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Scales of topographic maps and plans. Scale and its application Scale in modeling

Determine the map scale if the map area scale is 1:62500

In order to determine the scale of the map, we need to extract the root of the area scale: 79.056.

Therefore, the map scale is 1:79.

Calculate the azimuth if the north-west direction is 345?

The rhumb is the angle measured from the nearest end of the meridian to the line whose direction is being determined.

Let's draw through point A the meridian N - S and the line B - W (east - west). These mutually perpendicular lines with the designations of the cardinal points in Russian letters S, Yu, V, and Z (or in Latin on the plane are four quarters, numbered clockwise and names made up of the corresponding designations of the cardinal points. So the first quarter is called the northeastern ( NE), the second quarter - southeast (SE), the third quarter - southwest (SW), and the fourth - northwest (NW).

The rhumb of the line is 345?, the value of the rhumb indicates that the line is located in the fourth quarter; therefore, we report from the northern end of the meridian in a counterclockwise direction, since the direction is called NW, this line is located in the fourth quarter and the azimuth will be equal according to the formula:

r 4=360? - 345?= C Z:15?.

The azimuth is 15?.

Determine the distance on the ground, if on the map the scale is 1: 35000 they are as follows: 10 cm; 30 mm; 2 cm 45 mm

To construct a plan or map of the area, the calculated horizontal distances of the lines measured on the ground must be reduced. The degree of such reduction in line spacing is called scale. The scale is expressed by the ratio of the length S0 of a line segment on a plan (map) to the length S of the horizontal location of the corresponding line segment on the ground, i.e. S0:S.

For the sake of convenience of calculations, scales, i.e. ratios S0:S are represented by proper fractions with the numerator equal to one:

S0/S= 1/S:S0=1/M.

Such a scale (for example, 1/1000; 1/2000; 1/5000; 1/10000, etc.), where the numerator is expressed by one, is called a numerical scale.

The scales of plans or maps are used when solving the following problems:

1) Using the known length S of the laying of the terrain line, determine the length S0 of this laying on a plan having a numerical scale of 1/M;

2) Using the length S0 of a straight line segment on a 1/M scale plan, determine the distance S on the ground.

To solve our problem we need the formula: S=S0*M.

S= 10 cm * 35000= 350000 cm= 3500 m = 3 km 500 m.

S= 30mm * 35000= 1050000mm = 10500cm = 105 m.

S = 2cm 45mm = 2.45*35000 = 85750cm = 857m 50cm.

Generalization of maps

Generalization is a generalization of geoimages of small scales relative to larger ones, carried out in connection with the purpose, subject, study of the object or technical conditions for obtaining the geoimage itself. Cartographic generalization - selection, generalization, identification of the main typical features of an object, carried out in accordance with the qualifications and selection standards established by the cartographer or map editor, who, in addition, generalize the qualitative and quantitative indicators of the depicted objects, simplify the outlines, unite or exclude contours, sometimes important but very small objects are shown with some exaggeration. Remote generalization (remote sensing generalization, optical generalization) is a geometric and spectral generalization of the image in photographs, arising as a result of a complex of technologies. factors (method and height of survey, spectral range, scale, resolution) and natural features (nature of the area, atmospheric conditions, etc.). Automatic, or algorithmic generalization (automated generalization, algorithmic generalization) - formalized selection, smoothing (simplification) or filtering of an image in accordance with specified algorithms and formal criteria. Dynamic generalization is a mechanical generalization of animations that allows you to observe the main, most time-stable objects and phenomena by changing the speed of demonstration of animations.

Cartographic generalization is the selection and generalization of objects depicted on the map according to its purpose, scale, content and characteristics of the mapped territory.

The essence of the generalization process is to convey on the map the main, typical features of objects, their characteristic features and relationships.

Generalization is an integral property of all cartographic images, even the largest ones. When drawing maps of any scale, you constantly have to “compress” the image, giving up details and details.

Generalization is manifested in generalizing the qualitative and quantitative characteristics of objects, replacing individual concepts with collective ones, abstracting from particulars and details for the sake of a clear image of the main features of spatial arrangement.

All this allows us to assert that generalization is one of the manifestations of the process of abstraction of the reality displayed on the map.

The process of generalization itself is largely contradictory. Firstly, some elements cannot be shown on the map due to spatial conditions, but must be reflected on it due to their substantive significance. Secondly, a contradiction often arises between geometric accuracy and meaningful correspondence of the image, in other words, the spatial relationships of objects are conveyed correctly, but the geometric accuracy is violated. Thirdly, during generalization, not only the exclusion of image details and loss of information occurs, but also the appearance of new generalized information on the map. As abstraction progresses, particulars disappear and the most essential features of an object emerge more clearly, leading patterns and main relationships are revealed, and geosystems of increasingly larger rank are identified.

The generalization process is more difficult to formalize and automate than other cartographic processes. Not all stages and procedures can be algorithmized, and not all criteria can be formalized unambiguously.

The quality of generalization largely depends on the cartographer’s understanding of the substantive essence of the geographical objects and phenomena depicted and the ability to identify their main typical features.

Factors of generalization are the scale of the map, its purpose, subject matter, type, features and knowledge of the object being mapped, methods of graphic design of the map. Factors determine approaches to generalization, its conditions and nature.

Purpose of the card. The map shows only those objects that correspond to its purpose. The image of other objects that do not correspond to the purpose of the map only interferes with its perception and makes it difficult to work with the map.

The effect of scale is that when moving from a larger image to a smaller one, the area of the map decreases. Features that are important for large-scale maps lose their significance on small-scale maps and therefore must be excluded.

The topic and type of map determine which elements should be shown on the map in the greatest detail, and which can be more or less significantly generalized or even removed completely. Thus, on a soil map it is important to show the hydrological network in detail - it is directly related to the theme of the map. In this case, populated areas will be more subject to generalization.

Different types of cards have different generalizations. Analytical maps of the inventory type are the most detailed, and synthetic maps, especially inferential maps, are the most generalized and generalized.

The features of the object being mapped are reflected in the need to convey on the map the originality, remarkable characteristic elements of the objects or territory. For example, in steppe regions it is necessary to show all the small lakes, sometimes even with exaggeration if they do not “fit” to scale.

The degree of knowledge of objects influences generalization. Sufficiently studied objects are depicted on the map in as much detail as possible. If there is insufficient amount of factual material, the image becomes generalized and schematic. The knowledge factor is closely related to the quality and completeness of the sources used for mapping. Therefore, forecast maps compiled from incomplete data are the most generalized.

Complex abstraction processes associated with cartographic generalization are implemented in different types and forms. They relate to the generalization of spatial (geometric) and content characteristics, qualitative and quantitative indicators, selection and even exclusion of depicted objects. Usually all manifestations of generalization are present on the map together, in close combination.

Generalization of qualitative characteristics occurs due to the reduction of various objects, which is always associated with generalization and enlargement of classification characteristics, with the transition from simple concepts to complex ones.

Generalization of the qualitative characteristics of the phenomenon being mapped is, first of all, a generalization (generalization) of its classification. Therefore, this type of generalization begins with the map legend, with the transition from species to genera, from individual phenomena to their groups, from fractional taxonomic divisions to larger ones.

Generalization of quantitative characteristics is manifested in the enlargement of scales, the transition from continuous scales to more generalized step ones, from uniform to uneven. An example is the increase in the height of the relief section when generalizing a topographic map.

The type of generalization, the transition from simple concepts to complex ones, is associated with the introduction of integral concepts and collective designations. For example, when generalizing a geomorphological map, individual signs of karst forms are replaced by a general outline of the distribution of karst processes.

During generalization, objects that need to be shown on the map are always selected. Selection is always directly related to the generalization of qualitative and quantitative characteristics. It is conducted in accordance with the enlarged divisions of the legend. When selecting, two quantitative indicators are used: qualifications and standards.

The selection criterion is a restrictive parameter indicating the size or significance of objects preserved during generalization. For example, show all rivers longer than 1 cm on the map scale.

