The oldest mechanism for telling time. Sundial - the simplest device, but it contains the knowledge and observations of our ancient ancestors. Currently sundial used as landscape decoration. For example sundial parents teach their children the structure solar system, and the building itself DIY sundial- a most exciting activity for our children, for example, being on the beach. During production sundial you need to know some points and features of their design, which we will talk about in this article.
What is a sundial made of?
Sundial consist of a pointer hand that casts a shadow (this hand is called a gnomon) and a sundial dial. Time by sundial determined by the shadow cast by the gnomon on the dial. Everything is simple, but there are some peculiarities. Clock face sundial is divided into 24 hours, rather than 12 hours, as in conventional mechanical watches. The dial or gnomon must be tilted above the plane. Sundial do not take into account the transition to summer time. The sundial only works in clear or partly cloudy weather during daylight hours. That's all the restrictions sundial.
There are several types sundial. Let's deal with them in order.
You can do it right on the sand on the beach. First we need to know two things: what latitude we are at and where north is. If the second part can be installed by selection, then with the first you will have to be prepared. So, we have a compass and we know our latitude (St. Petersburg - 60, Moscow - 55, Nizhny Novgorod - 56, Ekaterinburg - 56, Sochi - 43, Rostov-on-Don - 47, Novosibirsk - 55, Vladivostok - 43 degrees north latitude). If we make a dial sundial on a portable surface - draw a circle and divide it into 24 parts. If we make a sundial on the ground, draw a circle, insert a stick (gnomon) into the center of the circle and tilt it north so that the angle between the surface of the earth and the gnomon is equal to our latitude, draw a line from the lower end of the gnomon exactly north - it will be 12 hours of the day astronomical time. We draw the remaining lines, dividing the entire circle into 24 equal sectors. Each sector sundial equal to 15 degrees.
An ambush awaits us here. After competently delineating the dial and tilting the gnomon, the time is shown sundial may differ from the time shown on local television. The problem lies in maternity time and time zones, which were artificially created for convenience. A portable dial will easily solve this problem by simply turning it until the time is correct. With a clock drawn on sand a little more complicated, this point must be taken into account when starting to paint the dial. For example, you can postpone marking the dial until 12 o'clock, when we will determine the north without a compass and accurately draw the main axis of the dial of our sundial. If you have no time to wait, and creativity is bursting out of you, paint the dial sundial in the draft version and adjust your dial to the error that you got.
In our latitudes sundial They work in the height of summer from 8 am to 8 pm, so it is almost pointless to divide the numbers between these values. Because of this, the base of the gnomon is often moved downward on a round dial.
The same horizontal clock, only the gnomon is set clearly vertically, and the dial itself is inclined to the surface of the earth at the angle of latitude where such a clock is installed.
Vertical sundial.
Vertical sundial usually mounted on the walls of houses. The same tilted gnomon and dial marked at 15 degrees.
Usually in cities they make a mixed type sundial, i.e. The dial is tilted half an angle, and the gnomon is tilted half an angle. This construction sundial look more impressive, in fact, that’s why they are made.
Construction sundial DIY will really captivate your child and, in addition, expand his horizons.
History of the sundial
Man invented a number of instruments for measuring time, for example, lunar, water, candle clocks, which were used until the 18th century, then hourglasses and from the 16th to the 18th centuries oil clocks. However, due to their dependence on external conditions and their fluctuations, as well as due to technical imperfections, these means of measuring time have not found universal use.
According to modern chronology, clocks of varying degrees of complexity already existed everywhere 4000 years ago. The first to try to make them were the Egyptians, who invented star clock charts, and it was possible to determine night time by observing the rise of the stars. Regarding daytime, the late Egyptians invented shadow clocks (sundial). The shadow from the cross beam gradually crossed a series of marks from sunrise to sunset. A set of instructions for making such a watch was found in the tomb of a pharaoh.
Seti I, who reigned around 1300 BC. Such simple shadow clocks were the predecessors solar.
Particularly favorable climatic conditions for measuring time using sundial had Egypt. News about the most ancient of ancient Egyptian sundial dates back to the reign of Thutmose III - the first half of the 15th century. BC. One type of sundial was a stepped clock in the form of an obelisk with two inclined surfaces oriented along an east-west axis and divided into steps. At sunrise, the shadow fell on the edge of the upper step of one of these surfaces - the eastern one, then gradually dropped until it completely disappeared by noon. Then, in the afternoon, the shadow again appeared in the lower part of the western surface, from where it continued to rise until, at sunset, it touched the edge of the upper step.
On the described sundial time was measured by the length, not the direction, of the shadow cast. However, the Egyptians had a sundial with a scale to determine the direction of the cast shadow. The famous Roman architect and builder Marcus Vitruvius, who worked during the reigns of Caesar and Augustus, describes at least 13 types of sundials in his work “Architecture”.
