Determining distances on a map in various ways. Determining directions and distances from a topographic map How to determine distances on a map by scale

The terrain on the map is always depicted in a reduced form. The degree to which the area is reduced is determined by the scale of the map.

Scale shows how many times the length of the line on the map is less than its corresponding length on the ground. The scale is indicated - on each sheet of the map under the southern (bottom) side of the frame in numerical and graphic form.

Numerical scale indicated on maps as the ratio of one to a number, showing how many times the lengths of lines on the ground are reduced when depicting them on the map.

Example : scale 1:50000 means that all terrain lines are depicted on the map with a reduction of 50,000 times, i.e. 1 cm on the map corresponds to 50,000 cm on the terrain.

The number of meters (kilometers) on the ground corresponding to 1 cm on the map is called the size of the scale. It is indicated on the map under the numerical scale.

It's a good rule to remember: if on the right side of the ratio we cross out the last two zeros of 1:50000, then the remaining number will show how many meters on the ground are contained in 1 cm on the map, i.e. the scale value.

When comparing several scales, the larger one will be the one with the smaller number on the right side of the ratio. The larger the scale of the map, the more detailed and accurate the terrain is depicted on it.

Linear scale - a graphical representation of a numerical scale in the form of a straight line with divisions (in kilometers, meters) for a direct report of distances measured on the map.

Methods for measuring distances on a map.

Distance on a map is measured using a numerical or linear scale.

The distance on the ground is equal to the product of the length of the segment measured on the map in centimeters and the scale value.

The distance between points along straight or broken lines is usually measured using a ruler, multiplying this value by the scale value.

Example 1: using a map 1:50000 (SNOW) measure the length of the road from the flour mill to the storage farm. Belichi (6511) to the intersection with the railway.

The length of the road on the map is 4.6 cm

Scale size - 500 m

The length of the road on the ground is 4.6x500 = 2300 m

Example 2: Using a 1:50000 map (SNOV), measure the length of the field road from Voronikha (7419) to the bridge over the Gubanovka River (7622). The length of the road on the map is 2 cm + 1 cm + 2.3 cm + 1.4 cm + 0.4 cm = 7.1 cm. The length of the field road on the ground is 7.1 x 500 = 3550 m.

Small straight sections are measured using a linear scale without any calculations. To do this, it is enough to use a compass to plot the distance between given points on the map and, applying the compass to a linear scale, take the finished reading in meters or kilometers.

Example 3: Using a map of 1:50000 (SNOV), determine the length of Lake Kamyshovoye (7412) using a linear scale.

The length of the lake is 575 m.

Example 4 : using a linear scale, determine the length of the Voronka River from the dam (6717) to its confluence with the Sot River.

The length of the Voronka River is 2175 m.

To measure curves and winding lines, use either a measuring compass or a special device - a curvimeter.

When using a measuring compass, it is necessary to set the compass opening corresponding to a whole number of meters (kilometers), and also commensurate with the curvature of the line being measured.

The measured line is passed with this solution, counting “steps”. Then, using the scale value, find the length of the line.

Example 5: Using a map 1:50000 (SNOW), measure the length of the section of the Andoga River from the railway bridge to the confluence of the Andoga and the Sot River.

The selected compass solution is 0.5 cm.

Number of steps - 6.

The remainder is 0.2 cm.

The scale is 500 m.

The length of the Andogi River section on the ground is (0.5 x 6) x 500 + (0.2 x 500) = 1500 m + 100 m = 1600 m.

To measure curves and winding lines, a special device is also used - odometer . The mechanism of this device consists of a measuring wheel connected to a pointer that moves along the dial. When the wheel moves along the line measured on the map, the arrow moves across the dial and indicates the distance traveled by the wheel in centimeters.

To measure curved lines with a curvimeter, you must first set the curvimeter needle to “0”, and then roll it along the line being measured, making sure that the curvimeter needle moves in a clockwise direction. By multiplying the curvimeter readings in cm by the scale value, the distance on the ground is obtained.

