How to determine the height of a pressure mountain. Counting in centimeters
How is the height of mountains determined? and got the best answer
Answer from ™Inextinguishable Star... ®[guru]
From books and maps we can find out the exact height of the mountains. How did a person manage to measure them, even those peaks that no one has managed to visit yet?
The height of mountains is measured by the most, perhaps, the oldest method - topographic survey, with which you can determine the shape and size of any formation or object on the earth's surface.
There are several ways to conduct such surveys, but they are all based on the "triangulation" method, in other words, in all cases, a trigonometric survey is carried out. When you start studying such a subject as geometry, you will learn about one interesting theorem, according to which, knowing the length of one side of a triangle and the size of its two angles, you can calculate the length of its other two sides.
Therefore, regardless of the area of the site that you want to measure: whether it be several tens or several thousand square meters, the measurement method remains the same. First you need to very accurately measure the distance between the two landmarks using a land surveyor or tape with divisions. This will be one side of the triangle. Now you need to select the third landmark and make it a conditional vertex of the triangle. After that, it is necessary to determine the magnitude of the angles that two imaginary lines from the top of the triangle form with the measured side. And now, according to the theorem, you can calculate the length of the other two sides of the triangle.
The magnitude of the angles is measured using a special device - theodolite. Having measured the area of one triangle, you can continue to divide the area into imaginary triangles until you determine its total area.
Theodolite measures angles not only in the horizontal plane, but also in the vertical one.
This method of measurement is called leveling, bringing to one level, and is carried out using a spirit level located at the base of the theodolite. The spirit level indicates when alignment has occurred.
By raising the sight (optical device) to any landmark on the mountain, you can measure the angles and ultimately determine its height.
Answer from Twilight[guru]
the height of the mountains is measured relative to the level of the ocean
Answer from User deleted[newbie]
Mountain heights are measured with an altimeter. It is based on a barometer, but the scale is graduated not in millimeters of mercury, but in meters. Altitude can also be determined using a conventional barometer. For calculations, you need to know that for every 10 meters, the pressure drops by approximately 1 mm Hg. Art.
Answer from ALEXanderr1[guru]
from sea level...
Answer from Vladimir Shi[expert]
Many ways: it can be done by eye, it can be done with a barometer (pressure difference according to the table), with the help of geometry and function, with the help of aircraft, etc.
Answer from Virtual mag[guru]
The best way is with a thermometer and a stopwatch! The thermometer is dropped from the top, and the fall time is measured with a stopwatch. Then calculate the height of the mountain is not difficult!
Answer from Ahila Ismailova[newbie]
Can be determined by the height scale on the map
Answer from Vadim Startsev[guru]
The most accurate way is to take a point whose height above sea level is already known. Using geodetic instruments, such as a theodolite, measure the angle to the horizon of a line directed from the observation point to the top. Using a range finder (laser, or more ancient, optical), measure the distance from the observation point to the top of the mountain. And then the school course of trigonometry. Determine the length of the leg, knowing the length of the hypotenuse and the magnitude of the opposite angle.
According to an old legend, when the Welsh surveyor and geographer Sir George Everest measured the height of Mount Chomolungma, he got exactly 29,000 feet high (8839.2 meters), and his team decided to add two feet to their measurement to make it more believable. The cloud giant was thought to be quietly rising, secluded from everything else, at an altitude of 29,002 feet above sea level.
Subsequently, the advent of sophisticated technology such as satellites has estimated the peak to be 29,029 feet high (8848.04 meters). However, Sir Everest's discovery is extremely remarkable, given that he did it in 1852 without the aid of the tools that geographers are currently equipped with.
Moreover, his team took measurements more than 100 miles from the peak, as the Nepalese government did not allow the British to enter their country. So how did they achieve this amazing dimension?
Trigonometry
As a child, the easiest method to determine the length was to scale the distance with your hand. The only unit of measure would be the distance between the thumb and little finger when the arm was moderately extended.
To measure, say, a table, you had to put your hand on it. Then the little finger moved forward, allowing the thumb to take its place, and so on until the entire length was taken into account.
In the end, the arms were replaced with rulers, but the methodology remains the same - stack one by one until the entire length is covered. No one will deny that measuring the height of Everest with a ruler is possible, but everyone will agree that the process will be very time consuming and cumbersome.
However, the method geographers rely on is not far from the use of rulers. In fact, Sir Everest and his team used school geometry to measure the height of Mount Everest. Yes, that's right, only their instruments were just fancier, more complex sets of rulers and protractors.
