Latitude 52 degrees
Height 1.75m (5' 9")
Semi-major axis = 5m (16' 5")
Whenever I happen by the analemmatic sundial on Janskerkhof in Utrecht, I step on the date strip and read the time. With its major axis of 10 meters (33 feet), this is a large dial.
Around noon in summer, my shadow is so far short of the hour points that reading the time becomes a problem. It is just like having a watch with hands a third of the usual length. Watch makers do not make those.
The figure below shows shadow lines at the start of each season, for a person of 1.75 meters height, on an analemmatic dial for 52 degrees latitude.
It would seem ideal to me if, on each date, every time of the day, my shadow reaches to or beyond the hour points. What should the ellipse size be? A small puzzle!
For the same analemmatic sundial and for the same person of 1.75 meters height, the semi-major axis should be shortened to about 1.80 meters to meet this requirement. See below.
Conclusion:
Bigger is not always better.
An equation for the arithmeticians:
Semi-major axis = (height of person) * cos 23.5 / cos (latitude - 23.5)
In our example, this gives a semi-major axis of 1.82 meters.
Hans de Rijk
English translation: RH