Example 6: on a map 1:50000 (SNOV) using a curvimeter, measure the length of the section railway Mirtsevsk - Beltsovo limited by the map frame.

Curvimeter needle reading - 33 cm

Scale size - 500 m

The length of the section of the Mirtsevsk - Beltsovo railway on the ground is: 33x500 = 16500 m = 16.5 km.

Accuracy of distance measurement on the map.

The accuracy of measuring distances on a map depends on its scale, errors in the compilation of the map itself, wrinkles and deformations of the paper, terrain, measuring instruments, human vision and accuracy.

The maximum graphic accuracy in topography is 0.5 mm, 5% of the map scale.

Distances measured on the map are always slightly shorter than the actual ones. This happens because horizontal lines are measured on the map, while the corresponding lines on the ground are inclined, i.e., longer than their horizontal lines.

Therefore, during calculations it is necessary to introduce appropriate corrections for the slope of the lines.

Line inclination - 10° correction - 2% of line length

Line inclination - 20° correction - 6% of line length

Line inclination - 30° correction - 15% of line length

Measuring areas on a map.

The areas of objects are most often measured by counting the squares of a coordinate grid. Each square of the map grid 1:10000 - 1:50000 on the ground corresponds to 1 km, 1:100000 - 4 km, 1:200000 - 16 km.

When measuring large areas using a map or aerial photograph, a geometric method is used, which consists of measuring the linear elements of the site and then calculating it using formulas.

If an area on the map has a complex configuration, it is divided by straight lines into rectangles ((a+b) x 2), triangles ((axb) : 2) and the areas of the resulting figures are calculated, which are then summed up.

It is convenient to measure the areas of small areas with an officer's ruler, which has special rectangular cutouts.

The area of ​​radioactive contamination of the area is calculated using the formula for determining the area of ​​a trapezoid:

where R is the radius of the infection circle, km

a - chord, km.

The concept of a coordinate system.

Coordinates are called linear or angular quantities that determine the position of a point on a plane or in space.

Coordinate system is a set of lines and planes relative to which the position of points, objects, targets, etc. is determined.

There are many coordinate systems that are used in mathematics, physics, technology, and military affairs.

IN military topography to determine the position of points (objects, targets) on earth's surface and the map uses geographic, flat rectangular and polar coordinate systems.

Geographic coordinate system.

In this system, the position of any point on the ground surface is determined by two angles - geographic latitude and geographic longitude, relative to the equator and the prime meridian.

Geographic latitude (B)- this is the angle formed by the equatorial plane and the responsible line at a given point on the earth’s surface.

Latitudes are measured along the arc of the meridian north and south of the equator from 0° at the equator to 90° at the poles. In the northern hemisphere - southern latitudes.

Geographical longitude (L)- the angle formed by the plane of the initial (zero) meridian and the plane of the meridian passing through a given point.

The prime meridian is taken to be the meridian passing through the astronomical observatory in Greenwich (near London). All points on globe, located to the east of the prime meridian have eastern longitude from 0° to 180° and to the west - western longitude, also from 0° to 180°. All points lying on the same meridian have the same longitude.

The difference in longitude of two points shows not only their relative positions, but also the difference in time at these points. Every 15° in longitude corresponds to 1 hour, since the Earth rotates 360° for 24 hours.

Thus, knowing the longitude of two points, it is easy to determine the difference in local time at these points.

Geographic grid on topographic maps.

Lines connecting points of the earth's surface of the same latitude are called parallels.

Lines connecting points on the earth's surface of the same longitude are called meridians.

Parallels and meridians are the frames of topographic map sheets.

The bottom and top sides of the frame are parallels, and the sides are meridians.

The latitudes and longitudes of the frame are signed on the corners of each sheet of the map (read and show on the map and poster). On large-scale and medium-scale topographic maps, the sides of the frames are divided into segments equal to one minute. The minute segments are shaded every other with black paint and separated by dots into 10-second sections.

