The timing principle of the sundial
The pole can measure the shadow, and the measurement can tell the time. This is the simplest principle of sundial timing.
To understand why the sundial can measure time, you first need to know some necessary astronomical knowledge, the most important of which is the relationship between the earth and the sun. We know that while the earth is revolving around the sun, it is still revolving around the earth’s axis. A week of revolution is a year, and four seasons are produced, and a week of rotation is a day, and day and night are produced.
Because the orbit of the earth’s revolution is not a perfect circle, but an approximately elliptical shape, affected by this, its distance from the sun in a year is short and the sun’s gravitational force is large or small, so the speed of the revolution is not constant. At the same time, when the earth rotates, the angle between the earth’s axis and the ecliptic plane (the earth’s orbital plane) is not vertical 90°, but about 66.5°, so the angle between the ecliptic plane and the equatorial plane (yellow-red angle) is about 23.5°. In other words, the earth revolves and rotates around the sun with its body swaying rapidly and slowly. Therefore, the relationship between the earth and the sun is far more complicated than what we are talking about here.
As the earth continues to rotate, we will see that the sun rises from the horizon every day, and sunlight is projected onto the surface of the earth through the atmosphere, and shadows are formed when objects are blocked. This shadow was called “sundial” in ancient China.
Since the positional relationship between the earth and the sun is relatively stable and changes according to a certain law, the shadow of a fixed object on the ground from the sun also changes regularly. According to the position of the shadow, that is, the angle and distance between the shadow and some fixed reference objects, people can judge or mark the time (including solar terms and time) at this moment. This is the basic principle of sundial timing.
▲ Schematic diagram of the yellow-red angle
▲ Schematic diagram of the positional relationship between the earth and the sun
Definition of sundial
According to the timing principle of the sundial, it is not difficult to get such a definition: a sundial-an astronomical instrument-is a tool that uses the position of the sun or the projection of the sun and the ground reference to measure time.
The reason for using such a definition that seems too broad is because the sundial is not exactly the style we have seen. In other words, the usual configurations such as the dial face and the dial are not necessarily the standard configuration of the sundial. In fact, according to the basic principles of the sundial, some special-structured sundials, such as projected sundials, can be completely free of dials and dials, but they still conform to the principle of sundial timing and should be counted as sundials. Furthermore, why should the Chinese standard watches and the shadow clocks of ancient Egypt be included in the sundial? Because the standard watch completely conforms to the timekeeping principle and method of the sundial, only the time unit is different; the shadow clock is only different in name.
Sundial and standard time
The sundial measures the time based on the positional relationship between the sun and the observation point on the earth. This measured result is generally called “sundial time”, and in astronomy called “true solar time”, that is, the observation point is local, at the time and the sun. The time point of the formation of the positional relationship. The length of time the sun passes through the same place twice is called the “true solar day”. Due to the unequal speed of the earth’s revolution and the existence of the yellow-red angle, the position where the sun passes through a certain point on the earth every day will be slightly different. Therefore, the “true solar day” is not exactly the same length in each day of the year.
▲ Astronomy enthusiasts regularly locate and photograph the sun’s position trajectory during the year
▲ Sundial time difference curve chart
▲ Analiema curve
▲ Earth-axis sundial marked with an Analeyma curve
▲ The equatorial sundial with the Anarema curve dial
In order to overcome this “flaw” in the relationship between the sun and the earth and allow time to serve human society accurately, people define the average of all “true solar days” as “average solar days”, which are the “days” used in daily life by modern people. “, the time point it contains is called “average solar time”, or “normal time” for short.
There is a time difference between “sundial time” and “normal time” that varies with the anniversary. This time difference is traceable and can be calculated: normal = sundial hour-time difference.
There is a way to draw the time difference curve between “sundial time” and “normal time”, that is, the famous “Anarema Curve”. According to the different position trajectories of the sun every day of the year, it uses a circular closed curve to form a figure similar to “8”, and then puts this figure into a coordinate system composed of “normal” and the sun’s declination, “sundial time” The time difference with “usual” is clear at a glance.
