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For other uses, see Sundial (disambiguation).
A combined analemmatic-equatorial sundial in Ann Morrison Park in Boise, Idaho, 43°36'45.5"N 116°13'27.6"W

A sundial is a device that tells the time of day by the apparent position of the Sun in the sky. In common designs such as the horizontal sundial, the sun casts a shadow from its style onto a surface marked with lines indicating the hours of the day. The style is the time-telling edge of the gnomon, often a thin rod or a sharp, straight edge. As the sun appears to move across the sky, the shadow-edge aligns with different hour-lines. Those sundials that directly measure the sun's hour-angle by the shadow of an edge must have that edge parallel to the axis of the Earth's rotation to tell the correct time throughout the year. The style's angle from the horizontal will thus equal the sundial's geographical latitude. It is common for inexpensive mass-produced decorative sundials to have incorrect hour angles, which cannot be adjusted to tell correct time.[1]











Apparent motion of the Sun[edit]


[citation needed]


Unlike the fixed stars, the Sun changes its position on the celestial sphere, being at a positive declination in spring and summer, and at a negative declination in autumn and winter, and having exactly zero declination (i.e., being on the celestial equator) at the equinoxes. The Sun's celestial longitude also varies, changing by one complete revolution per year. The path of the Sun on the celestial sphere is called the ecliptic. The ecliptic passes through the twelve constellations of the zodiac in the course of a year.[citation needed]






For more details on this topic, see History of sundials.
World's oldest sundial, from Egypt's Valley of the Kings (c. 1500 BC)

The earliest sundials known from the archaeological record are the obelisks (3500 BC) and shadow clocks (1500 BC) from ancient Egyptian astronomy and Babylonian astronomy. Presumably, humans were telling time from shadow-lengths at an even earlier date, but this is hard to verify. In roughly 700 BC, the Old Testament describes a sundial — the "dial of Ahaz" mentioned in Isaiah 38:8 and II Kings. The Roman writer Vitruvius lists dials and shadow clocks known at that time. A canonical sundial is one that indicates the canonical hours of liturgical acts. Such sundials were used from the 7th to the 14th centuries by the members of religious communities.Italian astronomer Giovanni Padovani published a treatise on the sundial in 1570, in which he included instructions for the manufacture and laying out of mural (vertical) and horizontal sundials. Giuseppe Biancani's Constructio instrumenti ad horologia solaria (ca. 1620) discusses how to make a perfect sundial.[citation needed] They have been commonly used since the 16th century.


A London type horizontal dial. The western edge of the gnomon is used as the style before noon, the eastern edge after that time. The changeover causes a discontinuity, the noon gap, in the time scale.







Sundials in the Southern Hemisphere[edit]


A sundial at a particular latitude in one hemisphere must be reversed for use at the opposite latitude in the other hemisphere. [5] A vertical direct south sundial in the Northern Hemisphere becomes a vertical direct north sundial in the Southern Hemisphere. To position a horizontal sundial correctly, one has to find true North or South. The same process can be used to do both. [6] The gnomon, set to the correct latitude, has to point to the true South in the Southern hemisphere as in the Northern Hemisphere it has to point to the true North. [7] Also the hour numbers go in opposite directions, so on a horizontal dial they run anti-clockwise rather than clockwise.[8]


Adjustments to calculate clock time from a sundial reading[edit]


Summer (daylight saving) time correction[edit]


Time-zone (longitude) correction[edit]


At its most extreme, time zones can cause official noon, including daylight savings, to occur up to three hours early (the sun is actually directly overhead at official clock time of 3 pm). This occurs in the far west of Alaska, China, and Spain. For more details and examples, see Skewing of time zones.

Equation of time correction[edit]

The Equation of Time - above the axis the equation of time is positive, and a sundial will appear fast relative to a clock showing local mean time. The opposites are true below the axis.
Main article: Equation of time

Although the Sun appears to rotate nearly uniformly about the Earth, it is not perfectly uniform. This is due to the ellipticity of the Earth's orbit (the fact that the Earth's orbit about the Sun is not perfectly circular) and the tilt (obliquity) of the Earth's rotational axis relative to the plane of its orbit. Therefore, sundials time varies from standard clock time. On four days of the year, the correction is effectively zero. However, on others, it can be as much as a quarter-hour early or late. The amount of correction is described by the equation of time. This correction is universal; it does not depend on the local latitude of the sundial. It does, however, change over long periods of time, centuries or more,[10] because of slow variations in the Earth's orbital and rotational motions. Therefore, tables and graphs of the equation of time that were made centuries ago are now significantly incorrect. The reading of an old sundial should be corrected by applying the present-day equation of time, not one from the period when the dial was made.




