A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Longitude by calculator -theodolite
From: Bruce J. Pennino
Date: 2013 Jul 1, 22:53 -0400
From: Bruce J. Pennino
Date: 2013 Jul 1, 22:53 -0400
Hello Paul, Antoine, and All:
The stop watch idea is a good one, and I'll look for one. But I like just reading my digital watch; simple. Someone please recommend a stop watch of the variety described by Paul. It would make tabulating data easier!
I want to take data in some daylight because I can see the cross hairs easily without using a flashlight. Adjusting the theodolite, reading time and recording data is complicated enough. The moon is big, convenient and just easy.
Because my theodolite body has a low height (a short pivot, hard to describe), I must select a celestial body at relatively small Hs (large zenith angle). Say it another way, I can't get my eye to instrument if I want to sight a large Hs. My maximum Hs is 30-35 degrees. I read the angle to nearest second, but the merest touch moves the hairline. So the value is realistically only good to a second or so. Deflection of the vertical is one of those errors that I just "lump into small errors difficult to quantify". That is why my accuracy as perceived by me can't be plus or minus three seconds. Any measurement where I am within 3 seconds , Hc-Ho, is just plain luck or happenstance. Averaging balances various errors, but good luck is difficult to trump. There are just too many embedded places where errors can result. I now believe I can probably, on average, measure a Hs to within 6 seconds, but I said 12 seconds just to give myself " some slack" and have confidence in the results.
For my measurements, I think recording normal weather or water conditions does not add much on any practical basis. Unusual conditions should be recorded. When I make dip measurements, I do record weather and water conditions.Antoine, when I did the moon celestial measurements, I did not bother to record any conditions. There was no significant wind ; it was a pleasant New England evening and I was standing in shirt sleeves 65-70 F. Normal air pressure conditions.
Thank you for data analysis. For the past three days we have had rain, fog, haze and mist. I'll try to sight some stars in near future and analyze; Hc-Ho.
On Sat, Jun 29, 2013 at 7:33 PM, Paul Hirose wrote:
Bruce J. Pennino wrote:
> Actually, for my
> next set of sights I'm going to use some early rising stars at twilight.
> Should work ok. Someone asked about my using the moon. I used the moon
> because I can't put any shades on the theodolite, and there would be
> optical distortion (maybe) as suggested.
Wouldn't it be more convenient to work in full darkness? Then you
wouldn't have to observe within a specific time window. The selection of
stars would be better too.
> I am measuring time to nearest whole second. So I'm probably accurate to
> plus or minus 1/2 second for a single measurement, at very best .
It helps to use a stopwatch with a split-action feature (to stop the
display without stopping the watch). Record the start time. Take a split
at each observation. After all the observations, take a final split
against your time standard to verify the start time.
I used to own a dedicated stopwatch with 10 memories to record the
splits. Sadly, it quit working several years ago. My wristwatch simply
displays the split for 10 seconds then resumes running. That's not as
convenient, but still usable.
> The theodolite is a "6 second gun", which
> means I can directly read to 3 seconds, and maybe estimate to the
> nearest second or so.
To realize the potential of that instrument, altitudes should be
computed to 1 second or better. By careful choice of stars you
can minimize refraction error. A stable temperature helps. That's
another reason to observe when the sky is fully dark. You avoid the
rapid temperature decrease around sunset.
I wonder if you have considered deflection of the vertical. At your
location, xi = -4.26 and eta = 1.37 seconds, according to the National
Geodetic Survey calculator:
That means an instrument, exactly level with respect to gravity,
actually has its vertical axis inclined 4.26 seconds south and 1.37
seconds east with respect to the ellipsoid. Its observations yield
astronomic latitude and longitude, different from the geodetic
coordinates on a map or GPS receiver.
At the precision to which you are working, I believe deflection of the
vertical will be a significant part of your error budget unless corrected.
For example, at 2013 June 30 0200 UTC, Antares is observed from N42
W072, 0 height above ellipsoid. UT1-UTC = +0.05773 s. Computed
unrefracted altitude from the Tinyac program:
20°45'10.0" no deflection of vertical
20°45'14.4" with deflection of vertical
One solution is to compute altitude at the geodetic position where a
perpendicular to the ellipsoid is parallel with the deflected plumb line
at the true position. The adjusted position is north latitude plus xi,
and east longitude plus (eta divided by cosine latitude). In this case,
the adjusted position is N41 59 55.74 W071 59 58.16.
The Tinyac program uses that simple method. I later realized it is
effective for altitude only. Azimuths are inaccurate, the error
increasing with latitude. Lunar3 does it right, though. Compare azimuth
and unrefracted altitude of Antares, including deflection of the vertical:
169°13'36.2" 20°45'14.4" Tinyac
169°13′35.0″ 20°45′14.4″ Lunar3
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