A sundial is a device that tells the time of day when there is
sunlight by the apparent position of the
Contents 1 Introduction 2 Apparent motion of the Sun 3 History 4 Terminology 5 Sundials in the Southern Hemisphere 6 Adjustments to calculate clock time from a sundial reading 6.1 Summer (daylight saving) time correction
6.2 Time-zone (longitude) correction
6.3
7 Sundials with fixed axial gnomon 7.1 Empirical hour-line marking 7.2 Equatorial sundials 7.3 Horizontal sundials 7.4 Vertical sundials 7.5 Polar dials 7.6 Vertical declining dials 7.7 Reclining dials 7.8 Declining-reclining dials/ Declining-inclining dials 7.8.1 Empirical method 7.9 Spherical sundials 7.10 Cylindrical, conical, and other non-planar sundials 8 Movable-gnomon sundials 8.1 Universal equinoctial ring dial 8.2 Analemmatic sundials 8.3 Foster-Lambert dials 9 Altitude-based sundials 9.1 Human shadows
9.2
10 Nodus-based sundials 10.1 Reflection sundials 11 Multiple dials 11.1
12 Unusual sundials 12.1 Benoy dials
12.2 Bifilar sundial
12.3 Digital sundial
12.4 Globe dial
12.5 Noon marks
12.6
13 Meridian lines
14
18.1 Citations 18.2 Sources 19 External links 19.1 National organisations 19.2 Historical 19.3 Other Introduction[edit] There are several different types of sundials. Some sundials use a shadow or the edge of a shadow while others use a line or spot of light to indicate the time. The shadow-casting object, known as a gnomon, may be a long thin rod or other object with a sharp tip or a straight edge. Sundials employ many types of gnomon. The gnomon may be fixed or moved according to the season. It may be oriented vertically, horizontally, aligned with the Earth's axis, or oriented in an altogether different direction determined by mathematics. Given that sundials use light to indicate time, a line of light may be formed by allowing the sun's rays through a thin slit or focusing them through a cylindrical lens. A spot of light may be formed by allowing the sun's rays to pass through a small hole or by reflecting them from a small circular mirror. Sundials also may use many types of surfaces to receive the light or shadow. Planes are the most common surface, but partial spheres, cylinders, cones and other shapes have been used for greater accuracy or beauty. Sundials differ in their portability and their need for orientation. The installation of many dials requires knowing the local latitude, the precise vertical direction (e.g., by a level or plumb-bob), and the direction to true North. Portable dials are self-aligning: for example, it may have two dials that operate on different principles, such as a horizontal and analemmatic dial, mounted together on one plate. In these designs, their times agree only when the plate is aligned properly. Sundials may indicate the local solar timeonly. To obtain the national clock time, three corrections are required: the orbit of the Earth is not perfectly circular and its rotational axis is not perpendicular to its orbit. The sundial's indicated solar time thus varies from clock time by small amounts that change throughout the year. This correction – which may be as great as 15 minutes – is described by the equation of time. A sophisticated sundial, with a curved style or hour lines, may incorporate this correction. The more usual simpler sundials sometimes have a small plaque that gives the offsets at various times of the year. the solar time must be corrected for the longitude of the sundial relative to the longitude of the official time zone. For example, a sundial located west of Greenwich, England but within the same time-zone, shows an earlier time than the official time. For example, it will show "noon" before the official noon. This correction can easily be made by rotating the hour-lines by a constant angle equal to the difference in longitudes, which makes this is a commonly possible design option. to adjust for daylight saving time, if applicable, the solar time must additionally be shifted for the official difference (usually one hour). This is also a correction that can be done on the dial, i.e. by numbering the hour-lines with two sets of numbers, or even by swapping the numbering in some designs. More often this is simply ignored, or mentioned on the plaque with the other corrections, if there is one. Apparent motion of the Sun[edit] Top view of an equatorial sundial. The hour lines are spaced equally
about the circle, and the shadow of the gnomon (a thin cylindrical
rod) rotates uniformly. The height of the gnomon is 5⁄12 the
outer radius of the dial. This animation depicts the motion of the
shadow from 3 a.m. to 9 p.m. (not accounting for Daylight Saving Time)
on or around Solstice, when the sun is at its highest declination
(roughly 23.5°). Sunrise and sunset occur at 3am and 9pm,
respectively, on that day at geographical latitudes near 57.05°,
roughly the latitude of
The principles of sundials are understood most easily from the Sun's
apparent motion.[3] The Earth rotates on its axis, and revolves in an
elliptical orbit around the Sun. An excellent approximation assumes
that the
This model of the Sun's motion helps to understand sundials. If the
shadow-casting gnomon is aligned with the celestial poles, its shadow
will revolve at a constant rate, and this rotation will not change
with the seasons. This is the most common design. In such cases, the
same hour lines may be used throughout the year. The hour-lines will
be spaced uniformly if the surface receiving the shadow is either
perpendicular (as in the equatorial sundial) or circular about the
gnomon (as in the armillary sphere).