Sundials with fixed axial gnomon[edit]



Some types of sundials are designed with a fixed gnomon that is not aligned with the celestial poles like a vertical obelisk. Such sundials are covered below under the section, "Nodus-based sundials".

Empirical hour-line marking[edit]

The formulas shown in the paragraphs below allow the positions of the hour-lines to be calculated for various types of sundial. In some cases, the calculations are simple; in others they are extremely complicated. There is an alternative, simple method of finding the positions of the hour-lines which can be used for many types of sundial, and saves a lot of work in cases where the calculations are complex.[13] This is an empirical procedure in which the position of the shadow of the gnomon of a real sundial is marked at hourly intervals. The equation of time must be taken into account to ensure that the positions of the hour-lines are independent of the time of year when they are marked. An easy way to do this is to set a clock or watch so it shows "sundial time"[b] which is standard time,[c] plus the equation of time on the day in question.[d][14] The hour-lines on the sundial are marked to show the positions of the shadow of the style when this clock shows whole numbers of hours, and are labelled with these numbers of hours. For example, when the clock reads 5:00, the shadow of the style is marked, and labelled "5" (or "V" in Roman numerals). If the hour-lines are not all marked in a single day, the clock must be adjusted every day or two to take account of the variation of the equation of time.

Equatorial sundials[edit]



   H_E = 15^{\circ}\times t (hours)

The uniformity of their spacing makes this type of sundial easy to construct. If the dial plate material is opaque, both sides of the equatorial dial must be marked, since the shadow will be cast from below in winter and from above in summer. With translucent dial plates (e.g. glass) the hour angles need only be marked on the sun-facing side, although the hour numberings (if used) need be made on both sides of the dial, owing to the differing hour schema on the sun-facing and sun-backing sides. Another major advantage of this dial is that equation of time (EoT) and daylight saving time (DST) corrections can be made by simply rotating the dial plate by the appropriate angle each day. This is because the hour angles are equally spaced around the dial. For this reason, an equatorial dial is often a useful choice when the dial is for public display and it is desirable to have it show the true local time to reasonable accuracy. The EoT correction is made via the relation :

 Correction^{\circ} = \frac{EoT (minutes) + 60 \times \Delta DST (hours)}{15}



Horizontal sundials[edit]

For a more detailed description of such a dial, see London dial and Whitehurst & Son sundial (1812).

In the horizontal sundial (also called a garden sundial), the plane that receives the shadow is aligned horizontally, rather than being perpendicular to the style as in the equatorial dial.[19] [20] [21] Hence, the line of shadow does not rotate uniformly on the dial face; rather, the hour lines are spaced according to the rule [22] [23]

\tan H_H = \sin L  \tan(15^{\circ} \times t)

Or in other terms:

\ H_H = \tan^{-1}[\sin L \times \tan(15^{\circ} \times t)]

where L is the sundial's geographical latitude (and the angle the style makes with horizontal),  H_H is the angle between a given hour-line and the noon hour-line (which always points towards true North) on the plane, and t is the number of hours before or after noon. For example, the angle  H_H of the 3pm hour-line would equal the arctangent of sin L, since tan 45° = 1. When L equals 90° (at the North Pole), the horizontal sundial becomes an equatorial sundial; the style points straight up (vertically), and the horizontal plane is aligned with the equatorial plane; the hour-line formula becomes  H_H = 15° × t, as for an equatorial dial. A horizontal sundial at the Earth's equator, where L equals 0°, would require a (raised) horizontal style and would be an example of a polar sundial (see below).

