home > Solitaire Mat > Practical work “Determining distances on maps using scale. Measurements using a topographic map Methods for determining distances using a topographic map

Practical work “Determining distances on maps using scale. Measurements using a topographic map Methods for determining distances using a topographic map

The scale can be expressed numerically (numerical scale) or graphically (linear, transverse scales) in the form of a graph. The design of the numerical and linear scales on the map is shown in Figure 100.

Figure 100 -

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

Numerical scale is the scale of the map, expressed as a fraction, the numerator of which is one, and the denominator is a number showing how many times the horizontal layouts of terrain lines are reduced on the map. The smaller the denominator, the larger the scale of the map. For example, a scale of 1:25,000 shows that all linear dimensions of terrain elements (their horizontal distribution on a level surface) when depicted on a map are reduced by 25,000 times

The distance on the ground in meters and kilometers corresponding to 1 cm on the map is called the scale value. It is indicated on the map under the numerical scale.

When using a numerical scale, the distance measured on the map in centimeters is multiplied by the denominator numerical scale in meters. For example, on a 1:50,000 scale map, the distance between two local objects is 4.7 cm; on the ground it will be 4.7x500=2350 m. If the distance measured on the ground needs to be plotted on the map, it must be divided by the denominator of the numerical scale.

For example, on the ground the distance between two local objects is 1525 m. On a map of scale 1:50,000 it will be 1525:500 = 3.05 cm. Linear scale is a graphic expression of a numerical 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.

Measurements on a linear scale are performed using a measuring compass (Figure 101). Long straight lines and curved lines on a map are measured in parts. To do this, set the solution (“step”) of the measuring compass equal to 0.5 - 1 cm, and with such a “step” they walk along the measured line (Figure 102), keeping count of the permutations of the legs of the measuring compass. The remainder of the distance is measured on a linear scale. The distance is calculated by multiplying the number of permutations of the compass by the “step” value in kilometers and adding the remainder to the resulting value. If you don’t have a measuring compass, you can replace it with a strip of paper on which a dash is used to mark the distance measured on the map or plotted to scale on it.

The transverse scale is a special graph engraved on a metal plate (Figure 103). Its construction is based on the proportionality of the segments parallel lines, intersecting the sides of the angle. The standard (normal) transverse scale has major divisions equal to 2 cm and minor divisions (on the left of the graph) equal to 2 mm. In addition, the graph contains segments between the vertical and inclined lines, equal to 0.2 mm along the first lower horizontal line, 0.4 mm along the second, 0.6 mm along the third, etc. d. Using a transverse scale, you can measure and plot distances on maps of any scale.

Figure 101 -

Figure 102

Figure 103 - Transverse scale: scale reference 2.36 cm

Distance measurement accuracy. Accuracy of measuring the length of straight segments on topographic map using a measuring compass and a transverse scale does not exceed 0.1 mm. This value is called the maximum graphic accuracy of measurements, and the distance on the ground corresponding to 0.1 mm on the map is the maximum graphic accuracy of the map scale.

The graphical error in measuring the length of a segment on a map depends on the deformation of the paper and the measurement conditions. Usually it ranges from 0.5 - 1 mm. To eliminate gross errors, measuring a segment on the map must be performed twice. If the results obtained do not differ by more than 1 mm, the average of the two measurements is taken as the final value of the length of the segment. Errors in determining distances from topographic maps of various scales are given in Table 43.

Table 43

Errors in determining distances on maps

Correction in distance for the slope of the line. The distance measured on the map on the ground will always be slightly less. This happens because the map measures horizontal applications, while the corresponding lines on the ground are usually inclined (Figure 104). The conversion coefficients from distances measured on the map to actual ones are given in Table 44.

Figure 104 -

D- distance on the plane (map); D- ground distance

As can be seen from the table, on flat terrain the distances measured on the map differ little from the actual ones. On maps of hilly and especially mountainous terrain, the accuracy of determining distances is significantly reduced. For example, the distance between two points, measured on a map, on terrain with a slope of 12°, is equal to 9270 m. The actual distance between these points will be 9270x1.02 = 9455 m.

Table 44

Distance conversion coefficients

Thus, when measuring distances on a map, it is necessary to introduce corrections for the slope of the lines (for the relief).

Determination of distances using coordinates taken from the map. Long straight distances in one coordinate zone can be calculated using the formula:

where 5 1 is the distance on the ground between two points, m;

*1 y- coordinates of the first point;
*2Ugh~ coordinates of the second point.

This method of determining distances is used in preparing data for the design of structures in other cases.

Measuring distances on a map. Study of a site. Reading a map along the route

Studying a site

Based on the relief and local objects depicted on the map, one can judge the suitability of a given area for organizing and conducting combat, for the use of military equipment in combat, for observation conditions, firing, orientation, camouflage, as well as cross-country ability.

Availability of a large number of settlements and individual tracts of forest, cliffs and gullies, lakes, rivers and streams indicate rough terrain and limited visibility, which will impede the movement of military and transport equipment off roads and create difficulties in organizing surveillance. At the same time, the rugged nature of the terrain creates good conditions for sheltering and protecting units from the effects of enemy weapons of mass destruction, and forests can be used to camouflage unit personnel, military equipment, etc.

By the nature of the layout, size and font of the signatures of settlements, we can say that some settlements belong to cities, others to urban-type settlements, and still others to rural-type settlements. The orange coloring of the blocks indicates the predominance of fire-resistant buildings. Black rectangles located close to each other inside the blocks indicate the dense nature of the development, and yellow shading indicates the non-fire resistance of the buildings.

In a populated area there may be a weather station, a power station, a radio mast, a fuel warehouse, a plant with a pipe, a railway station, a flour mill and other objects. Some of these local items can serve as good reference points.

The map can show a relatively developed network of roads of various classes. If there is a signature on a conventional highway sign, for example, 10 (14) B. This means that the paved part of the road has a width of 10 m, and from ditch to ditch - 14 m, the surface is cobblestone. A single-track (double-track) railway can pass through the area. Studying the route along railway, you can find on the map individual sections of roads that run along an embankment or in a excavation with a specified depth.

With a more detailed study of roads, it is possible to establish: the presence and characteristics of bridges, embankments, excavations and other structures; the presence of difficult areas, steep descents and ascents; possibility of leaving roads and driving near them.

Water surfaces are depicted on maps in blue or light blue, so they clearly stand out among the symbols of other local objects.

By the nature of the font of the river's signature one can judge its navigability. The arrow and number on the river indicate in which direction it flows and at what speed. The signature, for example: means that the width of the river in this place is 250 m, the depth is 4.8 m, and the bottom soil is sandy. If there is a bridge across the river, then next to the image of the bridge its characteristics are given.

If the river on the map is depicted with one line, then this indicates that the width of the river does not exceed 10 m. If the river is depicted in two lines, and its width is not indicated on the map, its width can be determined by the indicated characteristics of the bridges.

If the river is fordable, then the ford symbol indicates the depth of the ford and the soil of the bottom.

When studying the soil and vegetation cover, you can find forest areas of different sizes on the map. Explanatory symbols on the green fill of the forest area may indicate a mixed composition of tree species, deciduous or coniferous forest. The caption, for example: , says that the average height of the trees is 25 m, their thickness is 30 cm, the average distance between them is 5 m, which allows us to conclude that it is impossible for cars and tanks to move through the forest off roads.

Studying the terrain on a map begins with determining the general nature of the unevenness of the area on which it is to be carried out. combat mission. For example, if the map shows a hilly terrain with relative heights of 100-120 m, and the distance between horizontal lines (laying) is from 10 to 1 mm, this indicates a relatively small steepness of the slopes (from 1 to 10 °).

A detailed study of the terrain on a map is associated with solving problems of determining the heights and mutual elevation of points, the type, direction of steepness of slopes, characteristics (depth, width and length) of hollows, ravines, gullies and other relief details.