In other cases, the hour-lines are not spaced evenly, even though the
shadow rotates uniformly. If the gnomon is not aligned with the
celestial poles, even its shadow will not rotate uniformly, and the
hour lines must be corrected accordingly. The rays of light that graze
the tip of a gnomon, or which pass through a small hole, or reflect
from a small mirror, trace out a cone aligned with the celestial
poles. The corresponding light-spot or shadow-tip, if it falls onto a
flat surface, will trace out a conic section, such as a hyperbola,
ellipse or (at the
World's oldest sundial, from Egypt's Valley of the Kings (c. 1500 BC) The earliest sundials known from the archaeological record are shadow
clocks (1500 BC or BCE) from ancient
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. In general, sundials indicate the time by casting a shadow or throwing light onto a surface known as a dial face or dial plate. Although usually a flat plane, the dial face may also be the inner or outer surface of a sphere, cylinder, cone, helix, and various other shapes. The time is indicated where a shadow or light falls on the dial face, which is usually inscribed with hour lines. Although usually straight, these hour lines may also be curved, depending on the design of the sundial (see below). In some designs, it is possible to determine the date of the year, or it may be required to know the date to find the correct time. In such cases, there may be multiple sets of hour lines for different months, or there may be mechanisms for setting/calculating the month. In addition to the hour lines, the dial face may offer other data—such as the horizon, the equator and the tropics—which are referred to collectively as the dial furniture. The entire object that casts a shadow or light onto the dial face is known as the sundial's gnomon.[4] However, it is usually only an edge of the gnomon (or another linear feature) that casts the shadow used to determine the time; this linear feature is known as the sundial's style. The style is usually aligned parallel to the axis of the celestial sphere, and therefore is aligned with the local geographical meridian. In some sundial designs, only a point-like feature, such as the tip of the style, is used to determine the time and date; this point-like feature is known as the sundial's nodus.[4][a] Some sundials use both a style and a nodus to determine the time and date. The gnomon is usually fixed relative to the dial face, but not always; in some designs such as the analemmatic sundial, the style is moved according to the month. If the style is fixed, the line on the dial plate perpendicularly beneath the style is called the substyle,[4] meaning "below the style". The angle the style makes with the plane of the dial plate is called the substyle height, an unusual use of the word height to mean an angle. On many wall dials, the substyle is not the same as the noon line (see below). The angle on the dial plate between the noon line and the substyle is called the substyle distance, an unusual use of the word distance to mean an angle. By tradition, many sundials have a motto. The motto is usually in the form of an epigram: sometimes sombre reflections on the passing of time and the brevity of life, but equally often humorous witticisms of the dial maker.[5][6] A dial is said to be equiangular if its hour-lines are straight and spaced equally. Most equiangular sundials have a fixed gnomon style aligned with the Earth's rotational axis, as well as a shadow-receiving surface that is symmetrical about that axis; examples include the equatorial dial, the equatorial bow, the armillary sphere, the cylindrical dial and the conical dial. However, other designs are equiangular, such as the Lambert dial, a version of the analemmatic dial with a moveable style. Sundials in the Southern Hemisphere[edit] Southern-hemisphere sundial in Perth, Australia. Magnify to see that the hour marks run anticlockwise. Note graph of Equation of Time, needed to correct sundial readings. A sundial at a particular latitude in one hemisphere must be reversed
for use at the opposite latitude in the other hemisphere.[7] A
vertical direct south sundial in the
The Equation of
Main article: Equation of time The Whitehurst & Son sundial made in 1812, with a circular scale showing the equation of time correction. This is now on display in the Derby Museum. Although the
Sunquest sundial, designed by Richard L. Schmoyer, at the Mount Cuba Observatory in Greenville, Delaware The Sunquest sundial, designed by Richard L. Schmoyer in the 1950s, uses an analemmic inspired gnomon to cast a shaft of light onto an equatorial time-scale crescent. Sunquest is adjustable for latitude and longitude, automatically correcting for the equation of time, rendering it "as accurate as most pocket watches".[15][16][17][18] Similarly, in place of the shadow of a gnomon the sundial at Miguel Hernández University uses the solar projection of a graph of the equation of time intersecting a time scale to display clock time directly.