The selection rate is an indicator that determines the accepted degree of selection, the average per unit area value of objects preserved during generalization. Selection norms regulate the load of the card. This criterion is always differentiated according to the characteristics of the mapped territory. For example, when moving from a 1:200,000 scale map to 1:500,000 scale maps, the population load rate in densely populated areas is one third.

The geometric side of generalization is manifested in the smoothing of small meanders of rivers and coastlines, the elimination of bends in horizontal lines that draw small erosional incisions, etc. At the same time, however, it is necessary to ensure that the generalization of outlines is not mechanical and does not reduce to formal smoothing. The generalized image must certainly preserve a geographically plausible picture of the object. For example, meandering of rivers, types of erosion dissection. Another manifestation of the geometric side of generalization is the merging of contours. Small contours are combined into one large one. Thus, individual small areas of deposits of one mineral can be combined into one area.

From a geographical point of view, generalization is considered as the process of identifying geosystems of a larger rank on maps, their main components and interrelations. Among the variety of generalization conditions, the most significant are the following:

Scientifically based generalization of the legend;

Display of genetic and morphological characteristics of objects and phenomena;

Taking into account the internal and external relationships of the depicted objects, their hierarchical subordination;

Optimal selection of signs and visual aids.

The most important stage from which the process of generalization of any thematic map begins is the generalization of the legend. This means simplification of the legend, generalization of taxonomic categories, exclusion of certain groups of objects, reduction of quantitative divisions and scales.

Geographically correct selection and generalization of the cartographic drawing itself requires close attention to the transfer of the morphology and genesis of the depicted objects. For generalization, the entire arsenal of techniques is used. The main requirement for geographically reliable generalization is a scientifically based demonstration of the spatial structure and relationships of phenomena. It is necessary to preserve the morphological appearance, highlight and even emphasize the main elements, the characteristic relationships of objects, their subordination.

The basis of coordinated generalization is taking into account the geographical connections between the objects being mapped. When generalizing, the following types of connections must be taken into account:

between homogeneous objects (for example, a coordinated selection of rivers and lakes that are part of a single water system is necessary);

between objects of different nature or different cartographic layers (relief and hydrology);

between different maps (vegetation and landscapes).

Compliance with these requirements presupposes, first of all, the harmonization of qualifications and selection standards, the same detail of qualitative and quantitative characteristics, the unity of approaches to generalizing contours, and for different maps - also the mutual coordination (the same detail) of legends, which is especially important when generalizing a series of maps.

At the final stages of generalization, a thoughtful choice of design techniques is necessary. This makes it possible to emphasize different visual plans, combine individual layers of the image, and give expressiveness to especially significant objects.

Map scale is the ratio of the length of a segment on the map to its actual length on the ground.

Scale ( from German - measure and Stab - stick) is the ratio of the length of a segment on a map, plan, aerial or satellite image to its actual length on the ground.

Let's look at the types of scales.

Numerical scale

This is a scale expressed as a fraction, where the numerator is one and the denominator is a number indicating how many times the image is reduced.

Numerical scale is a scale expressed as a fraction in which:

the numerator is equal to one,
the denominator is equal to the number showing how many times the linear dimensions on the map are reduced.

Named (verbal) scale

This is a type of scale, a verbal indication of what distance on the ground corresponds to 1 cm on a map, plan, photograph.

A named scale is expressed by named numbers indicating the lengths of mutually corresponding segments on the map and in nature.

For example, there are 5 kilometers in 1 centimeter (5 kilometers in 1 cm).

Linear scale

This an auxiliary measuring ruler applied to maps to facilitate the measurement of distances.

Plan scale and map scale

The scale of the plan is the same at all points.

The map scale at each point has its own particular value, depending on the latitude and longitude of the given point. Therefore, its strict numerical characteristic is the numerical scale - the ratio of the length of an infinitesimal segment D on the map to the length of the corresponding infinitesimal segment on the surface of the ellipsoid of the globe.

However, for practical measurements on a map, its main scale is used.

Forms of expression of scale

The designation of scale on maps and plans has three forms - numerical, named and linear scales.

The numerical scale is expressed as a fraction in which:

numerator - unit,
denominator M - a number showing how many times the dimensions on the map or plan are reduced (1:M)

In Russia, standard numerical scales have been adopted for topographic maps

1:1 000 000
1:500 000
1:300 000
1:200 000
1:100 000
1:50 000
1:25 000
1:10 000
For special purposes, topographic maps are also created on scales 1:5 000 And 1:2 000

The main scales of topographic plans in Russia are

1:5000
1:2000
1:1000
1:500

In land management practice, land use plans are most often drawn up on a scale 1:10 000 And 1:25 000 , and sometimes - 1:50 000.

When comparing different numerical scales, the smaller one is the one with the larger denominator. M, and, conversely, the smaller the denominator M, the larger the scale of the plan or map.

Yes, scale 1:10000 larger than scale 1:100000 , and the scale 1:50000 smaller scale 1:10000 .

Note

The scales used in topographic maps are established by the Order of the Ministry of Economic Development of the Russian Federation “On approval of requirements for state topographic maps and state topographic plans, including requirements for the composition of information displayed on them, for the symbols of this information, requirements for the accuracy of state topographic maps and state topographic plans , to the format of their presentation in electronic form, requirements for the content of topographic maps, including relief maps" (No. 271 dated June 6, 2017, as amended on December 11, 2017).

Named scale

Since the lengths of lines on the ground are usually measured in meters, and on maps and plans in centimeters, it is convenient to express the scales in verbal form, for example:

There are 50 m in one centimeter. This corresponds to the numerical scale 1:5000. Since 1 meter is equal to 100 centimeters, the number of meters of terrain contained in 1 cm of a map or plan is easily determined by dividing the denominator of the numerical scale by 100.

Linear scale

It is a graph in the form of a straight line segment, divided into equal parts with signed values of the corresponding lengths of terrain lines. Linear scale allows you to measure or plot distances on maps and plans without calculations.

Scale accuracy

The maximum possibility of measuring and constructing segments on maps and plans is limited to 0.01 cm. The corresponding number of meters of terrain on the scale of a map or plan represents the maximum graphic accuracy of a given scale.

Since the accuracy of the scale expresses the length of the horizontal location of the terrain line in meters, to determine it, the denominator of the numerical scale should be divided by 10,000 (1 m contains 10,000 segments of 0.01 cm). So, for a scale map 1:25 000 scale accuracy is 2.5 m; for map 1:100 000 - 10 m, etc.

Scales of topographic maps

numerical scale cards	Name cards	1 cm on the map corresponds on the grounddistance	1 cm 2 on the map corresponds on the area's terrain
	five thousandth
1:10 000	ten-thousandth
1:25 000	twenty-five thousandth
1:50 000	fifty thousandth
1:1100 000	hundred thousandth
1:200 000	two hundred thousandth
1:500 000	five hundred thousandth, or half a millionth
1:1000000	millionth

Below are the numerical scales of the maps and the corresponding named scales:

Scale 1:100,000

1 mm on the map - 100 m (0.1 km) on the ground
1 cm on the map - 1000 m (1 km) on the ground
10 cm on the map - 10,000 m (10 km) on the ground

Scale 1:10000

1 mm on the map - 10 m (0.01 km) on the ground
1 cm on the map - 100 m (0.1 km) on the ground
10 cm on the map - 1000m (1 km) on the ground

Scale 1:5000

1 mm on the map - 5 m (0.005 km) on the ground
1 cm on the map - 50 m (0.05 km) on the ground
10 cm on the map - 500 m (0.5 km) on the ground

Scale 1:2000

1 mm on the map - 2 m (0.002 km) on the ground
1 cm on the map - 20 m (0.02 km) on the ground
10 cm on the map - 200 m (0.2 km) on the ground

Scale 1:1000

1 mm on the map - 100 cm (1 m) on the ground
1 cm on the map - 1000 cm (10 m) on the ground
10 cm on the map - 100 m on the ground

Scale 1:500

1 mm on the map - 50 cm (0.5 meters) on the ground
1 cm on the map - 5 m on the ground
10 cm on the map - 50 m on the ground

Scale 1:200

1 mm on the map - 0.2 m (20 cm) on the ground
1 cm on the map - 2 m (200 cm) on the ground
10 cm on the map - 20 m (0.2 km) on the ground

Scale 1:100

1 mm on the map - 0.1 m (10 cm) on the ground
1 cm on the map - 1 m (100 cm) on the ground
10 cm on the map - 10 m (0.01 km) on the ground

Example 1

Convert the numerical scale of the map to a named one:

1:200 000
1:10 000 000
1:25 000

Solution:

To more easily convert a numerical scale into a named one, you need to count how many zeros the number in the denominator ends with.