In addition, the intersections of the middle parallels and meridians are shown directly on the map and their digitization in degrees and minutes is given, and the outputs of the minute divisions are shown along the inner frame with 2-3 mm strokes.

This allows you to draw parallels and meridians on a map glued together from several sheets.

To determine geographical coordinates, any point along topographic map, you need to draw parallel and meridian lines through this point. Why, from this point, lower perpendiculars to the lower (upper) and side sides of the map frame. After this, calculate degrees, minutes and seconds using the latitude and longitude scales on the sides of the map frame.

Accuracy of determining geographical coordinates on large-scale maps it is about 2 seconds.

Example: geographical coordinates symbol airfield (7407) on the SNOV map will be respectively:

B = 54 45’ 23” - north latitude;

L = 18 00’ 20” - east longitude.

System of plane rectangular coordinates.

In topography, flat rectangular coordinates are linear quantities:

Abscissa X,

Ordinate U.

These coordinates are somewhat different from the Cartesian coordinates on a plane accepted in mathematics. The positive direction of the coordinate axes is taken to be north for the abscissa axis (axial meridian of the zone), and east for the ordinate axis (ellipsoid equator).

The coordinate axes divide the six-degree zone into four quarters, which are counted clockwise from the positive direction of the x-axis X. The position of any point, for example point M, is determined by the shortest distance to the coordinate axes, that is, along the perpendiculars.

The width of any coordinate zone is approximately 670 km at the equator, at latitude 40 - 510 km, at latitude 50 - 430 km. In the northern hemisphere of the Earth (I and IV quarter zones) the abscissa signs are positive. The ordinate sign in the fourth quarter is negative. In order not to have negative ordinate values ​​when working with topographic maps, at the origin point of each zone the ordinate value is taken equal to 500 km, and the ordinate of a point located to the west of the axial meridian of the zone will always be positive and in absolute value less than 500 km, and the ordinate of the point , located east of the axial meridian, will always be more than 500 km.

When you are in an unfamiliar area, especially if the map is not detailed enough with a conditional coordinate reference or with no such reference at all, it becomes necessary to navigate by 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, a hunter can accurately determine the distance to an animal in order to kill it with one shot. The distance is measured with a laser beam, the device runs on rechargeable batteries. By using this device on a hunt or under other circumstances, the ability to determine 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.

Determining distances on the ground is carried out in a variety of ways. Some of them fall into the category of sniper or military reconnaissance methods. In particular, when navigating the area, an ordinary tourist may find the following useful:

1. Measuring in steps

This method is often used to draw maps of the area. Typically, steps are counted in pairs. A mark is made after every pair or three 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 from 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, we can take the thumbnail of the hand extended forward, equal to 1 cm (1 degree), as the standard for measuring this angle. The entire index finger is a 10 degree reference. 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 by your thumbnail, then it is at an angle of 1 degree. Therefore, the distance from the observer to the object is approximately 60 m.

1. By a flash of light

The difference between the flash of light and the sound is determined using a stopwatch. From this the distance is calculated. Typically, this is calculated by finding a firearm.

1. By speedometer
2. By time 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 one end of it with the top of the object being identified. After this, you need to move your thumbnail to the base of the object and calculate the distance using 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 method of determining 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 and raise your thumb up. You need to close one eye, and if the target moves from left to right, the left eye closes and vice versa. At the moment when the target closes with your finger, you need to close the other eye, opening the one that was closed. In this case, the object will be moved back. Now you need to count the time (or steps, if the person is being observed) until the object is covered with your finger again. The distance to the target is calculated simply: the amount of time (or steps of the pedestrian) before closing the finger a second time, multiplied by 10. The resulting value is converted into meters.