Detail of horizontal sundial outside Kew Palace in London, United Kingdom

The chief advantages of the horizontal sundial are that it is easy to read, and the sun lights the face throughout the year. All the hour-lines intersect at the point where the gnomon's style crosses the horizontal plane. Since the style is aligned with the Earth's rotational axis, the style points true North and its angle with the horizontal equals the sundial's geographical latitude L. A sundial designed for one latitude can be adjusted for use at another latitude by tilting its base upwards or downwards by an angle equal to the difference in latitude. For example, a sundial designed for a latitude of 40° can be used at a latitude of 45°, if the sundial plane is tilted upwards by 5°, thus aligning the style with the Earth's rotational axis.[citation needed] Many ornamental sundials are designed to be used at 45 degrees north. Some mass-produced garden sundials fail to correctly calculate the hourlines and so can never be corrected. A local standard time zone is nominally 15 degrees wide, but may be modified to follow geographic or political boundaries. A sundial can be rotated around its style (which must remain pointed at the celestial pole) to adjust to the local time zone. In most cases, a rotation in the range of 7.5 degrees east to 23 degrees west suffices. This will introduce error in sundials that do not have equal hour angles. To correct for daylight saving time, a face needs two sets of numerals or a correction table. An informal standard is to have numerals in hot colors for summer, and in cool colors for winter.[citation needed] Since the hour angles are not evenly spaced, the equation of time corrections cannot be made via rotating the dial plate about the gnomon axis. These types of dials usually have an equation of time correction tabulation engraved on their pedestals or close by. Horizontal dials are commonly seen in gardens, churchyards and in public areas.

Vertical sundials[edit]


In the common vertical dial, the shadow-receiving plane is aligned vertically; as usual, the gnomon's style is aligned with the Earth's axis of rotation.[15] [24] [25] As in the horizontal dial, the line of shadow does not move uniformly on the face; the sundial is not equiangular. If the face of the vertical dial points directly south, the angle of the hour-lines is instead described by the formula[26] [27]

\tan H_V = \cos L \tan(15^{\circ} \times t)

where L is the sundial's geographical latitude,  H_H is the angle between a given hour-line and the noon hour-line (which always points due north) on the plane, and t is the number of hours before or after noon. For example, the angle  H_H of the 3pm hour-line would equal the arctangent of cos L, since tan 45° = 1. Interestingly, the shadow moves counter-clockwise on a South-facing vertical dial, whereas it runs clockwise on horizontal and equatorial north-facing dials.

Dials with faces perpendicular to the ground and which face directly South, North, East, or West are called vertical direct dials.[28] [29] It is widely believed, and stated in respectable publications, that a vertical dial cannot receive more than twelve hours of sunlight a day, no matter how many hours of daylight there are.[30] However, there is an exception. Vertical sundials in the tropics which face the nearer pole (e.g. north facing in the zone between the Equator and the Tropic of Cancer) can actually receive sunlight for more than 12 hours from sunrise to sunset for a short period around the time of the summer solstice. For example, at latitude 20 degrees North, on June 21, the sun shines on a north-facing vertical wall for 13 hours, 21 minutes.[31] Vertical sundials which do not face directly South (in the northern hemisphere) may receive significantly less than twelve hours of sunlight per day, depending on the direction they do face, and on the time of year. For example, a vertical dial that faces due East can tell time only in the morning hours; in the afternoon, the sun does not shine on its face. Vertical dials that face due East or West are polar dials, which will be described below. Vertical dials that face North are uncommon, because they tell time only during the spring and summer, and do not show the midday hours except in tropical latitudes (and even there, only around midsummer). For non-direct vertical dials — those that face in non-cardinal directions — the mathematics of arranging the style and the hour-lines becomes more complicated; it may be easier to mark the hour lines by observation, but the placement of the style, at least, must be calculated first; such dials are said to be declining dials.[32] [33] [34]



Pocket sundials[edit]


Polar dials[edit]

Polar sundial at Melbourne Planetarium




Vertical declining dials[edit]

Two sundials, a large and a small one, at Fatih Mosque, Istanbul dating back to the late 16th century. It is on the southwest facade with an azimuth angle of 52° N.