For example, on a scale of 1:500,000, there are five zeros in the denominator after the number 5. 

If after the number in the denominator there are five more zeros, then by covering (with a finger, a pen or simply crossing out) the five zeros, we get the number of kilometers on the ground corresponding to 1 centimeter on the map.

Example for scale 1:500,000

The denominator after the number has five zeros. Closing them, we get for a named scale: 1 cm on the map is 5 kilometers on the ground.

If there are less than five zeros after the number in the denominator, then by closing two zeros, we get the number of meters on the ground corresponding to 1 centimeter on the map.

If, for example, in the denominator of the scale 1:10 000 cover two zeros, we get:

in 1 cm - 100 m.

Answers :

1 cm - 2 km
1 cm - 100 km
in 1 cm - 250 m

Use a ruler and place it on the maps to make it easier to measure distances.

Example 2

Convert the named scale to a numerical one:

in 1 cm - 500 m
1 cm - 10 km
1 cm - 250 km

Solution:

To more easily convert a named scale to a numerical one, you need to convert the distance on the ground indicated in the named scale into centimeters.

If the distance on the ground is expressed in meters, then to obtain the denominator of the numerical scale, you need to assign two zeros, if in kilometers, then five zeros. 

For example, for a named scale of 1 cm - 100 m, the distance on the ground is expressed in meters, so for the numerical scale we assign two zeros and get: 1:10 000 .

For a scale of 1 cm - 5 km, we add five zeros to the five and get: 1:500 000 .

Answers :

1:50 000;
1:1 000 000;
1:25 000 000.

Types of maps depending on scale

Depending on the scale, maps are conventionally divided into the following types:

topographic plans - 1:400 - 1:5 000;
large-scale topographic maps - 1:10,000 - 1:100,000;
medium-scale topographic maps - from 1:200,000 - 1:1,000,000;
small-scale topographic maps - less than 1:1,000,000.

Topographic map

Topographical maps are those whose content allows them to solve various technical problems.

Maps are either the result of direct topographic survey of the area, or are compiled from existing cartographic materials.

The terrain on the map is depicted at a certain scale.

The smaller the denominator of a numerical scale, the larger the scale. Plans are drawn up on a large scale, and maps are drawn up on a small scale.

Maps take into account the “spherical shape” of the earth, but plans do not. Because of this, plans are not drawn up for areas larger than 400 km² (that is, areas of land approximately 20 km × 20 km).

Standard scales for topographic maps

The following scales of topographic maps are accepted in our country:

1:1 000 000
1:500 000
1:200 000
1:100 000
1:50 000
1:25 000
1:10 000.

This series of scales is called standard. Previously, this series included scales of 1:300,000, 1:5000 and 1:2000.

Large scale topographic maps

Scale maps:

1:10,000 (1cm =100m)
1:25,000 (1cm = 100m)
1:50,000 (1cm = 500m)
1:100,000 (1cm =1000m)

are called large-scale.

Other scales and maps

Topographic maps of the territory of Russia up to a scale of 1:50,000 inclusive are classified, topographic maps of a scale of 1:100,000 are chipboard (for official use), and smaller ones are unclassified.

Currently, there is a technique for creating topographic maps and plans of any scale that are not classified and intended for public use.

A tale about a map on a scale of 1:1

Once upon a time there lived a Capricious King. One day he traveled around his kingdom and saw how large and beautiful his land was. He saw winding rivers, huge lakes, high mountains and wonderful cities. He became proud of his possessions and wanted the whole world to know about them.

And so, the Capricious King ordered cartographers to create a map of the kingdom. The cartographers worked for a whole year and finally presented the King with a wonderful map, on which all the mountain ranges, large cities and large lakes and rivers were marked.

However, the Capricious King was not satisfied. He wanted to see on the map not only the outlines of mountain ranges, but also an image of each mountain peak. Not only large cities, but also small ones and villages. He wanted to see small rivers flowing into rivers.

The cartographers set to work again, worked for many years and drew another map, twice the size of the previous one. But now the King wanted the map to show passes between mountain peaks, small lakes in the forests, streams, and peasant houses on the outskirts of villages. Cartographers drew more and more maps.

The Capricious King died before the work was completed. The heirs, one after another, ascended the throne and died in turn, and the map was drawn up and drawn up. Each king hired new cartographers to map the kingdom, but each time he was dissatisfied with the fruits of his labor, finding the map insufficiently detailed.

Finally, the cartographers drew the Incredible Map! It depicted the entire kingdom in great detail - and was exactly the same size as the kingdom itself. Now no one could tell the difference between the map and the kingdom.

Where were the Capricious Kings going to keep their wonderful map? The casket is not enough for such a map. You will need a huge room like a hangar, and in it the map will lie in many layers. But is such a card necessary? After all, a life-size map can be successfully replaced by the terrain itself))))

It is useful to familiarize yourself with this

You can familiarize yourself with the units of measurement of land areas used in Russia.
For those who are interested in the possibility of increasing the area of land plots for individual housing construction, private household plots, gardening, vegetable farming, owned, it is useful to familiarize yourself with the procedure for registering additions.
From January 1, 2018, the exact boundaries of the plot must be recorded in the cadastral passport, since it will simply be impossible to buy, sell, mortgage or donate land without an accurate description of the boundaries. This is regulated by amendments to the Land Code. A total revision of borders at the initiative of municipalities began on June 1, 2015.
On March 1, 2015, the new Federal Law “On Amendments to the Land Code of the Russian Federation and certain legislative acts RF" (N 171-FZ dated June 23, 2014), according to which, in particular, the procedure for purchasing land plots from municipalities has been simplified.You can familiarize yourself with the main provisions of the law.
Regarding the registration of houses, bathhouses, garages and other buildings on land plots, owned by citizens, the new dacha amnesty will improve the situation.

INTRODUCTION

The topographic map is reduced a generalized image of the area showing elements using a system of symbols.
In accordance with the requirements, topographic maps are highly geometric accuracy and geographical relevance. This is ensured by them scale, geodetic basis, cartographic projections and a system of symbols.
The geometric properties of a cartographic image: the size and shape of areas occupied by geographical objects, the distances between individual points, the directions from one to another - are determined by its mathematical basis. Mathematical basis cards includes as components scale, geodetic basis, and map projection.
What a map scale is, what types of scales there are, how to construct a graphic scale and how to use scales will be discussed in the lecture.

6.1. TYPES OF SCALES OF TOPOGRAPHIC MAPS

When drawing up maps and plans, horizontal projections of segments are depicted on paper in a reduced form. The degree of such reduction is characterized by scale.

Map scale (plan) - the ratio of the length of a line on a map (plan) to the length of the horizontal location of the corresponding terrain line

m = l K : d M

The scale of the image of small areas throughout the topographic map is practically constant. At small angles of inclination of the physical surface (on a plain), the length of the horizontal projection of the line differs very little from the length of the inclined line. In these cases, the length scale can be considered the ratio of the length of a line on the map to the length of the corresponding line on the ground.

The scale is indicated on maps in different versions

6.1.1. Numerical scale

Numerical scale expressed as a fraction with numerator equal to 1(aliquot fraction).

