Journal of Geomancy vol. 1 no. 1, October 1976

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AN INVESTIGATION INTO THE DISTANCE OF THE HORIZON AT VARIOUS HEIGHTS

BY RUPERT PENNICK.

When we examine the trackways, ley lines, and Zodiacs of Britain, it is of interest to discover the distances which the constructors could see from various positions along the tracks.  We can, by the use of a Navigation Formula, calculate the distances seen under perfect weather conditions.  This does not eliminate the possibility of viewing beacons at night over similar distances.  The varying undulation of the earth’s surface and the interruption to clear viewing caused by higher elevations than the hill on which the observer is standing must be taken into account when using the Navigation Formulae, either along the trackways or leys, or when calculating visible distances using an Ordnance Survey map. 

I think it should be realised that this Navigation Formula is not limited to ground observations and may be used for calculations in balloon, plane, or any other aerial form of locomotion. 

The calculations are shown here mainly in feet and miles, as I feel most British and American readers will understand and memorize them more easily in this form.  Continentals, and others who are more familiar with the Metric system, may easily convert remembering that 1 foot = 0·3048 metre, and 1 mile = 1·6093 kilometres.  Thus, we obtain by the N.F. that at the height of 1000 feet the distance of the horizon is 39 miles.  When converted we find that at the height of 304·8 metres the distance of the horizon is 62·7627 kilometres,. 

The formula known as the Navigation Formula, or N.F., is as follows:–

Distance of the horizon in miles = 1·225√altitude in feet.  The following table which I have worked out will show the distance visible at various heights.  Intermediate heights may be calculated by the reader by use of the Navigation Formula.  (table overleaf). 

As the altitude of the observer increases, so the likelihood of any obstruction to viewing the horizon, in perfect weather conditions, decreases.  It is obvious that this work may be done in the field, or alternatively at home using any good map with contour lines.  As an example I have taken a point on Ordnance Survey Map 167.  The National Grid Reference is SU 031 251 (nearest name Mount Sorrel) height 281 feet; distance of possible horizon 20·82 miles.  Converted to Metric measurement this becomes an altitude of 85·65 metres and a horizon of 33·51 kilometres. 

If we travel due north that distance we arrive at the railway cutting 1 km due east of Crookwood Mill Farm; this 1 km east location on the National Grid Reference is SU 031 585.  This is the limit of observation if no higher elevation intervened; this is not the case for within less than a kilometre due north the hills restrict the view as they rise fairly steeply to 500 feet, only more distant hills to the north are visible as they rise fairly steeply to over 600 feet.  Looking however E by NE, the city of Salisbury, 12 km away, is visible, and as our eyes follow the valley of the River Ebble to the east they cross the Roman road near Stratford Tony and we see Dean Hill 22 km to the east.  The location of marker points may thus be estimated by the use of the Navigation Formula, and the Ordnance Survey map giving information where distance of horizon is limited by intervening heights.  I feel the use of the N.F. may prove invaluable in conjunction with published work on leys and landscape geometry. 

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