A declining dial is any non-horizontal, planar dial that does not face in a cardinal direction, such as (true) North, South, East or West. [32] [39] [34] As usual, the gnomon's style is aligned with the Earth's rotational axis, but the hour-lines are not symmetrical about the noon hour-line. For a vertical dial, the angle  H_\text{VD} between the noon hour-line and another hour-line is given by the formula below. Note that  H_\text{VD} is defined positive in the clockwise sense w.r.t. the upper vertical hour angle; and that its conversion to the equivalent solar hour requires careful consideration of which quadrant of the sundial that it belongs in.[40]

\tan H_\text{VD} = \frac{\cos L}{\cos D \cot(15^{\circ} \times t) - s_o \sin L \sin D }

where  L is the sundial's geographical latitude; t is the time before or after noon;  D is the angle of declination from true south, defined as positive when east of south; and s_o is a switch integer for the dial orientation. A partly south-facing dial has an s_o value of + 1; those partly north-facing, a value of -1. When such a dial faces South ( D  = 0^{\circ} ), this formula reduces to the formula given above for vertical south-facing dials, i.e.

\tan H_\text{V}  = \cos L \tan(15^{\circ} \times t)

When a sundial is not aligned with a cardinal direction, the substyle of its gnomon is not aligned with the noon hour-line. The angle  B between the substyle and the noon hour-line is given by the formula[40]

\tan B = \sin D  \cot L

If a vertical sundial faces true South or North ( D = 0^{\circ} or  D  = 180^{\circ} , respectively), the angle  B  = 0^{\circ} and the substyle is aligned with the noon hour-line.

The height of the gnomon, that is the angle the style makes to the plate,  G , is given by :

\sin G = \cos D  \cos L


Reclining dials[edit]


The sundials described above have gnomons that are aligned with the Earth's rotational axis and cast their shadow onto a plane. If the plane is neither vertical nor horizontal nor equatorial, the sundial is said to be reclining or inclining.[42] Such a sundial might be located on a South-facing roof, for example. The hour-lines for such a sundial can be calculated by slightly correcting the horizontal formula above[43]

\tan H_{RV} = \cos(L + R) \tan(15^{\circ} \times t)

where  R is the desired angle of reclining relative to the local vertical, L is the sundial's geographical latitude,  H_{RV} is the angle between a given hour-line and the noon hour-line (which always points due north) on the plane, and t is the number of hours before or after noon. For example, the angle  H_{RV} of the 3pm hour-line would equal the arctangent of cos(L + R), since tan 45° = 1. When R equals 0° (in other words, a South-facing vertical dial), we obtain the vertical dial formula above.


\tan H_{RV}  = \sin(L + I) \tan(15^{\circ} \times t)

The angle between the gnomon style and the dial plate, B, in this type of sundial is :

B = 90^{\circ} - (L + R)

Or :

B = 180^{\circ} - (L + I)

Declining-reclining dials/ Declining-inclining dials[edit]

Some sundials both decline and recline, in that their shadow-receiving plane is not oriented with a cardinal direction (such as true North or true South) and is neither horizontal nor vertical nor equatorial. For example, such a sundial might be found on a roof that was not oriented in a cardinal direction.

The formulae describing the spacing of the hour-lines on such dials are rather more complicated than those for simpler dials.

There are various solution approaches, including some using the methods of rotation matrices, and some making a 3D model of the reclined-declined plane and its vertical declined counterpart plane, extracting the geometrical relationships between the hour angle components on both these planes and then reducing the trigonometric algebra.[44] [45]

One system of formulas for Reclining-Declining sundials:[46]

The angle  H_\text{RD} between the noon hour-line and another hour-line is given by the formula below. Note that  H_\text{RD} advances anticlockwise with respect to the zero hour angle for those dials that are partly south-facing and clockwise for those that are north-facing.

\tan H_\text{RD} = \frac{\cos R \cos L  - \sin R \sin L \cos D - s_o  \sin R \sin D \cot(15^{\circ} \times t)}{\cos D \cot(15^{\circ} \times t) - s_o  \sin D \sin L }

within the parameter ranges :  D < D_c and  -90^{\circ} < R < (90^{\circ} - L) .

Or, if preferring to use inclination angle,  I , rather than the reclination,  R , where  I = (90^{\circ} + R)  :

  \tan H_\text{RD} = \frac{\sin I \cos L  + \cos I \sin L \cos D + s_o  \cos I \sin D \cot(15^{\circ} \times t)}{\cos D \cot(15^{\circ} \times t) - s_o  \sin D \sin L }

within the parameter ranges :  D < D_c and  0^{\circ} < I < (180^{\circ} - L) .

