Scale 1 5000 corresponds to a large-scale map. Scales of topographic maps and plans. Solving scale problems

The frames of maps of derived scales are constructed by dividing the base sheet along the lines of parallels and meridians into several equal parts, i.e. The layout of sheets is always based on a geographic coordinate grid. We consider the following scales of maps and plans to be standard:
Layout scheme and nomenclature of topographic maps of derivative scales for the main coordinate system SK-42 in the Russian Federation:

Scale	Base sheet	divided into	Designation	Frame size
1: 1 000 000			N-37	4 x 6 degrees
1: 500 000	1: 1 000 000	4 sheets (A, B, C, D)	N-37-B	2 x 3 degrees
1: 200 000	1: 1 000 000	36 sheets (I-XXXVI)	N-37-XXIII	40" x 60"
1: 100 000	1: 1 000 000	144 sheets (1-144)	N-37-89	20" x 30"
1: 50 000	1: 100 000	4 sheets (A, B, C, D)	N-37-44-B	10" x 15"
1: 25 000	1: 100 000	16 sheets (a,b,c,d)	N-37-114-GB	5" x 7" 30"
1: 10 000	1: 100 000	64 sheets (1,2,3,4)	N-37-78-Bv-3	2" 30" x 3" 45"

Topographic maps for which the base layout is a scale of 1: 1,000,000 are considered to be medium-scale, and those for which the base is a scale of 1: 100,000 are considered large-scale. Sheets of topographic maps of large scales from 1: 50,000 and 1: 10,000 are formed by sequentially dividing the sheet of the previous scale into 4 parts with the corresponding additions of letters to the nomenclature.
Topographic maps at a scale of 1: 200,000 and smaller are open to us, for a scale of 1: 100,000 the order of use is defined - for official use, all larger scales of topographic maps are closed.

	This figure shows the division of a sheet of scale 1: 1,000,000 On 4 sheets of scale 1: 500,000 (A, B, C, D), For 36 sheets of scale 1:200,000 (indicated by Roman numerals), and For 144 sheets, scale 1:100,000 (indicated by Arabic numerals).
		This figure shows the division of a sheet of scale 1: 100,000: For 4 sheets of scale 1: 50,000 (A, B, C, D are added); Scale sheet division 1: 50,000 on 4 sheets scale 1: 25,000 (a, b, c, d are added); Scale sheet division 1: 25,000 on 4 sheets scale 1: 10,000 (add 1, 2, 3, 4); Three-digit numbers from 1 to 256 show division into sheets of scale 1: 5,000, but maps of this scale are very rare in practice.

The domestic nomenclature of topographic maps larger than 1: 100,000 in practice often causes errors and confusion (Vb - Bv, ...) and, according to the authors, is not very successful - it is very difficult to estimate from just the nomenclature number which sheet will be next. To make it easier to navigate, we provide a reference table for dividing into sheets of scale 1: 10,000.
Although the frames of all topographic maps have boundaries along a geographic grid, on the topographic map sheets themselves, starting from a scale of 1: 200,000 and for all maps larger, it is no longer geographical, but a rectangular, so-called kilometer grid with a step of 4000 m for a scale of 1: 200,000 and up to 1000 m for a scale of 1: 10,000, which is a display of the rectangular Gauss-Kruger coordinate system.
On the standard SK-42 topographic maps there is complete information about the coordinates of the sheet both in the geographic coordinate system and in the rectangular Gauss-Kruger coordinate system. The fragment of the topographic map below shows a corner with information about its coordinates and explains how to understand it correctly. This is a sheet of topographic map at a scale of 1: 200,000 with the nomenclature number N-38-XXII, made in the SK-42 coordinate system.

Topographic map angle 1: 200,000 and coordinate information:

at the very corner of the sheet, the geographical coordinates of this corner are written, 46° 00" east longitude and 54° 00" north latitude; At the top frame, the numbers 48, 52, 56, 60 are the coordinates of the kilometer grid, and together with the small number 85 next to 60 they show the exact value of the Y coordinate of this vertical line in rectangular system Gauss-Kruger coordinates equal to 8,560,000 m; that is, this map is from zone 8, and the coordinate of the line is 60 km east of the middle meridian of the zone; In the right frame, the numbers 76, 80, 84 are also kilometer grid coordinates, and together with the small number 59 next to 80 they show the exact X coordinate value of this horizontal line in the rectangular Gauss-Kruger coordinate system, equal to 5,980,000 m; is the distance to that line from the equator.

