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Poor man's methods to determine azimuth

In this page some poor man's methods to determine the azimuth are discussed (so no theodolite), using as an example measurements done between Baltray and Rockabill (both in Ireland). The following methods are discussed: Some conclusions are available.
In case of a North Arrow in the document, please check what it is.As the below methods have a larger error than the Laplace correction between Astronomic and Geodetic azimuth, one can say that Astronomic azimuth ~ Geodetic azimuth.

Longitude/latitude

The longitude and latitude can be determined by: Using the longitude and latitude of two points (A and B), one can determine the azimuth using the great circle method.
A GPS does this already, except that it most of the time rounds it up to full degrees:-(, but the GPS Utility program provides accurate azimuth information (see for help this page).
A web page has been made to calculate the azimuth using this method.
In general the two points must be more than 400 m apart, otherwise the error becomes bigger than 30'. More info on GPS accuracy can be found here (make sure one averages the longitude and lattiude for at least for 2 minutes with the GPS).

The Geodetic azimuthl from Baltray stone towards the Rockabill (map references gotten from the OS map) is: 132° 37' +/- 1'.

Map grid

The map grid (in [m]) can be determined by:
Using the map grid of two points (A and B), one can determine the azimuth using the normal trigonometry. The map azimuth has to be compensated with the difference between Grid North and Geodetic North (the basic Convergence angle formula comes from A. Thom).
A GPS does this already, except that it most of the time rounds it up to full degrees:-(, but the GPS Utility program provides accurate azimuth information (see for help this page).
A web page has been made to calculate the azimuth using this method.
In general the two points must be more than 800 m apart, otherwise the error becomes bigger than 30'. More info on GPS accuracy can be found here (make sure one averages the longitude and latitude for at least for 2 minutes with the GPS).

The OS map coordinates are: Just using trigonometry you get:
map azimuth = 90 - arctan ((78170-62660)/(14476-32177)) = 131° 14'

The Convergence angle is: -1° 24' +/- 1'
So the Geodetic azimuthm is here: map azimuth - Convergence angle = 132° 38+/- 2'
 

Magnetic grid

The compass is using the Magnetic grid over the earth. Because Magnetic North is not the same as Astronomic North, one has to compensate the compass reading with the Magnetic declination (go to this web page to calculate an approximation of this Magnetic declination and its variance).
Remember to remove any magnetic material from body (watches, glasses, (even straw) hats, rings, piercings, etc). Also don't stand near fences, power cables, cars, etc. AND stones (because most stones generally contain some iron and will thus influence the magnetic grid). Change position and measure in reverse direction to see if there are anomalies.

Measurements done in the circle entrance path
of Circle B at Lough Gur

So looking at this result, one needs to stand at least 5 yards from a fence. The best way is to do a few measurements while stepping one step back and forward and measure in reverse direction. If these measurement differ much, there must be something around that disturbs the magnetic field.

More information on error determination of magnetic grid readings (such as using a reference measurements) check this page.


Compass measurement (using Suunto KB-20) was done from the dunes towards Rockabill (in line with Baltray): This gives a 139.2° +/- 15' magnetic azimuth (in 2000) which has to be compensated with Magnetic declination (-6° 12' +/- 30').
Thus the Geodetic azimuthc becomes: magnetic azimuth + Magnetic declination = 133° 0' +/- 35'
Some Javascript to help you:
    Astronomic Azimuth = Magnetic azimuth + Magnetic declination
                                                        (east is positive and west is negative)
    Magnetic azimuth: [°]
    Magnetic declination: [°](easterly is + and westerly is -)
    the Geodetic azimuth: [°]
Or when using information from a UK or Irish OS map (Magnetic-Grid difference= Magnetic declination+Convergence angle):
    Geodetic Azimuth = Magnetic azimuth + Magnetic-Grid difference - Convergence angle
                                                        (east is positive and west is negative)
    Magnetic azimuth: [°]
    Magnetic-Grid difference: [°](easterly is + and westerly is -)
    Convergence angle: [°](easterly is + and westerly is -)
    the Geodetic azimuth: [°]