An analemma may be added to many types of sundials to correct apparent
solar time to mean solar time or another standard time. These usually
have hour lines shaped like "figure eights" (analemmas) according to
the equation of time. This compensates for the slight eccentricity in
the Earth's orbit and the tilt of the Earth's axis that causes up to a
15-minute variation from mean solar time. This is a type of dial
furniture seen on more complicated horizontal and vertical dials.
Prior to the invention of accurate clocks, in the mid-17th Century,
sundials were the only timepieces in common use, and were considered
to tell the "right" time. The Equation of
The 1959
The most commonly observed sundials are those in which the
shadow-casting style is fixed in position and aligned with the Earth's
rotational axis, being oriented with true
An equatorial sundial in the Forbidden City, Beijing. 39°54′57″N
116°23′25″E / 39.9157°N 116.3904°E / 39.9157;
116.3904 (
The distinguishing characteristic of the equatorial dial (also called the equinoctial dial) is the planar surface that receives the shadow, which is exactly perpendicular to the gnomon's style.[23][24][25] This plane is called equatorial, because it is parallel to the equator of the Earth and of the celestial sphere. If the gnomon is fixed and aligned with the Earth's rotational axis, the sun's apparent rotation about the Earth casts a uniformly rotating sheet of shadow from the gnomon; this produces a uniformly rotating line of shadow on the equatorial plane. Since the sun rotates 360° in 24 hours, the hour-lines on an equatorial dial are all spaced 15° apart (360/24). H E = 15 ∘ × t (hours) . displaystyle H_ E =15^ circ times t text (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 ∘ = EoT (minutes) + 60 × Δ DST (hours) 4 . displaystyle text Correction ^ circ = frac text EoT (minutes) +60times Delta text DST (hours) 4 . Near the equinoxes in spring and autumn, the sun moves on a circle
that is nearly the same as the equatorial plane; hence, no clear
shadow is produced on the equatorial dial at those times of year, a
drawback of the design.
A nodus is sometimes added to equatorial sundials, which allows the
sundial to tell the time of year. On any given day, the shadow of the
nodus moves on a circle on the equatorial plane, and the radius of the
circle measures the declination of the sun. The ends of the gnomon bar
may be used as the nodus, or some feature along its length. An ancient
variant of the equatorial sundial has only a nodus (no style) and the
concentric circular hour-lines are arranged to resemble a
spider-web.[26]
Horizontal sundials[edit]
For a more detailed description of such a dial, see
Horizontal sundial in Minnesota. June 17, 2007 at 12:21. 44°51′39.3″N, 93°36′58.4″W 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.[27] [28] [29] Hence, the line of shadow does not rotate uniformly on the dial face; rather, the hour lines are spaced according to the rule [30] [31] tan H H = sin L tan ( 15 ∘ × t ) displaystyle tan H_ H =sin Ltan(15^ circ times t) Or in other terms:
H H = tan − 1 [ sin L × tan ( 15 ∘ × t ) ] displaystyle H_ H =tan ^ -1 [sin Ltimes tan(15^ circ times t)] where L is the sundial's geographical latitude (and the angle the gnomon makes with the dial plate), H H displaystyle 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 displaystyle H_ H of the 3pm hour-line would equal the arctangent of sin L, since tan
45° = 1. When L equals 90° (at the
H H displaystyle 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
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
Two vertical dials at
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.[23] [32] [33] 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[34] [35] tan H V = cos L tan ( 15 ∘ × t ) displaystyle tan H_ V =cos Ltan(15^ circ times t) where L is the sundial's geographical latitude, H V displaystyle H_ V 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 V displaystyle H_ V 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
"Double" sundials in Nové Město nad Metují, Czech Republic; the observer is facing almost due north. Vertical dials are commonly mounted on the walls of buildings, such as
town-halls, cupolas and church-towers, where they are easy to see from
far away. In some cases, vertical dials are placed on all four sides
of a rectangular tower, providing the time throughout the day. The
face may be painted on the wall, or displayed in inlaid stone; the
gnomon is often a single metal bar, or a tripod of metal bars for
rigidity. If the wall of the building faces toward the South, but does
not face due South, the gnomon will not lie along the noon line, and
the hour lines must be corrected. Since the gnomon's style must be
parallel to the Earth's axis, it always "points" true