These also include horizontal hollow hemispherical sundial- the so-called hemispheres. The inner surface of the hemisphere represented a celestial hemisphere with an equator line, two solstice lines and a twelve-hour time scale. The invention of such clocks is attributed to the famous ancient astronomer Aristarchus of Sames, who lived in 320 - 250. BC who also made sundial with semicircular scales divided into five parts (hours) of unequal length. In improving the Greek sundial The famous mathematician, doctor, founder of Greek astronomy Eudoxus of Knidos, who lived in 408 - 356, also took a great part. BC. The sharp end of the gnomon, which originally served the Egyptians to clearly limit the shadow on the scale, was later replaced by the Greeks with a small one round hole, the so-called solar eye, which threw a small point of light onto the scale. In addition to the above horizontal clocks, the Greeks also had more advanced vertical sundial, the so-called hemocycles, which they placed on public buildings. All ancient sundials were based on simple principle a gnomon, in which the length and direction of the cast shadow depended not only on the position of the Sun at a given moment in the sky, but also on the time of year.
With the Roman method of dividing day and night into 12 hours, daytime hours were lengthened in spring and summer, and shortened in autumn and winter. The ancient sundial, due to its imperfection, indicated the time, the main feature of which was that, under the influence of the changing inclination of the Sun, the length of the day and night hours changed throughout the year. Later antique and many medieval sundial had curvilinear scales that eliminated this drawback. Such clocks, with more complex and more accurate time scales calculated for quarterly or monthly intervals, were used until about the 15th century. A new era in the development of sundials was opened by an important invention dating back to 1431. Its principle was to install a shadow arrow in the direction of the earth's axis. This simple innovation achieved that the shadow of the hand, called the semi-axis, after this innovation rotated evenly around the semi-axis, turning 15 degrees every hour. This made it possible to introduce uniform time, which could be used throughout the year, and the segments corresponding to the hours were the same length, regardless of the changing altitude of the Sun. The next stage in development sundial became a sundial with a compass. To the first creator sundial an astronomer and a mathematician with a corrective compass
Regiomontan. with a dial parallel to the plane of the earth's equator and a gnomon perpendicular to it, they were, in essence, the simplest clocks with a uniform time scale. The creators of such watches usually assumed that they would be used in different geographical latitudes. Sometimes such watches had a geared hand and a small dial with an arrow for counting minute intervals with an accuracy of 1 to 3 minutes. Such clocks were called heliochronometers.
There were also equatorial clocks, designed so that their dial indicated directly the average solar time , not local solar time, like a regular equatorial watch. Varieties sundial were very diverse. Interesting roundabouts sundial- one of the options for travel sundials, which very often also served as a decorative pendant.
The main part of such sundial there was a brass ring several centimeters in diameter with another movable ring equipped with a hole for a sunbeam. On the outer surface of the main ring, the initial letters of the names of the months were usually engraved, and against them, on inner surface, there was an hour scale. Before measuring, it was necessary to turn the smaller, usually iron, ring so that the hole for the beam lay at the name of the corresponding month. When measuring time, the watch was held in a position that allowed the sun's ray to pass through the hole in the scale. The so-called equatorial rings were built on a similar principle - similar watches, on the main ring of which there were two more circles intersecting with each other. Later arose new option with a crossbar instead of a third ring.
On one side of this crossbar the months were indicated, and on the other - the signs of the zodiac. In the middle there was a jumper with a small hole for the passage of the sun's ray. Correct position of these clocks when measuring time was such when Sunbeam, passing through the hole, fell on the central line of the equatorial circle. To conclude this section, I would like to briefly dwell on one of the road models sundial, used by Indian travelers. They were wooden octagonal sticks with a metal tip 160 cm long with carved hour scales. A rod about 15 cm long was inserted into the hole above the scale for the corresponding month so that its tip would cast a shadow on the scale when the stick was in a vertical position. There should have been 12 scales on the stick. Since the same conditions were in effect for days removed from the solstice by the same time, it was enough to have 8 scales. These watches received the name ashadah according to the season (June-July) in which the travel was made. Sundial have never lost their meaning and continue to be constructed even today. The Romans perfected the sundial we are familiar with today, and even made solar portable watch, convenient for travel. They lasted for thousands of years and more for a long time remained a means of checking and coordinating for very unreliable wheel clocks until they were finally superseded by the invention of the spiral spring as a regulator (1674), but we will talk about this below.
We looked at the design and functioning of sundials, which have been improved and changed over the years. Sundial with a pole movable in height, a compass and scales with minute divisions, they were a simple and reliable solar time indicator, but they also suffered from some serious shortcomings. Their work was associated with sunny weather and with a limited period of work - between sunrise and sunset. Therefore, new instruments for measuring time were fundamentally different from sundials. While the unit of time according to the sundial was derived from the rotation of the Earth and its movement around the Sun, it was necessary to create an artificial standard for the unit of time, for example, in the form of the time interval required for the flow of a certain amount of matter in a chronometric device.
When traveling, sometimes it is necessary to navigate by the sun, for which you need to know the approximate time. If you don't have a watch with a dial, you can make your own sundial. Besides practical significance, this design will be an excellent decoration garden plot. Plus, making a solar time teller will be a fun activity for kids to follow the movement of the sun and know the time of day. How to make a sundial? You can find out more about this below.
Sundial
Solar time tellers are divided into three types: vertical, horizontal, equatorial. The first type is mounted on the walls of buildings; accordingly, it has a vertical dial directed strictly to the south. The rod for indicating the time is located above the center of the dial with a deviation of 90 degrees minus the latitude of a particular area.
