But really - how to measure the height of the mountain? After all, you will not measure the mountain with steps or a tape measure. But before looking for an answer to this question, we need to find out what kind of height we are talking about.
If we are interested in what is the height of the mountain from the bottom to the top, then we mean the relative height. Undoubtedly, this indicator is quite interesting and even important. However, based on the values of relative heights, it would be impossible to make accurate maps of the earth's surface. On such a map, the highest peak on the planet, Everest, would turn out to be lower than, for example, Mount McKinley. Therefore, it is very important to know the absolute height. Absolute altitude is the height of a place above sea level. This indicator is given on maps and reference books.
The concept of height above sea level is well known to everyone from the first lessons of geography or natural science. It would seem that everything is very simple - we take the height of the sea level as 0 m, and we measure the height of all other elements of the Relief relative to this level. However, the question arises - what exactly is the sea level we take as the zero altitude mark? After all, there are ebbs and flows on the seas, which means that the sea level is constantly changing. Therefore, heights on land are usually measured from the mean sea level, which is determined from long-term observations. Then the following question arises: and the average level of which sea is considered a zero mark? After all, as it turned out, these levels do not coincide in different seas and oceans, and even within the same sea or ocean. Then a volitional decision was made: for example, in the former USSR (and now in Russia), the absolute heights of land are calculated from the average level of the Baltic Sea, or rather, from the zero of the Kronstadt footstock (the footstock is a rail with divisions, which is installed at water measuring posts to monitor water level). In other countries, absolute heights are measured from the average level of their seas - as it suits you. However, the resulting differences in the assessment of absolute heights are significant only for a narrow circle of specialists.
So, how do you find out the height of the top? First, you can use a device called an altimeter. The principle of its operation is based on the fact that atmospheric pressure naturally changes with height: for every 100 m rise, its value decreases by 12 mm Hg. So, by measuring the atmospheric pressure at some peak, you can find out its height. This is exactly what the physicist Pascal argued, who in 1648 asked his friends to measure the atmospheric pressure at the foot and on the top of the Puy de Dome mountain in the Alps and, based on the results, calculated its absolute and relative height. But it took another 300 years, during which the best minds of mankind, among which were Newton, and Kepler, and Marriott, and Lomonosov, worked on improving this method and instruments for measuring pressure. As a result, a “complete barometric formula” was derived, which also takes into account the change in atmospheric pressure with a change in air temperature, and the method itself is still considered one of the most accurate methods for measuring the heights of a place.
However, in order to apply this method, it is necessary to climb to the top of the mountain, and this is not always an achievable task. But, it turns out, you can do without climbing.
It turns out that even in ancient Greece Thales of Miletus, who knows geometry well, came up with an ingenious way to measure the distances to distant objects. The wise Greek once thought about how to measure the distance, for example, from the coast to a ship standing in the sea. Standing on the pier, with the help of a goniometer, he noted the direction to the ship from two points of the pier, measured the distance between these points and, using three known elements (the side of the triangle and two angles adjacent to it), built a triangle on the chosen scale. It remains only to measure the two resulting sides of the triangle in the drawing and multiply them by the scale - this was the desired distance to the ship from one and from the other point of the pier.
This method of measuring distance was forgotten for a long time, but in the XVI century. He was remembered by the Dutch mathematician W. Snellius, who realized what richest possibilities geometry holds. After all, by accurately measuring a relatively small segment and putting it at the base of a triangle, at the top of which some distant object is located, you can calculate the distance to this object and put it at the base of the next triangle, and so on - and thus measure huge spaces. And all you need to know for this is the length of the initial segment and the angles of the resulting triangles. Snell's method he developed was called triangulation (from the Latin word papdi1us - "triangular") and put it into practice, measuring the entire western part of Holland. This method, combined with the determination of the coordinates of the vertices of some of the triangles (reference points), creates the mathematical basis for maps of the earth's surface. So the dimensions of the Earth were calculated and its shape was accurately determined: our planet turned out to be not a ball at all, but an ellipsoid somewhat flattened from the poles, for which we had to come up with a special name - the geoid. The science of determining the shape and size of the Earth was later called geodesy (from the Greek words meaning "earth" and "divide").
