Article of the month July
Projection for analemmatic
and horizontal sundial
Both figures below show the celestial globe with its axis. That axis is also the axis of the earth.
Square to the axis, the equator and some hour points are drawn. In reality there are 24 hour points, always 15 degrees apart.
Additionally, two lines on either side of the equator indicate the extreme values for the solar declination: plus and minus 23.5 degrees.
If many solar declinations were plotted, they would trace out, on the celestial axis, a complete date scale.
The equator is now projected onto the horizontal plane.
Left is drawn a parallel projection vertically down, to the right is a parallel projection along the celestial axis (which is really the axis of the earth).
In both drawings we arrive at an ellipse with hour points.
These ellipses are similar, only the scale differs. The ratio of semi-major to semi-minor axis equals the sine of the latitude.
The orientations of the ellipses are different. For the analemmatic sundial, the major axis lays East West; for the horizontal sundial it lays North South.
The date scale on the celestial axis is also projected.
For the analemmatic sundial, it becomes a date scale in the horizontal plane on which a vertical gnomon is placed.
In the horizontal sundial, the date scale collapses into a single point, where the pole style is placed under an angle equal to the latitude. The pole style, therefore, does not need to be adjusted for the date.
Because of this, hour lines may be drawn from the foot of the pole style to the hour points, whereas in an analemmatic sundial, only hour points on the ellipse can be used for readout.
If you have the pattern for an analemmatic sundial, you may construct a pole style sundial directly from it:
Draw hour lines from the centre to the hour points, turn the ellipse 90 degrees, and adjust the hour numerals.