Map measurements. Determining directions and distances from a topographic map How to measure distance on a map

Map scale. The scale of topographic maps is the ratio of the length of the line on the map to the length of the horizontal projection of the corresponding terrain line. On flat territories, at small angles of inclination of the physical surface, the horizontal projections of the lines differ very little from the lengths of the lines themselves, and in these cases, the ratio of the line length on the map to the length of the corresponding terrain line, i.e. the degree of reduction in the length of lines on the map relative to their length on the ground. The scale is indicated under the southern frame of the map sheet in the form of a ratio of numbers (numerical scale), as well as in the form of named and linear (graphic) scales.

Numerical scale(M) is expressed as a fraction, where the numerator is one, and the denominator is a number indicating the degree of reduction: M \u003d 1 / m. So, for example, on a map on a scale of 1:100,000, the lengths are reduced in comparison with their horizontal projections (or with reality) by 100,000 times. Obviously, the larger the scale denominator, the greater the reduction in length, the smaller the image of objects on the map, i.e. the smaller the scale of the map.

Named Scale- an explanation indicating the ratio of the lengths of the lines on the map and on the ground. At M= 1:100,000, 1 cm on the map corresponds to 1 km.

Linear scale serves to determine the lengths of lines in kind from maps. This is a straight line divided into equal segments corresponding to the "round" decimal numbers of the distances of the terrain (Fig. 5).

Rice. 5. Designation of the scale on the topographic map: a - the base of the linear scale: b - the smallest division of the linear scale; scale accuracy 100 m. Scale value - 1 km

Segments a to the right of zero are called scale base. The distance on the ground corresponding to the base is called linear scale value. To improve the accuracy of determining distances, the leftmost segment of the linear scale is divided into smaller parts in, called the smallest divisions of the linear scale. The distance on the ground, expressed by one such division, is the accuracy of a linear scale. As can be seen in Figure 5, with a numerical map scale of 1:100,000 and a linear scale base of 1 cm, the scale value will be 1 km, and the scale accuracy (at the smallest division of 1 mm) will be 100 m. Accuracy of measurements on maps and accuracy of graphic constructions on paper are related both to the technical capabilities of measurements and to the resolution of human vision. The accuracy of constructions on paper (graphic accuracy) is considered to be equal to 0.2 mm. The resolution of normal vision is close to 0.1 mm.

Ultimate Accuracy map scale - a segment on the ground corresponding to 0.1 mm on the scale of this map. At a map scale of 1:100,000, the limiting accuracy will be 10 m; at a scale of 1:10,000, it will be equal to 1 m. It is obvious that the possibilities of depicting contours in their actual outlines on these maps will be very different.

The scale of topographic maps largely determines the selection and detail of the display of the objects depicted on them. With zoom out, i.e. with an increase in its denominator, the detail of the image of terrain objects is lost.

Maps of different scales are needed to meet the diverse needs of the sectors of the national economy, science and defense of the country. For state topographic maps of the USSR, a number of standard scales based on the metric decimal system of measures have been developed (Table 1).

In the complex of maps named in Table. 1, there are actually topographic maps at scales of 1:5000-1:200,000 and survey topographic maps at scales of 1:500,000 and 1:1,000,000. maps are used for general familiarization with the terrain, for orientation when moving at high speed.

Measuring distances and areas using maps. When measuring distances on maps, it should be remembered that the result is the length of horizontal projections of lines, and not the length of lines on the earth's surface. However, at small angles of inclination, the difference in the length of the inclined line and its horizontal projection is very small and may not be taken into account. So, for example, at an inclination angle of 2°, the horizontal projection is shorter than the line itself by 0.0006, and at 5°, by 0.0004 of its length.

When measuring from distance maps in mountainous areas, the actual distance on a sloping surface can be calculated

according to the formula S = d cos α, where d is the length of the horizontal projection of the line S, α is the angle of inclination. The angles of inclination can be measured from a topographic map by the method specified in §11. Corrections for the lengths of oblique lines are also given in the tables.