Here L is the sundial's geographical latitude; s_o is the orientation switch integer; t is the time in hours before or after noon; and  R and  D are the angles of reclination and declination, respectively. Note that  R is measured with reference to the vertical. It is positive when the dial leans back towards the horizon behind the dial and negative when the dial leans forward to the horizon on the sun's side. Declination angle  D is defined as positive when moving east of true south. Dials facing fully or partly south have s_o = +1, while those partly or fully north-facing have an s_o value of -1. Since the above expression gives the hour angle as an arctan function, due consideration must be given to which quadrant of the sundial each hour belongs to before assigning the correct hour angle.

Unlike the simpler vertical declining sundial, this type of dial does not always show hour angles on its sunside face for all declinations between east and west. When a northern hemisphere partly south-facing dial reclines back (i.e. away from the sun) from the vertical, the gnomon will become co-planar with the dial plate at declinations less than due east or due west. Likewise for southern hemisphere dials that are partly north-facing. Were these dials reclining forward, the range of declination would actually exceed due east and due west. In a similar way, northern hemisphere dials that are partly north-facing and southern hemisphere dials that are south-facing, and which lean forward toward their upward pointing gnomons, will have a similar restriction on the range of declination that is possible for a given reclination value. The critical declination  D_c is a geometrical constraint which depends on the value of both the dial's reclination and its latitude :

\cos D_c  = \tan R \tan L = - \tan L \cot I

As with the vertical declined dial, the gnomon's substyle is not aligned with the noon hour-line. The general formula for the angle  B , between the substyle and the noon-line is given by :

\tan B = \frac {\sin D}{\sin R \cos D + \cos R \tan L} = \frac {\sin D}{\cos I \cos D - \sin I \tan L}

The angle  G , between the style and the plate is given by :

 \sin G = \cos L \cos D \cos R - \sin L \sin R = - \cos L \cos D \sin I + \sin L \cos I

Note that for  G = 0^{\circ}, i.e. when the gnomon is coplanar with the dial plate, we have :

 \cos D = \tan L \tan R = - \tan L \cot I

i.e. when  D = D_c , the critical declination value.

Empirical method[edit]

Because of the complexity of the above calculations, using them for the practical purpose of designing a dial of this type is difficult and prone to error. It has been suggested that it is better to locate the hour lines empirically, marking the positions of the shadow of a style on a real sundial at hourly intervals as shown by a clock.[13] See Empirical hour-line marking, above.

Spherical sundials[edit]



In the equatorial bow sundial, the gnomon is a bar, slot or stretched wire parallel to the celestial axis. The face is a semicircle, corresponding to the equator of the sphere, with markings on the inner surface. This pattern, built a couple of meters wide out of temperature-invariant steel invar, was used to keep the trains running on time in France before World War I.[50]



Precision sundial in Bütgenbach, Belgium. (Precision = ±30 seconds) 50°25′23″N 6°12′06″E﻿ / ﻿50.4231°N 6.2017°E﻿ / 50.4231; 6.2017﻿ (Belgium) (Google Earth)


As an elegant alternative, the style (which could be created by a hole or slit in the circumference) may be located on the circumference of a cylinder or sphere, rather than at its central axis of symmetry.

In that case, the hour lines are again spaced equally, but at twice the usual angle, due to the geometrical inscribed angle theorem. This is the basis of some modern sundials, but it was also used in ancient times; [e]

In another variation of the polar-axis-aligned cylindrical, a cylindrical dial could be rendered as a helical ribbon-like surface, with a thin gnomon located either along its center or at its periphery.

Movable-gnomon sundials[edit]


Universal equinoctial ring dial[edit]


A universal equinoctial ring dial (sometimes called a ring dial for brevity, although the term is ambiguous) is a portable version of an armillary sundial,[54] or was inspired by the mariner's astrolabe.[55] It was likely invented by William Oughtred around 1600 and became common throughout Europe.[56]




Analemmatic sundials[edit]

Main article: Analemmatic sundial


Foster-Lambert dials[edit]

The Foster-Lambert dial is another movable-gnomon sundial.[59] In contrast to the elliptical analemmatic dial, the Lambert dial is circular with evenly spaced hour lines, making it an equiangular sundial, similar to the equatorial, spherical, cylindrical and conical dials described above. The gnomon of a Foster-Lambert dial is neither vertical nor aligned with the Earth's rotational axis; rather, it is tilted northwards by an angle α = 45° - (Φ/2), where Φ is the geographical latitude. Thus, a Foster-Lambert dial located at latitude 40° would have a gnomon tilted away from vertical by 25° in a northerly direction. To read the correct time, the gnomon must also be moved northwards by a distance


where R is the radius of the Foster-Lambert dial and δ again indicates the Sun's declination for that time of year.