Measuring distances on a map

Measuring straight and curved lines using a map

To determine on a map the distance between terrain points (objects, objects), using a numerical scale, you need to measure on the map the distance between these points in centimeters and multiply the resulting number by the scale value.

Example, on a map of scale 1:25000 we measure the distance between the bridge and the windmill with a ruler; it is equal to 7.3 cm, multiply 250 m by 7.3 and get the required distance; it is equal to 1825 meters (250x7.3=1825).

Determine the distance between terrain points on the map using a ruler

A small distance between two points in a straight line is easier to determine using a linear scale. To do this, it is enough to apply a measuring compass, the opening of which is equal to the distance between given points on the map, to a linear scale and take a reading in meters or kilometers. In the figure, the measured distance is 1070 m.

Large distances between points along straight lines are usually measured using a long ruler or measuring compass.

In the first case, a numerical scale is used to determine the distance on the map using a ruler.

In the second case, the “step” solution of the measuring compass is set so that it corresponds to an integer number of kilometers, and an integer number of “steps” is plotted on the segment measured on the map. The distance that does not fit into the whole number of “steps” of the measuring compass is determined using a linear scale and added to the resulting number of kilometers.

In the same way, distances are measured along winding lines. In this case, the “step” of the measuring compass should be taken 0.5 or 1 cm, depending on the length and degree of tortuosity of the line being measured.

To determine the length of a route on a map, a special device called a curvimeter is used, which is especially convenient for measuring winding and long lines.

The device has a wheel, which is connected by a gear system to an arrow.

When measuring distance with a curvimeter, you need to set its needle to division 99. Holding the curvimeter in a vertical position, move it along the line being measured, without lifting it from the map along the route so that the scale readings increase. Having reached the end point, count the measured distance and multiply it by the denominator of the numerical scale. (In this example, 34x25000=850000, or 8500 m)

Accuracy of measuring distances on the map. Distance corrections for slope and tortuosity of lines

The accuracy of determining distances on a map depends on the scale of the map, the nature of the measured lines (straight, winding), the chosen measurement method, the terrain and other factors.

The most accurate way to determine the distance on the map is in a straight line.

When measuring distances using a measuring compass or a ruler with millimeter divisions, the average measurement error in flat areas usually does not exceed 0.7-1 mm on the map scale, which is 17.5-25 m for a map at a scale of 1:25000, scale 1:50000 - 35-50 m, scale 1:100000 - 70-100 m.

In mountainous areas with steep slopes, errors will be greater. This is explained by the fact that when surveying a terrain, it is not the length of the lines on the Earth’s surface that is plotted on the map, but the length of the projections of these lines onto the plane.

For example, With a slope steepness of 20° and a distance on the ground of 2120 m, its projection onto the plane (distance on the map) is 2000 m, i.e. 120 m less.

It is calculated that with an inclination angle (steepness of the slope) of 20°, the resulting distance measurement result on the map should be increased by 6% (add 6 m per 100 m), with an inclination angle of 30° - by 15%, and with an angle of 40° - by 23 %.

When determining the length of a route on a map, it should be taken into account that road distances measured on the map using a compass or curvimeter are in most cases shorter than the actual distances.

This is explained not only by the presence of ups and downs on the roads, but also by some generalization of road convolutions on maps.

Therefore, the result of measuring the length of the route obtained from the map should, taking into account the nature of the terrain and the scale of the map, be multiplied by the coefficient indicated in the table.

The simplest ways to measure areas on a map

An approximate estimate of the size of the areas is made by eye using the squares of the kilometer grid available on the map. Each grid square of maps of scale 1:10000 - 1:50000 on the ground corresponds to 1 km2, the square of the grid of maps of scale 1:100000 - 4 km2, the square of the grid of maps of scale 1:200000 - 16 km2.

More accurately, areas are measured with a palette, which is a sheet of transparent plastic with a grid of squares with a side of 10 mm applied to it (depending on the scale of the map and the required measurement accuracy).

Having applied such a palette to the measured object on the map, they first count from it the number of squares that completely fit inside the contour of the object, and then the number of squares intersected by the contour of the object. We take each of the incomplete squares as half a square. As a result of multiplying the area of one square by the sum of squares, the area of the object is obtained.

Using squares of scales 1:25000 and 1:50000, it is convenient to measure the area of small areas with an officer’s ruler, which has special rectangular cutouts. The areas of these rectangles (in hectares) are indicated on the ruler for each gharta scale.

Reading a map along the route

Reading a map means correctly and fully perceiving the symbolism of its conventional signs, quickly and accurately recognizing from them not only the type and varieties of objects depicted, but also their characteristic properties.

Studying a terrain using a map (reading a map) includes determining its general nature, the quantitative and qualitative characteristics of individual elements (local objects and landforms), as well as determining the degree of influence of a given area on the organization and conduct of combat.

When studying the terrain on a map, you should remember that since its creation, changes may have occurred in the area that are not reflected on the map, i.e. the contents of the map will to some extent not correspond to the actual state of the terrain on this moment. Therefore, it is recommended to begin studying the area using a map by familiarizing yourself with the map itself.

Familiarization with the map. When familiarizing yourself with the map, using the information placed in the outer frame, determine the scale, height of the relief section and the time of creation of the map. Data on the scale and height of the relief section will allow you to establish the degree of detail of the image on a given map of local objects, shapes and relief details. Knowing the scale, you can quickly determine the size of local objects or their distance from each other.

Information about the time of creation of the map will make it possible to preliminarily determine the correspondence of the contents of the map to the actual state of the area.

Then they read and, if possible, remember the values of the magnetic needle declination and direction corrections. Knowing the direction correction from memory, you can quickly convert directional angles into magnetic azimuths or orient the map on the ground along the kilometer grid line.

General rules and sequence of studying the area on the map. The sequence and degree of detail in studying the terrain is determined by the specific conditions of the combat situation, the nature of the unit's combat mission, as well as seasonal conditions and tactical and technical data of the military equipment used in carrying out the assigned combat mission. When organizing defense in a city, it is important to determine the nature of its planning and development, identifying durable buildings with basements and underground structures. In the case where the unit’s route passes through the city, there is no need to study the features of the city in such detail. When organizing an offensive in the mountains, the main objects of study are passes, mountain passages, gorges and gorges with adjacent heights, the shape of the slopes and their influence on the organization of the fire system.

The study of terrain, as a rule, begins with determining its general nature, and then studies in detail individual local objects, shapes and details of the relief, their influence on the conditions of observation, camouflage, cross-country ability, protective properties, conditions of fire and orientation.

Determining the general nature of the area is aimed at identifying the most important features of the relief and local objects that have a significant impact on the accomplishment of the task. When determining the general nature of an area based on familiarization with the topography, settlements, roads, hydrographic network and vegetation cover, the variety of the area, the degree of its ruggedness and closedness are identified, which makes it possible to preliminarily determine its tactical and protective properties.

The general character of the area is determined by a quick overview of the entire study area on a map.

At first glance at the map, one can tell that there are settlements and individual tracts of forest, cliffs and gullies, lakes, rivers and streams indicating rough terrain and limited visibility, which inevitably complicates the movement of military and transport equipment off roads and creates difficulties in organizing surveillance . At the same time, the rugged nature of the terrain creates good conditions for sheltering and protecting units from the effects of enemy weapons of mass destruction, and forests can be used to camouflage unit personnel, military equipment, etc.

