Analemmatic dials

Longwood Gardens, Kennett Square (Pennsylvania, USA)

Analemmatic dial, Longwood Gardens
(photo from Sky & Telescope)

This large dial is set in the beautiful gardens of this former country estate. The major axis is over 11 m (37 ft). It is unique among the analemmatic dials, as it reads civil time, in this case daylight saving time.

For me, the analemmatic dial is attractive because I can act myself as a gnomon. That balances the inaccuracy inherent from my imprecise placement on the date line or the width of my shadow. I don't mind an error of less than 10 minutes so much, or there's my watch. Only in October/November and around February there may be a little problem.
Some people aim higher, however. Among them Pierre du Pont, the former owner of the estate. He used a vertical rod as a gnomon, to obtain a more accurate reading. Just to learn that the dial deviated from the clock.

A dial that should read mean (or standard) time should take account of the equation of time. Many sundial types can do so, for instance by having analemmas substituted for the hour lines (example: Nijmegen), to give the gnomon a special shape (Lattrop), or to make the time scale adjustable (Roussillon).
The trick of replacing the date line by an analemma, as was done in Brou, doesn't work. By stepping beside the date line the reading may be correct around noon, but the correction will too small in the morning and the afternoon. One solution is to replace each hour point by an analemma, but then it is difficult to read the time from where one stands, and even more so in between hour points.

Separate analemmas for am and pm hours Kenneth Seidelman [ref.1] developed another solution for the Longwood dial in the 70's. Recognizing that a theoretically correct solution is impossible, he aimed at an approximation that would be good enough. He calculated separate analemmas for the morning and afternoon hours, on which to place the gnomon. The deviation is less than 1-2 minutes between 7 am and 5 pm. Outside these hours, the error is still only a couple of minutes.
Seidelman then cut the dial face in half and separated the two parts by a foot or so, to avoid confusion between the corresponding analemmas. Each day at 1 pm (DST) the gnomon is moved from the morning to the afternoon analemma.


Divisions per day (photo: Longwood website) The gnomon has to be placed very precisely in order to get at the calculated accuracy. Therefore the analemmas have divisions per day, as you can see alongside. The time scale along the ellipse should have a correspondingly fine grain, but I don't see much of that in the top picture.
Another problem is that the gnomon is not long enough for its shadow to always reach the time scale. Sawyer calculated that it would have to be more than 19 ft (almost 6 m). In fact it is about 6 ft (2 m).


The Seidelman paper [ref.1] is short in details on the procedure he used to find the optimum approximation. The article by Fred Sawyer [ref.2] is more informative in this respect. It gives an extensive account on the background of the problem and considers several options for calculating an optimum solution.

References

  1. P.K. Seidelman, A design for an analemmatic standard-time sundial.
    Sky and Telescope, December 1975, p. 368-369.
  2. F.W. Sawyer, Of analemmas, mean time and the analemmatic sundial.
    Published in several forms, but easiest found through this link.


Website: Longwood Gardens
Location: 39.9° N, 75.7° E
Design: Pierre S. du Pont/P. Kenneth Seidelman
Inauguration: 1939/1975