Altitude-based sundials[edit]

Altitude dials measure the height of the sun in the sky, rather than directly measuring its hour-angle about the Earth's axis. They are not oriented towards true North, but rather towards the sun and generally held vertically. The sun's elevation is indicated by the position of a nodus, either the shadow-tip of a gnomon, or a spot of light.

In altitude dials, the time is read from where the nodus falls on a set of hour-curves that vary with the time of year. Many such altitude-dials' construction is calculation-intensive, as also the case with many azimuth dials. But the capuchin dials (described below) are constructed and used graphically.

Altitude dials' disadvantages:

Since the sun's altitude is the same at times equally spaced about noon (e.g., 9am and 3pm), the user had to know whether it was morning or afternoon. At, say, 3:00 pm, that isn't a problem. But when the dial indicates a time 15 minutes from noon, the user likely won't have a way of distinguishing 11:45 from 12:15.

Additionally, altitude dials are less accurate near noon, because the sun's altitude isn't changing rapidly then.

Many of these dials are portable and simple to use. As is often the case with other sundials, many altitude dials are designed for only one latitude. But the capuchin dial (described below) has a version that's adjustable for latitude.[citation needed]

The book on sundials by Mayall & Mayall describes the Universal Capuchin sundial.

Human shadows[edit]





Shepherd dials – Timesticks[edit]

19th century Tibetan Shepherd's Timestick


Shepherd's dials appear in several works of literature. [g]

Similarly, the shepherd's dial is evoked in Shakespeare's Henry VI, Part 3, [h]


Timesticks, clock spear,[61] or shepherds' time stick,[61] are based on the same principles as dials.[61][62] The time stick is carved with eight vertical time scales for a different period of the year, each bearing a time scale calculated according to the relative amount of daylight during the different months of the year. Any reading depends not only on the time of day but also on the latitude and time of year.[62] A peg gnomon is inserted at the top in the appropriate hole or face for the season of the year, and turned to the Sun so that the shadow falls directly down the scale. Its end displays the time.[61]

Ring dials[edit]


Card dials (Capuchin dials)[edit]


The Capuchin sundials are constructed and used graphically, as opposed the direct hour-angle measurements of horizontal or equatorial dials; or the calculated hour angle lines of some altitude and azimuth dials.

In addition to the ordinary Capuchin dial, there is a universal Capuchin dial, adjustable for latitude.

Nodus-based sundials[edit]






Reflection sundials[edit]


Multiple dials[edit]


Diptych (tablet) sundial[edit]



Multiface dials[edit]

A common type of multiple dial has sundials on every face of a Platonic solid (regular polyhedron), usually a cube.[72]



A Polyhedral's dial faces can be designed to give the time for different time-zones simultaneously.

Prismatic dials[edit]

Prismatic dials are a special case of polar dials, in which the sharp edges of a prism of a concave polygon serve as the styles and the sides of the prism receive the shadow.[73] Examples include a three-dimensional cross or star of David on gravestones.

Unusual sundials[edit]

Benoy dials[edit]

Benoy Sun Clock showing 6:00 p.m.


Bifilar sundial[edit]

A bifilar dial showing the two wires
Main article: Bifilar sundial

Discovered by the German mathematician Hugo Michnik in 1922, the bifilar sundial has two non-intersecting threads parallel to the dial. Usually the second thread is orthogonal to the first. [76] The intersection of the two threads' shadows gives the local solar time.

Digital sundial[edit]

Digital sundial: graphic showing the masking
Main article: Digital sundial

A digital sundial uses light and no-light to "write" the time in numerals rather than marking time with position. The sundial consists of two closely spaced parallel masks. The first mask, facing the sun, has a regular array of thin vertical slits, which cast a striped light pattern onto the second mask. That mask, facing the user, is composed of narrow stripes, cut from the digits to be displayed. Using the final digit as an example, in one position of the sun, the stripes cut from the "0" are lit. Five minutes later the sun has moved over 1.25° and the stripes derived from the "5" are illuminated. Five minutes later, the stripes from the "0" are again illuminated as the light falling through a given slit has advanced one stripe to the left. A translucent screen behind the second mask helps diffusing the thin light lines and enables the numerals to be read from a broad angle.