The second type is located on the ground in a horizontal position. The clock rod has the shape of a triangle with an angle equal to the latitude of the area, called a gnomon. It points north. This clock shows exact time all year round, except winter and late autumn. The surface of the equatorial clock is inclined relative to ground level and turned to the north. The gnomon is a rod perpendicular to the dial, located parallel to the earth's axis. The dial is marked with divisions similar to a conventional clock, every 15 degrees. The disadvantage of equatorial clocks is that they will only show information during the period between the spring and autumn equinoxes in the northern hemisphere, and vice versa in the southern hemisphere. The advantage of this type of watch is its mobility. You can make a small structure that can be moved to the desired location.
How to make a sundial with your own hands: video
The most common are horizontal and equatorial sundials, but despite this it is worth describing the manufacture of each of the three types. Before manufacturing the structure, it is necessary to determine the location for its placement. This should be an area not blocked by buildings, trees or other objects. It is better to first observe the location of the future clock throughout the year so that it is constantly sunny. Depending on the location, it will depend on what type of watch to make - vertical, horizontal or equatorial. If a lot of shadows from pillars and fences fall on the site, the best option would be to make a vertical sundial that can be attached to the wall of the house or on a decorative post.
Equatorial sundial: manufacturing
As a basis, you need to take plywood or a piece of plastic, on which divisions are applied every 15 degrees. A metal rod or pin made of any other strong material is fixed in the center of the base. Its length varies depending on the size of the watch.
In order to give the correct tilt to the dial, it is placed on a special stand. To correctly calculate the angle of inclination, you need to subtract the degree of latitude of the area where the sundial is installed from 90 degrees.
Once the dial is installed, they need to be oriented so that the gnomon points north. This needs to be done this way: some time before noon, the rod (gnomon) is fixed on a horizontal plane. The place where the shadow from the rod will fall should be marked with a dot, then draw a circle using a compass. The center of this circle will be where the gnomon is fixed. The length of the shadow at the moment of observation will indicate the radius of the circle. Next you need to observe the movement of the shadow. Moving away from the drawn circle, it will gradually decrease, then grow again, crossing the circle again. In the place where it crosses it for the second time, you need to put a mark and connect it with the first mark. The resulting segment must be divided in half. The straight line that passes through the middle of the resulting segment and the center of the circle will indicate the north-south direction. Next, you need to mark the dial, for which the base is marked into 24 identical segments of 15 degrees each, and apply numerical markings.
For correct orientation of the equatorial homemade watch conditions must be met:
- The part of the dial on which the numbers from 6 to 18 are indicated must be strictly horizontal.
- The part of the dial with numbers 12-24 must coincide with a certain north-south direction.
- The dial must be tilted so that the angle is the local latitude.
How to make a horizontal sundial
Do-it-yourself sundials with a horizontal dial are even easier to make than equatorial ones.
The base is made of solid material, you can take plywood or plastic. It can be made round or square. The gnomon is made from the same material in the form of a triangle, one angle of which should be equal to 90 degrees, and the second to the latitude of a particular area. The triangular arrow is attached to the base, and is installed on the ground in in the right place. In order to turn the arrow to the north, they are guided by a compass. To indicate divisions on the dial, you need to set a timer and mark the shadow of the hand every hour.
Making a vertical sundial
Preparing to make a sundial It is better to place a vertical sundial on the south side. Making this type of sundial is more complex than the first two. The dial is positioned parallel to the horizon in a strict south direction for the northern hemisphere. Just above the central part of the base of the time indicator, you need to mark the location of the arrow, and from this point lower a plumb line along which you need to draw a line. This line will indicate the time of noon. Numerical designations are located symmetrically on the dial only if the rod is in a strictly perpendicular position relative to the dial. Fixing the rod in the wall is not so easy: first you need to drill a hole with a diameter larger than the gnomon. The part of the rod that will be fixed inside the wall needs to be slightly flattened in order to prevent it from turning. The attachment point is moistened, the rod is inserted there so that the bending point is exactly in the wall. The rod must be rotated so that it makes an angle of 90 degrees with the surface of the wall before the mortar at the attachment point hardens.
Sundials in our country are rather exotic, but if you make this device with your own hands, then it can be successfully used in the country as not only a device for telling the time, but also as an interesting architectural element. Sundials were used by people to determine time in ancient times, but they were gradually replaced by more modern devices. But even in our time, such watches can come in handy, especially since making them is a very exciting activity.
If you make a homemade sundial with your child, it will be a useful developmental activity for him to study the movement of the sun and telling time. The sundial options proposed in this article are current models, therefore, when manufacturing them, it is necessary to observe the right technology have some knowledge of trigonometry and astronomy.
Materials for sundials
It is also important that they are suitable for making sundials different materials, the main thing is that they are resistant to weather factors. You can use stone or cement, wood or iron, plastic or gravel for the dial. It is better to choose a light material - the shadow of the arrow (gnomon) is clearly visible on it. Marble, limestone or light pebbles are suitable for these purposes. For the gnomon (arrows), metal or plastic pins, long nails, knitting needles, etc. are used.