Reference object

An important poor man's method is of course using a reference object with known position on land or in the sky (like a church, sun, stars, moon)  as a means of providing the azimuth.
In the case of a celestial object one has to determine the time (use a clock as precise as possible, like GPS or NTP) the measurements were done. Using an ephemeris programs one can determine the azimuths (e.g. SkyMap or JPL ephemeris), an example of a JPL e-mail query can be found here.
The reference land object has to be determined by Longitude/latitude or Map grid.
The angle between this object and the intended object can be determined by photometric method.
A theodolite or transit will also use such a reference object.

In this case the reference object has been chosen as a celestial object: the Sun and the Moon. Make sure one gets the full horizontal width of the celestial object in the picture, this can then be used as a reference of the angle (around 30').
 
A picture was used from Michael Byrne who video taped the winter solstice sunrise event at Baltray on Dec. 21st, 1999.
This picture has been copied on this page and some photometry information is added:

Some photometry information is added
to the picture of Michael Byrne

From this picture one can determine (called photometry method), based on the width of the Sun (A) and the height above the horizon (B), an approximate time when it was taken (19:45 BST). Using the distance between the middle of the sun and Rockabill (C) one can then calculate the position of Rockabill. Doing that gives an Astronomic azimuthr of: 132° 24' +/- 10'.

Another picture has been taken on Dec. 21st, 2004 by Anthony Murhpy. If the centre of the Sun in this picture is indeed on the horizon, the Sun's azimuth is ~130° 50', furthermore the distance between Sun's centre and lighthouse Rockabill looks to be 3.25 times the diameter of the Sun, so around 3.25*0.542° = ~1° 46', thus the Astronomic azimuth of the lighthouse on Rockabill looks to be: ~132° 26'. Thus is again very close to the values calculated above.

In the below picture a trial has been made to show how the winter solstice Sun of 4000 years ago would have looked like  in relation to Rockabill (seen from Baltray). I have used the moon as a proxy;-)


Moon just above lighthouse at Rockabill
on July 17th, 2000 at 22:30 BST seen from Bettystown beach,
proxying the winter solstice Sun of 4000 years ago seen from Baltray.

It is also done from the beach of Bettystown but now with the Moon as celestial object. The Moon was directly above Rockabill at an azimuthr of 124° 45' +/- 1'.
In the above picture the Moon is precisely at the same position above Rockabill as the winter solstice Sun would have been 4000 years ago seen from Baltray.

Remote light source

The shadow of a celestial body can also be used to determine this (certainly when determining the sunniness/mooniness). One has to determine the time (use a clock as precise as possible, like GPS or NTP) the measurements were done. The azimuths of the sun/moon can be determined by ephemeris programs (e.g.SkyMap or JPL ephemeris). Remember that these programs determine the middle of the celestial object and normally the shadow is determined by the left or right rim of the object (for moon and sun this is around 16' difference). 

This method was not used for Baltray (can be difficult with alignments of one stone). But see a worked out example for Maeshowe.

Building survey

Use a good ground plan of the building (from literature or made yourself). Remember that an accurate direction must be provided by this ground plan (using one of the methods mentioned above). Information from ground plan can be input in the sunniness/mooniness page to determine azimuth (and apparent altitude)

This method was not used for Baltray (can be difficult with alignments of one or two stones). But see a worked out example for Maeshowe.

Conclusions

(Including results taken from Bettystown)

The Map grid en Reference object are some 8' from each other. Longitude/latitude and Reference object reading are some 4' off. The Magnetic grid has the most variation.
I assume that the Reference object reading is at the end the most accurate, but Longitude/latitude and Map grid can do in most instances.

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Last major content related changes: Aug. 6, 2000