Trigonometry was used by the Greeks to measure tall structures and by Victorian surveyors to measure the highest mountains before we used satellites. However, even satellites measure height, they essentially implement the same principle - they draw triangles.
triangles
Geographers measure height by drawing numerous triangles. Among the three sides, one is the height of the mountain to be measured. The base of the triangle is between the base of the mountain and a point, say, which is located at a certain distance from the base of the mountain. The third side can be formed by simply connecting point A and a vertex.
When forming a horizontal base, geographers must ensure that it is completely level to achieve accurate results. Accounting for any irregularities on the surface of the Earth is achieved using very thin instruments. Next, they must measure all three angles formed inside the triangle.
This is achieved by using a preliminary protractor known as a theodolite. Measuring even two angles is sufficient, as the third angle can be calculated by subtracting the sum of the two known angles from 180 degrees, since the sum of all three angles enclosed by a triangle is 180º.
Now you can understand the magic of a simple trigonometric miracle - knowing two angles and the length of one side can reveal the height of a mountain. Even the ancient Greeks measured height by "comparing the ratios of the two sides of a triangle."
For example, consider a very simple example where the angle formed at point A is 60º and we only know the distance between point A and the base of the mountain, which is, of course, the base of the triangle.
For simplicity, let's assume that the triangle is right-angled, where the base is perpendicular to the height. This means that the third angle formed at the top is 30º (180º-). Let's also label the sides of the triangle. Starting from the height and moving clockwise, we will denote them as X, Y and Z.
Now Sin(60º) represents the X/Y ratio, while Sin(30º) represents the Z/Y ratio. If we separate these ratios, notice that the two Ys cancel out and we are left with only the X/Z ratio.
The values of both sines 60º and 30º can be found out simply by referring to a high school math textbook. In addition, Z is the base of the triangle, the magnitude of which we already know. Multiply Z with Sine ratios and we have the height of the mountain - X.
George Everest drew several of these triangles, all with different A distances, since the measurements of a single triangle cannot be trusted. The team then averaged each height obtained from all triangles.
This resulted in them being given a value of 29,000 feet, a number rumored to have been increased to avoid any suspicion.
Later, in 1999, scientists using satellites measured the height of Everest as 8848 meters above mean sea level.
The accuracy of George Everest's measurements turned out to be amazing - the true height of the peak turned out to be only 8.23 meters higher than he predicted. Using only two corners and one side!
How are heights measured?
This question is followed by related ones. What is absolute and relative height? Why are there triangulation marks on the tops? When was the height first determined? What does "above sea level" mean? Does this level fluctuate? How is altitude measured from aircraft? What are command points?
Displaying the area in a reduced form on diagrams and maps, people have always paid attention to the mountains. They were conspicuous and necessary reference points. The geographical map did not appear immediately: it survived its development from clay, parchment, birch bark samples to perfect cartographic models. At first, much depended on the draftsman, his sense of space, his ability to mentally survey the Earth from a height. The mathematical reliability of the relief, of course, was absent.
Over time, the profession of renter appeared. A measuring cord, a measuring wheel, a compass went into action. In the 16th century, prototypes of measuring geodetic instruments were invented - a measuring scale, a theodolite, then - rangefinders, levels. To measure the height of the mountain, or, as topographers say, "to take vertical marks", physicists helped.
Blaise Pascal asked his acquaintances in Clermont to climb Mount Puy-de-Dome with a mercury pipe. The scientist's assumption was confirmed at a height: the mercury column dropped. Since then, it has become customary to measure the height of the area using a mercury barometer. Appeared devices for determining the height of the temperature of the vapor of boiling water: hypsometer, thermobarometer, hypsothermometer. The principle of operation is as follows: as you rise, the air pressure decreases. At the same time, the boiling point of water also decreases - about 0.27 mm of mercury column. According to the tables, atmospheric pressure is noted accordingly, and the height of the terrain is determined from it.
This is, one might say, a "field" method. But not every peak is so easy to climb for measurement. And in the 17th century, the Dutch astronomer Snellius proposed a triangulation method, when heights are determined “from the side”, using reference points. This method is also used for topographic surveys from aircraft and artificial satellites.
Altitude marks of peaks began to be distinguished: absolute - from sea level and relative - from the foot of the mountain, from the underlying plain. It is clear that the absolute heights of mountains are always greater than the relative ones. For the unity of the measurement system in geographical science, it is customary to count these measurements from the level of the World Ocean. So, after indicating the height, a conspicuous prefix “above sea level” appeared, or if it is not there, then it is simply implied. But we know the ebb and flow. The levels of the seas are unstable: they began to be distinguished: instantaneous, tidal, average daily, average annual, average long-term. This latter, according to the developed international agreements, has become the most stable in order to "tie" the height of the mountains to it.