It is believed that Snell was very lucky with the area he chose to measure. Holland is a very flat country, but in its expanse there are well-visible landmarks here and there: mills, cathedral spiers. It was them that Snellius used as strongholds. But his followers, geodesists, who conduct such measurements in wild, untrodden places: in the mountains, in the taiga, among the endless expanses of steppes and tundra, have to specially erect clearly visible signs above the reference points. They are called triangulation signs, and you may have seen these pyramid-like structures and wondered who and why needed to build them.
And after the surveyors are topographers (from the Greek words "topos" - "place" and "grapho" - "I write"), whose task is to measure and map the smallest characteristics of the earth's surface, including height. This painstaking and difficult, but very romantic work is called topographic survey. And the measurement of heights in geodesy and topography is called leveling (from the French word meaning "level").
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The height of the mountains is amazing. The majestic eight-thousanders look amazing even in photographs. It is not surprising that climbers are so eager to conquer these peaks, because climbing is a very special adventure that will be remembered for a lifetime. But how do you know how high you managed to climb? How do you measure the height of mountains? After all, people managed to measure even Everest, having received an indicator of 8848 meters above sea level.
How are such measurements made, what tools help people get accurate results when it comes to sky-high heights? Perhaps every curious person would like to know about it.
How were mountains measured in the past?
Considering the exact methods of measuring heights on the ground, it should be noted that topographic surveys were used to solve this problem. This method allows you to get the exact coordinates, dimensions and shape of any piece of land, including hills. There are several options for conducting geodetic research, but they all come down to triangulation, that is, to the trigonometric survey technique.
Related materials:
Why is it cold in the mountains, because warm air rises?
Remembering the basics of geometry, we can give a theorem according to which, given information about one of the sides of a triangular object and its two angles, the remaining two sides can be calculated. The scale of the measurement object does not play a role in this case, the triangle can be both small and many kilometers long. To use this theorem, it is necessary to make accurate measurements to obtain initial information. Two landmarks are taken, a mechanical measurement is made. This is how you get the side of the triangle. Next, another conditional reference point for the top is selected. Imaginary lines are drawn from the top, it is possible to get an angle. It remains only to use the theorem.
Angles are measured with a theodolite, the device is intended just for this purpose. Having received the coordinates of the first triangle, you can get the next ones by dividing the required area into these figures until the total area is found.
Interesting fact: theodolite measures both horizontal and vertical surfaces.
Leveling is another proven method for measuring space within which the spirit level at the base of the theodolite is applied - it allows you to bring everything to the same level, indicating the moment of alignment. Using a sighting device - an optical device, and raising it to the desired landmark located on the mountain, you can end up with a height indicator.
Related materials:
How are mountains formed?
Modern technology and accurate results
Amateur tourists and climbers who are not associated with geological surveys do not carry all this equipment with them. Modern technologies have allowed a person to carry a minimum - GPS navigation can be installed on a regular smartphone. There are also more reliable and accurate stand-alone GPS devices that allow you not to get lost, always know who and where is on the ground. They work vertically and horizontally, they can show the height. The latter is important for climbers, lovers of parachuting.
The height of the mountains is amazing. The majestic eight-thousanders look amazing even in photographs. It is not surprising that climbers are so eager to conquer these peaks, because climbing is a very special adventure that will be remembered for a lifetime. But how do you know how high you managed to climb? How do you measure the height of mountains? After all, people managed to measure even Everest, having received an indicator of 8848 meters above sea level.
How are such measurements made, what tools help people get accurate results when it comes to sky-high heights? Perhaps every curious person would like to know about it.
How were mountains measured in the past?
Considering the exact methods of measuring heights on the ground, it should be noted that topographic surveys were used to solve this problem. This method allows you to get the exact coordinates, dimensions and shape of any piece of land, including hills. There are several options for conducting geodetic research, but they all come down to triangulation, that is, to the trigonometric survey technique.