Denominator M numerical scale shows the degree of reduction in the lengths of lines on a map (plan) in relation to the lengths of the corresponding lines on the ground. Comparing numerical scales with each other, the larger one is the one with the smaller denominator.
Using the numerical scale of the map (plan), you can determine the horizontal location dm lines on the ground

Example.
Map scale 1:50,000. Length of the segment on the map lК= 4.0 cm. Determine the horizontal location of the line on the ground.

Solution.
By multiplying the size of the segment on the map in centimeters by the denominator of the numerical scale, we obtain the horizontal distance in centimeters.
d= 4.0 cm × 50,000 = 200,000 cm, or 2,000 m, or 2 km.

Please note that the numerical scale is an abstract quantity that does not have specific units of measurement. If the numerator of a fraction is expressed in centimeters, then the denominator will have the same units of measurement, i.e. centimeters.

For example, a scale of 1:25,000 means that 1 centimeter of map corresponds to 25,000 centimeters of terrain, or 1 inch of map corresponds to 25,000 inches of terrain.

To meet the needs of the economy, science and defense of the country, maps of various scales are needed. For state topographic maps, forest management tablets, forestry and afforestation plans, standard scales have been determined - scale series(Table 6.1, 6.2).

Scale series of topographic maps

Table 6.1.

Numerical scale	Card name	1cm card corresponds on the ground distance	1 cm2 card corresponds on the area's terrain
	Five thousandth		0.25 hectare
	Ten-thousandth
	Twenty-five thousandth		6.25 hectares
	Fifty thousandth
	One hundred thousandth
	Two hundred thousandth
	Five hundred thousandth
	Millionth

Previously, this series included scales 1: 300,000 and 1: 2,000.

6.1.2. Named scale

Named scale called a verbal expression of a numerical scale. Under the numerical scale on the topographic map there is an inscription explaining how many meters or kilometers on the ground correspond to one centimeter of the map.

For example, on the map under a numerical scale of 1:50,000 it is written: “there are 500 meters in 1 centimeter.” The number 500 in this example is named scale value .
Using a named map scale, you can determine the horizontal distance dm lines on the ground. To do this, you need to multiply the value of the segment, measured on the map in centimeters, by the value of the named scale.

Example. The named scale of the map is “2 kilometers in 1 centimeter”. Length of a segment on the map lК= 6.3 cm. Determine the horizontal location of the line on the ground.
Solution. By multiplying the value of the segment measured on the map in centimeters by the value of the named scale, we obtain the horizontal distance in kilometers on the ground.
d= 6.3 cm × 2 = 12.6 km.

6.1.3. Graphic scales

To avoid mathematical calculations and speed up work on the map, use graphic scales . There are two such scales: linear And transverse .

Linear scale

To construct a linear scale, select an initial segment convenient for a given scale. This original segment ( A) are called basis of scale (Fig. 6.1).

Rice. 6.1. Linear scale. Measured segment on the ground
will CD = ED + CE = 1000 m + 200 m = 1200 m.

The base is laid on a straight line the required number of times, the leftmost base is divided into parts (segment b), which will smallest linear scale divisions . The distance on the ground that corresponds to the smallest division of the linear scale is called linear scale accuracy .

How to use a linear scale:

place the right leg of the compass on one of the divisions to the right of zero, and the left leg on the left base;
the length of the line consists of two counts: the count of whole bases and the count of divisions of the left base (Fig. 6.1).
If a segment on the map is longer than the constructed linear scale, then it is measured in parts.

Transverse scale

For more accurate measurements use transverse scale (Fig. 6.2, b).

Figure 6.2. Transverse scale. Measured distance
PK = TK + PS + ST = 1 00 +10 + 7 = 117 m.

To construct it, several scale bases are laid out on a straight line segment ( a). Usually the length of the base is 2 cm or 1 cm. At the resulting points, perpendiculars to the line are installed AB and draw ten parallel lines through them at equal intervals. The leftmost base above and below is divided into 10 equal segments and connected by oblique lines. The zero point of the lower base is connected to the first point WITH top base and so on. Get a series of parallel inclined lines, which are called transversals.
The smallest division of the transverse scale is equal to the segment C 1 D 1 , (Fig. 6. 2, A). The adjacent parallel segment differs by this length when moving up the transversal 0С and along a vertical line 0D.
A transverse scale with a base of 2 cm is called normal . If the base of the transverse scale is divided into ten parts, then it is called hundredths . On the hundredth scale, the price of the smallest division is equal to one hundredth of the base.
The transverse scale is engraved on metal rulers, which are called scale rulers.

How to use a transverse scale:

use a measuring compass to record the length of the line on the map;
place the right leg of the compass on a whole division of the base, and the left leg on any transversal, while both legs of the compass should be located on a line parallel to the line AB;
the length of the line consists of three counts: the count of integer bases, plus the count of divisions of the left base, plus the count of divisions up the transversal.

The accuracy of measuring the length of a line using a transverse scale is estimated at half the value of its smallest division.

6.2. VARIETIES OF GRAPHIC SCALES

6.2.1. Transitional scale

Sometimes in practice you have to use a map or aerial photograph, the scale of which is not standard. For example, 1:17,500, i.e. 1 cm on the map corresponds to 175 m on the ground. If you build a linear scale with a base of 2 cm, then the smallest division of the linear scale will be 35 m. Digitization of such a scale causes difficulties in practical work.
To simplify the determination of distances on a topographic map, proceed as follows. The base of the linear scale is not taken as 2 cm, but is calculated so that it corresponds to a round number of meters - 100, 200, etc.

Example. It is required to calculate the length of the base corresponding to 400 m for a map of scale 1:17,500 (175 meters in one centimeter).
To determine what dimensions a 400 m long segment will have on a 1:17,500 scale map, we draw up the proportions:
on the ground on the plan
175 m 1 cm
400 m X cm
X cm = 400 m × 1 cm / 175 m = 2.29 cm.

Having solved the proportion, we conclude: the base of the transition scale in centimeters is equal to the value of the segment on the ground in meters divided by the value of the named scale in meters. The length of the base in our case
A= 400 / 175 = 2.29 cm.

If we now construct a transverse scale with the length of the base A= 2.29 cm, then one division of the left base will correspond to 40 m (Fig. 6.3).

Rice. 6.3. Transitional linear scale.
Measured distance AC = BC + AB = 800 +160 = 960 m.

For more accurate measurements, a transverse transitional scale is constructed on maps and plans.

6.2.2. Steps scale

This scale is used to determine distances measured in steps during visual surveying. The principle of constructing and using the step scale is similar to the transition scale. The base of the step scale is calculated so that it corresponds to the round number of steps (pairs, triplets) - 10, 50, 100, 500.
To calculate the base value of the step scale, it is necessary to determine the shooting scale and calculate the average step length Shsr.
The average step length (pairs of steps) is calculated from the known distance traveled in the forward and reverse directions. By dividing the known distance by the number of steps taken, the average length of one step is obtained. When the earth's surface is tilted, the number of steps taken in the forward and reverse directions will be different. When moving in the direction of increasing relief, the step will be shorter, and in the opposite direction - longer.

Example. A known distance of 100 m is measured in steps. 137 steps were taken in the forward direction, and 139 steps in the reverse direction. Calculate the average length of one step.
Solution. Total distance covered: Σ m = 100 m + 100 m = 200 m. The sum of steps is: Σ w = 137 w + 139 w = 276 w. The average length of one step is:

Shsr= 200 / 276 = 0.72 m.

It is convenient to work with a linear scale, when the scale line is marked every 1 - 3 cm, and the divisions are signed with a round number (10, 20, 50, 100). Obviously, the value of one step of 0.72 m on any scale will have extremely small values. For a scale of 1:2,000, the segment on the plan will be 0.72 / 2,000 = 0.00036 m or 0.036 cm. Ten steps, on the appropriate scale, will be expressed as a segment of 0.36 cm. The most convenient basis for these conditions, in the opinion of author, the value will be 50 steps: 0.036 × 50 = 1.8 cm.
For those who count steps in pairs, a convenient base would be 20 pairs of steps (40 steps) 0.036 × 40 = 1.44 cm.
The length of the base of the step scale can also be calculated from proportions or by the formula
A = (Shsr × KS) / M
Where: Shsr - average value of one step in centimeters,
KS - number of steps at the base of the scale ,
M - scale denominator.