The declination of the sun is the latitude value of the sun directly on the earth, and the value range is ±23° 26′, that is, the angle between the direct sunlight on the Tropic of Cancer. It can also be seen from the Analema graph that the sun (for a fixed observation point on the earth) is not a punctual guy. It “attends work” on time only 4 days of the year, and on the other days it is either early or late, and the difference between it and “punctuality” is 15 or 6 minutes at most. Of course, it is not the sun that is not on time, but the earth.
Copying the Anarema graph on the sundial surface can read the corrected time very intuitively (“normal”), so it is often seen in the sundial design.
In addition, the standard time we use in our daily lives is artificially specified based on the single longitude of the time zone where we are located, especially when one standard time is used across several time zones. For example, in China, the East 8th time zone (120°E) is uniformly used, that is, “Beijing Time”. However, most areas, including Beijing, are not exactly located on the longitude 120° east. Therefore, there is still a certain longitude time difference between “normal time” and standard time. Since each time zone differs by 15° and the time differs by 1 hour, the longitude differs by 1° and the time differs by 4 minutes. The calculation formula is longitude difference = (local longitude-time zone longitude) × 4 (minutes). Finally, use the sundial to get an accurate standard time through the following formula: standard time = sundial time-time difference-longitude difference.
Sundial of various shapes
The basic principle of sundial timing is relatively simple, but the specific methods of timing are varied, which makes the types and styles of sundial also diverse. The classification and naming of sundial helps us to better understand, learn, master and popularize the knowledge of sundial and inherit this legacy.
Here, I try to use my own research experience and refer to the names of some existing and reasonable sundials, and re-summarize, divide and name all kinds of sundials to form a set of as comprehensive and reasonable sundial classification as possible. , In order to share with many sundial enthusiasts, or you can also harvest surprises.
The sundial, especially the sundial that has appeared in modern times, is diverse and different in shape, but it never leaves its origins. All sundials must have a sundial that accepts sunlight or sunshade (not necessarily represented as a dial). Therefore, first, according to the shape of the sundial, which is a common but distinct feature, the sundial is divided into 5 major ones. Class, namely plane, elevation, inclined plane, different plane and mirrored sundial. Secondly, according to the relationship between the plane on which the dial is located and the earth, the three common types of sundial (plane, elevation, and slope) are divided into 7 types (types), and the different-faced sundial is divided into 3 types according to its own shape. The face sundial is classified into type 1. In summary, it is “5 types and 11 types.”
If divided by function, sundial can be divided into solar sundial (such as standard watch) and timed sundial. In English, it is usually collectively referred to as Sundial, and it is also called the Sun clock.
This article focuses on the three most common types of sundial in the timed sundial, namely, plane, elevation and inclined sundial. The commonality of these three types of sundial is that most of the sundial faces are straight (or originally straight). The difference lies in the setting method, namely the relationship between the sundial face and the ground (horizontal) plane, the meridian face of the earth, the unitary face or the axis of the earth. .
1. plane sundial – azimuthal
sundial sundial planes parallel to the horizontal. There is only a flat sundial for the plane sundial. According to the relationship between the sundial needle and the dial surface, the horizontal sundial is divided into two types: vertical needle and oblique needle. The time lines of the two horizontal sundials are unevenly distributed and symmetrical. The design parameters (that is, the angle of the time line distribution) generally can only be applied to the same latitude area.
▲ Horizontal needle sundial
▲ Horizontal oblique needle sundial
The horizontal needle sundial is the earliest type of sundial invented and used by mankind. Most other types of sundial can be regarded as derived from the horizontal needle sundial. The horizontal oblique needle sundial’s gnomon is placed obliquely, and the angle with the dial is equal to the local latitude, and the end of the needle points to the north celestial pole (equivalent to the sundial being parallel to the earth’s axis).