Polar sundial at Melbourne Planetarium In polar dials, the shadow-receiving plane is aligned parallel to the gnomon-style.[44][45][46] Thus, the shadow slides sideways over the surface, moving perpendicularly to itself as the sun rotates about the style. As with the gnomon, the hour-lines are all aligned with the Earth's rotational axis. When the sun's rays are nearly parallel to the plane, the shadow moves very quickly and the hour lines are spaced far apart. The direct East- and West-facing dials are examples of a polar dial. However, the face of a polar dial need not be vertical; it need only be parallel to the gnomon. Thus, a plane inclined at the angle of latitude (relative to horizontal) under the similarly inclined gnomon will be a polar dial. The perpendicular spacing X of the hour-lines in the plane is described by the formula X = H tan ( 15 ∘ × t ) displaystyle X=Htan(15^ circ times t) where H is the height of the style above the plane, and t is the time (in hours) before or after the center-time for the polar dial. The center time is the time when the style's shadow falls directly down on the plane; for an East-facing dial, the center time will be 6am, for a West-facing dial, this will be 6pm, and for the inclined dial described above, it will be noon. When t approaches ±6 hours away from the center time, the spacing X diverges to +∞; this occurs when the sun's rays become parallel to the plane. Vertical declining dials[edit] Effect of declining on a sundial's hour-lines. A vertical dial, at a
latitude of 51° N, designed to face due
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,
H VD displaystyle H_ text VD between the noon hour-line and another hour-line is given by the formula below. Note that H VD displaystyle 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.[48] tan H VD = cos L cos D cot ( 15 ∘ × t ) − s o sin L sin D displaystyle tan H_ text VD = frac cos L cos Dcot(15^ circ times t)-s_ o sin Lsin D where L displaystyle L is the sundial's geographical latitude; t is the time before or after noon; D displaystyle D is the angle of declination from true south, defined as positive when east of south; and s o displaystyle s_ o is a switch integer for the dial orientation. A partly south-facing dial has an s o displaystyle s_ o value of + 1; those partly north-facing, a value of -1. When such a
dial faces
D = 0 ∘ displaystyle D=0^ circ ), this formula reduces to the formula given above for vertical south-facing dials, i.e. tan H V = cos L tan ( 15 ∘ × t ) displaystyle tan H_ text V =cos Ltan(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 displaystyle B between the substyle and the noon hour-line is given by the formula[48] tan B = sin D cot L displaystyle tan B=sin Dcot L If a vertical sundial faces true
D = 0 ∘ displaystyle D=0^ circ or D = 180 ∘ displaystyle D=180^ circ , respectively), the angle B = 0 ∘ displaystyle 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 displaystyle G , is given by : sin G = cos D cos L displaystyle sin G=cos Dcos L [49] Reclining dials[edit] Vertical reclining dial in the Southern Hemisphere, facing due north, with hyperbolic declination lines and hour lines. Ordinary vertical sundial at this latitude (between tropics) could not produce a declination line for the summer solstice. 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.[50] 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[51] tan H R V = cos ( L + R ) tan ( 15 ∘ × t ) displaystyle tan H_ RV =cos(L+R)tan(15^ circ times t) where R displaystyle R is the desired angle of reclining relative to the local vertical, L is the sundial's geographical latitude, H R V displaystyle 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 R V displaystyle 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. Some authors use a more specific nomenclature to describe the orientation of the shadow-receiving plane. If the plane's face points downwards towards the ground, it is said to be proclining or inclining, whereas a dial is said to be reclining when the dial face is pointing away from the ground. Many authors also often refer to reclined, proclined and inclined sundials in general as inclined sundials. It is also common in the latter case to measure the angle of inclination relative to the horizontal plane on the sun side of the dial. In such texts, since I = 90° + R, the hour angle formula will often be seen written as : tan H R V = sin ( L + I ) tan ( 15 ∘ × t ) displaystyle 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 ∘ − ( L + R ) displaystyle B=90^ circ -(L+R) Or : B = 180 ∘ − ( L + I ) displaystyle 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