The length of the base for 50 steps on a scale of 1:2000 with the length of one step equal to 72 cm will be:
A= 72 × 50 / 2000 = 1.8 cm.
To construct a step scale for the example above, you need to divide the horizontal line into segments equal to 1.8 cm, and divide the left base into 5 or 10 equal parts.

Rice. 6.4. Step scale.
Measured distance AC = BC + AB = 100 + 20 = 120 sh.

6.3. SCALE ACCURACY

Scale accuracy (maximum scale accuracy) is a horizontal line segment corresponding to 0.1 mm on the plan. The value of 0.1 mm for determining scale accuracy is adopted due to the fact that this is the minimum segment that a person can distinguish with the naked eye.
For example, for a scale of 1:10,000 the scale accuracy will be 1 m. On this scale, 1 cm on the plan corresponds to 10,000 cm (100 m) on the ground, 1 mm - 1,000 cm (10 m), 0.1 mm - 100 cm (1 m). From the above example it follows that If the denominator of the numerical scale is divided by 10,000, we obtain the maximum accuracy of the scale in meters.
For example, for a numerical scale of 1:5,000, the maximum scale accuracy will be 5,000 / 10,000 = 0.5 m.

Scale accuracy allows you to solve two important problems:

determining the minimum sizes of objects and terrain that are depicted on a given scale, and the sizes of objects that cannot be depicted on a given scale;
establishing the scale at which the map should be created so that objects and terrain features with predetermined minimum dimensions are depicted on it.

In practice, it is accepted that the length of a segment on a plan or map can be estimated with an accuracy of 0.2 mm. The horizontal distance on the ground, corresponding at a given scale to 0.2 mm (0.02 cm) on the plan, is called graphic scale accuracy . Graphic accuracy in determining distances on a plan or map can only be achieved when using a transverse scale.
It should be borne in mind that when measuring the relative position of contours on a map, the accuracy is determined not by the graphical accuracy, but by the accuracy of the map itself, where errors can average 0.5 mm due to the influence of errors other than graphic ones.
If we take into account the error of the map itself and the measurement error on the map, we can conclude that the graphical accuracy of determining distances on the map is 5 - 7 times worse than the maximum scale accuracy, i.e. it is 0.5 - 0.7 mm on the map scale.

6.4. DETERMINING AN UNKNOWN MAP SCALE

In cases where for some reason there is no scale on the map (for example, it was cut off when gluing), it can be determined in one of the following ways.

By grid . It is necessary to measure the distance on the map between the grid lines and determine how many kilometers these lines are drawn through; This will determine the scale of the map.

For example, the coordinate lines are designated by the numbers 28, 30, 32, etc. (along the western frame) and 06, 08, 10 (along the southern frame). It is clear that the lines are drawn through 2 km. The distance on the map between adjacent lines is 2 cm. It follows that 2 cm on the map corresponds to 2 km on the ground, and 1 cm on the map corresponds to 1 km on the ground (named scale). This means that the scale of the map will be 1:100,000 (1 centimeter equals 1 kilometer).

According to the nomenclature of the map sheet. The notation system (nomenclature) of map sheets for each scale is quite definite, therefore, knowing the notation system, it is not difficult to find out the scale of the map.

A map sheet at a scale of 1:1,000,000 (millionths) is designated by one of the letters of the Latin alphabet and one of the numbers from 1 to 60. The designation system for maps of larger scales is based on the nomenclature of sheets of a millionth map and can be represented by the following diagram:

1:1 000 000 - N-37
1:500,000 - N-37-B
1:200,000 - N-37-X
1:100,000 - N-37-117
1:50 000 - N-37-117-A
1:25 000 - N-37-117-A-g

Depending on the location of the map sheet, the letters and numbers that make up its nomenclature will be different, but the order and number of letters and numbers in the nomenclature of a map sheet of a given scale will always be the same.
Thus, if the map has the nomenclature M-35-96, then, by comparing it with the diagram shown, we can immediately say that the scale of this map will be 1:100,000.
For more information on card nomenclature, see Chapter 8.

By distances between local objects. If there are two objects on the map, the distance between which on the ground is known or can be measured, then to determine the scale you need to divide the number of meters between these objects on the ground by the number of centimeters between the images of these objects on the map. As a result, we get the number of meters in 1 cm of this map (named scale).

For example, it is known that the distance from the settlement. Kuvechino to the lake Glubokoe 5 km. Having measured this distance on the map, we got 4.8 cm. Then
5000 m / 4.8 cm = 1042 m in one centimeter.
Maps at a scale of 1:104,200 are not published, so we round up. After rounding, we will have: 1 cm of the map corresponds to 1,000 m of terrain, i.e., the map scale is 1:100,000.
If there is a road with kilometer posts on the map, then it is most convenient to determine the scale by the distance between them.

According to the dimensions of the arc length of one minute of the meridian . The frames of topographic maps along meridians and parallels are divided in minutes of arc of the meridian and parallel.

One minute of meridian arc (along the eastern or western frame) corresponds to a distance of 1852 m (nautical mile) on the ground. Knowing this, you can determine the scale of the map in the same way as by the known distance between two terrain objects.
For example, the minute segment along the meridian on the map is 1.8 cm. Therefore, in 1 cm on the map there will be 1852: 1.8 = 1,030 m. By rounding, we get the map scale of 1:100,000.
Our calculations obtained approximate scale values. This happened due to the proximity of the distances taken and the inaccuracy of their measurement on the map.

6.5. TECHNIQUES FOR MEASURING AND POSTPUTING DISTANCES ON A MAP

To measure distances on a map, use a millimeter or scale ruler, a compass-meter, and to measure curved lines, a curvimeter.

6.5.1. Measuring distances with a millimeter ruler

Using a millimeter ruler, measure the distance between given points on the map with an accuracy of 0.1 cm. Multiply the resulting number of centimeters by the value of the named scale. For flat terrain, the result will correspond to the distance on the ground in meters or kilometers.
Example. On a map of scale 1: 50,000 (in 1 cm - 500 m) the distance between two points is 3.4 cm. Determine the distance between these points.
Solution. Named scale: 1 cm 500 m. The distance on the ground between points will be 3.4 × 500 = 1700 m.
At angles of inclination of the earth's surface of more than 10º, it is necessary to introduce an appropriate correction (see below).

6.5.2. Measuring distances with a measuring compass

When measuring a distance in a straight line, the needles of the compass are placed 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.

Rice. 6.5. Measuring distances with a measuring compass on a linear scale.

To get the length broken line sequentially measure the length of each of its links, and then sum up their values. Such lines are also measured by increasing the compass solution.
Example. To measure the length of a broken line ABCD(Fig. 6.6, A), the legs of the compass are first placed at the points A And IN. Then, rotating the compass around the point IN. move the hind leg from the point A to the point IN", lying on the continuation of the straight line Sun.
Front leg from point IN transferred to point WITH. The result is a compass solution B"C=AB+Sun. By similarly moving the back leg of the compass from the point IN" to the point WITH", and the front one WITH V D. get a compass solution
C"D = B"C + CD, the length of which is determined using a transverse or linear scale.

Rice. 6.6. Line length measurement: a - broken line ABCD; b - curve A 1 B 1 C 1;
B"C" - auxiliary points

Long curved segments measured along chords by steps of a compass (see Fig. 6.6, b). The pitch of the compass, equal to an integer number of hundreds or tens of meters, is set using a transverse or linear scale. When rearranging the legs of the compass along the measured line in the directions shown in Fig. 6.6, b use arrows to count steps. The total length of the line A 1 C 1 is the sum of the segment A 1 B 1, equal to the step size multiplied by the number of steps, and the remainder B 1 C 1 measured on a transverse or linear scale.