Thus, as a result of determining the general nature of the terrain, a conclusion is drawn about the accessibility of the area and its individual directions for the operations of units on vehicles, and they also outline boundaries and objects that should be studied in more detail, taking into account the nature of the combat mission to be performed in this area of the terrain.
A detailed study of the area aims to determine the qualitative characteristics of local objects, shapes and relief details within the boundaries of the unit’s operations or along the upcoming route of movement. Based on obtaining such data from a map and taking into account the relationship of topographic elements of the terrain (local objects and relief), an assessment is made of the conditions of cross-country ability, camouflage and surveillance, orientation, firing, and the protective properties of the terrain are determined.

Determination of the qualitative and quantitative characteristics of local objects is carried out using a map with relatively high accuracy and great detail.

When studying settlements using a map, the number of settlements, their type and dispersion are determined, and the degree of habitability of a particular area (district) of the area is determined. The main indicators of the tactical and protective properties of settlements are their area and configuration, the nature of the layout and development, the presence of underground structures, and the nature of the terrain on the approaches to the settlement.

By reading the map, using the conventional signs of settlements, they establish the presence, type and location of them in a given area of the area, determine the nature of the outskirts and layout, the density of buildings and the fire resistance of buildings, the location of streets, main thoroughfares, the presence of industrial facilities, prominent buildings and landmarks.

When studying the road network using a map, the degree of development of the road network and the quality of roads are clarified, the traffic conditions of a given area and the possibility of efficient use of vehicles are determined.

A more detailed study of roads establishes: the presence and characteristics of bridges, embankments, excavations and other structures; the presence of difficult areas, steep descents and ascents; possibility of leaving roads and driving near them.

When studying dirt roads, special attention is paid to identifying the carrying capacity of bridges and ferry crossings, since on such roads they are often not designed to accommodate heavy wheeled and tracked vehicles.

By studying hydrography, the presence of water bodies is determined from the map, and the degree of ruggedness of the area is specified. The presence of water bodies creates good conditions for water supply and transportation along waterways.

Water surfaces are depicted on maps in blue or light blue, so they clearly stand out among the symbols of other local objects. When studying rivers, canals, streams, lakes and other water barriers using a map, the width, depth, flow speed, nature of the bottom soil, banks and surrounding areas are determined; the presence and characteristics of bridges, dams, locks, ferry crossings, fords and areas convenient for crossing are established.

When studying the soil and vegetation cover, the presence and characteristics of forests and shrubs, swamps, salt marshes, sands, rocky placers and those elements of the soil and vegetation cover that can have a significant impact on the conditions of passage, camouflage, observation and the possibility of shelter are determined from the map.

The characteristics of the forest area studied from the map allow us to draw a conclusion about the possibility of using it for a secretive and dispersed location of units, as well as about the passability of the forest along roads and clearings. Good landmarks in the forest for determining your location and orienting yourself while moving are the forester’s house and clearings.

The characteristics of swamps are determined by the outline of symbols. However, when determining the passability of swamps on a map, one should take into account the time of year and weather conditions. During the period of rains and muddy roads, swamps, shown on the map as passable by a symbol, may actually turn out to be difficult to pass. In winter, during severe frosts, impassable swamps can become easily passable.

Studying the terrain on a map begins with determining the general nature of the unevenness of the area of the terrain on which the combat mission is to be carried out. At the same time, the presence, location and mutual relationship of the most typical typical forms and relief details for a given area are established, their influence on the conditions of cross-country ability, observation, firing, camouflage, orientation and organization of protection against weapons of mass destruction is determined in general terms. The general nature of the relief can be quickly determined by the density and outline of contours, elevation marks and symbols of relief details.

A detailed study of the terrain on a map is associated with solving problems of determining the heights and mutual elevation of points, the type and direction of the steepness of the slopes, the characteristics (depth, width and length) of hollows, ravines, gullies and other relief details.

Naturally, the need to solve specific tasks will depend on the nature of the assigned combat mission. For example, the determination of invisibility fields will be required when organizing and conducting surveillance reconnaissance; determining the steepness, height and length of the slopes will be required when determining terrain conditions and choosing a route, etc.

During the era of great geographical discoveries, travelers and discoverers faced two most important tasks: measuring distances and determining their location on earth's surface. The Greeks theoretically justified the solution to these problems, but they did not have sufficiently accurate instruments and maps.

Interesting fact. When Spain and Portugal decided to agree on dividing the New World into spheres of influence, they could not draw the dividing line on the map accurately enough, since at that time they did not know how to determine the longitude of a place and the distance on the map. In this regard, constant disputes and conflicts arose between states.

Measuring distances using a degree network. To calculate distances on a map or globe, you can use the following values: the arc length of 1° meridian and 1° equator is approximately 111 km. For meridians this is always true, and the length of an arc of 1° along the parallels decreases towards the poles (the arc size at 1° parallel at the equator is 111 km, at 20° north or south latitude - 105 km, etc.). At the poles it is equal to 0 (since a pole is a point). Therefore, it is necessary to know the number of kilometers corresponding to the length of 1° arc of each specific parallel. This number is written on each parallel on the hemisphere map. To determine the distance in kilometers between two points lying on the same meridian, calculate the distance between them in degrees, and then multiply the number of degrees by 111 km. To determine the distance between two points on the equator, you also need to determine the distance between them in degrees, and then multiply by 111 km.

Measuring distances using a scale. Length geographical feature can also be determined using scale. The map scale shows how many times the distance on the map is reduced relative to the actual distance on the ground. Therefore, by drawing a straight line (if you need to find out the distance in a straight line) between two points and using a ruler, measuring this distance in centimeters, you should multiply the resulting number by the scale value. For example, on a map of scale 1:100,000 (1 cm is 1 km) the distance is 5 cm, i.e. on the ground this distance is 1 × 5 = 5 (km). You can also measure distance on a map using a measuring compass. In this case, it is convenient to use a linear scale.

Measuring the length of a curved line (for example, the length of a river) from a map. To measure you can use measuring compass, curvimeter or thin wet thread. Suppose the measurement is carried out on a map of scale 1: 5,000,000 (50 km in 1 cm). The measuring compass is given a small opening (2-3 mm) in order to be able to measure small bends of the river, and they walk along the river, counting the steps. Then, multiplying the value of the compass opening (for example, 3 mm) by the number of steps (let's say 49), find the total length of the river on the map:

3 mm × 49 = 147 mm = 14.7 cm.

Thus, the length of the river will be 50 km × 14.7 = 735 km.

You can measure the length of the river curvimeter – a special device for measuring the lengths of curved lines on maps and plans. The curvimeter wheel is rolled along a curved line (rivers, roads, etc.), and the curvimeter counter counts the revolutions, indicating the desired length of the line.

You can measure the length of the curve with a damp thin thread. It is laid out along all the bends of the river. Then, straightening the thread without strong tension, measure its length in centimeters, and use the scale to determine the actual length of the river.

If the length of a river is measured using a small-scale map, the result obtained turns out to be less than the actual length of this river. This is due to the fact that on small-scale maps it is impossible to show all the small bends of its channel. Topographic maps provide a greater opportunity to reflect all the bends of the channel, and the distortions on them are very small. Therefore, the most accurate measurement results can be obtained from topographic maps.

Odometer

When developing a hiking route, an important criterion is its length. Depending on this, the complexity and duration of the upcoming route are calculated, the time required to complete it, the required average speed of movement, the supply of water and food are determined, and the minimum acceptable degree of preparedness of future participants is determined. The methods and methods of developing the route itself may be different, but it all depends on the distance that you are willing to cover in the time allotted for its completion. Much will depend on the accuracy of your measurements and calculations, in particular, whether you will catch the scheduled return train or whether you will have to look for a place in a hotel or sit on the platform waiting for the morning train.

There are many tools and methods for measuring distances on a map, but not all of them are equally applicable or convenient for accurately measuring the length of future routes along winding roads.