There is a patent for this type of sundial.[77]

Such a sundial is installed, e.g., in the Deutsches Museum in Munich and in the Sundial Park in Genk (Belgium), and a small version is available commercially.

Globe dial[edit]

The globe dial is a sphere aligned with the Earth's rotational axis, and equipped with a spherical vane.[78] Similar to sundials with a fixed axial style, a globe dial determines the time from the Sun's azimuthal angle in its apparent rotation about the earth. This angle can be determined by rotating the vane to give the smallest shadow.

Noon marks[edit]

Noon mark from the Greenwich Royal Observatory. The analemma is the narrow figure-8 shape, which plots the equation of time (in degrees, not time, 1°=4 minutes) versus the altitude of the sun at noon at the sundial's location. The altitude is measured vertically, the equation of time horizontally.

The simplest sundials do not give the hours, but rather note the exact moment of 12:00 noon. [79] In centuries past, such dials were used to correct mechanical clocks, which were sometimes so inaccurate as to lose or gain significant time in a single day.


Noon cannon[edit]


Meridian lines[edit]


Sundial mottoes[edit]

Further information: List of sundial mottoes


Using a sundial as a compass[edit]

If a horizontal-plate sundial is made for the latitude in which it is being used, and if it is mounted with its plate horizontal and its gnomon pointing to the celestial pole that is above the horizon, then it shows the correct time in apparent solar time. Conversely, if the directions of the cardinal points are initially unknown, but the sundial is aligned so it shows the correct apparent solar time as calculated from the reading of a clock, its gnomon shows the direction of True North or South, allowing the sundial to be used as a compass. The sundial can be placed on a horizontal surface, and rotated about a vertical axis until it shows the correct time. The gnomon will then be pointing to the North, in the northern hemisphere, or to the South in the southern hemisphere. This method is much more accurate than using a watch as a compass (see Cardinal direction#Watch face) and can be used in places where the magnetic declination is large, making a magnetic compass unreliable. An alternative method uses two sundials of different designs. (See #Multiple dials, above.) The dials are attached to and aligned with each other, and are oriented so they show the same time. This allows the directions of the cardinal points and the apparent solar time to be determined simultaneously, without requiring a clock.[citation needed]

See also[edit]

Angbuilgu, a portable sundial used in Korea during the Joseon period. The integrated magnetic compass aligns the instrument toward north pole.(National Museum of Korea)[81]


  2. ^ A clock showing sundial time always agrees with a sundial in the same locality.
  3. ^ Strictly, local mean time rather than standard time should be used. However, using standard time makes the sundial more useful, since it does not have to be corrected for time zone or longitude.
  4. ^ The equation of time is considered to be positive when "sundial time" is ahead of "clock time", negative otherwise. See the graph shown in the section #Equation of time correction, above. For example, if the equation of time is -5 minutes and the standard time is 9:40, the sundial time is 9:35.
  5. ^ An example of such a half-cylindrical dial may be found at Wellesley College in Massachusetts.[53]
    Since eleven feet, a little more or less,
    my shadow at the time did fall,
    Considering that I myself am six feet tall.
    And lat us dyne as sone as that ye may;
    for by my chilindre it is pryme of day."
    To be no better than a homely swain;
    To sit upon a hill, as I do now,
    To carve out dials, quaintly, point by point,
    Thereby to see the minutes, how they run--
    How many makes the hour full complete,
    How many hours brings about the day,
    How many days will finish up the year,
    How many years a mortal man may live.