6.5.3. Measuring distances with a curvimeter

Curve segments are measured with a mechanical (Fig. 6.7) or electronic (Fig. 6.8) curvimeter.

Rice. 6.7. Mechanical curvimeter

First, by rotating the wheel by hand, set the arrow to the zero division, then roll the wheel along the measured line. The reading on the dial opposite the end of the hand (in centimeters) is multiplied by the map scale and the distance on the ground is obtained. A digital curvimeter (Fig. 6.7.) is a high-precision, easy-to-use device. The curvimeter includes architectural and engineering functions and has an easy-to-read display. This device can process metric and Anglo-American (feet, inches, etc.) 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.

Rice. 6.8. Curvimeter digital (electronic)

To increase the accuracy and reliability of the results, it is recommended to carry out all measurements twice - in the forward and reverse directions. In case of minor differences in the measured data, the arithmetic mean of the measured values is taken as the final result.
The accuracy of measuring distances using these methods using a linear scale is 0.5 - 1.0 mm on the map scale. The same, but using a transverse scale is 0.2 - 0.3 mm per 10 cm of line length.

6.5.4. Conversion of horizontal distance to slant range
It should be remembered that as a result of measuring distances on maps, the lengths of horizontal projections of lines (d) are obtained, and not the lengths of lines on the earth's surface (S) (Fig. 6.9).

Rice. 6.9. Slant range ( S) and horizontal distance ( d)

The actual distance on an inclined surface can be calculated using the formula:

where d is the length of the horizontal projection of line S;
v is the angle of inclination of the earth's surface.

The length of a line on a topographic surface can be determined using a table (Table 6.3) of the relative values of corrections to the length of the horizontal distance (in %).

Table 6.3

Tilt angle

Rules for using the table

1. The first line of the table (0 tens) shows the relative values of corrections at tilt angles from 0° to 9°, the second - from 10° to 19°, the third - from 20° to 29°, the fourth - from 30° up to 39°.
2. To determine the absolute value of the correction, it is necessary:
a) in the table based on the angle of inclination, find the relative value of the correction (if the angle of inclination of the topographic surface is not given by an integer number of degrees, then the relative value of the correction must be found by interpolating between the table values);
b) calculate the absolute value of the correction to the length of the horizontal distance (i.e., multiply this length by the relative value of the correction and divide the resulting product by 100).
3. To determine the length of a line on a topographic surface, the calculated absolute value of the correction must be added to the length of the horizontal alignment.

Example. The topographic map shows the horizontal length to be 1735 m, and the angle of inclination of the topographic surface to be 7°15′. In the table, the relative values of the corrections are given for whole degrees. Therefore, for 7°15" it is necessary to determine the nearest larger and nearest smaller values that are multiples of one degree - 8º and 7º:
for 8° the relative value of the correction is 0.98%;
for 7° 0.75%;
difference in table values of 1º (60′) 0.23%;
the difference between a given angle of inclination of the earth's surface 7°15" and the nearest smaller tabulated value of 7º is 15".
We make up the proportions and find the relative value of the correction for 15":

For 60′ the correction is 0.23%;
For 15′ the correction is x%
x% = = 0.0575 ≈ 0.06%

Relative correction value for inclination angle 7°15"
0,75%+0,06% = 0,81%
Then you need to determine the absolute value of the correction:
= 14.05 m approximately 14 m.
The length of the inclined line on the topographic surface will be:
1735 m + 14 m = 1749 m.

At small angles of inclination (less than 4° - 5°), the difference in the length of the inclined line and its horizontal projection is very small and may not be taken into account.

6.6. MEASUREMENT OF AREA BY MAPS

Determining the areas of plots using topographic maps is based on the geometric relationship between the area of a figure and its linear elements. The scale of the areas is equal to the square of the linear scale.
If the sides of a rectangle on a map are reduced by n times, then the area of this figure will decrease by n 2 times.
For a map of scale 1:10,000 (1 cm 100 m), the scale of the areas will be equal to (1: 10,000) 2 or 1 cm 2 will be 100 m × 100 m = 10,000 m 2 or 1 hectare, and on a map of scale 1 : 1,000,000 per 1 cm 2 - 100 km 2.

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

6.6.1. Measuring the area of a plot with straight boundaries

When measuring the area of a plot with straight boundaries, the plot is divided into simple geometric shapes, the area of each of them is measured geometrically and, by summing the areas of individual plots calculated taking into account the map scale, the total area of the object is obtained.

6.6.2. Measuring the area of a plot with a curved contour

An object with a curved contour is divided into geometric shapes, having previously straightened the boundaries in such a way that the sum of the cut off sections and the sum of the excesses mutually compensate each other (Fig. 6.10). The measurement results will be, to some extent, approximate.

Rice. 6.10. Straightening the curved boundaries of the site and
breaking down its area into simple geometric shapes

6.6.3. Measuring the area of a site with a complex configuration

Measuring plot areas, having a complex irregular configuration, are often performed using palettes and planimeters, which gives the most accurate results. Grid palette It is a transparent plate with a grid of squares (Fig. 6.11).

Rice. 6.11. Square mesh palette

The palette is placed on the contour being measured and the number of cells and their parts inside the contour is counted. The proportions of incomplete squares are estimated by eye, therefore, to increase the accuracy of measurements, palettes with small squares (with a side of 2 - 5 mm) are used. Before working on this map, determine the area of one cell.
The area of the plot is calculated using the formula:

P = a 2 n,

Where: A - side of the square, expressed in map scale;
n- the number of squares falling within the contour of the measured area

To increase accuracy, the area is determined several times with arbitrary rearrangement of the palette used to any position, including rotation relative to its original position. The arithmetic mean of the measurement results is taken as the final area value.

In addition to mesh palettes, dot and parallel palettes are used, which are transparent plates with engraved dots or lines. The points are placed in one of the corners of the cells of the grid palette with a known division value, then the grid lines are removed (Fig. 6.12).

Rice. 6.12. Spot palette

The weight of each point is equal to the cost of dividing the palette. The area of the measured area is determined by counting the number of points inside the contour and multiplying this number by the weight of the point.
Equally spaced parallel lines are engraved on the parallel palette (Fig. 6.13). The area being measured, when the palette is applied to it, will be divided into a number of trapezoids with the same height h. The parallel line segments inside the contour (midway between the lines) are the midlines of the trapezoid. To determine the area of a plot using this palette, it is necessary to multiply the sum of all measured center lines by the distance between the parallel lines of the palette h(taking into account scale).

P = h∑l

Figure 6.13. A palette consisting of a system
parallel lines

Measurement areas of significant plots is carried out using cards using planimeter.

Rice. 6.14. Polar planimeter

A planimeter is used to determine areas mechanically. The polar planimeter is widely used (Fig. 6.14). It consists of two levers - pole and bypass. Determining the contour area with a planimeter comes down to the following steps. Having secured the pole and positioned the needle of the bypass lever at the starting point of the contour, a count is taken. Then the bypass pin is carefully guided along the contour to the starting point and a second reading is taken. The difference in readings will give the area of the contour in divisions of the planimeter. Knowing the absolute value of the planimeter division, the contour area is determined.
The development of technology contributes to the creation of new devices that increase labor productivity when calculating areas, in particular the use of modern devices, including electronic planimeters.

Rice. 6.15. Electronic planimeter

6.6.4. Calculating the area of a polygon from the coordinates of its vertices
(analytical method)

This method allows you to determine the area of a plot of any configuration, i.e. with any number of vertices whose coordinates (x,y) are known. In this case, the numbering of vertices should be done clockwise.
As can be seen from Fig. 6.16, the area S of the polygon 1-2-3-4 can be considered as the difference between the areas S" of the figure 1y-1-2-3-3y and S" of the figure 1y-1-4-3-3y
S = S" - S".

Rice. 6.16. To calculate the area of a polygon from coordinates.