H RD displaystyle H_ text RD between the noon hour-line and another hour-line is given by the formula below. Note that H RD displaystyle H_ text RD advances counterclockwise 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 RD = cos R cos L − sin R sin L cos D − s o sin R sin D cot ( 15 ∘ × t ) cos D cot ( 15 ∘ × t ) − s o sin D sin L displaystyle tan H_ text RD = frac cos Rcos L-sin Rsin Lcos D-s_ o sin Rsin Dcot(15^ circ times t) cos Dcot(15^ circ times t)-s_ o sin Dsin L within the parameter ranges : D < D c displaystyle D<D_ c and − 90 ∘ < R < ( 90 ∘ − L ) displaystyle -90^ circ <R<(90^ circ -L) . Or, if preferring to use inclination angle, I displaystyle I , rather than the reclination, R displaystyle R , where I = ( 90 ∘ + R ) displaystyle I=(90^ circ +R) : tan H RD = sin I cos L + cos I sin L cos D + s o cos I sin D cot ( 15 ∘ × t ) cos D cot ( 15 ∘ × t ) − s o sin D sin L displaystyle tan H_ text RD = frac sin Icos L+cos Isin Lcos D+s_ o cos Isin Dcot(15^ circ times t) cos Dcot(15^ circ times t)-s_ o sin Dsin L within the parameter ranges : D < D c displaystyle D<D_ c and 0 ∘ < I < ( 180 ∘ − L ) displaystyle 0^ circ <I<(180^ circ -L) . Here L displaystyle L is the sundial's geographical latitude; s o displaystyle s_ o is the orientation switch integer; t is the time in hours before or after noon; and R displaystyle R and D displaystyle D are the angles of reclination and declination, respectively. Note that R displaystyle 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 displaystyle D is defined as positive when moving east of true south. Dials facing fully or partly south have s o displaystyle s_ o = +1, while those partly or fully north-facing have an s o displaystyle 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 displaystyle 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 displaystyle cos D_ c =tan Rtan L=-tan Lcot 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 displaystyle B , between the substyle and the noon-line is given by : tan B = sin D sin R cos D + cos R tan L = sin D cos I cos D − sin I tan L displaystyle tan B= frac sin D sin Rcos D+cos Rtan L = frac sin D cos Icos D-sin Itan L The angle G displaystyle 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 displaystyle sin G=cos Lcos Dcos R-sin Lsin R=-cos Lcos Dsin I+sin Lcos I Note that for G = 0 ∘ displaystyle 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 displaystyle cos D=tan Ltan R=-tan Lcot I i.e. when D = D c displaystyle D=D_ c , the critical declination value.[54] 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.[21] See Empirical hour-line marking, above. Spherical sundials[edit] Equatorial bow sundial in Hasselt,
The surface receiving the shadow need not be a plane, but can have any
shape, provided that the sundial maker is willing to mark the
hour-lines. If the style is aligned with the Earth's rotational axis,
a spherical shape is convenient since the hour-lines are equally
spaced, as they are on the equatorial dial above; the sundial is
equiangular. This is the principle behind the armillary sphere and the
equatorial bow sundial.[55] [56] [57] However, some equiangular
sundials — such as the Lambert dial described below — are based on
other principles.
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.[58]
Among the most precise sundials ever made are two equatorial bows
constructed of marble found in Yantra mandir.[59] [60] This collection
of sundials and other astronomical instruments was built by Maharaja
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) Other non-planar surfaces may be used to receive the shadow of the
gnomon.
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]
Sundials can be designed with a gnomon that is placed in a different
position each day throughout the year. In other words, the position of
the gnomon relative to the centre of the hour lines varies. The gnomon
need not be aligned with the celestial poles and may even be perfectly
vertical (the analemmatic dial). These dials, when combined with
fixed-gnomon sundials, allow the user to determine true
Universal ring dial. The dial is suspended from the cord shown in the upper left; the suspension point on the vertical meridian ring can be changed to match the local latitude. The center bar is twisted until a sunray passes through the small hole and falls on the horizontal equatorial ring. See Commons annotations for labels. 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,[62] or was inspired by the mariner's astrolabe.[63]
It was likely invented by
Analemmatic sundials are a type of horizontal sundial that has a vertical gnomon and hour markers positioned in an elliptical pattern. There are no hour lines on the dial and the time of day is read on the ellipse. The gnomon is not fixed and must change position daily to accurately indicate time of day. Analemmatic sundials are sometimes designed with a human as the gnomon. 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.[66] Foster-Lambert dials[edit] The Foster-Lambert dial is another movable-gnomon sundial.[67] 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 Y = R tan α tan δ displaystyle Y=Rtan alpha tan delta , 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.[68]
The book on sundials by Mayall & Mayall describes the Universal
Capuchin sundial.