As a means of measuring segments on the map, you can use the usual ruler or compass. But as you might guess, all these devices are designed to measure straight sections, and a bicycle route is rarely a series of straight lines, unless you are riding along city streets. When measuring a route along winding roads and paths using linear instruments, you will certainly be faced with the need for additional calculations, including determining the magnitude of the error in your measurements, since the usual smooth bend of the road when measured with a ruler will look like a broken line consisting of many short straight lines segments. At the same time, the longer and more winding the route, the greater the error will be allowed in your measurements and the more approximately the total length of the route will be determined, especially if you use a small-scale map to plot the route.

More accurate results can be obtained by using a thread with transverse markings corresponding to the centimeter scale previously applied to it using the same ruler. However, in this case, the accuracy of the measurement will directly depend on your accuracy and patience when laying out the thread on the surface of the card.

Fortunately, a special simple device has long existed, designed specifically for taking measurements on a map of both straight and winding segments called a curvimeter. Curvimeter (from Latin curvus - curve and... meter), a device for measuring the lengths of segments of curves and winding lines on topographic plans, maps and graphic documents.

The curvimeter is made with circular and linear scales. Each type of curvimeter is available in two versions: with a fixed dial and a moving arrow or index; with a movable dial and a fixed index. To measure the length of a line, the Curvimeter wheel is rolled along this line. The distance measured by the Curvimeter per revolution corresponds to a scale length of 100 cm. The error in measuring a straight line segment with a length of at least 50 cm is no more than 0.25 cm.

The mechanical curvimeter (shown in the figure) has a metric and inch scale. The metric scale division corresponds to 1 cm, and the inch scale to 0.05 inches. The error in measuring a segment 50 cm long does not exceed 0.5%.

Thus, when using a curvimeter, you can measure the winding section of the route you need at the lowest cost and with the greatest accuracy. However, here too you should remember a few simple rules for measuring a route using this device.

First, when measuring the total length of a route, do not try to measure its entire length from start to finish at once. It is better to measure in segments - from one important landmark to another. And the point is not at all that you may not have enough scale length. It’s just that as the length of the measured segment increases, the degree of measurement error increases; an uncomfortable position, fatigue or trembling of the hand can also have a detrimental effect on the accuracy of measurements.

Secondly, use a larger scale map if possible. In practice, a map at a scale of 1:50,000 (five hundred meters) or 1:100,000 (kilometers) will do just fine. Just don’t be lazy and carefully trace all the curves of the road with a curvimeter.

Thirdly, don’t be too lazy to measure each segment several times. This way you will eliminate accidental errors. If you are using a conventional mechanical curvimeter, and not an electronic analogue that allows you to measure with tenths and even thousandths, determining the remaining “tail” by eye, which is very important on maps with a scale of less than 1:100,000, do not always try to round in one direction ( more or less) use at least approximate tenths.

Fourthly, in the segments between the main landmarks, do not be too lazy to separately measure the distances to secondary landmarks along the route, for example, a bridge across a channel, a road intersection, a deep ravine, etc. Thus, as mentioned above, you will be able to constantly monitor your location on the route and have an accurate idea of the distance remaining to the finish even without a GPS receiver, but only with the help of a map with distances to landmarks marked on it.

When plotting measurement results on a map, it seems convenient to use the fractional notation A/B, where A is the distance from the previous landmark, and B is the distance from the starting point of the route. This method makes it easy to navigate in space without unnecessary mathematical calculations. This is relevant, for example, when you need to inform your fellow travelers, especially those who like to get ahead of the main group, the exact distance to a landmark near which you need to turn, wait for the group, etc. In addition, if you made radial forays on any part of the route or accidentally made an unplanned detour, for example, bypassing a washed-out section of the road, you will not have to make adjustments to pre-marked marks on the map, rewrite them or constantly keep in mind the number of “extra” kilometers, which will have to be constantly adjusted.

An example of measuring and plotting its results on a map:

Start (0/0) - turn right, exit from the asphalt highway onto a dirt road (3/3) - bridge over the river (2/5) - Dubki village (7/13) - Lesnoy village (14/27) - bridge across stream (5/32) – intersection with asphalt highway (8/40) – railway station Terminus (10/50).

And a few words about the variety of shapes and varieties of curvimeters that are presented on the Russian market today.

As mentioned above, there are two main types of curvimeters: mechanical and electronic.

In the design of mechanical curvimeters, regardless of the specific model, there are no particular fundamental differences, with the exception of the type of scale (rectilinear and circular) and the principle of displaying measurement results (with a fixed dial and a movable arrow or index; with a movable dial and a fixed index). As a rule, this is a plastic device weighing about 50 grams of rather modest dimensions. For example, the Russian-made KU-A curvimeter shown in the figure has dimensions of 50x20x100 (in a case).

This curvimeter has been produced in our country for decades in an unchanged form, except now without the USSR quality mark, and was included in the mandatory list of items as part of an officer’s tablet. It was standardized back in Soviet times and complies with TU 25-07-1039-74. The cost of this copy is about 500 rubles.

The curvimeter of the Swedish company is designed in approximately the same way. Silva. However, the fixed dial has more complex markings for measurements on eight scales.

The cost of such a curvimeter is about 1000 rubles.

Another example of a Russian-made mechanical curvimeter made in the form of a keychain and additionally equipped with a compass.

The dial of the curvimeter has scales for maps of scale 1:5000, 1:20000 and 1:50000. as well as a metric scale, the division value of which corresponds to 1 centimeter.

Its cost is 120 rubles.

another sample from survive.com

Distance measurement in mm, cm, NM and km.
- Measuring range: 10 m (current size)
- Features: setting the scale
- Metal wheel for measurements

Diameter 4.5cm

Length 9.7cm

Materials: plastic, steel, plastic glass.

price 215.00 rub.

In general, mechanical curvimeters have several main advantages:
- simplicity of design and use;
- the absence of electronic circuits and other complex elements implies the possibility of its use in any climatic, weather and temperature conditions;
- complete energy independence due to the absence of batteries as such;
- good impact resistance and the impossibility of disabling it as a result of water procedures.

All of the above makes a mechanical curvimeter most suitable for use in field conditions. The main and probably the only drawback of such a curvimeter is the need to determine tenths of the division price “by eye”.

Now let's turn to the variety of electronic curvimeters. Here, the cost of one copy ranges from three hundred to five thousand rubles, depending on the complexity of the device and the number of basic and additional functions in it. As in the production of many other electronic devices, manufacturers of electronic curvimeters rarely avoid the temptation to endow them with a lot of additional functions, both useful and not so useful.

For example, one of the simplest electronic curvimeters from the same Swedish company Silva, entitled "Silva Digital Map Measurer" made in the form of a keychain, and in addition to performing the main function - measuring distance on a map, it is additionally equipped with:

Calculator;
- mini flashlight;
- compass.

Its cost is about >2000 rubles.

A much more complex high-precision curvimeter made in the USA called "Scal Master II", designed to perform complex graphic measurements and calculations, has its own software, the ability to connect to a personal computer and has 91 architectural and engineering functions.

This device processes 50 Anglo-American values (feet, inches, etc.) and 41 metric values, allowing you to work with any maps and drawings. You can enter your most frequently used measurement type and the instrument will automatically convert to scale measurements. Has the ability to save data. It can be connected to a computer using a PC-Interface Kit. Compatible with Windows. Works with Excel, Lotus.

Technical characteristics of the curvimeter Scale Master II:

Size: 182 x 41 x 15 mm
Weight: 54 g
Wheel material: solid polymer
Email power supply: 2 X 3 Volt - lithium
Usage life: up to 400 hours
Automatic shutdown: 5 min.
Number of buttons: 12
Operating temperatures: 0 – 55О С
Display size: 19 x 64 mm.