In turn, each of the areas S" and S" is the sum of the areas of trapezoids, the parallel sides of which are the abscissas of the corresponding vertices of the polygon, and the heights are the differences in the ordinates of the same vertices, i.e.

S " = square 1у-1-2-2у + square 2у-2-3-3у,
S" = pl. 1у-1-4-4у + pl. 4у-4-3-3у
or: 2S " = (x 1 + x 2) (y 2 - y 1) + (x 2 + x 3 ) (y 3 - y 2)
2 S " = (x 1 + x 4) (y 4 - y 1) + (x 4 + x 3) (y 3 - y 4).

Thus,
2S = (x 1 + x 2) (y 2 - y 1) + (x 2 + x 3 ) (y 3 - y 2) - (x 1 + x 4) (y 4 - y 1) - (x 4 + x 3) (y 3 - y 4). Opening the brackets, we get
2S = x 1 y 2 - x 1 y 4 + x 2 y 3 - x 2 y 1 + x 3 y 4 - x 3 y 2 + x 4 y 1 - x 4 y 3

From here
2S = x 1 (y 2 - y 4) + x 2 (y 3 - y 1)+ x 3 (y 4 - y 2) + x 4 (y 1 - y 3) (6.1)
2S = y 1 (x 4 - x 2) + y 2 (x 1 - x 3)+ y 3 (x 2 - x 4)+ y 4 (x 3 - x 1) (6.2)

Let us represent expressions (6.1) and (6.2) in general view, denoting through i the serial number (i = 1, 2, ..., n) of the vertices of the polygon:
(6.3)
(6.4)
Therefore, the doubled area of a polygon is equal to either the sum of the products of each abscissa and the difference between the ordinates of the subsequent and previous vertices of the polygon, or the sum of the products of each ordinate and the difference between the abscissas of the previous and subsequent vertices of the polygon.
Intermediate control of calculations is the satisfaction of the conditions:

0 or = 0
Coordinate values and their differences are usually rounded to tenths of a meter, and products - to whole square meters.
Complex formulas for calculating the area of a plot can be easily solved using Microsoft XL spreadsheets. An example for a polygon (polygon) of 5 points is given in tables 6.4, 6.5.
In Table 6.4 we enter the initial data and formulas.

Table 6.4.

y i (x i-1 - x i+1)

Double area in m2

SUM(D2:D6)

Area in hectares

In Table 6.5 we see the results of the calculations.

Table 6.5.

				y i (x i-1 -x i+1)






	Double area in m2
	Area in hectares

6.7. EYE MEASUREMENTS ON THE MAP

In the practice of cartometric work, eye measurements are widely used, which give approximate results. However, the ability to visually determine distances, directions, areas, slope steepness and other characteristics of objects from a map helps to master the skills of correctly understanding a cartographic image. The accuracy of visual determinations increases with experience. Visual skills prevent gross miscalculations in measurements with instruments.
To determine the length of linear objects on a map, one should visually compare the size of these objects with segments of a kilometer grid or divisions of a linear scale.
To determine the areas of objects, squares of a kilometer grid are used as a kind of palette. Each grid square of maps of scales 1:10,000 - 1:50,000 on the ground corresponds to 1 km 2 (100 hectares), scale 1:100,000 - 4 km 2, 1:200,000 - 16 km 2.
The accuracy of quantitative determinations on the map, with the development of the eye, is 10-15% of the measured value.

Video

Scale problems

Tasks and questions for self-control

What elements does the mathematical basis of maps include?
Expand the concepts: “scale”, “horizontal distance”, “numerical scale”, “linear scale”, “scale accuracy”, “scale bases”.
What is a named map scale and how do I use it?
What is a transverse map scale, and what is its purpose?
What transverse map scale is considered normal?
What scales of topographic maps and forest management tablets are used in Ukraine?
What is a transition map scale?
How is the transition scale base calculated?

Scale(German) Massstab, lit. "measuring stick": Maß"measure", Stab"stick") - in the general case, the ratio of two linear dimensions. In many areas of practical application, scale is the ratio of the size of the image to the size of the depicted object.

The concept is most common in geodesy, cartography and design - the ratio of the size of the image of an object to its natural size. A person is not able to depict large objects, such as a house, in life-size, therefore, when depicting a large object in a drawing, drawing or model, the size of the object is reduced several times: two, five, ten, one hundred, a thousand, and so on. The number showing how many times the depicted object is reduced is the scale. Scale is also used when depicting the microworld. A person cannot depict a living cell, which he examines through a microscope, in natural size and therefore increases the size of its image several thousand times. The number showing how many times the real phenomenon is increased or decreased when depicting it is defined as scale.

Scale in geodesy, cartography and design

Scale shows how many times each line drawn on a map or drawing is smaller or larger than its actual dimensions. There are three types of scale: numerical, named, graphic.

Scales on maps and plans can be presented numerically or graphically.

Numerical scale written as a fraction, the numerator of which is one, and the denominator is the degree of reduction of the projection. For example, a scale of 1:5,000 shows that 1 cm on the plan corresponds to 5,000 cm (50 m) on the ground.

The larger scale is the one whose denominator is smaller. For example, a scale of 1:1,000 is larger than a scale of 1:25,000. In other words, with more on a large scale the object is depicted larger (larger), with more small scale- the same object is depicted smaller (smaller).

Named scale shows what distance on the ground corresponds to 1 cm on the plan. It is written, for example: “There are 100 kilometers in 1 centimeter”, or “1 cm = 100 km”.

Graphic scales are divided into linear and transverse.

Linear scale- this is a graphic scale in the form of a scale bar divided into equal parts.
Transverse scale is a graphic scale in the form of a nomogram, the construction of which is based on the proportionality of segments of parallel straight lines intersecting the sides of an angle. The transverse scale is used for more accurate measurements of the lengths of lines on plans. The transverse scale is used as follows: a length measurement is laid down on the bottom line of the transverse scale so that one end (the right one) is on the whole division OM, and the left one goes beyond 0. If the left leg falls between the tenth divisions of the left segment (from 0), then Raise both legs of the meter up until the left leg hits the intersection of any transvensal and any horizontal line. In this case, the right leg of the meter should be on the same horizontal line. The smallest DP = 0.2 mm, and the accuracy is 0.1.

Scale accuracy- this is a horizontal line segment corresponding to 0.1 mm on the plan. The value of 0.1 mm for determining scale accuracy is adopted due to the fact that this is the minimum segment that a person can distinguish with the naked eye. For example, for a scale of 1:10,000, the scale accuracy will be 1 m. On this scale, 1 cm on the plan corresponds to 10,000 cm (100 m) on the ground, 1 mm - 1,000 cm (10 m), 0.1 mm - 100 cm (1 m).

The scales of images in the drawings must be selected from the following range:

When designing master plans for large objects it is allowed to use a scale of 1:2,000; 1:5 000; 1:10,000; 1:20,000; 1:25,000; 1:50,000.
If necessary, it is allowed to use magnification scales (100n):1, where n is an integer.

Scale in photography

Main article: Linear increase

When taking photographs, scale is understood as the ratio of the linear size of the image obtained on photographic film or a light-sensitive matrix to the linear size of the projection of the corresponding part of the scene onto a plane perpendicular to the direction of the camera.

Some photographers measure scale as the ratio of the size of an object to the size of its image on paper, screen, or other media. The correct technique for determining scale depends on the context in which the image is being used.

Scale is important when calculating depth of field. Photographers have access to a very wide range of scales - from almost infinitely small (for example, when photographing celestial bodies) to very large (without the use of special optics it is possible to obtain scales of the order of 10:1).

Macro photography traditionally refers to shooting at a scale of 1:1 or larger. However, with the widespread use of compact digital cameras, this term also began to refer to shooting small objects located close to the lens (usually closer than 50 cm). This is due to the necessary change in the operating mode of the autofocus system in such conditions, however, from the point of view of the classical definition of macro photography, such an interpretation is incorrect.