Human shadows[edit]
The length of a human shadow (or of any vertical object) can be used
to measure the sun's elevation and, thence, the time.[69] The
19th century Tibetan Shepherd's Timestick A shepherd's dial — also known as a shepherd's column dial,[70][71]
pillar dial, cylinder dial or chilindre — is a portable cylindrical
sundial with a knife-like gnomon that juts out perpendicularly.[72] It
is normally dangled from a rope or string so the cylinder is vertical.
The gnomon can be twisted to be above a month or day indication on the
face of the cylinder. This corrects the sundial for the equation of
time. The entire sundial is then twisted on its string so that the
gnomon aims toward the sun, while the cylinder remains vertical. The
tip of the shadow indicates the time on the cylinder. The hour curves
inscribed on the cylinder permit one to read the time. Shepherd's
dials are sometimes hollow, so that the gnomon can fold within when
not in use.
The shepherd's dial is evoked in Shakespeare's Henry VI, Part 3, [g]
among other works of literature. [h]
The cylindrical shepherd's dial can be unrolled into a flat plate. In
one simple version,[73] the front and back of the plate each have
three columns, corresponding to pairs of months with roughly the same
solar declination (June–July, May–August, April–September,
March–October, February–November, and January–December). The top
of each column has a hole for inserting the shadow-casting gnomon, a
peg. Often only two times are marked on the column below, one for noon
and the other for mid-morning/mid-afternoon.
Timesticks, clock spear,[70] or shepherds' time stick,[70] are based
on the same principles as dials.[70][71] 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.[71] A peg gnomon is inserted at the top in the appropriate hole
or face for the season of the year, and turned to the
Kraków. 50°03′41″N 19°56′24″E / 50.0614°N 19.9400°E / 50.0614; 19.9400 (Kraków sundial) The shadow of the cross-shaped nodus moves along a hyperbola which shows the time of the year,indicated here by the zodiac figures. It is 1:50 p.m. on 16 July, 25 days after the summer solstice. Another type of sundial follows the motion of a single point of light or shadow, which may be called the nodus. For example, the sundial may follow the sharp tip of a gnomon's shadow, e.g., the shadow-tip of a vertical obelisk (e.g., the Solarium Augusti) or the tip of the horizontal marker in a shepherd's dial. Alternatively, sunlight may be allowed to pass through a small hole or reflected from a small (e.g., coin-sized) circular mirror, forming a small spot of light whose position may be followed. In such cases, the rays of light trace out a cone over the course of a day; when the rays fall on a surface, the path followed is the intersection of the cone with that surface. Most commonly, the receiving surface is a geometrical plane, so that the path of the shadow-tip or light-spot (called declination line) traces out a conic section such as a hyperbola or an ellipse. The collection of hyperbolae was called a pelekonon (axe) by the Greeks, because it resembles a double-bladed ax, narrow in the center (near the noonline) and flaring out at the ends (early morning and late evening hours).
There is a simple verification of hyperbolic declination lines on a
sundial: the distance from the origin to the equinox line should be
equal to harmonic mean of distances from the origin to summer and
winter solstice lines.[76]
Nodus-based sundials may use a small hole or mirror to isolate a
single ray of light; the former are sometimes called aperture dials.
The oldest example is perhaps the antiborean sundial (antiboreum), a
spherical nodus-based sundial that faces true North; a ray of sunlight
enters from the
The diptych consisted of two small flat faces, joined by a hinge.[80]
Diptychs usually folded into little flat boxes suitable for a pocket.
The gnomon was a string between the two faces. When the string was
tight, the two faces formed both a vertical and horizontal sundial.
These were made of white ivory, inlaid with black lacquer markings.