The eye distance recognition method is the simplest, but requires practice. This is the most common method because it does not require the use of any devices. There are several ways to visually determine the distance to a target: by segments of terrain, the degree of visibility of the object, as well as its approximate size, which appears to the eye. To train your eye, you need to practice by comparing the apparent distance to the target with double-checking on a map or steps (you can use a pedometer). With this method, it is important to fix in memory certain standards of distance measures (50,100,200,300 meters), which are then mentally laid down on the ground, and estimate the approximate distance, comparing the real value and the reference value. Consolidating specific distance segments in memory also requires practice: for this you need to remember the usual distance from one object to another. It should be taken into account that the length 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 maximum distances, based 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 determination of the distances of objects. So, if, in accordance with the table, a person’s facial features become distinguishable from a hundred meters, this means that in reality the distance to him is not exactly 100 m, and no more. For a person with low visual acuity, it is necessary to make individual adjustments regarding the reference table.

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

• Brightly lit objects, as well as objects marked with bright colors, appear closer to their true distance. This should be taken into account if you notice a fire, fire or distress signal. The same applies to large objects. Small ones seem smaller.
• At twilight, on the contrary, all objects seem further away. A similar situation occurs during fog.
• After rain, in the absence of dust, the target always seems closer than it actually is.
• If the sun is in front of the observer, the desired target will appear closer than it actually is. If it is located behind, the distance to the desired target is greater.
• A target located on a flat bank will always appear closer than one located on a hilly one. This is explained by the fact that uneven terrain conceals the distance.
• When looking down from a high point, objects will appear closer than when looking at them from below.
• Objects located on a dark background always seem further away than on a light background.
• The distance to an object appears shorter 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 an error in the calculations is. In addition, the more trained the eye is, the higher the accuracy of calculations can be achieved.

Sound guidance

In cases where it is impossible to determine the distance to the target by eye, for example, in conditions of poor visibility, very rough terrain or at night, you can navigate by sounds. This ability must also be trained. Identification of target range by sounds is determined by various weather conditions:

• The clear sound of human speech can be heard from afar on a quiet summer night, if the space is open. Audibility can reach 500m.
• Speech, steps, and 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 clear but diffuse.
• In a windless forest and over calm water, sounds travel very quickly, and rain greatly muffles them.
• Dry soil transmits sound better than air, especially at night.

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

This article was produced by our experienced team of editors and researchers, who reviewed it for accuracy and comprehensiveness.

Number of sources used in this article: . You will find a list of them at the bottom of the page.

A topographic map is a two-dimensional map that depicts a three-dimensional terrain, with the elevation of the earth's surface indicated using contour lines. As with any map, the distance between two points on a topographic map is measured along a straight line connecting them, as if a bird were flying between the points. This is done first, and only then the surface topography and other terrain features that may affect the total length of the route are taken into account. Learn how to measure distance along a straight line.

Steps

Measuring distance using a linear scale

Attach a strip of paper to the map and mark points on it. Place a strip of paper with a straight edge on the card. Align this edge simultaneously with the first (“point A”) and second (“point B”) points, the distance between which you want to measure, and mark the location of these points on paper.

• Take a strip of paper long enough to cover the distance between the points of interest. Please note that this method is better suited for measuring relatively short linear distances.
• Press a strip of paper onto the map and try to mark the location of two points on it as accurately as possible.

1. Place a strip of paper on the linear scale. Find the linear scale on the topographic map - it is usually located in the lower left corner of the map. Place a strip of paper with two marks on it to determine the distance between them. Use this method to measure short distances, which fit on a linear scale.

   Determine b O most of the distance on the main scale. Place the strip of paper on the scale so that the right mark matches the whole number on the scale. In this case, the left mark should be on the additional scale.

   • The point on the main scale where the right mark will be is determined by the condition that the left mark must fall on the additional scale. In this case, it is necessary to align the right mark with the integer on the main scale.
   • The integer corresponding to the right mark on the main scale indicates that the distance being measured is at least that many meters or kilometers. The remaining distance can be more accurately determined using an additional scale.

2. Move to an additional scale where the scale base is divided into parts. Determine the length of the smaller part of the distance using the additional scale. The left mark will coincide with the whole number on the additional scale - this number should be divided by ten and added to the distance determined on the main scale.

