues, but terminology
got in the way. I am not, however, clear on why the rating duration
should affect the use of uniform time vs. non-uniform time.

To answer your question, “And what "standard" should that be? GMT? UT1?
Atomic Time? GPS Time?”

Uniform time scale:
*Atomic Time (TAI)? Yes.
*TAI plus a constant? Yes

Non-uniform time scales:
*UTC or Greenwich *Civil* Time? No, we can do better.
*GMT (Greenwich *Mean* Time)? No, 12 hours off UTC/GCT. Why bother?
*UT1? Yes, nominally within 0.1 s of Earth time. UT2 would be overkill
for cel nav.
*Time ball or cannon (my addition)? Heck, why not? It's so nautical.

Undetermined:
GPS time? No. If I understand correctly, this is the b_stard step child
of TAI and UTC. Atomic clocks in the satellites that do not add leap
seconds. Transitioning from their atomic clocks to UTC is the province
of the GPS receiver. In my observations the GPS time display can be up
to 1.5 s off UTC, often leapfrogging a second on the display. A Garmin
engineer stated this was due to the majority of the unit's
hardware/firmware horsepower being dedicated to location etc. Time
display takes a back seat.

Hopefully we are on the same page at this point, and I can turn my
attention to polishing my “Pedantic” lapel pin.

"Time is an illusion. Lunchtime doubly so." "Very deep," said Arthur,
"you should send that in to the Reader's Digest. They've got a page for
people like you." –Douglas Adams, The Hitchhiker’s Guide to the Galaxy

Bill B

PS. I do have one bone to pick with a man of science and letters. The
use of "As we all know..." in "As we all know, the rotational period of
the earth is not constant, and is gradually slowing down..." I certainly
didn't know that when I joined the discussion group with Celestaire's
build-it-yourself cardboard sextant, an HO 229 instructional book, 229
tables for my latitude, and the NA. Perhaps other new members did not
know either. If you are a betting man and poll the general population
I'd wager you get either a blank stare or, "OMG, are we going to fall
off the Earth!" Lord help you if you run into a flat earther.

IMHO "We all know" is a kissing cousin to "It goes without saying"
before the speaker says it. If it goes without saying, why say it? If we
all know it.... I also consider the above to linked to female speak, as
in "never" or "always." 

A side bar: An OCD female companion of mine stated her children were
"always" in bed by 9:00. I tallied that for 2 months and presented her
with the results. “Always” was roughly 54%, so “never” must be close to
46%. She explained that on weekends they could stay up later, sometimes
they had school projects to finish, their grandparents were visiting....
  No wonder I’ve only been married 9 out of 65 years! Not complaining
though, even if married men live longer than bachelors, and house cats
live longer than....















On 6/1/2013 3:22 AM, Geoffrey Kolbe wrote:
> ------------------------------------------------------------------------
> Bill B wrote:
>
>
>> Navigation or not, he has
>> to compare the watch's time to some standard.
>
> And what "standard" should that be? GMT? UT1? Atomic Time? GPS Time?
>
> I would argue that the most useful "standard" to which a chronometer
> used for celestial navigation should be compared is 'Earth Time', or the
> observed mean solar day. (This is often called UT1, but these days the
> definition of UT1 is not actually based on observations of the sun, so
> it is not directly linked to the mean solar day.) As we all know, the
> rotational period of the earth is not constant, and is gradually slowing
> down in a way which is not predictable in the short term. As a result,
> there is no way to accurately predict how 'Earth Time' compares with
> other standards based on atomic clocks. The only way to determine Earth
> Time is to derive it from observations of the sun, moon and planets as
> compared to those predicted in the ephemerides for a given time.
>
> UTC (broadcast time, which is derived from atomic clocks) is currently
> forced to keep pace with this 'Earth Time' (or more specifically, UT1)
> by the intercalation of leap seconds as required, usually once every
> year or so. This means we can use UTC to extract the positions of the
> planets, moon and sun from the ephemerides, so long as we are prepared
> to accept an accuracy of half a second or so.
>
> Where you are rating a chronometer over periods that are short compared
> with a year, like a few weeks, and there has been the insertion of a
> leap second in the interim, then of course that leap second should be
> taken into account. But where you are looking at a drift of your
> chronometer against UTC over periods as long as ten years then I would
> argue that whether leap seconds have been inserted or not in the
> intervening period is not of any concern. Moreover, I would argue that
> rating chronometers over periods as long as ten years does not
> necessarily mean that the derived rate is accurate for keeping track of
> 'Earth Time' as currently paced out by the rotation of the earth. It
> will have slowed significantly over that period.
>
> However, where you are rating a chronometer by its timekeeping over
> periods comparable to one year, I would argue that how you deal with the
> intercalation of leap seconds is not trivial and needs careful thought.
>
> Geoffrey Kolbe
>
>
> : http://fer3.com/arc/m2.aspx?i=124242
>

   

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