The cost of such a device + Kit for connecting to a PC is >11,000 rubles

Summarizing the information about electronic curvimeters, we can conclude that their use in the field, especially more complex analogues, is associated with some difficulties. Susceptibility to external influences such as cold and moisture, dependence on the presence of batteries and significantly lower impact resistance suggest the use of such a device primarily in greenhouse conditions of urban premises for the preliminary development of routes. At the same time, the undeniable advantage of an electronic curvimeter will be the maximum accuracy of measurements and the ability to immediately process them, for example, converting them into kilometers depending on the previously set scale.

Measuring distances
Measuring route length
Definition of areas

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 scale can be expressed in numerical form (numerical scale) or graphically (linear, transverse scales) - in the form of a graph. Numerical and linear scales are displayed on the bottom edge of the topographic map.

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

Numerical scale- this is the scale of the map, expressed as a fraction, the numerator of which is one, and the denominator is a number showing how many times the horizontal layouts of terrain lines are reduced on the map. The smaller the denominator, the larger the scale of the map. For example, a scale of 1:25,000 shows that all linear dimensions of terrain elements (their horizontal distribution on a level surface) when depicted on a map are reduced by 25,000 times.

Distances on the ground in meters and kilometers corresponding to 1 cm on the map are called scale values. It is indicated on the map under the numerical scale.

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, on a 1:50,000 scale map, the distance between two local objects is 4.7 cm; on the ground it will be 4.7 x 500 = 2350 m. If the distance measured on the ground needs to be plotted on the map, it must be divided by the denominator of the numerical scale. For example, on the ground the distance between two local objects is 1525 m. On a 1:50,000 scale map it will be 1525:500 = 3.05 cm.

A linear scale is a graphical expression of a numerical scale. On the linear scale, segments corresponding to distances on the ground in meters and kilometers are digitized. This simplifies the process of measuring distances, since no calculations are required.

In simple terms, scale is the ratio of the length of a line on a map (plan) to the length of the corresponding line on the ground.

Measurements on a linear scale are performed using a measuring compass. Long straight lines and curved lines on a map are measured in parts. To do this, set the solution (“step”) of the measuring compass equal to 0.5-1 cm, and with such a “step” they walk along the measured line, counting the permutations of the legs of the measuring compass. The remainder of the distance is measured on a linear scale. The distance is calculated by multiplying the number of permutations of the compass by the “step” value in kilometers and adding the remainder to the resulting value. If you don’t have a measuring compass, you can replace it with a strip of paper on which a dash is used to mark the distance measured on the map or plotted to scale on it.

The transverse scale is a special graph engraved on a metal plate. Its construction is based on the proportionality of segments of parallel lines intersecting the sides of the angle.

The standard (normal) transverse scale has major divisions equal to 2 cm and minor divisions (left) equal to 2 mm. In addition, on the graph there are segments between the vertical and inclined lines, equal to 0.5 mm along the first lower horizontal line, 0.4 mm along the second, 0.6 mm along the third, etc. Using a transverse scale, you can measure distances on maps of any scale.

Distance measurement accuracy. The accuracy of measuring the length of straight segments on a topographic map using a measuring compass and a transverse scale does not exceed 0.1 mm. This value is called the maximum graphic accuracy of measurements, and the distance on the ground corresponding to 0.1 mm on the map is the maximum graphic accuracy of the map scale.

The graphical error in measuring the length of a segment on a map depends on the deformation of the paper and the measurement conditions. Usually it varies between 0.5 - 1 mm. To eliminate gross errors, measuring a segment on the map must be performed twice. If the results obtained do not differ by more than 1 mm, the average of the two measurements is taken as the final value of the length of the segment.

Errors in determining distances from topographic maps of various scales are shown in the table.

Correction to distance for line slope. The distance measured on the map on the ground will always be slightly less. This happens because the map measures horizontal distances, while the corresponding lines on the ground are usually inclined.

The conversion coefficients from distances measured on the map to actual ones are given in the table.

As can be seen from the table, on flat terrain the distances measured on the map differ little from the actual ones. On maps of hilly and especially mountainous terrain, the accuracy of determining distances is significantly reduced. For example, the distance between two points, measured on a map, on terrain with an angle of 12 5o 0, is equal to 9270 m. The actual distance between these points will be 9270 * 1.02 = 9455 m.

Thus, when measuring distances on a map, it is necessary to introduce corrections for the slope of the lines (for the relief).

Determining distances using coordinates taken from the map.

Long straight distances in one coordinate zone can be calculated using the formula

S=L-(X 42 0- X 41 0) + (Y 42 0- Y 41 0) 52 0,

Where S— distance on the ground between two points, m;

X 41 0,Y 41 0— coordinates of the first point;

X 42 0,Y 42 0— coordinates of the second point.

This method of determining distances is used when preparing data for artillery firing and in other cases.

Measuring route length

The length of the route is usually measured on the map with a curvimeter. A standard curvimeter has two scales for measuring distances on a map: on the one hand, metric (from 0 to 100 cm), on the other, inch (from 0 to 39.4 inches). The curvimeter mechanism consists of a bypass wheel connected by a gear system to a pointer. To measure the length of a line on a map, you must first rotate the deflection wheel to set the curvimeter needle to the initial (zero) division of the scale, and then roll the deflection wheel strictly along the line being measured. The resulting reading on the curvimeter scale must be multiplied by the map scale.

The correct operation of the curvimeter is checked by measuring a known line length, for example the distance between the kilometer grid lines on a map. The error in measuring a line 50 cm long with a curvimeter is no more than 0.25 cm.

The length of the route on the map can also be measured with a measuring compass.

The length of the route measured on the map will always be somewhat shorter than the actual one, since when drawing up maps, especially small-scale ones, roads are straightened. In hilly and mountainous areas, in addition, there is a significant difference between the horizontal layout of the route and its actual length due to ascents and descents. For these reasons, a correction must be made to the route length measured on the map. Correction factors for different types of terrain and map scales are not the same; they are shown in the table.

The table shows that in hilly and mountainous areas the difference between the distance measured on the map and the actual length of the route is significant. For example, the length of the route measured on a 1:100,000 scale map of a mountainous region is 150 km, but its actual length will be 150 * 1.20 = 180 km.

A correction to the length of the route can be entered directly when measuring it on the map with a measuring compass, setting the “step” of the measuring compass taking into account the correction factor.

Definition of areas

The area of a terrain area is determined from a map, most often by counting the squares of the coordinate grid covering this area. The size of the square fractions is determined by eye or using a special palette on an officer’s ruler (artillery circle). Each square formed by the lines of the coordinate grid on a map of scale 1:50,000 corresponds on the ground to 1 km 52 0, on a map of scale 1:100,000 - 4 km 2, on a map of scale 1:200,000 - 16 km 2.

When measuring large areas using a map or photographic documents, a geometric method is used, which consists of measuring the linear elements of a site and then calculating its area using geometry formulas. If the area on the map has a complex configuration, it is divided by straight lines into rectangles, triangles, trapezoids and the areas of the resulting figures are calculated.

The area of destruction in the area of a nuclear explosion is calculated using the formula P=pR. The radius R is measured using a map. For example, the radius of severe destruction at the epicenter of a nuclear explosion is 3.5 km.

P=3.14 * 12.25 = 38.5 km 2.

The area of radioactive contamination of the area is calculated using the formula for determining the area of a trapezoid. This area can be approximately calculated using the formula for determining the area of a sector of a circle

Where R— radius of the circle, km;

A— chord, km.

Determination of azimuths and directional angles

Azimuths and directional angles. The position of an object on the ground is most often determined and indicated in polar coordinates, that is, the angle between the initial (given) direction and the direction to the object and the distance to the object. The direction of the geographic (geodesic, astronomical) meridian, magnetic meridian or vertical line of the map coordinate grid is chosen as the initial direction. The direction to some distant landmark can also be taken as the initial one. Depending on which direction is taken as the initial direction, a distinction is made between geographical (geodetic, astronomical) azimuth A, magnetic azimuth Am, directional angle a (alpha) and position angle 0.