It is clear that many peaks and ridges in the oceans that do not come to the surface are measured differently. The highest marine seamount ever discovered was in 1953 near the Tonga Trench off New Zealand. It rises from the bottom of the sea to 8690 m, and its peak is 365 m below the surface of the water. And if we do not proceed from sea level, but measure the height from the underwater base, then the highest mountain in the world is Mauna Kea (“White Mountain”) in the Hawaiian Islands. Its total height is 10,203 m, of which only 4,205 m are above sea level.
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.
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Remembering the basics of geometry, we can give a theorem according to which, given the knowledge of 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.
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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 difference in the heights of two adjacent horizontals is called the height of the relief section. Knowing this value, the number of contour lines can be used to calculate both the absolute and relative height of the terrain.
As a result, many lists have appeared (both for the whole Earth and for individual regions), where the value of the relative height of the peak has become an inclusion criterion. The main problem with using the relative height of a peak as an indication of the notability of a mountain is the following. The relative height of the summit does not take into account the steepness of the slopes, which makes a significant contribution to the impression of the mountain. In this case, it is much more difficult to calculate the relative height of the peak, and a computer is usually used for this.
home > Science > How the height of a mountain is determined
The height of mountains is measured by the most, perhaps, the oldest method - topographic survey, with which you can determine the shape and size of any formation or object on the earth's surface. Therefore, regardless of the area of the site that you want to measure: whether it be several tens or several thousand square meters, the measurement method remains the same. How to measure the height of a mountain Description: But really - how to measure the height of a mountain? After all, you will not measure the mountain with steps or a tape measure. If we are interested in what is the height of the mountain from the bottom to the top, then we mean the relative height. However, based on the values of relative heights, it would be impossible to make accurate maps of the earth's surface. It would seem that everything is very simple - we take the height of the sea level as 0 m, and the height of all other elements of the Relief ... When going to the mountains, take an altimeter (altimeter) with you, which will allow you to always be informed about the height of your location.
Plains with a height of 200 to 500 m (for example, Valdai) are called uplands and are usually indicated in yellow. There are land areas that are located below sea level (for example, the southern part of the Caspian lowland). To designate them, brown or red is usually chosen, and the greater the height of the mountains, the darker and richer the shade. 3 Within the category of high mountains, there is also a color division: mountains over 3000 meters high, over 5000, and even higher.
It is unfortunately not possible to use systems for determining absolute, and not relative height (as in the instruments mentioned above), until they are released for general use. How to measure the height of a building with a barometerMeasuring the height of a building with a barometer is a non-trivial physics problem that shows how important it is for a physicist to think outside the usual categories. How to measure height In construction work, it is regularly necessary to measure height. How to find out the height above sea level The ability to determine the height of your own location is necessary when orienting in mountainous areas when visibility is insufficient. How to determine the height of a plain It is customary to determine the location in space of any geographical point by its coordinates: latitude, longitude and height.
Man learned how to determine the height of a mountain long before conquering it. The technique of triangulation, with which the survey is carried out, is widely used in many fields of science and technology. The length or distance is determined by a surveyor, angles - by a theodolite. Determining the height of a mountain with a sight is similar to the topographic method. In both the first and second cases, a landmark is selected on the mountain, the angles are measured, and an unknown height (the side of the triangle) is determined.
This method of measurement is called leveling, bringing to one level, and is carried out using a spirit level located at the base of the theodolite. By raising the sight (optical device) to any landmark on the mountain, you can measure the angles and ultimately determine its height. The most accurate way is to take a point whose height above sea level is already known. Using a range finder (laser, or more ancient, optical), measure the distance from the observation point to the top of the mountain. And then the school course of trigonometry.
The height of the mountain and other objects can be found using a physical map next to which there is a scale of depths and heights in meters. If you are not satisfied with the answer or there is none, then try to use the search on the site and find similar answers in the subject of Geography.
Elbrus. the top of the Dividing Range of the Greater Caucasus on the border of Azerbaijan and Russia (Dagestan). The height is 4466 m. And at an altitude of about 3900 m there is a modern small church. The literal translation is "white mountain". The height is 5204 m, that is, in height it is second only to Elbrus in the Caucasus. Mountains of the world. Mount Sugarloaf. Ural mountains. Mount Ushba. Mount Aires - rock. Mountains on the coast of the Red Sea. Eastern Sayans. Andes. Large watershed.
Usually about high mountains, when they are mentioned in various media, we are always told about their exact height, which is indicated in meters. How do people manage to calculate their height, and even so accurately, especially if the mountain has not yet been mastered by a single person? You can calculate the height of the mountain using one of the ancient methods, which has long been in service with surveyors, surveyors, if in a modern way.
When high mountains are mentioned in newspapers or books, we are usually given their exact height in meters. Geodesy is the science that determines the shape and size of any part of the earth's surface.