Analemmatic sundials are a type of horizontal sundial that has a vertical gnomon 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. [1] As with most sundials, analemmatic sundials mark solar time rather than clock time.
An analemmatic sundial is completely defined by [2] [3]
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. [1]
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 or the analemma 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. [4] 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." [5]
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. [6] 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
where t is the time (in hours) before or after noon. [7]
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
where W is half the width of the ellipse and δ is the Sun's declination at that time of year. [8] 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.
| month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| declination | -23.13 | -17.3 | -8 | 4.25 | 15 | 22 | 23.00 | 18 | 8.50 | -2.9 | -14 | -21.7 |
| Mean values on the first of the month. This averages out the effect of leap years. [9] | ||||||||||||
In astronomy, declination 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 the celestial equator, along the hour circle passing through the point in question.
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 pole, with 0° at the Equator. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth.
A sundial is a horological device that tells the time of day 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 flat plate and a gnomon, which casts a shadow onto the dial. As the Sun appears to move through the sky, the shadow aligns with different hour-lines, which are marked on the dial to indicate the time of day. The style is the time-telling edge of the gnomon, though a single point or nodus may be used. The gnomon casts a broad shadow; the shadow of the style shows the time. The gnomon may be a rod, wire, or elaborately decorated metal casting. The style must be parallel to the axis of the Earth's rotation for the sundial to be accurate throughout the year. The style's angle from horizontal is equal to the sundial's geographical latitude.
A diptych is any object with two flat plates which form a pair, often attached by hinge. For example, the standard notebook and school exercise book of the ancient world was a diptych consisting of a pair of such plates that contained a recessed space filled with wax. Writing was accomplished by scratching the wax surface with a stylus. When the notes were no longer needed, the wax could be slightly heated and then smoothed to allow reuse. Ordinary versions had wooden frames, but more luxurious diptychs were crafted with more expensive materials.
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 figure eight. Earth often display an analemma as a two-dimensional figure of equation of time vs. declination of the Sun.
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.
The equation of time describes the discrepancy between two kinds of solar time. The word equation is used in the medieval sense of "reconciliation of a difference". The two times that differ are the apparent solar time, which directly tracks the diurnal motion of the Sun, and mean solar time, which tracks a theoretical mean Sun with uniform motion along the celestial equator. Apparent solar time can be obtained by measurement of the current position of the Sun, as indicated by a sundial. Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time would have a mean of zero.
The solar zenith angle is the zenith angle of the sun, i.e., the angle between the sun’s rays and the vertical direction. It is the complement to the solar altitude or solar elevation, which is the altitude angle or elevation angle between the sun’s rays and a horizontal plane. At solar noon, the zenith angle is at a minimum and is equal to latitude minus solar declination angle. This is the basis by which ancient mariners navigated the oceans.
Polar alignment is the act of aligning the rotational axis of a telescope's equatorial mount or a sundial's gnomon with a celestial pole to parallel Earth's axis.
François-Lamathe Dom Bédos de Celles de Salelles was a Benedictine monk best known for being a master pipe organ builder.
Astronomical rings, also known as Gemma's rings, are an early astronomical instrument. The instrument consists of three rings, representing the celestial equator, declination, and the meridian.
The Whitehurst & Son sundial was produced in Derby in 1812 by the nephew of John Whitehurst. It is a fine example of a precision sundial telling local apparent time with a scale to convert this to local mean time, and is accurate to the nearest minute. The sundial is now housed in the Derby Museum and Art Gallery.
The Noon mark is a type of sundial that at its simplest is a vertical line on a south facing wall or a north-south line on a horizontal pavement. When the shadow of a point crosses the line it will be midday. Noon in local standard time is defined as when the sun is overhead, however clocks and watches use mean time which varies from standard time by a few minutes each day. The difference is calculated using the equation of time and this can be shown on the noon mark by drawing an analemma, or using a correction table.
The position of the Sun in the sky is a function of both the time and the geographic location of observation on Earth's surface. As Earth orbits the Sun over the course of a year, the Sun appears to move with respect to the fixed stars on the celestial sphere, along a circular path called the ecliptic.
A bifilar dial is a type of sundial invented by the German mathematician Hugo Michnik in 1922. It has two non-touching threads parallel to the dial. Usually the second thread is orthogonal-(perpendicular) to the first. The intersection of the two threads' shadows gives the local apparent time.
Giovanni Francesco Zarbula was a mural painter and sundial designer from Piedmont Italy who created a hundred or more vertical and vertical declining sundials in the French and Italian Alpes between 1830 and 1881. He worked exclusively in Savoy, in Piémont, the Valley of the Ubaye, le Queyras and around Briançon.
Dialing scales are used to lay out the face of a sundial geometrically. They were proposed by Samuel Foster in 1638, and produced by George Serle and Anthony Thompson in 1658 on a ruler. There are two scales: the latitude scale and the hour scale. They can be used to draw all gnomonic dials – and reverse engineer existing dials to discover their original intended location.
A London dial in the broadest sense can mean any sundial that is set for 51°30′ N, but more specifically refers to a engraved brass horizontal sundial with a distinctive design. London dials were originally engraved by scientific instrument makers. The trade was heavily protected by the system of craft guilds.
A schema for horizontal dials is a set of instructions used to construct horizontal sundials using compass and straightedge construction techniques, which were widely used in Europe from the late fifteenth century to the late nineteenth century. The common horizontal sundial is a geometric projection of an equatorial sundial onto a horizontal plane.
Vertical declining dials are sundials that indicate local apparent time. Vertical south dials are a special case: as are vertical north, vertical east and vertical west dials. The word declining means that the wall is offset from one of these 4 cardinal points. There are dials that are not vertical, and these are called reclining dials.
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