Geographic (geodetic, astronomical) is a dihedral angle between the meridian plane of a given point and a vertical plane passing in a given direction, measured from the direction north clockwise (geodetic azimuth is a dihedral angle between the geodetic meridian plane of a given point and the plane passing through the normal to it and containing the given direction. The dihedral angle between the plane of the astronomical meridian of a given point and a vertical plane passing in a given direction is called astronomical azimuth).

Magnetic azimuth A 4m is a horizontal angle measured from the north direction of the magnetic meridian in a clockwise direction.

Directional angle a is the angle between the direction passing through a given point and a line parallel to the abscissa axis, measured from the north direction of the abscissa axis clockwise.

All of the above angles can have values from 0 to 360 0.

The position angle 0 is measured in both directions from the direction taken as the initial one. Before naming the position angle of the object (target), indicate in which direction (right, left) from the initial direction it is measured.

In maritime practice and in some other cases, directions are indicated by bearings. The rhumb is the angle between the north or south direction of the magnetic meridian of a given point and the determined direction. The value of the rumba does not exceed 90 0, therefore the rumba is accompanied by the name of the quarter of the horizon to which the direction refers: NE (northeast), NW (northwest), SE (southeast), and SW (southwest). The first letter shows the direction of the meridian from which the rhumb is measured, and the second in which direction. For example, the rhumb NW 52 0 means that this direction makes an angle of 52 0 with the northern direction of the magnetic meridian, which is measured from this meridian to the west.

Measurement on the map of directional angles and geodetic azimuths is carried out with a protractor, artillery circle or chord angle meter.

Using a protractor, directional angles are measured in this order. The starting point and the local object (target) are connected by a straight grid line that must be greater than the radius of the protractor. Then the protractor is aligned with the vertical line of the coordinate grid, in accordance with the angle. The reading on the protractor scale against the drawn line will correspond to the value of the measured directional angle. The average error in measuring an angle using an officer's ruler protractor is 0.5 0 (0-08).

To draw on the map the direction specified by the directional angle in degrees, you need to go through the main point symbol starting point, draw a line parallel to the vertical grid line. Attach a protractor to the line and place a dot against the corresponding division of the protractor scale (reference), equal to the directional angle. After this, draw a straight line through two points, which will be the direction of this directional angle.

Directional angles on the map are measured with an artillery circle in the same way as with a protractor. The center of the circle is aligned with the starting point, and the zero radius is aligned with the north direction of the vertical grid line or a straight line parallel to it. Against the line drawn on the map, read the value of the measured directional angle in divisions of the protractor on the red inner scale of the circle. The average measurement error with an artillery circle is 0-03 (10 0).

A chord angle meter measures angles on a map using a measuring compass.

A chord angle meter is a special graph engraved in the form of a transverse scale on a metal plate. It is based on the relationship between the radius of the circle R, the central angle 1a (alpha) and the length of the chord a:

The unit is taken to be the chord of the angle 60 0 (10-00), the length of which is approximately equal to the radius of the circle.

On the front horizontal scale of the chord angle meter, the chord values corresponding to angles from 0-00 to 15-00 are marked at 1-00. Small divisions (0-20, 0-40, etc.) are signed with numbers 2, 4, 6, 8. Numbers 2, 4, 6, etc. on the left vertical scale the angles are indicated in protractor division units (0-02, 0-04, 0-06, etc.). Digitization of divisions on the lower horizontal and right vertical scales is intended to determine the length of chords when constructing additional angles up to 30-00.

Angle measurement using a chord angle meter is performed in this order. Through the main points of the symbols of the starting point and local subject, at which the directional angle is determined, draw a thin straight line on the map with a length of at least 15 cm.

From the point of intersection of this line with the vertical line of the coordinate grid of the map, using a measuring compass, make marks on the lines that formed an acute angle, with a radius equal to the distance on the chord angle meter from 0 to 10 major divisions. Then measure the chord - the distance between the marks. Without changing the angle of the measuring compass, its left corner is moved along the leftmost vertical line of the chord angle meter scale until the right needle coincides with any intersection of the inclined and horizontal lines. The left and right needles of the measuring compass should always be on the same horizontal line. In this position of the needles, a reading is taken using a chord angle meter.

If the angle is less than 15-00 (90 0), then large divisions and tens of small divisions of the protractor are counted on the upper scale of the chordogonometer, and units of divisions of the protractor are counted on the left vertical scale.

If the angle is greater than 15-00, then measure the addition to 30-00, readings are taken on the lower horizontal and right vertical scales.

The average error in measuring an angle with a chord angle meter is 0-01 - 0-02.

Meridian convergence. Transition from geodetic azimuth to directional angle.

Meridian convergence y is the angle at a given point between its meridian and a line parallel to the x-axis or axial meridian.

The direction of the geodetic meridian on a topographic map corresponds to the sides of its frame, as well as straight lines that can be drawn between the same minute divisions of longitude.

The convergence of meridians is counted from the geodetic meridian. The convergence of meridians is considered positive if the northern direction of the x-axis is deviated to the east of the geodetic meridian and negative if this direction is deviated to the west.

The amount of meridian convergence indicated on the topographic map in the lower left corner refers to the center of the map sheet.

If necessary, the amount of convergence of the meridians can be calculated using the formula

y=(L — L4 0) sin B,

Where L— longitude of a given point;

L 4 0 — longitude of the axial meridian of the zone in which the point is located;

B— latitude of a given point.

The latitude and longitude of a point are determined from the map with an accuracy of 30`, and the longitude of the axial meridian of the zone is calculated using the formula

L 4 0 = 4 06 5 0 0N - 3 5 0,

Where N— zone number

Example. Determine the convergence of meridians for a point with coordinates:

B = 67 5о 040` and L = 31 5о 012`

Solution. Zone number N = ______ + 1 = 6;

L 4o 0= 4 06 5o 0 * 6 - 3 5o 0 = 33 5o 0; y = (31 5о 012` - 33 5о 0) sin 67 5о 040` =

1 5о 048` * 0.9245 = -1 5о 040`.

The convergence of meridians is zero if the point is on the axial meridian of the zone or on the equator. For any point within one coordinate six-degree zone, the convergence of the meridians in absolute value does not exceed 3 5o 0.

The geodetic direction azimuth differs from the directional angle by the amount of convergence of the meridians. The relationship between them can be expressed by the formula

A = a + (+ y)

From the formula it is easy to find an expression for determining the directional angle based on the known values of the geodetic azimuth and the convergence of the meridians:

a= A - (+y).

Magnetic declination. Transition from magnetic azimuth to geodetic azimuth.

The property of a magnetic needle to occupy a certain position at a given point in space is due to the interaction of its magnetic field with the Earth’s magnetic field.

The direction of the established magnetic needle in the horizontal plane corresponds to the direction of the magnetic meridian at a given point. The magnetic meridian generally does not coincide with the geodetic meridian.

The angle between the geodetic meridian of a given point and its magnetic meridian directed north is called declination of the magnetic needle or magnetic declination.

Magnetic declination is considered positive if the northern end of the magnetic needle is deviated east of the geodetic meridian (eastern declination), and negative if it is deviated to the west (western declination).

The relationship between geodetic azimuth, magnetic azimuth and magnetic declination can be expressed by the formula

A = A 4m 0 = (+ b)

Magnetic declination changes with time and location. Changes can be permanent or random. This feature of magnetic declination must be taken into account when accurately determining magnetic azimuths of directions, for example, when aiming guns and launchers, orienting technical reconnaissance equipment using a compass, preparing data for working with navigation equipment, moving along azimuths, etc.

Changes in magnetic declination are caused by the properties of the Earth's magnetic field.

The Earth's magnetic field is the space around the earth's surface in which the effects of magnetic forces are detected. Their close relationship with changes in solar activity is noted.