Types of sundials
Such watches can be different types, but there are mainly three types:
- Equatorial. Their dial (cadran) is located parallel to the equator, and the part that casts the shadow - the gnomon), in the form of a metal rod, is parallel to the earth's axis. The markings on the dial of such a watch are every 15 degrees.
- Horizontal. In them, the plane of the frame is parallel to the horizon, and the gnomon is made in the form of a triangle, with the side inclined to the plane of the dial at an angle equal to the geographic latitude of the given area. The arrow is directed north, and divisions into sectors (hours) are made according to the formula. Such clocks show time all year round, but in winter and late autumn their readings are not entirely accurate.
- Vertical. Their dial is located vertically and is placed on the walls of buildings, pillars, fences and other vertical planes. The frame in them should be directed strictly south and should be perpendicular to the noon line or at an acute angle to it. The gnomon in such a sundial is fixed above the center of the dial and must be deflected by an angle equal to 90 degrees minus geographical latitude of this area.
How to make a sundial
We will look at how to make two types of sundials - equatorial (oblique) and horizontal. These are the watches that are most common in everyday life.
Equatorial sundial
- Plywood or plastic is used as a base. A dial is drawn on it with divisions every 15 degrees.
- A metal pin or rod made of any strong material is fixed in the center of the dial.
- The clock must be set correctly. To do this, the dial is tilted using a stand. The angle of this inclination is calculated for each area individually: 90 degrees minus the degree of latitude of the area.
- After installing the dial, the sundial must be oriented to the area - point the clock hand to the north.
- It is worth remembering that such a sundial will only show time in certain seasons, and in winter, for example, it will not be unsuitable.
Horizontal sundial
This watch is very simple and quick to make, so you can make it together with your child.
- Plastic or plywood is also used for the dial; a gnomon in the form of a triangular arrow is made from the same materials. One of its angles must be equal to 90 degrees, and the second is taken equal to the latitude of a particular area.
- This triangle, along with the dial, is installed in the place where the sundial will be used. In this case, you need to navigate north using a compass.
- Next, start the timer, and every hour the shadow of the hand is noted and thus the divisions are made on the dial.
- Horizontal clocks can be made large and placed on a flower bed, lawn or on an island in the middle of a decorative pond. If you do it very big clock, then you can use boulders or tree stumps as divisions.
IN modern world sundials look, at least, exotic, and in most cases they are a banal decoration - a decoration for a dacha or a plot of a residential building. But we should not forget that in ancient times it was a very useful and functional thing, the accuracy of which even some may well envy modern products this type. If the sundial is made correctly, it may well compete with yours. wristwatch. You can make them three different ways, which is what we will talk about in this article. Together with the site, we will get acquainted with the question of how to make a sundial with your own hands - we will talk about three varieties of these items and their correct manufacture.
Equatorial sundial: DIY production
This is a very simple sundial to make - this is due to the fact that the divisions of its dial are the same and amount to 15 degrees, which corresponds to one hour. In principle, this is where everything simple in this watch ends and the difficulties begin - a watch of this type must be installed correctly, which in itself is difficult. Such a clock must be installed simultaneously in two planes.
As for the actual production of equatorial sundials, everything is very simple. It is better to use a hard material like plastic for them. First you make a dial with a gnomon, then you think about how you can install it at an angle, but also orient it to the north, after which the clock will work. By the way, the angle of inclination of the gnomon can be easily adjusted with a protractor and rulers - drawing tool has a special lock that allows you to install between a pair of rulers desired angle. By the way, for our hemisphere, the clock needs to be directed towards the true north pole, but if you make a clock while in the southern hemisphere, then the gnomon and dial should point towards the true south pole. In this case, the dial will be a little different - it will be a mirror image of a sundial for the northern hemisphere of the Earth.
You can see what a sundial can be like in this video.
DIY horizontal sundial
A distinctive feature of this type of watch is the horizontal arrangement of the dial - the gnomon is oriented exclusively towards the true pole of the Earth. On the one hand this is good ( simpler technology manufacturing), but on the other hand, not very well, since setting the clock looks very problematic. In such watches, the shadow from the gnomon does not move the same distance over the course of an hour, so you need to be patient and wristwatch. The divisions will have to be applied in accordance with a mechanical or electronic chronometer. Such watches are made as follows.
During even hours, we simply place marks where the shadow of the gnomon points.
Once the dial markings are completed, the watch can be used fully. In principle, they can be used immediately after installation, only without divisions you can determine the time exclusively intuitively.
How to make a polar sundial for the garden
The beauty of this solar chronometer lies in its dial - it is not round, like most illogical devices, but linear. The shadow from the gnomon moves along it in a straight line, which greatly simplifies the technology of making sundials. By by and large, this is still the same equatorial sundial, only its gnomon is not a pin, but a stick located across the so-called dial. The divisions in such watches are also applied unevenly, which makes it possible to assert that a sundial of this type is some kind of hybrid between the first two options. Do-it-yourself polar sundials are made as follows.
In principle, there is a fourth option for sundials, which are very difficult to manufacture and configure - these are vertical, or, as they are also called, wall sundials. They are more convenient to use, but their assembly requires very precise calculations and very precise (no less precise) manufacturing.
