I've got an email into Jerry Wahl, who pretty much wrote the book on Polaris shots, and used his spreadsheet to find the star. He might shed light on how to use the spreadsheet to correct the backlight azimuth based on the direction to Polaris.
In the meantime, I'm not clear on how to reduce the data:
I have taken three sets, Backsight and star, Direct and Reverse.
If I reduce the D&R for each set, I can get three angles. I've done that, and found one outlier and discarded it.
But do I "mean" the two times as well, and use the ephemeris data for the star location at that time, then compare it to the mean of the two measurements?
Or, treat each individual measurement (6 in all), compare each to the known location of the star at that time, then reduce them all.
FYI, I've read Fink and Wahl's "The advantages of Polaris...", as well as the Sokkia document, but they all seem to talk about just a single measurement calculation.
You have several ways to do this as you are alluding to.
1. You can mean your Direct and Reverse and calculate the Azimuth using current ephemeris data; OR
2. Use each pointing (as you have stated) and calculate the azimuth.
The advantage of using #2 above is you can isolate errors in any one pointing and timing errors.
I would speculate you are doing this for practice because at least 4 D&R are required for 3rd order work. Also doing #2 above would give you more practice in
reducing (calculating) the azimuth.
JOHN NOLTON
Tombstone, AZ.
> I would speculate you are doing this for practice because at least 4 D&R are required for 3rd order work. Also doing #2 above would give you more practice in
> reducing (calculating) the azimuth.
That would be correct, Sir. I was well on my way to 4 D&R when my iPhone went dark with 12% left in the frozen battery. I contemplated sprinting back to the car 500' through a foot of snow to put a quick charge back in it, when my laptop slipped off the TS case into the snow; then, in a quick effort to right that situation, bumped the tripod leg! Temps were heading down fast towards single digits too. Mission over. Definitely my first rodeo here with Polaris.
I did learn that it's very easy to see in daylight through the gun, and not rocket science at all to find, if you have an approximate azimuth to start with. Another day, I'll try it mid day.
Thanks for the suggestions above.
The "right" way is to do a calculation for each sighting and mean the resulting azimuths.
For the slow apparent motion of Polaris, you can get away with averaging D&R and using the mean time in one azimuth calculation, if not a lot of time has elapsed.
Try it both ways to see for yourself if it makes a difference.
rfc; Its always good to learn but I am sure glad I was not with you in all that snow
and cold. What books are you using to learn from? What Instrument are you using?
The reason I ask about the Inst. is sometimes in the daylight using a Wild T2 theodolite I could not find Polaris. If I set up my Wild T3 or Kern DKM3 or Wild T3000 (larger diameter objective lens) I could find it with ease.
Have fun and keep us posted of your results.
JOHN NOLTON
Tombstone, AZ.
I've never been able to find Polaris during full daylight through Topcon optics. I've found it as soon as it starts to get a little dusky.
I reduce each pointing then mean them in sets. I use Wolf and Brinker ninth edition.
Bill93 I would like you to show me (reference book or paper)where it says the "right way" according to you on how to reduce "Polaris observations".
JOHN NOLTON
Tombstone, AZ.
Averaging the times is making the assumption that the azimuth of Polaris changes linearly with time. This is a reasonable approximation unless the time difference is large, but it IS an approximation.
And it is done with separate computations in some books, even if they don't say that's the only way. For instance, Wolf & Ghilani, 11th ed., Example 18.2 in section 18.11 records an observation time for each sighting and does a separate computation for each.
I like the advice in the Elgin, Knowles, and Senne handbook (aka Leitz ephemeris) linked here: http://www.rollanet.org/~eksi/Handbook.htm
We always observed the target then Polaris reverse scope then Polaris then target DD-RR. We would mean times and horizontal angles. We would observe multiple sets (we did 12 sets).
Each set would be computed individually then each set compared against the mean.
Fun, fun out west with clear skies. Less so near cities or other well illuminated areas. Not much snow time work for me.
The reference above has the algorithms and some HP 41 code. I converted it to Matlab. If interested, please advise.
Cheers,
DMM
> rfc; Its always good to learn but I am sure glad I was not with you in all that snow
> and cold. What books are you using to learn from? What Instrument are you using?
Ghilani and Wolfe; Davis, Foote and Kelly.
I'm using a Topcon GTS-255.
Admittedly, mid day observations might be optimistic, but when I found it, it was a full hour before dark. I took care to pre-establish focus and marked it with matching "dots" on the focus ring. Also, I think it's as much about your eyes as it is the optics (although they are very important). A trick I learned during my sailing days, is, at dusk, observe off center in the scope...allowing the rod sensors to be used more...they either are more low light sensitive, or come "on line" sooner at dusk than the cones (in the center of the eye).