2. facade sundial – meridional formula
facade sundial sundial perpendicular to the horizontal plane and parallel to the Earth’s meridian plane (meridional plane), thus constituting the face east, and west facade surfaces, respectively, for the determination of the morning and afternoon time. The dial is perpendicular to the dial surface, and the length of the shadow of the needle is used to indicate the time, and the slope indicates the solar terms. In practical applications, the meridian sundial can be an independent sundial standing on a horizontal plane (combined surface), showing the east and west sides, or it can be installed on the east and west walls of the building, each showing one side (Faceted). The disadvantage is that the sundial is invisible due to direct sunlight on the side of the facade at noon, and it is difficult to express around 12 o’clock.
▲ Meridian Sundial
▲ Meridian faceted sundial with Annaremar curve
3. Facade sundial – Maoyou formula
sundial surface of a single-sided, south (north in the southern hemisphere), perpendicular to the horizontal, with the earth and prime vertical plane (the equatorial plane) in parallel.
According to the direction of the sundial, the Maoyou-style sundial is divided into two types: flat and oblique. The former is parallel to the horizontal plane and perpendicular to the dial, and the time line does not meet the pinhole; the latter is parallel to the earth’s axis (the angle with the dial is equal to the complementary angle of the local latitude), and the time line meets the pinhole. The time lines of the two sundials are unevenly distributed, but symmetrical, and both left and right symmetrical solar terms can be designed. The slope of the needle shadow indicates the time, and the length of the needle shadow indicates the solar terms. The disadvantage of the Maoyou-style sundial is that there is no shadow in the afternoon, that is, during the half-year (Northern Hemisphere) from the vernal equinox to the autumnal equinox, the afternoon sun does not shine on the south-facing sundial, and it turns to the north. It may be necessary to add another one for this The sundial facing north.
4. Facade sundial – Offset
called offset is relative to the fixed direction “upright” meridian and the prime vertical sundial according to the formula. Although the offset sundial surface is perpendicular to the horizontal plane, its orientation is either eastward or westward. It does not coincide with the meridian or Maoyou surface, but is somewhere in between. The time line and the solar term line are unevenly and asymmetrically distributed. Although the calculation and determination of the time line and solar term of the offset sundial are more complicated, the orientation angle of the sundial can be determined according to the orientation of the building, which varies from wall to wall, so it avoids the trouble of choosing and installing the wall. At the same time, because the sundial can be offset, the problem of “no shadow in the afternoon” can be avoided. The offset sundial is also divided into flat and oblique needles.
▲ Offset flat needle sundial
▲ Offset oblique needle sundial
The ramp sundial – equatorial
sundial plane parallel to the equatorial plane, the elevation angle and the horizontal plane is equal to the local latitude. The dial is perpendicular to the dial surface (parallel to the axis of the earth), and the two ends point to the north and south celestial poles. Time lines (or points) are equally distributed. The equatorial sundial is divided into two types: disk-shaped and ring-shaped according to the shape of the dial.
▲ Equatorial disc-shaped sundial
▲ Equatorial ring sundial
The equatorial disc-shaped sundial is the first type of sundial created by the Chinese, and it is also one of the outstanding contributions of the Chinese nation to world civilization. It is simple to make, and the dial map is 12 or 24 bisecting lines. It can be applied to all latitudes and does not require complicated calculations. However, it is accurate in timing and easy to read. It was widely used in ancient China and was particularly loved. The dial surface is divided into two sides, and the concentric dial surface passes through the surface of the disc, showing that there is one on each side, and the inclination of the shadow of the needle is used to indicate the time. After the equinox, the time value of the needle shadow on the north is read clockwise, and the time value of the needle shadow on the south is read counterclockwise after the autumnal equinox; the opposite is true for the southern hemisphere. The solar term line can be designed to indicate the solar term with the length of the needle shadow. On the day of the vernal equinox and the autumnal equinox, because the sun is directly on the equator, that is, on the side of the plane of the dial, there is no shadow of the dial.