Rice. 6. The position of the measuring compass when measuring distances on the map using a linear scale

To determine the length of a straight line segment between two points, a given segment is taken from the map into the compass-measuring solution, transferred to the linear scale of the map (as shown in Figure 6) and the line length is obtained, expressed in land measures (meters or kilometers). Similarly, the lengths of broken lines are measured, taking each segment separately into the compass solution and then summing up their lengths. Distance measurements along curved lines (roads, borders, rivers, etc.) are more complex and less accurate. Very smooth curves are measured as broken lines, having previously been divided into straight segments. Winding lines are measured with a small constant solution of a compass, rearranging it (“stepping”) along all the bends of the line. Obviously, finely sinuous lines should be measured with a very small compass opening (2-4 mm). Knowing what length the compass solution corresponds to on the ground, and counting the number of its installations along the entire line, its total length is determined. For these measurements, a micrometer or a spring compass is used, the solution of which is regulated by a screw passed through the legs of the compass.

Rice. 7. Curvimeter

It should be borne in mind that any measurements are inevitably accompanied by errors (errors). According to their origin, errors are divided into gross blunders (arise due to the inattention of the person making the measurements), systematic errors (due to errors in measuring instruments, etc.), random errors that cannot be fully taken into account (their reasons are not clear). Obviously, the true value of the measured quantity remains unknown due to the influence of measurement errors. Therefore, its most probable value is determined. This value is the arithmetic average of all individual measurements x - (a 1 + a 2 + ... + a n): n \u003d ∑ a / n, where x is the most likely value of the measured value, a 1, a 2 ... a n are the results of individual measurements ; 2 - sum sign, n - number of measurements. The more measurements, the closer the probable value to the true value of A. If we assume that the value of A is known, then the difference between this value and the measurement a will give the true measurement error Δ=A-a. The ratio of the measurement error of any quantity A to its value is called the relative error -. This error is expressed as a proper fraction, where the denominator is the proportion of the error from the measured value, i.e. ∆/A = 1/(A:∆).

So, for example, when measuring the lengths of curves with a curvimeter, a measurement error of the order of 1-2% occurs, i.e., it will be 1/100 - 1/50 of the length of the measured line. Thus, when measuring a line with a length of 10 cm, a relative error of 1-2 mm is possible. This value on different scales gives different errors in the lengths of the measured lines. So, on a 1:10,000 scale map, 2 mm corresponds to 20 m, and on a 1:1,000,000 scale map it will be 200 m. It follows that more accurate measurement results are obtained when using maps of large scales.

Determination of areas plots on topographic maps is based on the geometric relationship between the area of ​​the figure and its linear elements. The area scale is equal to the square of the linear scale. If the sides of a rectangle on the map are reduced by n times, then the area of ​​this figure will decrease by n2 times. For a map with a scale of 1:10,000 (1 cm - 100 m), the area scale will be equal to (1:10,000) 2 or 1 cm 2 - (100 m) 2, i.e. in 1 cm 2 - 1 ha, and on a map of a scale of 1: 1,000,000 in 1 cm 2 - 100 km 2.

To measure areas on maps, graphical and instrumental methods are used. The use of one or another measurement method is dictated by the shape of the area being measured, the given accuracy of the measurement results, the required speed of obtaining data, and the availability of the necessary instruments.

Rice. 8. Straightening the curvilinear boundaries of the site and breaking down its area into simple geometric shapes: dots indicate cut off sections, hatching - attached sections

When measuring the area of ​​a site with rectilinear boundaries, the site is divided into simple geometric shapes, the area of ​​each of them is measured geometrically and, summing up the areas of individual sections calculated taking into account the scale of the map, the total area of ​​the object is obtained. An object with a curvilinear contour is divided into geometric shapes, having previously straightened the boundaries in such a way that the sum of the cut-off sections and the sum of the excesses mutually compensate each other (Fig. 8). The measurement results will be approximate to some extent.

Rice. 9. Square grid palette superimposed on the measured figure. Plot area Р=a 2 n, a - side of the square, expressed on the scale of the map; n is the number of squares that fall within the contour of the measured area

Measurement of the areas of areas with a complex irregular configuration is often carried out using pallets and planimeters, which gives the most accurate results. A grid palette (Fig. 9) is a transparent plate (made of plastic, organic glass or tracing paper) with an engraved or drawn grid of squares. The palette is placed on the measured contour and the number of cells and their parts inside the contour is counted. The proportions of incomplete squares are estimated by eye, therefore, to improve the accuracy of measurements, palettes with small squares (with a side of 2-5 mm) are used. Before working on this map, the area of ​​\u200b\u200bone cell is determined in land measures, i.e. the price of the division of the palette.