> Bill93 I would like you to show me (reference book or paper)where it says the "right way" according to you on how to reduce "Polaris observations".
>
Davis, foot and Kelly come close to what bill93 is suggesting...although they do say meaning D&R as well as the time between them (if it's short)is usual and customary.
They don't say what "short" is. It took me about 3 minutes between D&R, so I don't know if that constitutes "short".
But they also go on about doing 12 sets! And also mounting the instrument on a concrete pier! Whoa! I want to know my Azimuth sure enough, but it's not like I'm setting up a new NGS Azimuth Pair Bench mark!
D,F,& K was written for people using a half-minute transit. There was a lot of room for improvement by averaging instrument readings before you get down to the other types of error. Other errors being personal sighting errors, slight wiggle in the tripod, etc.
Modern instruments being much more accurate get you to the level of other errors with less averaging of the instrument errors.
That said, understanding what D,F, & K are teaching on most subjects helps a great deal in understanding what modern instruments and software are doing for you so you understand the foundations and the assumptions.
I've always processed each observation individually as this allows me to see the distribution of the residuals which can be telling. Averages give you one answer.
I remember once that I miss entered the latitude (I think it was) and the residuals were a string instead of a random cluster. It was apparent that there was a problem.
Polaris & curvature correction
Bill93 one of the corrections made to an astronomic observation on Polaris would be "curvature correction" of which you are alluding to. There are tables that have the correction in them and one such table would be Table XIV on page 192 of
Manual of Geodetic Astronomy, Special Publication # 237 by NGS. This table shows that if your difference in pointing on Polaris between a D&R (or R&D) is 6 minutes then the correction could reach 1.0 seconds of arc (this would be when Polaris is at East or West Elongation; and less of a correction when it is closer to the pole).
JOHN NOLTON
Tombstone, AZ.
For rfc and others.
Some other books that are good to learn Astronomic observation from would be:
1. A Manual on Astronomic and Grid Azimuth by R.B. Buckner (good for 3rd order azimuth)
When you really get into the subject and want to know 1st and 2nd order work look at the following.
1. Manual of Geodetic Astronomy, Special Publication #237 By NGS (old but still good)
2. Spherical and Practical Astronomy by Prof. I.I. Mueller
3. Geodatische Astronomie by Albert Schodlbauer (in German but very good).
There are more but this will keep you busy for some time.
JOHN NOLTON
Tombstone, AZ.
Another book
In my above post about books on astronomic azimuth observation I left out.
The Elements of Astronomy for Surveyors by J. B. Mackie
JOHN NOLTON
Tombstone,AZ.
free set of lecture notes
www2.unb.ca/gge/Pubs/LN49.pdf
The link above is to the lecture notes for the course Introduction to Geodetic Astronomy by D. B. Thomson (December 1981) provided by the University of New Brunswick. Check out Chapter 7. He readily acknowledges his debt to I. Mueller recommended in Mr. Nolton's note.
I understand the course in Geodetic Astronomy at The Ohio State University has been discontinued (course text in the late 1980s was the Mackie text).
Interesting to see the continuing interest in using astronomical observations. The Leitz ephemeris I linked was the product of three PhD professor/surveyors. In the 1980s they gave workshops at ACSM meetings on solar observations. Very practical information for those interested more in the doing than understanding.
BTW, if interested in current uses of astronomical techniques so web search for the article "Status of Geodetic Astronomy at the Beginning of the 21st Century" by Christian Hirt and Beat Bu?rki. Some of the equipment mentioned was (will be?) used in NGS geoid slope validation surveys.
free set of lecture notes
> www2.unb.ca/gge/Pubs/LN49.pdf
>
> The link above is to the lecture notes for the course Introduction to Geodetic Astronomy by D. B. Thomson (December 1981) provided by the University of New Brunswick. Check out Chapter 7. He readily acknowledges his debt to I. Mueller recommended in Mr. Nolton's note.
That's very interesting, as are the references Mr. Nolton points out. Unfortunately, most are pretty expensive (given all the other stuff on my "must get" list, lol.)
> Interesting to see the continuing interest in using astronomical observations. The Leitz ephemeris I linked was the product of three PhD professor/surveyors. In the 1980s they gave workshops at ACSM meetings on solar observations. Very practical information for those interested more in the doing than understanding.
I've read the Leitz book and it does indeed have information for those who don't want to spend all their time reading books (that includes me).
It seems that the advent of GPS and OPUS has pretty much done away with astronomical observations.