When practical problems of creating cartographic foundations for mapping regions are solved, it turns out that even in the Central European part of the Russian Federation, only rare regions lie entirely within the same Gauss-Kruger projection zone. To solve this problem, it is possible to expand the standard 6-degree zone, but with the caveat that area distortions will increase in the expansion zone. To ensure the possibility of combining adjacent map sheets from different zones, kilometer grid marks of the adjacent zone can be applied to the outer sheets, as shown in the figure. When using maps in GIS, this information seems to be of little use.

Transverse scale, unlike a linear scale, allows you to measure and transfer lines to a map or plan with greater accuracy.

Usually the transverse scale is drawn on a metal plate, but it can also be drawn on paper.

Start of construction transverse scale similar to constructing a linear scale.

The two outer perpendiculars are divided into 10 equal parts and lines parallel to the base of the scale are drawn through the resulting points.

The upper left base, as well as the lower left base, is divided into 10 equal parts.

The division points of the upper left base and the lower left base are connected by inclined lines as shown in the figure. These slanted lines are called transversals.

Near the transversals, mark divisions that are equal to a hundredth of the base of the scale (100 m / 100 = 1 m).

The picture shows transverse scale with a base of 2 cm corresponding to a numerical scale of 1:5000 (2 cm * 5000 = 10000 cm = 100 m).

Thus, the transverse scale allows you to measure and plot lines on a map or plan with an accuracy of one hundredth of the base of the scale (1 m for a numerical scale of 1:5000).

Transverse scale used as follows:

1). into the measuring compass solution, take a segment from a map or plan, the length of which must be determined;

2). apply a compass to transverse scale so that its right needle is on the zero or other perpendicular to the right of zero, and the left needle is on the same horizontal line with the right needle;

3). sum up the readings along the perpendiculars on the right and left needles of the compass to the right and left of the zero perpendicular.

In the figure, the lengths of the measured segments according to the 1:5000 scale plan are 252 meters and 477 meters.

Betuganov Astemir

Project Manager:

Shopagova Alla Sergeevna

Institution:

MCOU "Secondary School No. 27" Nalchik

In the presented research paper in mathematics on the topic "Scale and its application" I will try to find out at what scale it will be convenient to place objects on an A4 sheet. Working on a research project about scale will help me consolidate my knowledge in mathematics.

In my mathematics research project "Scale and Its Applications" I will need to clarify and compare the mathematical calculations with the data obtained.

During research work in mathematics about scale and its application, I hope that the scales that I set will allow me to place objects on album sheet A4.

Also, in the practical part of my work, I will consider and mathematically solve interesting problems involving distance and scale.

Introduction
Main part
1. Definition of scale.
2. Solving interesting problems at scale.
conclusions
Applications.

Introduction

In mathematics lessons in the 6th grade, we covered this interesting topic, from which we learned how, using a scale, you can find a distance on the ground, knowing the length of the segment on the map corresponding to this distance on the ground, and vice versa.

When drawing images of objects on paper, we are most often forced to change their actual sizes: large objects have to be depicted in a reduced form, and small ones have to be enlarged.

Sites earth's surface depicted on paper in a reduced form. An example of such an image is any map or plan. Small details are shown enlarged in the drawings.

But a drawing, map or plan should give an idea of ​​the actual dimensions of objects. Therefore, a special entry is made on drawings and maps showing the ratio of the length of the segment on the map or drawing to its real length.

The topic of my research project in mathematics is " Scale and its application».

Objective of the project: find out at what scale it will be convenient to place objects on an A4 sheet.

Project objectives:

1. consolidate school knowledge in mathematics;
2. clarify whether mathematical calculations are comparable with the data obtained.

Hypothesis: It is most effective to draw patterns at 1:10, apartment layout at 1:100; house passport 1:1000; city ​​map 1:10000; area map 1:100000.

Expected Result: The scales I have specified will allow me to place objects on a landscape sheet.

Equipment:
ruler, pencil, compass, calculator, map.
sheet A 4, ruler, pencil.

Definition of scale

Scale is a fraction where the numerator is one, and the denominator is a number that shows how many times the distance on the terrain plan is reduced than on the ground.

For example: 1:1000 (one thousandth) means that all distances on the ground are reduced by a thousand times. The larger the number in the denominator of the fraction, the greater the reduction and the greater the coverage of the area.

• numerical, expressed in numbers 1:1000;
• named, is expressed in words, that is, cm is converted to m: 1cm is 10m, 10m is the scale value;
• linear, knowing the scale, we can determine the distances.

