Analemmatic sundials are a type of horizontal

sundial A sundial is a horological device that tells the time of day (referred to as civil time in modern usage) when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a f ...

that has a vertical

gnomon A gnomon (; ) is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields. History A painted stick dating from 2300 BC that was excavated at the astronomical site of Taosi is the ...

and hour markers positioned in an elliptical pattern. The gnomon is not fixed and must change position daily to accurately indicate time of day. Hence there are no hour lines on the dial and the time of day is read only on the ellipse."Analemmatic sundials: How to build one and why they work"
C.J. Budd and C.J. Sangwin, maths.org, 1 June 2000 As with most sundials, analemmatic sundials mark

solar time Solar time is a calculation of the passage of time based on the position of the Sun in the sky. The fundamental unit of solar time is the day, based on the synodic rotation period. Two types of solar time are apparent solar time (sundial ti ...

rather than clock time.

Description

An analemmatic sundial is completely defined by # The size of its ellipse (chosen by the designer). # The latitude of its location (determines the location of the hour markers on the ellipse). # The declination of the sun (determines the daily gnomon position). Analemmatic sundials are sometimes designed with a human as the gnomon. In this case the size of the hour marker ellipse is constrained by human height and the latitude of the sundial location, since the human gnomon shadow must fall on the hour marker ellipse to accurately indicate the time of day. Human gnomon analemmatic sundials are not practical at lower latitudes where a human shadow is quite short during the summer months. A 66-inch tall person casts a 4-inch shadow at 27 deg latitude on the

summer solstice The summer solstice, also called the estival solstice or midsummer, occurs when one of Earth's poles has its maximum tilt toward the Sun. It happens twice yearly, once in each hemisphere (Northern and Southern). For that hemisphere, the summer ...

. The use of the adjective "analemmatic" to describe this class of sundial can be misleading, because there is no use of the

equation of time In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in F ...

or the

analemma In astronomy, an analemma (; ) is a diagram showing the position of the Sun in the sky as seen from a fixed location on Earth at the same mean solar time, as that position varies over the course of a year. The diagram will resemble a figur ...

in the design of an analemmatic sundial. Mayall refers to the analemmatic sundial as "the so-called Analemmatic Dial", implying a lack of connection to the analemma. The dial of Brou in front of the church of Brou in Bourg-en-Bresse, France is an example of the erroneous use of the analemma in the construction of an analemmatic sundial. Rohr states "The gnomon is displaced on the short axis of the ellipse and not on the meridian, whose presence here in the shape of an 8 is a mistake."

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. Therefore, the analemmatic sundial is an

ellipse In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in ...

, 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 In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opp ...

sin(Φ) of the local geographical

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north ...

, 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 :

\tan \theta = \frac

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 daily northwards from the centre by the distance :

Y = W \cos \phi \tan \delta \,

where ''W'' is half the width of the ellipse and δ is the Sun's

declination In astronomy, declination (abbreviated dec; symbol ''δ'') is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declination's angle is measured north or south of th ...

at that time of year.Rohr (1965), pp. 103, 111; Waugh (1973), p. 111. The declination measures how far the sun is above the

celestial equator The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. This plane of reference bases the equatorial coordinate system. In other words, the celestial equator is an abstract proj ...

; at the

equinox A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and se ...

es, δ=0 whereas it equals roughly ±23.5° at the summer and winter

solstice A solstice is an event that occurs when the Sun appears to reach its most northerly or southerly excursion relative to the celestial equator on the celestial sphere. Two solstices occur annually, around June 21 and December 21. In many count ...

References

External links

Analemmatic sundial generatorAnalemmatic and Horizontal Sundials of the Bronze AgeSun declination tables (mean)
{{DEFAULTSORT:Analemma Calendar Calendars Sundials Sculptures

Description

Construction

See also

References

External links