Rice. 10. Dot palette - a modified square palette. P \u003d a 2 n

In addition to grid palettes, dot and parallel palettes are used, which are transparent plates with engraved dots or lines. Points are placed in one of the corners of the cells of the grid palette with a known division value, then the grid lines are removed (Fig. 10). The weight of each point is equal to the price of the division of the palette. The area of ​​the measured area is determined by counting the number of points inside the contour, and multiplying this number by the weight of the point.

Rice. 11. A palette consisting of a system of parallel lines. The area of ​​the figure is equal to the sum of the lengths of the segments (middle dashed), cut off by the contour of the area, multiplied by the distance between the lines of the palette. P = p∑l

Equidistant parallel lines are engraved on the parallel palette. The measured area will be divided into a series of trapeziums with the same height when the palette is applied to it (Fig. 11). Segments of parallel lines inside the contour in the middle between the lines are the middle lines of the trapezoid. Having measured all the middle lines, multiply their sum by the length of the gap between the lines and get the area of ​​\u200b\u200bthe entire plot (taking into account the areal scale).

Measurement of the areas of significant areas is carried out on maps using a planimeter. The most common is the polar planimeter, which is not very difficult to work with. However, the theory of this device is quite complex and is discussed in surveying manuals.

When you are in an unfamiliar area, especially if the map is not detailed enough with a conditional reference of coordinates or with no such at all, it becomes necessary to focus on the eye, determining the distance to the target in various ways. For experienced travelers and hunters, determining distances is carried out not only with the help of many years of practice and skills, but also with a special tool - a rangefinder. Using this equipment, the hunter can accurately determine the distance to the animal in order to kill it with one shot. The distance is measured by a laser beam, the device is powered by rechargeable batteries. By using this device for hunting or in other circumstances, the ability to determine the distance by eye is gradually developed, since when using it, the real value and the reading of the laser rangefinder are always compared. Next, methods for determining distances without the use of special equipment will be described.

Determination of distances on the ground is carried out in a variety of ways. Some of them belong to the category of sniper methods or military intelligence. In particular, during orientation on the ground, the following may be useful to an ordinary tourist:

1. Measuring in steps

This method is often used to map the area. As a rule, steps are considered in pairs. A mark is made after each pair or triple of steps, after which the distance in meters is calculated. To do this, the number of pairs or triples of steps is multiplied by the length of one pair or triple.

1. Angle measurement method.

All objects are visible at certain angles. Knowing this angle, you can measure the distance between the object and the observer. Considering that 1 cm from a distance of 57 cm is visible at an angle of 1 degree, it is possible to take the nail of the thumb of the outstretched hand equal to 1 cm (1 degree) as the standard for measuring this angle. The entire index finger is a reference of 10 degrees. Other standards are summarized in a table that will help you navigate the measurement. Knowing the angle, you can determine the length of the object: if it is covered with a thumbnail, then it is at an angle of 1 degree. Therefore, from the observer to the object is approximately 60 m.

1. By a flash of light

The difference between a flash of light and a sound is determined by a stopwatch. Based on this, the distance is calculated. As a rule, in this way, it is calculated by finding a firearm.

1. By speedometer
2. Time travel speed
3. By match

Divisions equal to 1 mm are applied to the match. Holding it in your hand, you need to pull it forward, hold it horizontally, while closing one eye, then combine its one end with the top of the object being determined. After that, you need to advance the thumbnail to the base of the object and calculate the distance according to the formula: the distance to the object, equal to its height, divided by the distance from the observer's eyes to the match, equal to the marked number of divisions on the match.

