When going on an interesting trip or simply looking at maps on the Internet, every person is faced with such a concept as scale. However, not everyone knows what it is, what types of scales there are and how to calculate it correctly.
What is scale
The word “scale” came into Russian from the language of precision - German - and is literally translated as a stick for measuring. However, in cartography, this term refers to the number by how many times a given map or other image is reduced in comparison with the original. The scale is present on every map and is also an integral part of any drawing.
Why do you need a scale?
So why do people need scale in practice? What does the scale show? In fact, this concept is associated practically and theoretically with many fields: mathematics, architecture, modeling and, of course, cartography. After all, not a single map, even an ultra-modern digital one, can display a geographical object in its real size. Therefore, when drawing images of certain cities, rivers, mountains or even entire continents on the map, all these objects are proportionally reduced. And how many times this is done is the scale that is indicated in the margins of the map. 
In the old days, when cartography did not yet use scale, but reduced the depicted objects at their own discretion, the resulting maps were very inaccurate and were rather approximate. So travelers using them often got into trouble. Who knows, perhaps the map that Christopher Columbus used also had the wrong scale, and that’s why he sailed to America instead of India?
Another industry that simply cannot exist without the use of scale is modeling. After all, when creating a drawing of a future building or aircraft, an engineer does this on a certain scale, reducing or enlarging the image depending on the need. So not a single detail, even the smallest one, can be made without using a drawing, and not a single drawing can do without a scale.
Main types of scales
Despite the simplicity of the concept of “scale,” there are several types of it. On maps it is usually indicated either using numbers (numerical) or graphically. Graphic scales are divided into two subtypes: linear and transverse. 
There are also scale subtypes that are more related to map types. Depending on the size of the scales, maps are distinguished:
- Large-scale - from one to two hundred thousand and less.
- Medium-scale - from one in a million to one in two hundred thousand.
- Small-scale - up to one in a million.
Naturally, some details are not shown on small-scale maps, while large-scale maps may contain names of streets and even small alleys. In modern electronic maps, the user can adjust the scale himself, in an instant turning the map from small-scale to large-scale, and vice versa.
Numerical and named scale
Scale data can be specified in different ways. If on a map or drawing the scale is indicated using a fraction (1:200, 1:20,000, etc.), then this type of scale is called numerical. When calculating this size, it is worth taking into account the fact that the larger scale will be the one with the smaller number in the denominator. In other words, objects on a map with a scale of 1:200 will be larger than on a map with a scale of 1:20,000.
The named scale not only indicates the size of the image reduction, but also names the units of measurement with which this is done. For example, on a terrain plan it is indicated that 1 centimeter on it is equal to 1 meter. Named scales are rarely used for small-scale maps, or for maps in general. It is more practical for various drawings. Especially if it is a tiny detail or, conversely, a huge residential complex.
Graphic scale
Graphic types of scales, as mentioned above, come in two variants.
Linear is a scale depicted as a uniformly graphed two-color ruler. As a rule, it is used on large-scale terrain plans and makes it possible to measure distances on it using a paper strip or compass. This graphical scale option can help you find out the length of rivers, roads and other curved lines.
Transverse is an improved version of the linear scale. Its purpose is to determine the distance indicated on the plan as accurately as possible. This graphical option is usually used on specialized cards.
Drawing scales
Having considered the most common types of scales in cartography, it is worth mentioning that this concept is also integrally associated with drawing and architectural graphics. Whether they are engineering drawings of tiny mechanical parts or, conversely, drawings of huge architectural ensembles, in any case, specialized drawing scales are applied to them. Each drawing form has a column in which the scale of the designed product must be indicated.
It is noteworthy that even if an engineer creates a full-size drawing of a part, the information about it still indicates a 1:1 scale. Unlike maps, in drawings the scale can be not only reduced (1:5), but also enlarged (5:1) if the depicted product is tiny in size.
Today, only narrow specialists need the ability to correctly calculate the scale without the help of machines. Thanks to modern programs and devices, other people no longer need to have a good understanding of the scale of a particular map - the computer will do everything for them. But still, everyone should have at least an approximate idea of what scale shows, how to calculate it correctly and what types of it exist - after all, this is a component of basic literacy and human culture.
- this is a reduced image of the earth's surface on a plane using conventional symbols. The maps show both visible terrain objects and various geographical phenomena (precipitation, air temperature, wind, etc.) (Fig. 2).
The main differences between a site plan and a geographical map can be formulated as follows:
- Local plans depict small areas of the earth's surface, so their scale is large, and geographic maps show huge spaces, so their scale is small;
- When drawing up plans, the curvature of the Earth's surface is not taken into account; when constructing maps, it is always taken into account;
- On maps there is always a degree network, but on plans there is none. On plans, the direction north is considered the direction upward. On maps, the north-south direction is determined by meridians, the west-east direction by parallels;
- On maps, some objects (settlements, volcanoes) are depicted without preserving their sizes and outlines; on plans, these objects are shown as they actually are, but only to scale.