DIY sundial photo
To conclude the topic of how to make a sundial with your own hands, I will say a few words about the materials. Their choice depends entirely on the purposes of production. If this is pampering or just Toolkit for children, the chronometer can be made from cardboard. If you really want to make working model and use it to determine time, then you need to choose more reliable materials. In this case, the dial can be made of concrete (alternatively, cut off the surface natural stone large size), and the gnomon is made of steel - such a watch can be safely left in the fresh air, and at the same time it will last a very long time.
A typical gnomon in its original form
It is also customary to call a gnomon the part of a sundial that casts a shadow on the dial.
Gnomonics is the science that studies sundials. Today, gnomonics is nothing more than a scientific hobby, since more accurate and easy-to-use instruments have been created to determine the true meridian and time.
Theoretical information
Let us list some facts based on knowledge of astronomy that will help you understand the principle of operation of the gnomon.
Fact No. 1. The sun always moves from east to west, which means the shadow from the gnomon moves in the opposite direction, that is, from west to east.
Fact No. 2. During sunrise and sunset, when it is directly above the horizon, the shadow from the gnomon is the longest, and at solar noon it is the shortest.
Fact No. 3. The shortest shadow from a gnomon is obtained when the Sun is at its zenith, that is highest point trajectory of its movement across the sky. At this moment, the Sun crosses the true meridian, that is, the line connecting north to south.
Fact No. 4. The fastest change in shadow length is observed during the hours of sunrise and sunset over the horizon. In the middle of the day, the rate of change in shadow length is minimal.
Fact No. 5. Due to the inclination of the Earth's rotation axis relative to the plane of the Earth's orbit at an angle of approximately 23.5 degrees, as well as due to the rotation of the Earth around the Sun, the observed movement of the Sun across the sky occurs below the celestial equator (in the northern hemisphere from September to March) , then above it (in the northern hemisphere from March to September). And only on the days of the spring and autumn equinoxes does the movement of the Sun coincide with the plane of the celestial equator. Moreover, the trajectory of the Sun's movement lies farthest from the celestial equator on the days of the winter and summer solstices.
By the way, the celestial equator is a large circle of the celestial sphere located perpendicular to the Earth’s axis of rotation, the plane of which coincides with the plane of the Earth’s equator.
Fact No. 6. The sun moves across the sky at an angular speed of approximately 15 degrees per hour.
Fact No. 7. Average “terrestrial” time does not always coincide with astronomical time for a number of reasons.
Fact No. 8. The diameter of the Sun visible from Earth is approximately thirty arcminutes. This makes the shadows of objects blurry.
Fact No. 9. If you stand in such a way that the north is in front of your face, then the south will be behind you, the east will be on your right, and the west will be on your left.
Understanding the processes underlying the operation of the gnomon and sundial is necessary not only in order to make these devices yourself, but also in order to use them correctly. Once I happened to observe a funny picture: a man, having bought a sundial, could not understand why the time on it and on the clock on his phone was different. The video shows this example:
How to use a gnomon to determine the true meridian
The gnomon in this case is a pillar, column or other straight vertical object located on a flat horizontal area open to the Sun. It is believed that increasing the length of the gnomon will increase the accuracy of measurements, since in this case changes in the length of the shadow become more noticeable. However, do not forget that as the length increases, the clarity of the cast shadow will decrease, which can negatively affect the accuracy of measurements. Also, the accuracy of the results is affected by the thickness of the upper part of the gnomon, which is why it is often made pointed.
On a clear sunny day, the shortest shadow from the gnomon indicates the onset of astronomical noon and points north (in the middle and high latitudes of the northern hemisphere) and south (in the middle and high latitudes of the southern hemisphere). In the tropics and at the equator, the situation can change throughout the year, as we have discussed in detail here.
Thus, by the shortest shadow it is possible to determine both true noon and the direction of the true meridian. Among other things, knowing the height of the gnomon (B) and the length of the shadow (L), it is not difficult to calculate the angular height (H) of the Sun above the horizon. To do this, use the formula tgH=B/L.
However, due to the slight change in the length of the shadow from the gnomon during lunch hours, it is not always possible to accurately determine the shortest shadow. If you need to obtain more accurate results, you can use another method. To do this, determine the bisector between two identical shadows of the gnomon, measured in the morning and evening, when the rate of change in the length of the shadow is more significant. It is this method that underlies one of the methods of orientation by the shadow of the Sun.
Knowing the true meridian, you can easily navigate the area by determining the direction north or south, and then all other cardinal directions.
How to use a gnomon to determine the latitude of an area
In addition to determining the true meridian, using a gnomon you can approximately calculate the latitude of the area in which measurements are taken. Next, we will consider several methods that arise from knowledge of astronomy.
Method number 1. On the day of the autumn or spring equinox at true noon, the angular altitude of the Sun is determined using the previously discussed formula. The resulting value is subtracted from 90 degrees. The result of the calculations will be the latitude of the area.