Let's look at the map. The scale is indicated at the top (1: 500,000). They say that the map was made on a scale of one five hundred thousandth. This means that 1 cm on the map corresponds to 500,000 cm on the ground. This means that a 1 cm segment on the map corresponds to a 5 km segment on the ground.

And if I take a segment 3 cm long on the map, then on the ground it will be a segment 15 km long.

I downloaded a map of the Kabardino-Balkarian Republic from the Internet. Map of the republic with a scale of 1:10000, that is, 1 cm 100 meters, and the scale of the surrounding area is 1:100000 in 1 cm 1 kilometer. I immediately found my native village using it.

So, scale (German. Massstab, lit. " measuring stick»: Maß « measure», Stab « stick") - in general, the ratio of two linear dimensions.

In many areas of practical application scale is the ratio of the image size to the size of the depicted object .

The concept of scale is most common in geodesy, cartography and design - the ratio of the natural size of an object to the size of its image.

A person is not able to depict large objects, for example a house, in life-size, and therefore, when depicting a large object in a drawing, drawing, layout, etc., a person reduces the size of the object several times: two, five, ten, one hundred, a thousand and so on again. 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 its natural size and therefore increases the size of its image several times.

The number showing how many times the real phenomenon is increased or decreased when depicting it is defined as scale.

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.

conclusions

Compared my assumptions put forward in my hypothesis with inscriptions on patterns, maps and technical plans of the house and apartment. It turned out that in some places I was mistaken 10 and even 100 times.

• patterns are most effectively drawn at 1:10;
• apartment layout 1:100;
• house passport 1:1000;
• city ​​map 1:10000;
• area map 1:100000.

In fact, the apartment plan is usually taken at a scale of 1:200; the scale of the maps turned out to be exactly the same as in the original, but they are located on as many as 6 landscape sheets!

So once again, I am convinced that before making assumptions, you need to recalculate several times.

Thus, we formed the concept of scale, map, drawing, and practiced solving problems for calculating the length of a segment on the ground and on the map.

Solving scale problems

Task 1. The distance between the two cities is 400 km. Find the length of the segment connecting these cities on a map made at a scale of 1:5000000.

Solution:
400km = 400000m = 40000000cm
40000000: 5000000 = 40: 5 = 8 (cm)

Task 2. The distance from Moscow to St. Petersburg in a straight line is approximately 635 km from center to center. The length of the route along the highway is 700 km.
How many times must this distance be reduced so that it can be depicted on a slide as a segment 14 cm long?

Solution:
700km = 700000m = 70000000cm
70000000cm: 14cm = 5000000(times)

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 consider 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 its 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

Used in topographic maps ah, the scales are established by Order of the Ministry economic development RF “On approval of requirements for state topographic maps and state topographic plans, including requirements for the composition of information displayed on them, for symbols specified 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 of 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 area
	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. 1:200 000
2. 1:10 000 000
3. 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. 1 cm - 2 km
2. 1 cm - 100 km
3. 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:

1. in 1 cm - 500 m
2. 1 cm - 10 km
3. 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. 1:50 000;
2. 1:1 000 000;
3. 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. 1:1 000 000
2. 1:500 000
3. 1:200 000
4. 1:100 000
5. 1:50 000
6. 1:25 000
7. 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. 1:10,000 (1cm =100m)
2. 1:25,000 (1cm = 100m)
3. 1:50,000 (1cm = 500m)
4. 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 were marked, big cities and large lakes and rivers.

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 of the Russian Federation” (N 171-FZ dated June 23, 2014) came into force, according to which, in particular, the procedure for purchasing land plots has been simplified from municipalities.You can familiarize yourself with the main provisions of the law.
• With regard to the registration of houses, bathhouses, garages and other buildings on land plots owned by citizens, the new dacha amnesty will improve the situation.

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This publication takes into account proposals from organizations that carry out surveys and use topographic maps. Coordination has been carried out with Conventional signs for topographic plans of scales 1:5000-1:500. Designations for topographical objects shown in all cases and according to additional requirements of sectors of the national economy have been delineated

Settlements and individual buildings

Examples of images of settlements

Industrial, agricultural and socio-cultural facilities

Railways and structures attached to them

Highways and dirt roads

Examples of combinations of conventional road network signs

Hydrography

Hydraulic and water transport facilities

Water supply facilities

Bridges and crossings

Vegetation

Main agricultural land

Soils and microforms of the earth's surface

Swamps and salt marshes

Examples of combining images of vegetation and soil

Examples of combining images of agricultural land