| The gnonom (shown in green) casts a
shadow on the base of the horizontal sundial indicating the time of the day. The angle θ must be equal to the latitude. Where should one place the hourly markings on the sundial? In other words, at 1:00 PM what is β, the angle from due North? What is it at 2:00 PM, etc? It turns out that there is a very simple formula relating time t, the number of hours before or after noon, with θ and β given by: |
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tan(β) = sin(θ) tan(t*15o) |
| This formula is derived below along
with a table and diagram for any given latitude. The vector from (a, b, 0) to the tip of the gnomon (shown as a dashed red line) is given by v = (-a, Lcos(θ) - b, Lsin(θ)) and points in the direction of the sun. The position of the sun is given by (x', y', z'). The equations and their derivation for x', y', and z' are found at the web page: sunpositformulas.htm. |