   Measuring distance on a numerical scale

   1. Mark the distance on a strip of paper. Place a strip of paper with a straight edge on the map and align this edge with the points between which you want to measure the distance. Mark “point A” and “point B” on paper.

      • Press the strip of paper against the card without bending it to get the most accurate results possible.
      • If desired, you can use a ruler or measuring tape instead of paper. In this case, record the measured distance between the points in millimeters.

   2. Measure the distance with a ruler. Place a ruler or measuring tape on the paper and determine the distance between the two marks. Use this method to measure large distances that fall outside the linear scale, or if you want to calculate the distance as accurately as possible.

      • Try to determine the distance to the nearest millimeter.
      • Find the scale at the bottom of the map. Here the ratio of lengths should be given, as well as a segment (linear scale) with centimeters marked on it. As a rule, for convenience, the scale is chosen in whole numbers, for example 1 centimeter = 1 kilometer.

   3. Calculate the distance along a straight line. For this, use the distance measured on the map in millimeters and a numerical scale, which is the ratio of lengths. Multiply the measured distance by the denominator of the scale.

When creating topographic maps, the linear dimensions of all terrain objects projected onto a level surface are reduced by a certain number of times. The degree of this reduction is called the map scale. The map scale can be expressed in numerical form (numerical scale) or graphically (linear, transverse scales), in the form of a graph.

Distances on a map are usually measured using a numerical or linear scale. More accurate measurements can be made using transverse scale.

On the linear scale, segments corresponding to distances on the ground in meters or kilometers are digitized. This simplifies the process of measuring distances, since no calculations are required.

Determination of distances and areas from a map. Measuring distances.

When using a numerical scale, the distance measured on the map in centimeters is multiplied by the denominator of the numerical scale in meters.

For example, the distance from the GGS point elev. 174.3 (sq. 3909) to the road fork (sq. 4314) on the map is 13.96 cm, on the ground it will be: 13.96 x 500 = 6980 m (scale map 1: 50,000 U-34-85 -A).

If the distance measured on the ground needs to be plotted on the map, then it must be divided by the denominator of the numerical scale. For example, the distance measured on the ground is 1550 m, on a map of scale 1: 50,000 it will be 3.1 cm.

Measurements on a linear scale are performed using a measuring compass. Using a compass solution, connect two contour points on the map, between which you need to determine the distance, then apply it to a linear scale and get the distance on the ground. Curvilinear sections are determined in parts or using a curvimeter.

In practice, numerical, linear and transverse scales are most often used.

Numerical scale denoted as a fraction:

1: M = 1: 25,000.

For example, 1: M = 1: 25,000 means that a distance of 1 cm on the map corresponds to 250 m of a horizontal line on the ground. In this case, M is the denominator of the numerical scale. The denominator of the numerical scale shows the degree of reduction in the horizontal layout of terrain lines, while the larger the denominator of the scale, the smaller the scale.

Scale accuracy t. A segment of at least 0.1 mm in length can be discerned on the map with the naked eye. In accordance with this, scale accuracy is defined as the horizontal location of the terrain line corresponding to a distance of 0.1 mm on a map of a given scale. For example, for a scale of 1:5000 the accuracy is 0.5 m (t = 0.5 m); for scale 1: 10,000 – t = 1 m.

The scale is used to measure the lengths of lines on a map and to draw a line on a map whose length is known on the ground.

Example 1. It is necessary to plot on a map of scale 1: 10,000 in a given direction the horizontal distance S = 346 m.

From the definition it follows that the length of the segment on the map can be found from the relation:

D = 346: 10,000 = 3.46 cm.

Example 2. On a map of scale 1: 10,000, the length of the line is measured d = 2.17 cm, the length of this line on the ground will be equal to:

S = d M (1.2)

S = 2.17 · 10,000 = 217 m.

Working with a numerical scale requires calculations.

Therefore, in order to avoid significant work on calculations, graphic scales are used - linear and transverse.