The way to determine the distance on the ground using the thumb helps to calculate the location of both a moving and a stationary object. To calculate, you need to stretch your hand forward, raise your thumb up. It is necessary to close one eye, while if the target moves from left to right, the left eye closes and vice versa. At the moment when the target is closed with a finger, you need to close the other eye, opening the one that was closed. In this case, the object will be pushed back. Now you need to make a count of the time (or steps, if the observation is for a person), until the moment when the object is again closed with a finger. The distance to the target is calculated simply: the amount of time (or pedestrian steps) before closing the finger a second time, multiplied by 10. The resulting value is converted to meters.

The distance recognition method by eye is the simplest, but requires practice. This is the most common method, since it does not require the use of any devices. There are several ways to visually determine the distance to the target: by segments of the terrain, the degree of visibility of the object, as well as its approximate value, which seems to the eye. To train the eye, you need to practice comparing the apparent distance to the target with a cross-check on the map or steps (you can use a pedometer for this). With this method, it is important to fix in memory some standards of measure of distance (50,100,200,300 meters), which are then mentally set aside on the ground, and evaluate the approximate distance by comparing the real value and the reference one. Fixing in memory specific segments of the distance also requires practice: for this you need to remember the usual distance from one object to another. In this case, it should be taken into account that the value of the segment decreases with increasing distance to it.

The degree of visibility and distinguishability of objects affects the setting of the distance to them with the naked eye. There is a table of limiting distances, focusing on which, you can imagine the approximate distance to an object that can be seen by a person with normal visual acuity. This method is designed for an approximate, individual finding of the ranges of objects. So, if, in accordance with the table, the facial features of a person become distinguishable from a hundred meters, this means that in reality the distance to him is not exactly 100 m, but no more. For a person with low visual acuity, it is necessary to make individual corrections regarding the reference table.

When establishing the distance to an object using an eye gauge, the following features should be taken into account:

• Brightly lit objects, as well as brightly colored objects, appear closer to the true distance. This must be taken into account if you notice a bonfire, fire or distress signal. The same applies to large objects. Small ones seem smaller.
• At dusk, on the contrary, all objects appear farther away. A similar situation develops during fog.
• After rain, in the absence of dust, the target always seems closer than it really is.
• If the sun is in front of the observer, the desired target will appear closer than it really is. If it is located behind, the distance to the desired target is greater.
• A target located on a level bank will always appear closer than one on a hilly one. This is due to the fact that uneven terrain hides the distance.
• When viewed from a high point downwards, objects will appear closer than when viewed from the bottom up.
• Objects located on a dark background always appear further than on a light background.
• The distance to the object appears less if there are very few observed targets in the field of view.

It should be remembered that the greater the distance to the target being determined, the more likely the error in the calculations. In addition, the more the eye is trained, the higher the accuracy of calculations can be achieved.

sound orientation

In cases where determining the distance to the target with an eye is impossible, for example, in conditions of poor visibility, rugged terrain or at night, you can navigate by sounds. This ability must also be trained. Identification of the target range by sounds is due to various weather conditions:

• The clear sound of human speech is heard from afar in a quiet summer night, if the space is open. Audibility can reach 500m.
• Speech, steps, various sounds are clearly audible on a frosty winter or autumn night, as well as foggy weather. In the latter case, it is difficult to determine the direction of the object, since the sound is distinct but diffuse.
• In a calm forest and over calm water, sounds travel very quickly, and the rain muffles them greatly.
• Dry ground transmits sounds better than air, especially at night.

To determine the location of the target, there is a table of correspondence between the range of audibility and the nature of the sound. If you apply it, you can focus on the most common objects in each area (shouts, steps, vehicle sounds, shots, conversations, etc.).

Algorithm for determining directions from a topographic map.

1. On the map we mark the point where we are and the point to which we need to determine the direction (azimuth).

2. We connect these two points.

3. Through the point at which we are, we draw a straight line: north - south.

4. Using a protractor, we measure the angle between the north-south line and the direction to the desired object. Azimuth is measured from the north direction in a clockwise direction.

Algorithm for determining distances from a topographic map.

1. We measure the distance between the given points using a ruler.

2. The obtained values ​​​​(in cm) are converted into a distance on the ground using a named scale. For example, the distance between points on the map is 10 cm, and the scale: 1 cm is 5 km. We multiply these two numbers and get the desired result: 50 km is the distance on the ground.