Method number 2. On the day of the winter solstice at true noon, the angular altitude of the Sun is determined. Since at this moment the Sun is below the celestial equator by an angle, equal to angle tilt of the earth's axis, that is, by 23.5 degrees, then by adding this angle to the angular height of the Sun obtained from the formula, we can obtain the angular height of the celestial equator. When subtracting the height of the celestial equator from 90 degrees, a value corresponding to the latitude of the area is obtained.
The movement of the Sun across the sky in summer at high latitudes.
This method can also be used on the summer solstice. To do this, you need to subtract 23.5 degrees from the angular altitude of the Sun to obtain the angle of inclination of the celestial equator, and knowing the angle of inclination, the latitude of the area.
The movement of the Sun in high latitudes in summer, when it does not set beyond the horizon.
Method No. 3. At true noon, shadow length measurements are taken daily. As a result of these measurements, you need to get the longest or shortest shadow, which will correspond to the winter or summer solstice, respectively, and then proceed according to the second method. Or, having determined the longest and shortest shadow, find the average length value, calculate the angular height of the Sun using the formula, focusing on the obtained average value, and act in accordance with the algorithm of the first method.
When obtaining results using one of the above methods, it should be remembered that the apparent height of the Sun above the horizon is to some extent influenced by the effect of light refraction - refraction, which we talked about here. Because of this effect, everything celestial bodies may appear higher than where they are actually located. And the more pronounced this effect will be, the closer to the horizon the observed object is located.
It follows from this that near the poles on the days of the spring and autumn equinoxes, when the Sun passes low above the horizon, the measurement results may differ slightly from the real ones towards lower latitude.
Now let's look at how to determine the time and date using a gnomon.
Gnomon and sundial
A sundial is an ancient instrument that allows you to determine time by the shadow of the Sun during daylight hours.
One of the very first sundials appeared in Egypt. They were a stone block approximately 30 cm long. This block was located along the east-west direction. On one side of this clock there was a “T”-shaped block, the shadow from which, decreasing, “crept” along the block from morning to noon, after which the sundial was turned 180 degrees and the shadow “crept” in the opposite direction. The time was determined by the notches made on the block.
Sketch of an "Egyptian" sundial.
The very first notes about sundials are found in Egyptian manuscripts and date back to 1306-1290 BC. The discovered Egyptian sundial, according to scientists, was made long before the found manuscripts describing them - back in 1479-1425 BC.
One of the first sundials.
Other models of ancient sundials were also discovered in Egypt, different from the model described, but their age, according to the testimony of scientists, is younger, so it is not necessary to consider them as the most ancient sundials.
Reconstruction of an ancient sundial in Egypt, exhibit of the Cairo Museum.
Regardless of Egypt, sundials appeared in other parts of the world, for example, ancient China and in Ancient Greece, from where their idea migrated to Ancient Rome.
In Rus', cathedral towers that cast shadows began to be used as sundials. But all this was already practiced in the 11th century AD.
However, such watches could not show the exact time, since the notches were made by evenly dividing the scale into a fixed number of parts.
And only many centuries later, humanity came up with a sundial that showed more accurate time. They were more similar to modern analog watches, with the only exception that their scale was designed only for a period of time from morning to evening and looked more compressed.
Such sundials can still be found today: it has become fashionable to decorate squares with them. Sometimes sundials can be found on garden and summer cottages, where they can look good at the intersection of paths.
Sundial as a decorative element.
The gnomon is an integral part of the sundial. It is he who casts a shadow on the dial, forming the “arrow”.
You need to understand that a sundial can show both astronomical and average “terrestrial” time: it all depends on the markings when constructing them. Therefore, when creating a homemade watch, you need to decide in advance what time we want to see on such a watch.
In addition to the time, the sundial can also show the date and month. To do this, additional markings are applied to them.
It is important to understand that such watches can correctly indicate the date and month only if they are “calibrated” strictly for a specific installation location.
But there is no need to place high hopes on a homemade sundial: due to a number of inaccuracies associated with the design of the clock, the unevenness of the surface for installation, the orientation of the clock in space, the angular diameter of the Sun, the equation of time and other factors, one cannot expect particularly accurate readings from such clocks .
Let's look at several basic models of sundials that you can construct with your own hands from wood, plastic or cardboard.
Equatorial sundial
This sundial got its name due to the fact that the plane of its dial is parallel to the plane of the celestial equator.
The tilt of the scale of these watches is required so that even the Sun standing at full zenith casts a shadow.
It is advisable to make such a watch in the form of a flat circle, in the center of which a gnomon is stuck, and in such a way that one part of it rises on one side of the dial, and the other sticks out on the other. If this is not done, then from September to March (in the middle and high latitudes of the northern hemisphere) you will not be able to use such a watch, because the Sun will drop below the celestial equator, which means the upper part of the watch will no longer be illuminated by its rays.
The equatorial clock is set so that the gnomon in relation to the horizon is raised at an angle corresponding to the latitude of the area, and points to the geographic north. In this case, the plane of the dial will be parallel to the plane of the celestial equator.
There is often a recommendation to set a sundial using a compass. However, this often creates an additional error, since the geographic north does not always coincide with the magnetic north, which the arrow points to. magnetic compass, which was described in detail in. Besides, additional error in this case may arise due to various magnetic deviations.
