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A method for determining True North

Many field archaeological surveys are probably done using systems with magnetic compasses, either incorporated into surveyors' transits or pocket transits such as the Brunton, or by use of small hand compasses, to obtain True North. In many areas local magnetic variation makes compasses unreliable, and ties to geodetic survey markers or other fixed objects like hill tops,churches, etc. to obtain True North can sometimes be difficult to find.

The system reported herein was developed for use in the field in an effort to obtain alignments relative to True North of a number of widely separated sites in Portugal, where ties to geodetic markers would be difficult, especially for a lone worker. The requirement for headings accurate to less than one degree, preferably to less than 0.5°, was met using an older model "midget" transit capable of reading reliably to 10 minutes of arc. The azimuth circle on the transit is engraved in degrees 0-90-0-90-0. The telescope of this transit can only be elevated to 45° above horizontal, unfortunately.

The method uses solar azimuths obtained from a calculator available online at the web site of the United States Naval Observatory. The calculator can produce solar altitudes and azimuths, in degrees and tenths, at intervals of one minute or longer at the user's choice, for the entire period the sun is above the horizon. The technique is as follows:
The transit, mounted on its tripod, is set up at the point from which a True North heading is desired. After leveling carefully, and consulting the table of azimuths, at the precise time from the table the telescope is pointed at the sun, using a solar filter, and the sun is centered on the vertical cross hair, or the sun's image is projected through the eyepiece onto a piece of paper and centered on the shadow of the telescope barrel. If the sun's altitude is too high for the telescope's altitude setting, the shadow of the telescope barrel can be used to aim the telescope at the sun, with a slight sacrifice in accuracy. When the telescope is aimed satisfactorily at the sun, the azimuth motion is locked.

Looking down at the transit's azimuth circle, always read and work counterclockwise (cc). Reading the azimuth on the circle, if the heading is decreasing cc, add it to 90; this takes you cc past the first 0 to the following 90. Then subtract the result from the table heading, and subtract the second result from 90 to give the True North heading. If this third result is greater than 90, continue cc past the 0 degree index the amount in excess of 90°.
For example: at 11:55 the solar azimuth from the table is 178.2°; the solar azimuth heading on the transit is read as 71.1° decreasing cc.  71.1+90=161.1°; 178.2-161.1=17.1°; 90-17.1=72.9°. Rotate the transit scope cc from 71.1 to 0 to 90 to 72.9 and the scope is now pointing True North.

If the heading is increasing cc, subtract it from 90, then add 90 to the result; this takes you cc past the first 90 to the following 0. Subtract the second result from table azimuth to obtain the True North heading. If this amount is more than 90, continue cc past the next 90° index the amount in excess of 90°.
For example: at 11:55 the solar azimuth from the table is 178.2°; the solar azimuth heading on the transit is read as 71.1° increasing cc. 90-71.1=18.9+90=108.9°; 178.2-108.9=69.3°. Rotate the transit scope cc from 71.1 to 90 to 0 to 69.3 and the scope is now pointing True North.

Both of these procedures are necessary because it is nearly impossible to set up and level the transit so that a 0° or 90° index is zeroed on the sun's azimuth; this method makes such a step unnecessary.

In tests of the method, True North, checked by sighting the North star, was obtained to an accuracy of about 1/3°. Accurate site location information can be obtained using a GPS receiver.

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