Linear scale is constructed as follows. Several segments [a] of equal length are laid out on a straight line, which are called linear scale base(Fig. 1.16). Usually the base is taken to be 2 cm. The length of the scale base corresponds to an integer number of hundreds of meters on the ground. The horizontal location of the terrain line corresponding to the base is called at the cost of scale base.

For example, for scale 1: M = 1: 5,000, the price of the scale base with a value of a = 2 cm is equal to 100 m.

The end of the first segment is signed with a “0” sign, and the next ones are digitized for a certain numerical scale. So, for 1: M = 1: 5,000, you need to sign 100, 200 m, etc. The leftmost segment from the zero stroke of the scale base is divided into smaller parts (usually 10 or 20). The horizontal location of the terrain line corresponding to the smallest division of the scale base is called at the cost of dividing the scale. In Fig. 1.16 the base is divided into 10 divisions, so the price of the smallest division is 10 m.

To determine distance on a linear scale it is necessary to attach the legs of the meter so that the right leg of the meter falls on the graph line indicating the whole base, and the left one is between the small divisions. The distance measured on the map in Fig. 1.16 will be composed of the number of whole bases and small divisions (Smeas = 200 + 5.8 10 = 258 m).

The accuracy of the linear scale is equal to half the smallest division of the base of the transverse scale.

To plot, for example, 257 m on a map, you need to place one leg of the compass on a segment of 200 m, and place the second so that it is 57 m, i.e. 5 small divisions and 0.7 divisions (estimated by eye).

Transverse scale is more accurate, unlike linear, which does not provide sufficient accuracy. The transverse scale was created to improve the accuracy of measuring base fractions.

The transverse scale is a system of mutually perpendicular lines forming a nomogram 12 or 20 cm long and 3 cm high. Special scale rulers are used for measurements. Vertical lines are drawn through distances equal to the scale base. The nomogram is divided by height into equal m divisions. The extreme base of the scale is divided horizontally into n equal parts. In addition, the nomogram displays transversals– inclined lines used for more accurate measurement of distances. For a scale of 1: 25,000 with a base equal to AB = 500 m with m = 10 and n = 10, the smallest division of the transverse scale will be 5 m.

To determine distances on a transverse scale the meter is placed so that the right leg of the meter is on the whole mark of the base of the scale, and it is raised simultaneously with the left leg until the latter crosses the transversal. The measured line consists of three parts; the first is equal to the number of integer bases of scale; the second - the number of whole small divisions (n) to the extreme base; the third part is determined by the number m of divisions.

Example. On a map of scale 1: 10,000, you need to plot a segment equal to 258.6 m. We determine that with a = 2 cm, the smallest division of the transverse scale will be 2 m.

Then the legs of the compass should be positioned as shown in Fig. 1.17.

1.2.2. Task execution sequence

1. Determine the accuracy of the linear scale.

The accuracy of the map (plan) scale can be determined by the formula:

t = 0.1 mm M, (1.4)

where M is the denominator of the numerical scale.

Draw and sketch a transverse scale in accordance with the given numerical scale.

2. Place points 1 and 2 on the map at given rectangular coordinates, points 3 and 4 at given geographic coordinates.

3. Determine the geographic coordinates of points 1 and 2 and the rectangular coordinates of points 3 and 4.

4. Determine rectangular coordinates for point 3 in the adjacent zone. Show on the drawing how many kilometers and on which side of the axial meridian it is located.

5. Measure the distances in the quadrilateral 1-2-3-4 on the map (1-2, 2-3, 3-4, 4-1), using linear and transverse scales; Express the results in meters and enter them in the table. 1.1; explain the resulting discrepancies between two measurements of the same line.

6. Give a description of the situation on the map along the route in a strip 4 cm wide. Write the description of the situation in the table. 1.2.

When determining distances on a map, numerical or linear (Fig. 9) and transverse scales are used.