The vertical plane passing through the magnetic axis of the arrow, freely placed on the tip of the needle, is called the plane of the magnetic meridian. Magnetic meridians converge on Earth at two points called the north and south magnetic poles (M and M 41 0), which do not coincide with the geographic poles. The magnetic north pole is located in northwestern Canada and moves in a north-northwest direction at a rate of about 16 miles per year.

The south magnetic pole is located in Antarctica and is also moving. Thus, these are wandering poles.

There are secular, annual and daily changes in magnetic declination.

Secular changes in magnetic declination represent a slow increase or decrease in its value from year to year. Having reached a certain limit, they begin to change in the opposite direction. For example, in London 400 years ago the magnetic declination was + 11 5o 020`. Then it decreased and in 1818 reached - 24 5о 038`. After this, it began to increase and is currently about 11 5o 0. It is assumed that the period of secular changes in the magnetic declination is about 500 years.

To make it easier to take into account the magnetic declination at different points on the earth's surface, special magnetic declination maps are drawn up, on which points with the same magnetic declination are connected by curved lines. These lines are called izogons. They are plotted on topographic maps at scales of 1:500,000 and 1:1000,000.

The maximum annual changes in magnetic declination do not exceed 14 - 16`. Information about the average magnetic declination for the territory of a map sheet, relating to the time of its determination, and the annual change in magnetic declination is placed on topographic maps at a scale of 1:200,000 and larger.

During the day, the magnetic declination undergoes two fluctuations. By 8 o'clock the magnetic needle occupies its extreme eastern position, after which it moves to the west until 14 o'clock, and then moves to the east until 23 o'clock. Until 3 o'clock it moves again to the west, and by sunrise it again occupies the extreme eastern position. The amplitude of such fluctuations for middle latitudes reaches 15`. As the latitude of the place increases, the amplitude of the oscillations increases.

It is very difficult to take into account daily changes in magnetic declination.

Random changes in magnetic declination include disturbances of the magnetic needle and magnetic anomalies. Disturbances of the magnetic needle, covering vast areas, are observed during earthquakes, volcanic eruptions, auroras, thunderstorms, the appearance of a large number of sunspots, etc. At this time, the magnetic needle deviates from its usual position, sometimes up to 2-3 5o 0. The duration of the disturbances ranges from several hours to two or more days.

Deposits of iron, nickel and other ores in the bowels of the Earth have a great influence on the position of the magnetic needle. Magnetic anomalies occur in such places. Small magnetic anomalies are quite common, especially in mountainous areas. Areas of magnetic anomalies are marked on topographic maps with special symbols.

Transition from magnetic azimuth to directional angle. On the ground, using a compass (compass), magnetic azimuths of directions are measured, from which they then proceed to directional angles. On the map, on the contrary, directional angles are measured and from them they proceed to the magnetic azimuths of directions on the ground. To solve these problems, it is necessary to know the magnitude of the deviation of the magnetic meridian at a given point from the vertical line of the map coordinate grid.

The angle formed by the vertical grid line and the magnetic meridian, which is the sum of the convergence of the meridians and the magnetic declination, is called deviation of the magnetic needle or direction correction (DC). It is measured from the north direction of the vertical grid line and is considered positive if the northern end of the magnetic needle deviates east of this line, and negative if the magnetic needle deviates to the west.

The direction correction and its constituent meridian convergence and magnetic declination are shown on the map under the southern side of the frame in the form of a diagram with explanatory text.

The direction correction in the general case can be expressed by the formula

PN = (+ b) - (+y)&

If the directional angle of direction is measured on the map, then the magnetic azimuth of this direction on the ground

A 4m 0 = a - (+PN).

The magnetic azimuth of any direction measured on the ground is converted into the directional angle of this direction according to the formula

a = A 4m 0 + (+PN).

To avoid errors when determining the magnitude and sign of the direction correction, you need to use a diagram of the directions of the geodetic meridian, magnetic meridian and vertical grid line placed on the map.

1.1.Map scales

Map scale shows how many times the length of a line on a map is less than its corresponding length on the ground. It is expressed as a ratio of two numbers. For example, a scale of 1:50,000 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 (or 500 m) on the terrain.

Rice. 1. Design of numerical and linear scales on topographic maps and city plans

The scale is indicated under the bottom side of the map frame in digital terms (numerical scale) and in the form of a straight line (linear scale), on the segments of which the corresponding distances on the ground are labeled (Fig. 1). The scale value is also indicated here - the distance in meters (or kilometers) on the ground, corresponding to one centimeter on the map.

It is useful to remember the rule: if you cross out the last two zeros on the right side of the ratio, the remaining number will show how many meters on the ground correspond to 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. Let’s assume that there are maps at scales of 1:25000, 1:50000 and 1:100000 for the same area. Of these, a scale of 1:25,000 will be the largest, and a scale of 1:100,000 will be the smallest.
The larger the scale of the map, the more detailed the terrain is depicted on it. As the scale of the map decreases, the number of terrain details shown on it also decreases.

The detail of the terrain depicted on topographic maps depends on its nature: the fewer details the terrain contains, the more fully they are displayed on maps of smaller scales.

In our country and many other countries, the main scales for topographic maps are: 1:10000, 1:25000, 1:50000, 1:100000, 1:200000, 1:500000 and 1:1000000.

The maps used by the troops are divided into large-scale, medium-scale and small-scale.

Map scale	Card name	Classification of cards
		by scale	for main purpose
1:10 000 (in 1 cm 100 m)	ten-thousandth	large scale	tactical
1:25,000 (in 1 cm 250 m)	twenty-five thousandth
1:50,000 (in 1 cm 500 m)	five thousandth
1:100,000 (1 cm 1 km)	hundred thousandth	medium-scale
1:200,000 (in 1 cm 2 km)	two hundred thousandth		operational
1:500,000 (1 cm 5 km)	five hundred thousandth	small-scale
1:1 000 000 (1 cm 10 km)	millionth

1.2. Measuring straight and curved lines using a map

Example, on a map of scale 1:25000 we measure the distance between the bridge and the windmill with a ruler (Fig. 2); it is equal to 7.3 cm, multiply 250 m by 7.3 and get the required distance; it is equal to 1825 meters (250x7.3=1825).

Rice. 2. Determine the distance between terrain points on the map using a ruler.

A small distance between two points in a straight line is easier to determine using a linear scale (Fig. 3). To do this, it is enough to apply a measuring compass, the opening of which is equal to the distance between given points on the map, to a linear scale and take a reading in meters or kilometers. In Fig. 3 the measured distance is 1070 m.

Rice. 3. Measuring distances on a map with a measuring compass on a linear scale

Rice. 4. Measuring distances on a map with a compass along winding lines

Large distances between points along straight lines are usually measured using a long ruler or measuring compass.

In the first case, a numerical scale is used to determine the distance on the map using a ruler (see Fig. 2).

In the same way, distances are measured along winding lines (Fig. 4). In this case, the “step” of the measuring compass should be taken 0.5 or 1 cm, depending on the length and degree of tortuosity of the line being measured.

Rice. 5. Distance measurements with a curvimeter

To determine the length of a route on a map, a special device is used, called a curvimeter (Fig. 5), which is especially convenient for measuring winding and long lines.

The device has a wheel, which is connected by a gear system to an arrow.

1.3. Accuracy of measuring distances on the map. Distance corrections for slope and tortuosity of lines

Accuracy of determining distances on the map depends on the scale of the map, the nature of the measured lines (straight, winding), the chosen measurement method, the terrain and other factors.

The most accurate way to determine the distance on the map is in a straight line.

For example, With a slope steepness of 20° (Fig. 6) and a distance on the ground of 2120 m, its projection onto the plane (distance on the map) is 2000 m, i.e. 120 m less.