Related materials:
Why is it cold in the mountains, because warm air rises?
Remembering the basics of geometry, we can give a theorem according to which, given information about one of the sides of a triangular object and its two angles, the remaining two sides can be calculated. The scale of the measurement object does not play a role in this case, the triangle can be both small and many kilometers long. To use this theorem, it is necessary to make accurate measurements to obtain initial information. Two landmarks are taken, a mechanical measurement is made. This is how you get the side of the triangle. Next, another conditional reference point for the top is selected. Imaginary lines are drawn from the top, it is possible to get an angle. It remains only to use the theorem.
Angles are measured with a theodolite, the device is intended just for this purpose. Having received the coordinates of the first triangle, you can get the next ones by dividing the required area into these figures until the total area is found.
Interesting fact: theodolite measures both horizontal and vertical surfaces.
Leveling is another proven method for measuring space within which the spirit level at the base of the theodolite is applied - it allows you to bring everything to the same level, indicating the moment of alignment. Using a sighting device - an optical device, and raising it to the desired landmark located on the mountain, you can end up with a height indicator.
Related materials:
How are mountains formed?
Modern technology and accurate results
Amateur tourists and climbers who are not associated with geological surveys do not carry all this equipment with them. Modern technologies have allowed a person to carry a minimum - GPS navigation can be installed on a regular smartphone. There are also more reliable and accurate stand-alone GPS devices that allow you not to get lost, always know who and where is on the ground. They work vertically and horizontally, they can show the height. The latter is important for climbers, lovers of parachuting.
There are many different ways to solve the problem of measuring the height of architectural structures and multi-storey buildings. A curious story happened to the famous Danish physicist, Nobel Prize winner Niels Bohr, who in his student years at the exam solved this very problem using a barometer. At the same time, he offered more than twenty solutions. In addition to quite reasonable methods, there were those that cause a smile, showing the wit and originality of the thinking of the famous scientist, for example: “Dig the tower into the ground. Take out the tower. Fill the resulting hole with barometers. Knowing the diameter of the tower and the number of barometers per unit volume, calculate the height of the tower. If Galileo Galilei had been in place of Niels Bohr, he would have dropped the barometer from the tower and determined the height of the tower by the time of free fall. True, in this case the barometer would have become unusable. If a mathematician were to solve our problem, he would measure the length of the shadow from the tower and from the barometer and, knowing the size of the barometer, using proportions, would determine the height of the tower. However, none of these methods is suitable for measuring the height of a mountain or area above sea level. Let's try to figure out how to measure the height of a mountain using a barometer.
The direct purpose of a barometer is to measure atmospheric pressure. Its existence was discovered back in the 17th century by the Italian physicist and mathematician Evangelista Torricelli, who also created the first barometer. Somewhat later, the French physicist Blaise Pascal not only confirmed the existence of atmospheric pressure, but also discovered its decrease with height, which makes it possible to determine the height using a barometer. The dependence of pressure on altitude is determined by the so-called barometric formula:
where is the atmospheric pressure at height , is the atmospheric pressure at height , is the molar mass of air, is the free fall acceleration¸ is the universal gas constant, is the air temperature. After small mathematical transformations, equating to 0, we get:
For example, if in summer at a temperature of 27 0 С the pressure at the foot of the mountain was 750 mm Hg. (torr), and at the top - 650 mm Hg. (torr), then the height of the mountain will be approximately 1255 m. The barometric formula is rather cumbersome and not very convenient for quick calculations, therefore, when measuring relatively low mountains, it is better to use a less accurate, but more convenient ratio: when lifting every 12 m, atmospheric pressure decreases by about 1 mm Hg.
Another interesting fact should also be noted. As the atmospheric pressure decreases as the altitude above sea level increases, the boiling point of water also decreases. So at an altitude of 5000 m, atmospheric pressure decreases to about 400 mm Hg, so the boiling point of water at this height is slightly more than 80 0 C, while at normal atmospheric pressure water boils at 100 0 C. This must be remembered going to the mountains.
We invite you to find your original way of solving the problem of measuring height.