Formulae, programmes



A representative selection of individual sets of data for several sites is given in 'Raw Data'.    From this must be found first the sun's azimuth and from it the azimuth of the plate zero (A.P.Z.) as follows

The azimuth of the observed horizon feature (usually the ‘referred object’ or R.O.) is found using the formula below.

Both limbs of the sun are measured and time of each noted.  These are averaged and any adjustments necessary for watch time is made, thus giving the G.M.T.    The Greenwich hour angle for the nearest previous hour  is taken from the Nautical Almanac (available online ), and adjusted for minutes and seconds.  Applying the longitude gives the local hour angle H.

To obtain the Sun’s azimuth A we use:-

Cot A = sin φ/ tan H – cos φ tan δ / sin H

Where φ is the latitude and δ the sun’s declination (also from the Nautical Almanac)

Deducting the corresponding mean plate bearing (P.B.) gives the azimuth of the plate zero (A.P.Z.).     Normally 3 or 4 sets of solar observations are made.    These are averaged to give the mean A.P.Z.     The azimuth of the R.O. is then obtained by adding its P.B. to the mean A.P.Z.

A worked example of azimuth calculation from the raw data for Ford is given here.

The calculation of A (sun azimuth) using a calculator is slow and liable to mistakes.  It is greatly eased by using an excel programme such as:-  Thomas_Calculator(2)


Having found the azimuth of a desired horizon point, the declination δ is found by

sin δ = sin Φ sin h + cos Φ cos h cos A

where Φ = latitude, A = azimuth, and h = horizon elevation corrected for refraction.

Clive Ruggles has on his website a useful programme for this calculation called GETDEC4.  This programme automatically allows for standard refraction.   It is however in 16 bit format