The equatorial ring-shaped sundial evolved from the disc-shaped sundial. Its biggest feature is that the thick disc surface of the disc-shaped sundial is removed from the structure, and a ring or even a half-circle ring is used instead, and the sundial is a whole body. The function of the circular ring or semicircular ring is equivalent to only retaining the edge of the disc, but it can still be used to receive needle shadows and indicate time. As a result of the removal of the solid disk, the problem of “looking at both the north and the south for two and a half years” no longer exists, and the drawbacks of the vernal and autumnal equinoxes of the sundial being invisible on the sundial are also discarded. Therefore, the equatorial ring sundial is highly respected in Europe and the United States, and it is also the most common type of modern sundial works.
6. ramp sundial – the shaft
sundial facing south (north in the southern hemisphere), one surface perpendicular to the equatorial plane, and parallel to the axis (i.e., the angle formed between the horizontal sundial is equal to the local latitude). The sundial is generally flat, but it can also be deformed and designed as a curved surface. The dial is generally parallel to the surface of the dial, or it can be just a point. The time line is unevenly distributed, but symmetrical, and the solar term line can be designed. The left and right (east-west) shadow positions of the sundial are used to indicate the time, and the upper and lower (south-north) shadow positions of the center of the sundial are used to indicate solar terms.
▲ Earth-axis plane sundial
▲ Earth-axis arc sundial
7. bevel sundial – any backstroke
called any Yang, means with respect to the equatorial sundial and according to a fixed elevation axis sundial set, the can “Yang arbitrarily set.” The elevation angle of its sundial (in theory) can be within the range that can receive sunlight in one day (all year). The northern hemisphere is facing south and the southern hemisphere is facing north, but the longitudinal axis of the dial and the direction of the hand remain in the meridian plane. The time line is symmetrical from east to west, generally unevenly distributed, and the design parameters are different for different latitude areas and different elevation angles. The advantage is that when set outdoors, it is not restricted by factors such as fixed elevation angles like other sundials, and it is easy to integrate with the environment. There are also standing needles and oblique needles for the Renyang sundial.
▲Right-up style vertical needle sundial (adjustable type)
▲ Ren Yang style oblique needle sundial
▲ Spherical sundial (outer spherical surface)
▲ Spherical sundial (inner spherical surface)
8. Different Surfaces sundial – type spherical
shape is a sphere, namely the surface of a sphere sundial. The sundial needle can be installed or not, and the position of the shadow of the sphere itself is used to indicate the time. The time line is an even and symmetrical arc, similar to the melon line or the meridian on the globe. The spherical sundial can be divided into an outer spherical surface and an inner spherical surface. The latter is also called the upside-down sundial, which is named for the shape of a pot facing the sky.
9. Different Surfaces sundial – tapered formula
sundial surface is a surface of a cone, the conical tip is typically placed gnomon, time line, the line according to the position of the throttle of the gnomon, to be determined. Divided into two kinds of cone and square cone.
▲ Cone Sundial
▲ Square cone sundial
▲ Inner cylindrical sundial
▲ Outer cylindrical sundial
10. Different Surfaces sundial – cylindrical formula
sundial surface is a surface of a cylinder, and the outer cylindrical surface is divided into two kinds of inner cylindrical surface. The design method of time line and solar terms is more complicated.
11. Ying sundial surface – projection type
enantiomer i.e. the projection plane sundial sundial, which uses a direct or indirect sunlight projected surface to mark a particular enantiomer time divided transmission (direct) and two kinds of refraction. The transmission sundial is a more “alternative” type of sundial. It does not use the shadow of the dial to mark the time like most sundials. Strictly speaking, it has neither a dial nor a dial, but only a transmissive surface, directly marking the time with the daylight itself that passes through the transmissive surface and is reflected on the object. Of course, it can also be understood that it is a shadow formed by a shield on the transmission surface to block light that does not need to pass through.