Analemmatic sundial
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Analemmatic sundial
Analemmatic sundials are a common feature at science museums , planetariums and occasionally in public places. They exploit the fact that the sun travels in a predictable pattern over the course of a year called the analemma and trace the projection of an object's shadow to measure time, not only the hours, as in normal sundials, but also weeks and months.
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Description
Accurate dials of this type are popular in public places, using a ball at the tip of a flagpole as the nodus, with the sundial face painted on or inlaid in the pavement. A less accurate version of the sundial is to lay out the hour marks on a pavement, and then let the user stand in a square marked with the month. The user's head then forms the gnomon of the dial. In middle latitudes, the ellipse with the hour-marks will be about six meters wide, so the shadow of the head of the beholder falls near it most of the time.[1] The month standing positions are arranged to correct the sundial for the time of year. [2]
Construction
An analemmatic sundial uses a vertical gnomon and its hour lines are the vertical projection of the hour lines of a circular equatorial sundial onto a flat plane.[3] Therefore, the analemmatic sundial is an ellipse, where the short axis is aligned North-South and the long axis is aligned East-West. The noon hour line points true North, whereas the hour lines for 6am and 6pm point due West and East, respectively; the ratio of the short to long axes equals the sine sin(Φ) of the local geographical latitude, denoted Φ. All the hour lines converge to a single centre; the angle θ of a given hour line with the noon hour is given by the formula[4]
where t is the time (in hours) before or after noon. However, the vertical gnomon does not always stand at the centre of the hour lines; rather, to show the correct time, the gnomon must be moved northwards from the centre by the distance[5]
where W is half the width of the ellipse and δ is the Sun's declination at that time of year. The declination measures how far the sun is above the celestial equator; at the equinoxes, δ=0 whereas it equals roughly ±23.5° at the summer and winter solstices.
See also
- Equation of time
- Fajada Butte in Chaco Canyon
References
- ^ "Analemmatic sundials: How to build one and why they work" by C.J. Budd and C.J. Sangwin
- ^ Sunclocks - Human Sundials, using your own shadow to tell correct time
- ^ Rohr (1965), pp. 100–106; Waugh (1973), pp. 108–115; Mayall and Mayall, p. 60–61, 186–190.
- ^ Rohr (1965), p. 106; Waugh (1973), p. 113.
- ^ Rohr (1965), pp. 103, 111; Waugh (1973), p. 111.
External links
- Analemmatic sundial at Tanglewood (Lenox, Massachusetts)]
- Analemmatic sundial generator
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