Rice. 6. Projection of the length of the slope onto a plane (map)

This is explained not only by the presence of ups and downs on the roads, but also by some generalization of road convolutions on maps.

1.4. The simplest ways to measure areas on a map

An approximate estimate of the size of the areas is made by eye using the squares of the kilometer grid available on the map. Each grid square of maps of scales 1:10000 - 1:50000 on the ground corresponds to 1 km2, a grid square of maps of scale 1 : 100000 - 4 km2, the square of the map grid at a scale of 1:200000 - 16 km2.

Areas are measured more accurately palette, which is a sheet of transparent plastic with a grid of squares with a side of 10 mm applied to it (depending on the scale of the map and the required measurement accuracy).

2. Azimuths and directional angle. Magnetic declination, convergence of meridians and direction correction

True azimuth(Au) - horizontal angle, measured clockwise from 0° to 360° between the northern direction of the true meridian of a given point and the direction to the object (see Fig. 7).

Magnetic azimuth(Am) - horizontal angle, measured clockwise from 0e to 360° between the northern direction of the magnetic meridian of a given point and the direction to the object.

Directional angle(α; DU) - horizontal angle, measured clockwise from 0° to 360° between the northern direction of the vertical grid line of a given point and the direction to the object.

Magnetic declination(δ; Sk) - the angle between the northern direction of the true and magnetic meridians at a given point.

If the magnetic needle deviates from the true meridian to the east, then the declination is eastern (counted with a + sign); if the magnetic needle deviates to the west, then the declination is western (counted with a - sign).

Rice. 7. Angles, directions and their relationships on the map

Meridian convergence(γ; Sat) - the angle between the northern direction of the true meridian and the vertical grid line at a given point. When the grid line deviates to the east, the convergence of the meridian is eastern (counted with a + sign), when the grid line deviates to the west - western (counted with a - sign).

Direction correction(PN) - the angle between the northern direction of the vertical grid line and the direction of the magnetic meridian. It is equal to the algebraic difference between the magnetic declination and the convergence of the meridians:

3. Measuring and plotting directional angles on the map. Transition from directional angle to magnetic azimuth and back

On the ground using a compass (compass) to measure magnetic azimuths directions, from which they then move to directional angles.

On the map on the contrary, they measure directional angles and from them they move on to magnetic azimuths of directions on the ground.

Rice. 8. Changing directional angles on the map with a protractor

Directional angles on the map are measured with a protractor or chord angle meter.

Measuring directional angles with a protractor is carried out in the following sequence:

the landmark at which the directional angle is measured is connected by a straight line to the standing point so that this straight line is greater than the radius of the protractor and intersects at least one vertical line of the coordinate grid;
align the center of the protractor with the intersection point, as shown in Fig. 8 and count the value of the directional angle using the protractor. In our example, the directional angle from point A to point B is 274° (Fig. 8, a), and from point A to point C is 65° (Fig. 8, b).

In practice, there is often a need to determine the magnetic AM from a known directional angle ά, or, conversely, the angle ά from a known magnetic azimuth.

Transition from directional angle to magnetic azimuth and back

The transition from the directional angle to the magnetic azimuth and back is carried out when on the ground it is necessary to use a compass (compass) to find the direction whose directional angle is measured on the map, or vice versa, when it is necessary to put on the map the direction whose magnetic azimuth is measured on the ground with using a compass.

To solve this problem, it is necessary to know the deviation of the magnetic meridian of a given point from the vertical kilometer line. This value is called the direction correction (DC).

Rice. 10. Determination of the correction for the transition from directional angle to magnetic azimuth and back

The direction correction and its constituent angles - the convergence of meridians and magnetic declination are indicated on the map under the southern side of the frame in the form of a diagram that looks like that shown in Fig. 9.

Meridian convergence(g) - the angle between the true meridian of a point and the vertical kilometer line depends on the distance of this point from the axial meridian of the zone and can have a value from 0 to ±3°. The diagram shows the average convergence of meridians for a given map sheet.

Magnetic declination(d) - the angle between the true and magnetic meridians is indicated on the diagram for the year the map was taken (updated). The text placed next to the diagram provides information about the direction and magnitude of the annual change in magnetic declination.

To avoid errors in determining the magnitude and sign of the direction correction, the following technique is recommended.

From the tops of the corners in the diagram (Fig. 10), draw an arbitrary direction OM and designate with arcs the directional angle ά and the magnetic azimuth Am of this direction. Then it will be immediately clear what the magnitude and sign of the direction correction are.

If, for example, ά = 97°12", then Am = 97°12" - (2°10"+10°15") = 84°47 " .

4. Preparation according to the data map for movement in azimuths

Movement in azimuths- This is the main way to navigate in areas poor in landmarks, especially at night and with limited visibility.

Its essence lies in maintaining on the ground the directions specified by magnetic azimuths and the distances determined on the map between the turning points of the intended route. Directions of movement are determined using a compass, distances are measured in steps or using a speedometer.

The initial data for movement along azimuths (magnetic azimuths and distances) are determined from the map, and the time of movement is determined according to the standard and drawn up in the form of a diagram (Fig. 11) or entered into a table (Table 1). Data in this form is given to commanders who do not have topographic maps. If the commander has his own working map, then he draws up the initial data for moving along azimuths directly on the working map.

Rice. 11. Scheme for movement in azimuth

The route of movement along azimuths is chosen taking into account the terrain's passability, its protective and camouflage properties, so that in a combat situation it provides a quick and covert exit to the specified point.

The route usually includes roads, clearings and other linear landmarks that make it easier to maintain the direction of movement. Turning points are chosen at landmarks that are easily recognizable on the ground (for example, tower-type buildings, road intersections, bridges, overpasses, geodetic points, etc.).

It has been experimentally established that the distances between landmarks at turning points of the route should not exceed 1 km when traveling on foot during the day, and 6–10 km when traveling by car.

For driving at night, landmarks are marked along the route more often.

To ensure a secret exit to a specified point, the route is marked along hollows, tracts of vegetation and other objects that provide camouflage of movement. Avoid traveling on high ridges and open areas.

The distances between landmarks chosen along the route at turning points are measured along straight lines using a measuring compass and a linear scale, or, perhaps more accurately, with a ruler with millimeter divisions. If the route is planned along a hilly (mountainous) area, then a correction for the relief is introduced into the distances measured on the map.

Table 1

5. Compliance with standards

No. norm.	Name of the standard	Conditions (procedure) for compliance with the standard	Category of trainees	Estimation by time
No. norm.	Name of the standard	Conditions (procedure) for compliance with the standard	Category of trainees	"excellent"	"choir."	"ud."
1	Determining direction (azimuth) on the ground	The direction azimuth (landmark) is given. Indicate the direction corresponding to a given azimuth on the ground, or determine the azimuth to a specified landmark. The time to fulfill the standard is counted from the statement of the task to the report on the direction (azimuth value). Compliance with the standard is assessed “unsatisfactory” if the error in determining the direction (azimuth) exceeds 3° (0-50).	Serviceman	40 s	45 s	55 s
5	Preparing data for azimuth movement	The M 1:50000 map shows two points at a distance of at least 4 km. Study the area on a map, outline a route, select at least three intermediate landmarks, determine directional angles and distances between them. Prepare a diagram (table) of data for movement along azimuths (translate directional angles into magnetic azimuths, and distances into pairs of steps). Errors that reduce the rating to “unsatisfactory”: the error in determining the directional angle exceeds 2°; the error in distance measurement exceeds 0.5 mm at the map scale; corrections for the convergence of meridians and the declination of the magnetic needle are not taken into account or incorrectly introduced. The time to fulfill the standard is counted from the moment the card is issued to the presentation of the diagram (table).	Officers	8 min	9 min	11 min

30.10.2021

Solitaire Mat

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