From the point of attachment of the gnomon to the dial in the northern direction (for middle and high latitudes of the northern hemisphere), a straight line is drawn along the dial. The shadow of the gnomon will cross this line at true (astronomical) noon.
Using a protractor or any other in an accessible way Other divisions are also applied to the dial in the form of rays with the center at the place where the gnomon is attached. The angle between adjacent “rays” should correspond to 15 degrees - it is this angular distance, as we remember, that the Sun, and accordingly the shadow, travel in one hour.
The number “12” is placed above the central marking corresponding to noon. Rays located to the west are numbered reverse order, that is, “11”, “10”, “9” and so on, and the rays located to the east are numbered in ascending order, that is, “13”, “14”, “15” and so on. The result is a dial.
A similar scale is made on the bottom of the clock.
Such a clock can be quickly made from a protractor, but in this case, instead of the numbers corresponding to the hours, you will need to use corner marks. Thus, a mark of 90 degrees will correspond to 12 o’clock in the afternoon, and for each hour the shadow of the gnomon will shift either in one direction or the other by 15 degrees, from which it can be concluded how much time has passed or should pass for the “arrow” to be on 90 degrees, that is, it made it clear that it was noon. This is not very convenient, but it will take a minimum of time to build such a sundial.
By the way, in the area of the equator such a watch will stand vertically, like a wheel. And at the poles - horizontally, like a top during its rotation.
The video shows how such watches are made by hand:
Despite the simplicity of the design, such watches have a drawback: they are difficult to use on days close to the spring and autumn equinoxes, since the plane of the Sun's movement across the sky in this case is parallel to the plane of the dial of the equatorial sundial.
When turning to numerous Internet sources, I came across information that equatorial sundials cannot work on the specified days, and I never came across information on how to determine the time in these cases. Therefore, I will share my thoughts. In fact, everything is simple: you need to make a small side protruding above the surface on the side of the dial opposite to the direction of the Sun. On this side the shadow of the gnomon will be visible even on the days of the equinox.
Equatorial sundials are convenient for their versatility, since they will work anywhere on the Earth on a clear sunny day. However, it will be difficult to determine the date and month with their help due to the too long shadow and limited dimensions of the dial. But the calendar function is easily handled by a horizontal sundial, which we’ll talk about later.
Horizontal sundial
In a horizontal sundial, the dial is positioned horizontally. The gnomon in this case, by analogy with the equatorial clock, is located in the northern (for middle and high latitudes of the northern hemisphere) direction at an angle to the horizon equal to the latitude of the area.
Antique copper sundial on a fortress wall at St Michael's Mount, Cornwall, UK.
Such sundials are also located strictly according to the geographical cardinal directions.
The mark on the dial corresponding to 12 o'clock in the afternoon is made by analogy with the previous version of the sundial. At the moment of crossing the shadow of the gnomon of this mark, the time is recorded on an ordinary clock. After this, exactly an hour later the next note is made. And so on until the Sun disappears below the horizon. All marks are connected by straight lines to the location of the gnomon - a kind of ray is obtained.
The rays corresponding to the morning hours are drawn on the dial as a mirror image of the evening ones. Next, each ray is numbered by analogy with the previous version of the sundial.
You can also make marks on this dial to determine the date. For this:
- On the day of the summer solstice, during the day, every hour, marks are applied to the dial, corresponding to the end of the shadow of the gnomon.
- The marks are connected by a smooth curve.
- The date and month on which the notes were made are signed next to the resulting curve.
- Similar actions are repeated exactly a month later and so on until the day of the winter solstice arrives.
- On the opposite side of the curves, dates and months corresponding to the period from December to June are plotted. So, July will correspond to May, August to April, September to March, October to February, and November to January.
In order to approximately determine the date from such a clock, you need to look at which curve the end of the gnomon's shadow is on or between which curves, and then use the interpolation method to determine the approximate date and month. To do this, of course, you need to know at least what period the measurement is being taken, because, for example, on November 21 the shadow will be approximately the same length as on January 21.
Vertical sundial
A vertical sundial, as the name suggests, has a vertical dial. Such a dial is often attached to a pillar or wall of a building. However, it should be noted that for convenience, such a dial should be positioned strictly south (for middle and high latitudes of the northern hemisphere) or strictly north (for middle and high latitudes of the southern hemisphere).
Moscow region, facade of the Temple of Seraphim of Sarov, vertical sundial made of Inkerman limestone. The size of the plate is 100x50 cm.
The gnomon in this case, as in the previous one, should be inclined at an angle relative to the horizon equal to the latitude of the area where the sundial is installed.
The markings of the dial and calendar in this watch are carried out similarly to a horizontal sundial.
The main disadvantage of vertical sundials is the impossibility of using them in the tropical and equatorial zones, when the position of the Sun at noon shifts from north to south or vice versa. In this case, you can proceed by analogy with the equatorial sundial, making its dial double-sided. However, you won’t be able to use a calendar with this watch because the gnomon’s shadow is too long.
In fact, at the equator, a vertical sundial is a special case of an equatorial sundial, since here the plane of its dial is parallel to the celestial equator, and the gnomon is perpendicular to this plane.