  1. ^ Moss, Tony. "How do sundials work". British Sundial society. Retrieved 21 September 2013. This ugly plastic ‘non-dial’ does nothing at all except display the ‘designer’s ignorance and persuade the general public that ‘real’ sundials don’t work. 
  2. ^ a b c British Sundial, Society. "BSS Glossary". Archived from the original on 2007-10-10. Retrieved 2011-05-02. 
  3. ^ Rohr 1965, pp. 126–129.
  4. ^ Waugh 1973, pp. 124–125.
  6. ^ Michelle B. Larson. "Making a sundial for the Southern hemisphere". Retrieved 2008-07-11. 
  8. ^ British Sundial, Society. "The Sundial Register". Retrieved 2014-10-13. 
  9. ^ Waugh 1973, pp. 48–50.
  13. ^ a b Waugh 1973, pp. 106–107.
  14. ^ Waugh 1973, p. 205.
  15. ^ a b Rohr 1965, pp. 46–49.
  17. ^ Waugh 1973, pp. 29–34.
  18. ^ Schaldach K (2004). "The arachne of the Amphiareion and the origin of gnomonics in Greece". Journal of the History of Astronomy 35: 435–445. doi:10.1177/002182860403500404. ISSN 0021-8286. 
  19. ^ Rohr 1965, pp. 49–53.
  21. ^ Waugh 1973, pp. 35–51.
  22. ^ Rohr 1965, p. 52.
  23. ^ Waugh 1973, p. 45.
  25. ^ Waugh 1973, pp. 52–99.
  26. ^ Rohr 1965, p. 65.
  27. ^ Waugh 1973, p. 52.
  28. ^ Rohr 1965, pp. 54–55.
  29. ^ Waugh 1973, pp. 52–69.
  30. ^ Waugh 1973, p. 83.
  32. ^ a b Rohr 1965, pp. 55–69.
  33. ^ Mayall & Mayall 1938, p. 58.
  34. ^ a b Waugh 1973, pp. 74–99.
  35. ^ Waugh 1973, p. 55.
  36. ^ Rohr 1965, p. 72.
  37. ^ Mayall & Mayall 1938, pp. 58, 107–112.
  38. ^ Waugh 1973, pp. 70–73.
  40. ^ a b Rohr 1965, p. 79.
  41. ^ Mayall & Mayall 1938, p. 138.
  45. ^ [ Sundial Design Considerations.] Donald L. Snyder, NASS Compendium, Vol 22, No. 1, Mar 2015..
  46. ^ *Fennerwick, Armyan. ", the Netherlands, Revision of Chapter 5 of Sundials by René R.J. Rohr, New York 1996 declining inclined dials part D Declining and Inclined Dials by Mathematics using a new figure". unknown. Netherlands: user on Retrieved 1 May 2015. 
  47. ^ Rohr 1965, pp. 114, 1214–125.
  49. ^ Waugh 1973, pp. 174–180.
  50. ^ Rohr 1965, p. 17.
  51. ^ Rohr 1965, pp. 118–119.
  52. ^ Mayall & Mayall 1938, pp. 215–216.
  53. ^ Mayall Mayall, p. 94.
  54. ^ Waugh 1973, p. 157.
  56. ^ Turner 1980, p. 25.
  59. ^ Mayall & Mayall 1938, pp. 190–192.
  64. ^ Waugh (1973), pp. 166–167.
  67. ^ Belk T (September 2007). "Declination Lines Detailed" (PDF). BSS Bulletin. 19(iii): 137–140. 
  68. ^ Rohr 1965, p. 14.
  69. ^ Waugh (1973), pp. 116–121.
  71. ^ Waugh (1973), p. 155.
  73. ^ Waugh 1973, pp. 181–190.
  74. ^ List correct as of British Sundial Register 2000. British Sundial, Society. "The Sundial Register". Retrieved 2008-01-05. 
  75. ^ St. Edmundsbury, Borough Council. "Telling the story of time measurement". Retrieved 2008-01-05. [dead link]
  76. ^ Michnik, H (1922). "Title: Theorie einer Bifilar-Sonnenuhr". Astronomische Nachrichten (in German) 217 (5190): 81–90. Bibcode:1922AN....217...81M. doi:10.1002/asna.19222170602. Retrieved 17 December 2013. 
  77. ^ Digital sundial
  78. ^ Rohr 1965, pp. 114–115.
  79. ^ Waugh 1973, pp. 18–28.
  80. ^ Mayall & Mayall 1938, p. 26.
  81. ^ "Portable Hemispherical Sundial". National Museum of Korea. Archived from the original on May 30, 2015. Retrieved May 30, 2015. 


  • Mayall, RN; Mayall, MW (1938). Sundials: Their Construction and Use (3rd (1994) ed.). Cambridge, MA: Sky Publishing. ISBN 0-933346-71-9. 

External links[edit]

National organisations[edit]