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Phases

Map of Phase III

Map of Phase III
The Human Sundial
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Phase I & II
Phase III

Details of the Analemmatic Sundial

Most garden sundials are horizontal sundials that consist of a circular or square dial plane and a fixed gnomon. Hour lines on the dial plane radiate at specific angles from an origin. The gnomon must be inclined at an angle equal to the latitude of the sundial's location for the sundial to work properly. (For example, in Calgary the gnomon should be inclined at 51 degrees.) When the gnomon is inclined in this manner, the gnomon is then parallel to the earth's axis of rotation and the direction of a shadow at any given hour of the day is constant, regardless of the season. However, this does present a problem if you wish the gnomon to be a person, as there may be some difficulty in standing at such an angle!

That is the reason for the using the analemmatic sundial. This particular sundial takes into account the fact that the gnomon is vertical. However, in doing so, two imortant changes must be made to the sundial. First, the gnomon position is different for every day of the year. This makes sense, as you would expect to stand closer to the time numbers in June, when the sun is high overhead and shadows are shorter, and farther away in December, when the sun is low in the sky and shadows are longer. For a practical application, we obviously cannot paint a gnomon position for every day of the year, but we can show the foot positions for the first day of each month. Students can then interpolate for dates in-between. Second, the hour times for an analemmatic sundial are points unevenly spaced around an ellipse, in contrast to the time lines on a horizontal sundial.

The above paragraph may make the creation of a human sundial seem daunting, but rest assured that mathematicians have the analemmatic sundial all figured out, and leave behind several simple formulas for us to use to calculate the time and gnomon positions.

Details of the Analemmatic Sundial

Installing an Analemmatic Sundial

Equation of Time

References

Appendix