Converting astronomical time to local time
In order to find out “earthly” time, knowing the astronomical time determined by a sundial, you need to take into account two main points: the longitude of the area where time is measured, and the equation of time. We talked about why this is important and how it affects the difference in time readings on regular and sundials here.
In order to correct for the first moment associated with longitude, you need to remember that the Earth rotates around its axis at an angular speed of approximately 15 degrees per hour. Thus, it is possible to determine the difference between astronomical time in this area and astronomical time in the prime meridian, that is, Greenwich.
To take into account the correction associated with the equation of time, you need to have a table or graph of the equation of time. It is convenient to apply it directly to the sundial in a place where it will not interfere with other measurements.
This graph shows how much earlier or later than 12 “earthly” hours on a given day the Sun will be at its zenith, that is, it shows the difference in astronomical and “earthly” time on a given day at the “average” longitude by which the time zone is determined.
By correcting for longitude and the equation of time, you can get Greenwich “earthly” time. And knowing Greenwich time and your time zone, it’s easy to calculate the local “earthly” time.
Of course, you can go the other way, without trying to calculate Greenwich time, but then you will have to focus on time zones, which do not always clearly correspond to astronomical readings due to the political component, and therefore the explanation will be more confusing.
In this regard, let’s look at the previously mentioned algorithm using an example.
The measurements are carried out on an area with a longitude of 32 degrees 30 minutes east longitude. The date on the calendar is February 20. The reading on the sundial is 16 o'clock. It is necessary to determine the average “terrestrial” time.
The solution looks like this:
- The difference with Greenwich time is calculated: 32°30′ / 15 = 2 hours 9 minutes. Since the longitude is eastern, this means that the clock in the prime meridian, compared to the clock in the given area, will be 2 hours 9 minutes behind.
- A correction is made for the equation of time. According to the table of the equation of time for February 20, the indicator is found - it corresponds to +13.9. That is, astronomical time on this day lags behind “earthly” by 13.9 minutes, which corresponds to 13 minutes 54 seconds. This means that “earthly” time (but not averaged over the time zone) will currently correspond to 16 hours + 13 minutes 54 seconds = 16 hours 13 minutes 54 seconds. Round up to the nearest minute - it turns out to be 16 hours 14 minutes.
- Knowing the “earthly” (not average) time in a given area and the difference in hours with the prime meridian, Greenwich time is determined: 16 hours 14 minutes – 2 hours 9 minutes = 14 hours 5 minutes.
- Knowing the time zone of the area (+2) in which the measurements are taken, the average “earthly” time in this area is determined: 14 hours 5 minutes + 2 hours = 16 hours 5 minutes.
If the sundial is not planned to be moved to an area with a different longitude, the correction for longitude can be written on the clock itself so as not to recalculate it every time.
It is also important when converting astronomical time to “terrestrial time” not to forget that in some regions clocks are set to summer time. If this is not done, the error may be 1 hour.
Is it possible to buy a sundial?
Today you can see many on sale various models sundial. Unfortunately, many of them perform purely decorative function and are not suitable for accurate time measurements. Personally, I was lucky enough to see such a model only once, with the help of which you can really tell time.
When purchasing a “working” sundial, the first thing you should pay attention to is what type it is. The equatorial type of sundial, as mentioned earlier, is universal, which means that it is likely that they can be installed normally in any area and ensure correct operation.
Such watches should be equipped with a mechanism that allows you to adjust the tilt of the dial, and, if possible, a rotating scale, allowing you to use it in any location.
There are also companies that manufacture custom-made sundials, but their services, as far as I know, are very expensive.
Based on this, it seems to me that it is easier to make a sundial yourself from cardboard or plywood. In this case, a person will not only acquire a really working tool, but will also better understand the principles on which these watches work. And these principles are the fundamental thing of all methods of orientation by the Sun, stars and Moon, so necessary for travelers who consider the risks of emergency situations and study ways to overcome them.
To summarize all of the above, several points can be noted.
For a person who finds himself in wildlife, sundial and gnomon in particular will allow you to navigate the area. In this regard, a portable sundial is a more universal tool, as it makes it possible to find the approximate location of the cardinal directions at any moment of the day, if the time and coordinates of the area are known, and the Sun is not hidden by clouds. With a stationary sundial everything is even simpler: they make it possible to navigate in cloudy weather and even at night, since, as a rule, they are oriented strictly to the cardinal points.
Sundial functions such as time and date are not so necessary in tourism and emergency survival situations. At least, I have never heard of anyone being seriously injured without knowing the calendar day or local time. If, however, you still need to navigate in time by the Sun, as for me, it is easier to do this if you know the cardinal directions and the direction to the Sun at the moment. Yes, the result will not be very accurate, and in low latitudes this method will be of little help, however, you also won’t have to carry a bulky sundial with you or waste time building one on the ground from scrap materials.
If, nevertheless, there is an urgent need for a sundial, then you should orient it not by a compass, but by the North Star or by the cardinal directions determined using a gnomon. As mentioned earlier, the magnetic poles do not coincide with the geographic ones, and the area where the sundial is installed may be located in the zone of a magnetic anomaly. All this will not make it possible to correctly set the sundial using a magnetic compass.