3. When measuring distances, you can use a compass, but then the named scale will be replaced by a linear scale. In this case, our task is simplified, we can immediately determine the desired distance on the ground.

№5 1) Time zones in Russia. Local and standard time.

Solar time at points located on the same meridian is called local. Due to the fact that at each moment of the day it is different on all meridians, it is inconvenient to use it. Therefore, according to the international agreement, standard time was introduced. To do this, the entire surface of the Earth was divided along the meridians into 24 zones of 15 ° longitude. Standard time (the same within each zone) is the local time of the median meridian of this zone. The zero belt is a belt whose median meridian is the Greenwich (zero) meridian. The same belt is the 24th. From it, the belts are counted to the east. Russia is located in 11 time zones: from the second (in which Moscow is located and whose time is called Moscow) to the twelfth (islands in the Bering Strait). The time difference between these zones is 10 hours, i.e. when it is midnight in Moscow, in the 12th time zone it is 10 am. The difference in time between zones is equal to the difference between the numbers of time zones. For convenience, the 11th and 12th time zones have been combined into one. The boundaries of time zones do not run strictly along the meridians, but coincide with the boundaries of administrative units (regions, republics) so that one administrative unit is located in one time zone.

2) Fuel industry: composition, location of the main areas of fuel production, development problems. Fuel industry and problems of environmental protection.

The fuel industry consists of three main branches: gas, oil and coal.

Gas industry. Russia ranks first in the world in terms of natural gas reserves and production. Compared to oil and coal, gas production is cheaper, and besides, gas is the most environmentally friendly type of fuel. In the last decade, the role of gas in Russia has grown significantly.

The gas is used in thermal power plants, public utilities and the chemical industry.

The main gas production area in Russia is the northern part of the West Siberian Plain (Urengoy and Yamburg fields). Gas is produced in the Ural-Volga region (Orenburg field, in the Saratov region), in the North Caucasus, in the Pechora river basin, in some areas of Eastern Siberia, off the coast of Sakhalin and on the shelf of the Barents and Kara Seas.

Gas is transported through pipelines: from Western Siberia to the European part of Russia, to the countries of Central, Eastern and Western Europe. The gas pipeline was laid along the bottom of the Black Sea to Turkey (the Blue Stream project). A project is under way to build a gas pipeline to Japan (along the bottom of the Sea of ​​Japan) and to China (from the Kovylkinsky field in Eastern Siberia).

In Russia, gas is produced, transported and processed by the Gazprom concern (the largest Russian monopoly). The main partners of Gazprom are the German Ruhrgaz and the Ukrainian Naftagaz.

Oil industry. In terms of oil reserves, Russia is among the top five countries in the world, and in terms of production, it ranks 1-3rd. At present, oil production in Russia is declining due to the depletion of some rich deposits, an increase in the cost of oil production, and a lack of investment in geological exploration.

The main oil production area is the central part of the West Siberian Plain. Recently, the role of fields located on the sea shelf (Caspian, Barents and Okhotsk Seas) has increased. Oil was discovered at the bottom of the Black and Bering Seas.

Almost the entire oil industry in Russia is run by private companies (Lukoil, Tatneft, Sibneft, Yukos, etc.).

Coal industry. Coal reserves in Russia are distributed unevenly. Most of it is concentrated in Siberia and the Far East (Tunguska basin). At present, the main coal basin of Russia is the Kuznetsk. Then follow the Pechora, South Yakutsk basins and part of the Donbass. The largest active brown coal basin is the Kansko-Achinsk.

The ecological situation in the areas where thermal power plants and oil refineries are located is usually unfavorable, an example is one of the most environmentally polluted cities - Dzerzhinsk (Moscow Basin), which has a high degree of morbidity and a low average life expectancy of the population. Oil and gas production in Western Siberia, especially in the tundra zone, causes great damage to nature.

Problems of development of the fuel industry.

1. An increase in the cost of fuel due to the shift of oil and gas production centers to the Far North.

2. Depletion of reserves and lack of exploration and exploration work.

3. The closure of unprofitable mines, leading to mass unemployment in this industry and an increase in social tension.

4. Depreciation of mining equipment.