Scale in modeling

Main article: Scale (modeling)

For each type of large-scale (bench) modeling, scale series are defined, consisting of several scales of varying degrees of reduction, and for different types Modeling (aircraft modeling, ship modeling, railway, automobile, military equipment) has its own historically established scale series, which usually do not intersect.

Scale in modeling is calculated using the formula:

Where: L - original parameter, M - required scale, X - desired value

For example:

At a scale of 1/72, and the original parameter is 7500 mm, the solution will look like;

7500 mm / 72 = 104.1 mm.

The resulting value of 104.1 mm is the desired value at a scale of 1/72.

Time scale

In programming

In time-sharing operating systems, it is extremely important to provide individual tasks with the so-called “real-time mode”, in which the processing of external events is ensured without additional delays and omissions. For this purpose, the term “real time scale” is also used, but this is a terminological convention that has nothing to do with the original meaning of the word “scale”.

In film technology

Main article: Time-lapse photography#Time scale Main article: Slow Motion#Time Zoom

Time scale is a quantitative measure of slowing down or accelerating movement, equal to the ratio of the projection frame rate to the shooting frame rate. So, if the projection frame rate is 24 frames per second, and the film was shot at 72 frames per second, the time scale is 1:3. A 2:1 time scale means the process on the screen is twice as fast as normal.

In mathematics

Scale is the ratio of two linear dimensions. In many areas of practical application, scale is the ratio of the size of the image to the size of the depicted object. In mathematics, scale is defined as the ratio of a distance on a map to the corresponding distance on the real terrain. A scale of 1:100,000 means that 1 cm on the map corresponds to 100,000 cm = 1,000 m = 1 km on the ground.

/ WHAT IS SCALE

Scale. Types of scale

Geography. 7th grade

What is scale?

The scale shows how many times the distance on the map is less than the corresponding distance on the ground.

A scale of 1:10,000 (one ten-thousandth is read) shows that each centimeter on the map corresponds to 10,000 centimeters on the ground.

What does scale mean?

Types of scale

What types of scale are shown here? Which one is missing?

Record in 1 cm –

Since there are 100 centimeters in 1 meter, you need to remove two zeros

Since there are 1000 meters in 1 kilometer, you need to remove three more zeros (if possible)

Write the remaining number after the dash, indicate meters or kilometers

How to convert a numerical scale to a named scale


			1 cm – 5 m
			in 1 cm – 200 m
			1 cm – 30 km

Converting scale from numerical to named

Check the answers

h1 cm – 5 m

h1 cm – 15 m

h1 cm – 500 m

in 1 cm – 2 km

in 1 cm – 30 km

h1 cm – 600 km

in 1 cm – 15 km

Exercises. Convert scale from numeric to named

How to calculate 1:50 scale?

Scale is used to place on a drawing an area that is actually many times larger. At a scale of 1:50, all dimensions are taken 50 times smaller than in reality. For example, the drawing is drawn at a scale of 1:50. On it, a size of 50 meters is taken as 1 meter. If you want to depict a shop 5 meters long, then in the drawing its length will be 10 cm. Such a small scale is used in construction drawings to graphically depict a small area (landscape design). Conclusion: when making a drawing with a scale of 1:50, all original dimensions must be divided by 50.

Mirra-mi

A scale of 1 to 50 means that in the drawing all objects and lines are reduced 50 times than they actually are. That is, 1 cm in the drawing is 50 cm in reality. Therefore, when reading such a drawing, each centimeter must be multiplied by 50:

1 cm is 50 cm,

2 cm is 100 cm,

10 cm is 500 cm, etc.

A scale of 1:50 means that the object (drawing, map, graph, drawing, object, sketch, etc.) that we see is reduced fifty times compared to its original dimensions. Where the length is shown, for example, one centimeter in the original means fifty centimeters.

Zolotynka

To understand what 1:50 scale is, let's look at an example: Let's say we have a car model produced at 1:50 scale. This means that the real car is 50 times larger than our model.

The same applies to maps: when we depict a certain area to scale on a piece of paper or a computer screen, we reduce the distances by 50 times, but we make sure to preserve all the features of the area and all the proportions. The scale clearly demonstrates the relationship between distances on the map and distances on the ground. This makes the map useful for us, as we get visual information with which we can easily calculate ground distances.

Those. in order to create a model on a scale of 1 to 50 (anything - an object, a location), you need to divide the actual size by 50.

Azamatik

To do this, let's use an example.

A scale of 1 to 50 means, for example, that 50 kilometers is taken as 1 kilometer; 50 meters is taken as 1 meter; 50 centimeters is the same as 1 centimeter, etc.

Let's take a real football field, whose length is 100 meters and its width is 50 meters.

To depict this field on a sheet of paper on a scale of 1 to 50, we divide both the width and length by 50 (50 m).

Therefore, this football field on a scale of 1:50 will be 2 meters long and 1 meter wide.

Moreljuba

Scale is a very necessary and important thing. It is very important when creating terrain drawings and maps. If we are talking about a scale of 1:50, then this means that all real objects, when transferred to our drawing, must be reduced in size by 50 times. In other words, the sizes of objects must be divided by 50. For example, if you need to draw an object 100 centimeters long, we reduce it to 2 centimeters (100/50).

Quite simply, if this is some kind of drawing, this means that all the details, say, of a ship model, are reduced by 50 times and in order to represent the true size of the ship from which this drawing was made, you will need to enlarge the model by 50 times, that is, multiply the size 50 of all parts.

Raziyusha

If you need to make rooms or some object on a scale of 1:50, then you need to do it like this: divide each length by 50 cm, draw the result on paper. Let's say a wall 6 m long in the drawing will be 12 cm long. How is this calculated:

6 m = 600 cm,

600: 50 = 12 cm.

Pollock tail

It turns out that all objects in the picture are reduced by fifty times. In order to calculate the scale of an object, you need to measure the picture with a regular ruler after 1 cm, multiply by 50. Actually, this is the real scale of the object.

The question borders on fantasy. A scale of one to fifty is the ratio of one scale unit containing 50 real scale units. For example, 1 cm of the established scale contains 50 cm of the real one.

What is scale?

Daria Remizova

Scale
(German Maßstab, from Maß - measure, size and Stab - stick), the ratio of the lengths of segments in a drawing, plan, aerial photograph or map to the lengths of the corresponding segments in nature. The numerical scale defined in this way is an abstract number greater than 1 in cases of drawings of small parts of machines and instruments, as well as many micro-objects, and less than 1 in other cases when the denominator of the fraction (with a numerator equal to 1) shows the degree of reduction in the size of the image of objects relative to their real ones sizes. The scale of plans and topographic maps is a constant value; The scale of geographical maps is a variable value. For practice, a linear scale is important, that is, a straight line divided into equal segments with captions indicating the lengths of the corresponding segments in real life. For more accurate drawing and measurement of lines on the plans, a so-called transverse scale is built. A transverse scale is a linear scale, parallel to which a number of equally spaced horizontal lines are drawn, intersected by perpendiculars (verticals) and oblique lines (transversals). The principle of constructing and using a transverse scale. is clear from the figure given for a numerical scale of 1: 5000. The section of the transverse scale, marked in the figure with dots, corresponds on the ground to the line 200 + 60 + 6 = 266 m. A transverse scale is also called a metal ruler on which the image of such a drawing is carved with very thin lines , sometimes without any inscriptions. This makes it easy to use in the case of any numerical scale used in practice.
A scale of 1:200 means that 1 unit of measurement in a picture or drawing corresponds to 200 units of measurement in space. For example: a topographic map - atlas of the Tver region has a scale of 1:200000. This means that 1 centimeter on the map is equal to 2 kilometers on the ground.

Dmitry Mosendz

A scale of 1:200 means that 1 unit of measurement in a picture or drawing corresponds to 200 units of measurement in space. For example: a topographic map - atlas of the Tver region has a scale of 1:200000. This means that 1 centimeter on the map is equal to 2 kilometers on the ground.

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