The gnomons were black braided silk, linen or hemp string. With a knot
or bead on the string as a nodus, and the correct markings, a diptych
(really any sundial large enough) can keep a calendar well-enough to
plant crops. A common error describes the diptych dial as
self-aligning. This is not correct for diptych dials consisting of a
horizontal and vertical dial using a string gnomon between faces, no
matter the orientation of the dial faces. Since the string gnomon is
continuous, the shadows must meet at the hinge; hence, any orientation
of the dial will show the same time on both dials.[81]
Multiface dials[edit]
A common type of multiple dial has sundials on every face of a
Benoy
The Benoy Dial was invented by Walter Gordon Benoy of Collingham in Nottinghamshire. Light is used to replace the shadow-edge of a gnomon. Whereas a gnomon casts a sheet of shadow, an equivalent sheet of light can be created by allowing the Sun's rays through a thin slit, reflecting them from a long, slim mirror (usually half-cylindrical), or focusing them through a cylindrical lens. For illustration, the Benoy Dial uses a cylindrical lens to create a sheet of light, which falls as a line on the dial surface. Benoy dials can be seen throughout Great Britain, such as[84] Carnfunnock Country Park Antrim Northern Ireland
Upton Hall
Bifilar sundial[edit] A bifilar dial showing the two wires Main article: Bifilar sundial
Invented 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.[86] The intersection of
the two threads' shadows gives the local solar time.
Digital sundial[edit]
Main article: Digital sundial
A digital sundial indicates the current time with numerals formed by
the sunlight striking it. Sundials of this type are installed in the
The simplest sundials do not give the hours, but rather note the exact
moment of 12:00 noon. [89] 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.
In some U.S. colonial-era houses, a noon-mark can often be found
carved into a floor or windowsill.[90] Such marks indicate local noon,
and provide a simple and accurate time reference for households that
do not possess accurate clocks. In modern times, in some Asian
countries, post offices set their clocks from a precision noon-mark.
These in turn provide the times for the rest of the society. The
typical noon-mark sundial was a lens set above an analemmatic plate.
The plate has an engraved figure-eight shape, which corresponds to
plotting the equation of time (described above) versus the solar
declination. When the edge of the sun's image touches the part of the
shape for the current month, this indicates that it is 12:00 noon.
Angbuilgu, a portable sundial used in Korea during the
Equation clock
Shadows — free software for calculating and drawing sundials.
Foucault pendulum
Francesco Bianchini
Horology
Moondial
Nocturnal — device for determining time by the stars at night.
Notes[edit] ^ In some technical writing, the word "gnomon" can also mean the
perpendicular height of a nodus from the dial plate. The point where
the style intersects the dial plate is called the gnomon root.
^ A clock showing sundial time always agrees with a sundial in the
same locality.
^ 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.
^ 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 #
References[edit] Citations[edit] ^ "Flagstaff Gardens, Victorian Heritage Register (VHR) Number H2041,
Heritage Overlay HO793". Victorian Heritage Database. Heritage
Victoria. Retrieved 2010-09-16.
^ Moss, Tony. "How do sundials work". British
Sources[edit] Daniel, Christopher St.J.H. (2004). Sundials. Shire Album. 176 (2nd
revised ed.). Shire Publications. ISBN 978-0747805588.
Earle AM (1971). Sundials and Roses of Yesterday. Rutland, VT: Charles
E. Tuttle. ISBN 0-8048-0968-2. LCCN 74142763. Reprint
of the 1902 book published by Macmillan (New York).
Heilbron, J. L. : The sun in the church: cathedrals as solar
observatories, Harvard University Press, 2001
ISBN 978-0-674-00536-5.
A.P. Herbert, Sundials Old and New, Methuen & Co. Ltd, 1967.
Kern, Ralf : Wissenschaftliche Instrumente in ihrer Zeit. Vom 15.
– 19. Jahrhundert. Verlag der Buchhandlung Walther König 2010,
ISBN 978-3-86560-772-0
Mayall, RN; Mayall, MW (1938). Sundials: Their Construction and Use
(3rd (1994) ed.). Cambridge, MA:
External links[edit] Wikimedia Commons has media related to Sundials. National organisations[edit] Asociación Amigos de los Relojes de Sol (AARS) - Spanish Sundial
Society
British
Historical[edit] "The Book of Remedies from Deficiencies in Setting Up
Other[edit] Register of Scottish Sundials
Derbyshire Sundials -
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