1:50000

1 centimeter is 500 meters

Rice. 9.Numerical and linear scales placed on the map

Numerical scale - map scale, expressed as a fraction, the numerator of which is one, and the denominator is a number showing the degree of reduction of terrain lines on the map (more precisely, their horizontal layouts); the smaller the denominator of the scale, the

larger map scale. The inscription of the numerical scale on maps is usually accompanied by an indication of the scale value - the distance on the ground (in meters or kilometers) corresponding to one centimeter of the map. The scale value in meters corresponds to the denominator of the numerical scale without the last two zeros,

When determining a distance using a numerical scale, a line on a map is measured with a ruler and the resulting result in centimeters is multiplied by the scale value.

Linear scale - graphic expression of the numerical scale; it represents a straight line divided into certain

Rice. 10.Measuring distances using a linear scale

parts that are accompanied by captions indicating distances on the ground. A linear scale is used to measure and plot distances on a map. In Fig. 10 distance between points A And IN equals 1850 m.

Transversescale - a graph (usually on a metal plate) for measuring and plotting distances on a map with extreme graphical accuracy (0,1 mm).

Standard (normal) transverse scale (Fig. II ) has major divisions equal to 2 cm, and small divisions (on the left on the graph), equal to 2 mm", in addition, on the graph there are segments between the vertical and inclined lines, equal along the first horizontal line - 0.2 mm, for the second - 0.4 mm, on the third - 0.6 mm etc. Using a standard transverse scale, you can measure and plot distances on a map of any (metric) scale. The distance reading on the transverse scale consists of the sum of the reading based on the graph and the reading of the segment between the vertical and inclined lines. In Fig. 11 distance between points A And IN(with map scale 1:100,000) equals 5500 m (4 km+1400 m+100 m).

Rice. II.Measuring distances on a transverse scale

Measuring distances with a measuring compass. At When measuring a distance in a straight line, the needles of the compass are set at the end points, then, without changing the opening of the compass, the distance is measured using a linear or transverse scale. In the case when the opening of the compass exceeds the length of the linear or transverse scale, the whole number of kilometers is determined by the squares of the coordinate grid, and the remainder is determined in the usual order according to the scale.

It is convenient to measure broken lines by sequentially increasing the compass solution in straight segments, as shown in Fig. 12.

The measurement of the lengths of curved lines is carried out by sequentially plotting the “step” of the compass (Fig. 13). The value of the “step” of the compass depends on the degree of tortuosity of the line, but, as a rule, should not exceed 1 cm. To eliminate systematic error, the length of the “step” of the compass, determined by scale or ruler, should be checked by measuring a line of a kilometer grid with a length of 6-8 cm.

The length of a winding line measured on a map is always somewhat less than its actual length, since it is not the curved line that is measured, but the chords of individual sections of this curve; therefore, a correction has to be introduced into the results of measurements on the map - coefficients for increasing distances (see table. 29).

Rice. 13.Measuring distances by “step” of a compass

Measuring distances with a curvimeter. By rotating the wheel, the curvimeter needle is set to the zero division, and then the wheel is rolled along the measured line with uniform pressure from left to right (or from bottom to top); the resulting reading in centimeters is multiplied by the scale value of this map.

Determining distances using rectangular coordinates within one zone can be produced using the formula

Where D- line length, l;

Xi, Yi-coordinates of the starting point of the line;Xi, yi -coordinates of the end point of the line.

Determination of areas by squares of a kilometer grid. The area of ​​the plot is determined by counting whole squares and their shares, estimated by eye. Each square of the kilometer grid corresponds to: on maps of scale 1:25000 and 1:50000-1 sq. km, on maps of scale 1:100,000 - 4 sq. km, on maps at scale 1:200000-16 sq. km.

Determination of areas using a geometric method. The area is divided by straight lines into rectangles, triangles and trapezoids. The areas of these figures are calculated using geometry formulas, having previously measured the necessary quantities. Formulas for calculating areas P geometric shapes: - rectangle with sides a and b:

P=a-b-,

- right triangle with legs a and b: