Scales. Scales How to translate from one scale to another

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 an 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 full size, therefore, when depicting a large object in a drawing, drawing or layout, the size of the object is reduced several times: two, five, ten, one hundred, one thousand, and so on. The number showing how many times the depicted object is reduced is the scale. The scale is also used when depicting the microworld. A person cannot depict a living cell, which he examines through a microscope, in full size and therefore increases the size of its image by several thousand times. The number showing how many times the real phenomenon is enlarged or reduced when it is depicted is defined as a scale.

Scale in geodesy, cartography and engineering

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

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

Numerical scale is 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 1:5000 shows that 1 cm on the plan corresponds to 5000 cm (50 m) on the ground.

Larger is the scale with the smaller denominator. For example, a scale of 1: 1,000 is larger than a scale of 1: 25,000. In other words, with more large scale the object is depicted larger (bigger), 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 subdivided into linear and transverse.

  • Linear scale- this is a graphical scale in the form of a scale bar, divided into equal parts.
  • Cross scale- this is a graphical scale in the form of a nomogram, the construction of which is based on the proportionality of segments of parallel lines intersecting the sides of the angle. The transverse scale is used for more accurate measurements of the lengths of lines on the plans. The transverse scale is used as follows: they postpone the length measurement on the bottom line of the transverse scale so that one end (right) is at the whole division of 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 a transvensal and some horizontal line. In this case, the right leg of the meter should be on the same horizontal line. The smallest CD = 0.2 mm, and the accuracy is 0.1.

Scale Accuracy- this is a segment of the horizontal line, corresponding to 0.1 mm on the plan. The value of 0.1 mm for determining the accuracy of the scale 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. In 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 should be selected from the following range:

When designing master plans for large objects, it is allowed to use scales of 1:2,000; 1:5000; 1:10,000; 1:20,000; 1:25,000; 1:50,000.
In necessary cases, it is allowed to use magnification scales (100n):1, where n is an integer.

Scale in photography

Main article: Linear zoom

When photographing, scale is understood as the ratio of the linear size of the image obtained on a photographic film or photosensitive matrix to the linear size of the projection of the corresponding part of the scene onto a plane perpendicular to the direction to 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 scaling technique depends on the context in which the image is used.

Scale is important in calculating the depth of field. A very wide range of scales is available to photographers - from almost infinitely small (for example, when shooting 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 is traditionally understood as shooting at a scale of 1: 1 or larger. However, with the widespread use of compact digital cameras, this term has also been used to refer to shooting close to the lens (usually closer than 50 cm) small objects. This is due to the necessary change in the mode of operation 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 scale (bench) modeling, scale series are defined, consisting of several scales of varying degrees of reduction, and for different types of modeling (aircraft modeling, ship modeling, railway, automotive, military equipment) their own, historically established, scale series are defined, which usually do not intersect .

The scale in modeling is calculated by the formula:

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

For instance:

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

7500 mm / 72 = 104.1 mm.

The resulting value is 104.1 mm, there 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 gaps. The term “real time scale” is also used for this, however, this is a terminological convention that has nothing to do with the original meaning of the word “scale”.

In film technology

Main article: Fast motion filming#Time scale Main article: Time Lapse#Timescale

Time scale - a quantitative measure of slowing down or speeding up movement, equal to the ratio of the projected frame rate to the shooting one. So, if the projection frame rate is 24 frames per second, and the filming was done at 72 frames per second, the time scale is 1:3. The 2:1 time scale means twice the speed of the process on the screen compared to the usual one.

In mathematics

Scale is the ratio of two linear dimensions. In many areas of practical application, scale is the ratio of the size of an image to the size of the depicted object. In mathematics, the scale is defined as the ratio of the distance on the map to the corresponding distance in the real area. 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. Scale types

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 (read one ten-thousandth) shows that each centimeter on the map corresponds to 10,000 centimeters on the ground.



What does scale mean



Scale types

What kind of scale is shown here? Which one is missing?



Write 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 one

in 1 cm - 5 m

in 1 cm - 200 m

in 1 cm - 30 km




Scale conversion from numerical to named



Check answers

in 1 cm - 5 m

in 1 cm - 15 m

in 1 cm - 500 m

in 1 cm - 2 km

in 1 cm - 30 km

in 1 cm - 600 km

in 1 cm - 15 km



Exercises. Convert scale from numerical to named

How to calculate scale 1:50?

The scale is used to place in the 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 on a scale of 1:50. On it, the size of 50 meters is taken as 1 meter. If you want to depict a shop 5 meters long, then in the figure its length will be 10 cm. Such a small scale is used in construction drawings for a graphic representation of a small area (landscape design). Conclusion: when drawing with a scale of 1:50, all initial dimensions must be divided by 50.

Mirra mi

A scale of 1 to 50 means that in the drawing all objects, lines are reduced by 50 times what they actually are. That is, 1 cm in the drawing is 50 cm in reality. Therefore, while 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 the original size. Where the length is shown, for example, one centimeter in the original means fifty centimeters.

Zolotynka

To understand what a 1:50 scale is, consider an example: suppose we have a model car produced in 1:50 scale. This means that the real car is 50 times larger than our model.

The same applies to maps: when we draw a locality to scale on a piece of paper or a computer screen, we reduce the distances by 50 times, but be sure to preserve all the features of the terrain and all proportions. The scale clearly shows the relationship between distances on the map and distances on the ground. This makes the map convenient for us, as we get visual information that can be used to easily calculate ground distances.

Those. in order to create a model on a scale of 1 to 50 (anything - an object, terrain), you need to divide the real 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 as 1 centimeter and so on.

Let's take a real football field, which is 100 meters long and 50 meters wide.

To depict this field on a piece of paper on a scale of 1 to 50, we divide both the width and the 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 drawings of the area 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 dimensions of the objects should be divided by 50. For example, if we need to put an object 100 centimeters long on the drawing, we reduce it to 2 centimeters (100/50).

Quite simply, if this is some kind of drawing, then this means that all the details, say, a model of a ship, 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 increase the model by 50 times, that is, multiply the size all parts for 50.

Razyusha

If you need to make rooms, some kind of object on a scale of 1:50, then you need to do it this way: 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.

Pollack tail

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

The question is on the verge of fantasy. The 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 length of segments in a drawing, plan, aerial photograph or map to the lengths of their corresponding segments in kind. The numerical Scale defined in this way is an abstract number, greater than 1 in the cases of drawings of small parts of machines and devices, as well as many micro-objects, and less than 1 in other cases, when the denominator of the fraction (with the numerator equal to 1) shows the degree of reduction in the size of the image of objects relative to their actual 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 segments corresponding to them in kind. For more accurate drawing and measurement of lines on plans, a so-called transverse scale is built. The transverse scale is a linear scale parallel to which a series of equally spaced horizontal lines crossed by perpendiculars (verticals) and oblique lines (transverses) is drawn. The principle of construction and use of the transverse scale. is clear from the figure given for a numerical scale of 1: 5000. The segment of the transverse scale, marked in the figure with dots, corresponds on the ground to the line 200 + 60 + 6 = 266 m. A metal ruler is also called a transverse scale, on which an image of such a pattern is carved with very thin lines , sometimes without any inscriptions. This makes it easy to use it in the case of any numerical scale used in practice.
Scale 1:200 means that 1 unit of measurement in the figure 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

Scale 1:200 means that 1 unit of measurement in the figure 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.

On any geographical map, you can see approximately the following inscription: "Scale 1: 100,000." Traditionally, the first number is 1, and the second can vary. If there is no inscription, then there is certainly a tiny ruler, divided into equal segments, or a nomogram. These signs indicate the ratio of the size of an object on a map or plan to its actual size.

You will need

  • Roulette or compasses
  • Ruler

Instruction

1. If you have a plan on which different objects are fairly accurately plotted, and you need to find out at what scale this plan was made, start with measurements. Select an object, one that is nearby. Measure it on the plan and write down the results.

2. Measure the actual object. Use a tape measure for this. In order to avoid mistakes, make a peg and hook a tape measure loop on it. Drive a peg into the ground so that the zero mark of the tape measure is on the tier of the starting point of the length or width of the object.

3. Determine the scale. It is more convenient for everyone to write it down in numbers. Write down the size of the object on the plan, after that - the one that turned out when measured on the territory. Let's say you have a barn 5 meters long on the plan occupies 2.5 cm. Convert meters to centimeters. That is, it turns out that you have 500 cm in 2.5 cm. Calculate how many centimeters of territory are contained in 1 cm on the plan. To do this, divide the larger number by the smaller one. It turns out 2.5:500 = 1:200, that is, 1 cm on the plan corresponds to 2 m on the territory.

4. In order to determine the scale more correctly, take several measurements. Let's say measure the barn on the site and the distance from the gate to the pond. The plans are different, and the dimensions of one or another object can be applied unsatisfactorily correctly. If there are discrepancies, make another frosted. The image of the object, the one that does not correspond to the other two, correct on the plan.

Scale is a numerical designation of parameters related to real objects that are unthinkable to depict in natural size. The figure applies their layouts.

Instruction

1. The scale is written in several ways, say, numerically - 1: 1000000. The size ratio can also be indicated in this form: 1 cm 10 km is a named scale. The linear display method is shown by a ticked line.

2. When considering scale in relation to cartography, the appearance of a particular map will depend on the ratios used. The larger it is, the more detailed the area will be depicted. The detail is also influenced by the nature of the territory, which is sparsely inhabited, say, easier to depict. Maps are large, medium and small scale. Large-scale maps are when 1 cm is from 100 to 2000 meters, medium-scale maps are 1 cm to 10 km, small-scale maps are 1 cm more than 10 km.

3. Scale matters in photography as well. With the help of lenses, photographers change the size from hefty small to hefty large. The methodology of the metamorphosis of scale depends on the specifics of the surveys. If these are small objects, say, insects, the scale increases, if they are huge, it decreases.

4. The representation is also used in many sciences. In mathematics it is the ratio of numbers, in programming it is the scale of time, in astronomy it is the scale of the universe. The meaning of the word is also used in the construction industry.

5. Firms are distinguished by the scale of their activities. There are, say, territorial organizations, but there are also federal tiers. Different in scale and people. True, not from a physical point of view, there is a psychological representation of the “scale of the figure”. This refers to human qualities, goals and results of activities.

Related videos

Note!
The size of a reduced object is relative to its natural size. The distance between objects can be changed by several centimeters, meters, kilometers. The scale of reality changes a lot, but all parameters must remain proportional. If proportions are not observed, it will be unthinkable to analyze the distances and sizes of objects.

With the need to present the real dimensions of the object depicted in the drawing, a person is faced more closely at school. In a drawing lesson, it may be necessary to draw a detail on a scale of 1:2 or 1:4, in a geography lesson - to calculate the exact distance between two cities. In order to cope with the task, you need to know how the scale is translated.

You will need

  • - geographic map;
  • – detail drawing;
  • - calculator;
  • - drawing accessories.

Instruction

1. If you need to draw details on a 1:1 scale, this means that 1 cm of the surface will correspond to 1 cm in the drawing. Measure the surface you want to depict and draw it on paper at natural size.

2. Other scales are also used in drawing. 1:2 means that the detail in the drawing should be half as large as in reality. If the scale is 1; 4, this means that 1 cm in the drawing is equal to 4 cm of the part. It also happens the other way around. It is possible to draw a completely small object, say, on a scale of 4:1, 10:1, etc. If you see a similar designation in front of you, it means that in the picture the object is four or ten times larger than it actually is.

3. In geography, scale conversion is also required. Look at the geographic map. In one of the lower corners, you will see either a ruler with numbers, or primitive numbers - say, 1:50,000. The numbers, finally, are larger than in the drawing, but the rule for translating them is exactly the same, that is, in the above example, per 1 cm of the map 50,000 cm of the earth's surface is brought, that is, 500 m. This is a map of a relatively huge scale. Looking at the atlas of the world, you will see much more impressive figures.

4. Quite often it is necessary to scale not a linear measure, but a square one, that is, to determine how many square centimeters. To do this, measure the area you need by any comfortable method. Say, with palette support. In order to find out the real area of ​​the territory, you need to convert the linear scale into a square one, that is, build the number of centimeters contained in 1 cm of the map into a square. Multiply the resulting number by the area of ​​the plot shown on the map. This way you will find out how many square meters the territory that concerns you occupies.

5. Occasionally there is a need to translate the scale of a three-dimensional object. For example, at a labor lesson, a teacher can give the task to make a part depicted in a technical drawing on a certain scale. You need to find out how much material this will require. The translation thesis will be the same. First, find out how many real centimeters this or that line in the drawing corresponds to. Determine the volume of the part from the drawing. This is a simple mathematical problem, the method of solving it depends on the shape of a particular part. The number that indicates the scale, cube, and then multiply by the volume of the part, calculated according to the drawing.

Useful advice
You can try to draw a simple plan on your own, setting yourself a certain scale. Let's say a 1:10 scale for a room plan would absolutely fit. Measure the length of the walls and large objects, determine their relative position and draw a plan in strict accordance with the data received.

Note!
The scale is the larger, the smaller the denominator of the fraction with which it is written. 1:100 is larger than 1:2,000. It is more comfortable to measure an object with an assistant. If there is no assistant, and there was no peg at hand, firmly press the tape measure against the wall of the object. It is more comfortable to measure everyone on the ground - say, on the bottom of the wall.

how to scale? please help and got the best answer

Answer from Elena[guru]
The scale shows how many times the distances on the plan are reduced in relation to the real distances.
e.g. scale
1:1000
this means that in 1 cm on the map there are 1000 real cm, i.e. 10 meters
or
1: 500000
this means that in 1 cm on the map there are 500,000 real cm, i.e. 5000 m or 5 km
The basic principle is this: if the left side is in mm, then the right side means the number of real mm, then you translate them into cm, m, or km,
if the left part is in cm, then the right part shows the number of real cm, then you translate them into m or km
To get meters from cm, divide them by 100, the resulting meters are divided by 1000 - you get km

Answer from 2 answers[guru]

Hey! Here is a selection of topics with answers to your question: how to scale? please help

Answer from Angelina Khaprova[newbie]


Answer from Patra[guru]
M 1:1, that is, 1 mm corresponds to 1 mm drawn in the drawing. M 1:2, that is, 1 mm corresponds to 0.5 mm in the drawing (reduction by half, any size is ideally drawn twice as small in the drawing). M 2:1, that is, 1 mm corresponds to 2 mm in the drawing (an increase of two times in the drawing from the actual dimensions of the object).


Answer from Yaisiya Konovalova[guru]
1. If this is a numerical scale, then you translate centimeters into meters, and then meters into kilometers. Divide by 100 and then by 1000. 1:500,000. There are 5 km in 1 cm.
And if it's easier, then
If there are five zeros in the denominator after the first digit, then by closing 5 zeros with your finger, we get the number of kilometers on the ground corresponding to 1 centimeter on the map. Example for scale 1: 500,000. In the denominator after the number there are five zeros, closing them, we get for the named scale: 1 cm on the map is 5 kilometers on the ground.
If after the number in the denominator there are less than five zeros, 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 we close two zeros, we get: in 1 cm - 100 m.
To convert named to numeric:
if written in 1 cm 5 km - add 5 zeros - 1:500000

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 - 10000 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 - 1000cm (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 - 10m (0.01 km) on the ground

Convert the map's numerical scale to a named one:

Solution:

To make it easier to translate a numerical scale into a named one, you need to calculate 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 there are five or more zeros in the denominator after the number, then by closing (with a finger, a pen or simply crossing out) five zeros, we get the number of kilometers on the ground corresponding to 1 centimeter on the map.

Example for scale 1: 500,000

There are five zeros in the denominator after the number. Closing them, we get for the named scale: 1 cm on the map 5 kilometers on the ground.

If after the number in the denominator there are less than five zeros, 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 we close two zeros, we get:

in 1 cm - 100 m.

Answers:

    in 1 cm - 2 km;

    in 1 cm - 100 km;

    in 1 cm - 250 m.

Use a ruler, overlay on maps to make it easier to measure distances.

Convert a named scale to a numerical one:

    in 1 cm - 500 m

    in 1 cm - 10 km

    in 1 cm - 250 km

Solution:

For easier translation of a named scale into a numerical scale, you need to convert the distance on the ground indicated in the named scale to centimeters.

If the distance on the ground is expressed in meters, then to get 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 a numerical scale we assign two zeros and get: 1: 10,000.

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

Answers:

Maps, depending on the scale, 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.

Scale maps:

    1:10,000 (1cm=100m)

    1:25,000 (1cm=100m)

    1:50,000 (1cm=500m)

    1:100,000 (1cm=1000m)

called large scale.

Tale about the map in scale 1:1

Once upon a time there was a Capricious King. One day he traveled around his kingdom and saw how great 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 the cartographers to create a map of the kingdom. Cartographers worked for a whole year and finally presented the King with a wonderful map, on which all mountain ranges, large cities and large lakes and rivers were indicated.

However, the Capricious King was not satisfied. He wanted to see on the map not only the outlines of the mountain ranges, but also the 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 wished that the map showed passes between mountain peaks, small lakes in the forests, streams, peasant houses on the outskirts of villages. Cartographers drew more and more new maps.

The capricious King died without waiting for the end of the work. Successors one by one came to 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 remained dissatisfied with the fruits of labor, finding the map insufficiently detailed.

Finally the cartographers drew an Incredible map!!! The map 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 store their wonderful map? The casket for such a card is not enough. You will need a huge room like a hangar, and in it the map will lie in many layers. Do you really need such a card? After all, a life-size map can be successfully replaced by the terrain itself ..))))

The scale of the map, at a given point and in a given direction, is the ratio of the length of a line taken near this point in a given direction on the map to the corresponding length on a ball or ellipsoid.

The scale value remains constant only on the plan and cannot be constant on all parts of the map. However, on maps, as well as on plans, a single scale value is usually placed. This is the main scale. On large-scale maps, deviations of private scales from the main one (due to their insignificance) are practically neglected, i.e., the scale can be considered, like the scales of plans, as a constant value.

Scales are shown in two ways: 1) by directly indicating the distance on the ground, corresponding to a unit of length on the map (for example, 1 cm on the map is equal to 10 km on the ground); 2) in the form of a fraction (whose numerator is equal to one), showing the relationship between the distance on the map and the distance on the ground, for example 1/1000000. Such a scale is called numerical; it is more convenient to write it, especially in text typing, in one line (1: 1,000,000 or 1/1,000,000); the sometimes used form of the fraction 1/1000000 is less convenient; for it you have to take small numbers that are difficult to read.

The order of transition from one type of scale to another is easily learned from the following examples:

1. Given a numerical scale of 1: 1,000,000; find the number of kilometers on the ground corresponding to 1 cm on the map.

One kilometer contains 100,000 cm. Divide the denominator of the numerical scale by this number and get the desired value:

1,000,000 / 100,000 \u003d 10, i.e. 10 km in 1 cm.

2. It is indicated that 1 cm on the map is equal to 10 km on the ground, find the numerical scale.

We multiply the number of centimeters in 1 km by 10 and get the denominator of the numerical scale: 100,000 * 10 = 1,000,000, i.e., the numerical scale is 1: 1,000,000.

It is just as easy to convert one type of scale to another in cases where the map is based on non-metric measures of length.

For example, it is stated that 1 inch on the map is equal to 2 versts on the ground; find the numerical scale.

1 verst contains 500 fathoms, each fathom has 84 inches; therefore, the denominator of the numerical scale is: 2 * 500 * 84 = 84,000, i.e. the numerical scale will be 1: 84,000.

At present, in the USSR, where, like in most other countries, the metric system of measures is adopted, the following scales are used: 1: 10,000, 1: 25,000, 1: 50,000, 1: 1,000,000, etc. In order to get a correct idea of ​​the meaning of the above numerical scales, you should remember some numbers from the following table:

Numerical Popular card name 1 cm on the map

corresponds to the terrain

 1 cm 2 on the map

corresponds

on the ground
1: 10 000 ten thousand card

twenty-five thousandth card fifty thousandth card

100,000th card

200,000th card

Five hundred thousand card

Million card

 100 m 1 ha \u003d 0.01 km 2

6.25 ha \u003d 0.0625 km 2

25 ha \u003d 0.25 km 2

In addition to metric scales, it is useful to know the scales in old Russian measures (1 verst = 500 sazhens = 42,000 inches) and in measures adopted in Great Britain, its colonies and some dominions (1 statute mile = 63,360 inches). The first were adopted for Russian maps of pre-revolutionary times (some of which have not lost their significance to this day); English cards, on the other hand, are widely popular due to the large territory of the British Empire.

Scales of Russian pre-revolutionary maps

English map scales

Metric scales, with their round figures, are of considerable convenience in the practical use of maps; this predetermines their gradual wide distribution.

Drawing a numerical scale on the map is mandatory. The inconvenience caused by its absence can be judged from the example of some reference cards published in the Union of South Africa. These maps indicate only that one inch of the map corresponds to 1000 Cape births on the ground. For the reader of the map, who is not familiar with the system of measures used in the Union of South Africa, this phrase gives very little. Reference books usually mention the English genus, equal to 5,029 m; and only in rare sources can one find that 1 Cape genus corresponds to 3,778 m, and from this a numerical scale of 1: 149,000 can be obtained - an expression understandable to any user of the map.

In cartography, the word scale has two meanings. On the one hand, this is the relationship between the length of the line on the map and the length of the corresponding lines on the ground, on the other hand, it is a graphical construction for converting distances on the map into the corresponding distances on the ground, expressed in any unit of length. Such a graph is called a linear scale. It is built in such a way that a certain length, taken from the map with a compass, can be directly translated in scale into the corresponding distance on the ground.

Example: given a map at a scale of 1:63,360 (one mile in 1 inch). We need to build a scale to measure distances in kilometers. 1 km on the ground will be expressed on the map as 100,000 / 63,360 = 1.58 cm. We set aside segments equal to 1.58 cm in succession on a straight line. We additionally divide the leftmost of them using parallel lines into 10 equal parts. To directly read the distance taken by the compass from the map, set one leg of the compass to an integer division so that the other leg falls on the leftmost segment, which has additional divisions. The distance on the ground, read on the scale, will be equal to 2.14 km.

Measuring distances on a map using a linear scale

In conclusion, we note that the use of linear scales gives relatively accurate results only on large-scale maps, on which deviations of particular scales from the main one are insignificant. On small-scale maps with significant deviations of private scales from the main one, a linear scale is usually absent (not drawn).

 

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