Selection and generalization of objects and phenomena shown on the map - cartographic generalization- must correspond to the purpose and scale of the map, as well as the size of the territory depicted on it (Fig. 3).
They occupy an intermediate position between a site plan and a geographical map. The scale of a topographic map is larger than the scale of a geographic map, but much smaller than the scale of a site plan.
Topographic maps are detailed geographic maps, unified in content, design and mathematical basis, displaying natural and socio-economic objects (relief, vegetation, settlements, roads, etc.), having a degree network and a stable system. Since the topographic map depicts small areas, there are practically no distortions associated with the sphericity of the Earth. This map is best used when exploring your area. You can use it to navigate and map out your route. Topographic maps are used by builders, the military, and land surveyors.
Rice. 1. Sample site plan
Rice. 2. Sample geographical map
Rice. 3. Cartographic generalization
Mathematical basis of cards are scale And map projection. The scale determines the degree of reduction in the size of objects and the distances between them on the hag in relation to the real ones on the ground, and the cartographic projection determines the magnitude and nature of distortions that are inevitable when a ball (ellipsoid) is depicted on a plane.
The materials used in making maps are called cartographic sources. They can be very diverse - statistical, topographical, aerospace, etc.
A miniature model of the Earth is globe. The linear and areal dimensions, angles and shapes of the depicted geographical objects (oceans, continents, lakes, rivers, etc.) are preserved on the globe. The scale of the globe is the same at all its points.
In order to measure distance on a plan, map or globe, you must be able to use a scale.
Numerical scale
Scale- this is an indicator of the degree of reduction in distance on a plan, map, globe compared to the true distance on the ground. Scale happens numeric, named And linear(Fig. 4).
Numerical scale expressed as a fraction, for example 1: 100,000. The larger the denominator of the fraction, the smaller the fraction itself, and therefore the smaller the scale. For example, a scale of 1:100,000 is smaller than a scale of 1:10,000.
Named scale
A scale of 1: 100,000 means that the reduction is made by a factor of 100,000, i.e. 1 cm of map contains 100,000 cm of terrain. This explanation is called named scale.
It is very easy to move from a numerical scale to a named one: if the numerical scale is 1: 100,000, then the named scale is: 1 cm 100 000 cm, or 1 cm 1000 m, or 1 cm 1 km.
Linear scale
In order to determine the distance in meters or kilometers from a map or plan, you can use linear scale - This is a scale that is depicted as a straight line divided into parts, each of which corresponds to a certain distance on the ground.
The distance on the ground corresponding to the base is called the magnitude of the linear scale. To accurately determine distances, the leftmost base is divided into smaller parts - the smallest divisions of the linear scale. With a map numerical scale of 1:100,000 and a linear scale base of 1 cm, the scale value will be 1 km and the scale accuracy will be 100 m.
You must be able to convert a linear scale to a named or numerical scale. In the first case, the denominator of the numerical scale can be converted into larger measures - meters or kilometers (if the numerical scale of the plan is I: 5000, then 1 cm on the plan corresponds to 5000 cm, or 50 m, on the ground). To convert to a numerical scale, you need to calculate how many times the linear scale division is less than the actual distance (a division of 1 cm corresponds to 1 km, a division of 1 cm corresponds to 1000 m, or 100,000 cm). Therefore, the numerical scale is 1:100,000.
Rice. 4. Design of numerical, named and linear scales
Scales of topographic maps
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
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
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
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
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
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
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
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
Measuring distances using a map and plan
Measuring distances on maps is done like this.
When measuring in a straight line between two points, a given segment is put off the map (or plan) into a compass-measuring solution, transferred to the linear scale of the map (Fig. 5) and the length of the corresponding line on the ground, expressed in meters or kilometers, is obtained.
The larger the map scale, the more accurate the measurement result.
Rice. 5. Position of the measuring compass when measuring distances on a map using a linear scale
Without it, it is impossible to construct a single geographical map. What is scale? And what types of scales exist in cartography and geodesy? This will be discussed in this article.
What is scale?
Scale is a German word (masstab), which consists of two parts: mass - “measure, magnitude” and stab - “stick, pole”. Measuring pole - this is how this term can be translated.
What is scale? In a general interpretation, this is a mathematical value that shows how many times the model (image) is reduced in comparison to the original. This concept is actively used in mathematics, cartography, modeling, geodesy and design, photography, and programming.
In other words, scale is the ratio of two linear dimensions. In cartography, it shows how many times a segment on a map (or plan) is reduced compared to the actual length of the same segment. When compiling any geographical map, it is impossible to depict objects (forest, village, building, etc.) in real size. Therefore, all values are reduced many times (by 5, 10, 100, 1000 times, and so on). The scale of the map is precisely this value expressed as a number.
Types of scales
Scale is shown on maps and drawings using numbers or graphically. Accordingly, several types are distinguished.
The numerical scale is in the form of a fraction. It is most common in cartography. Many of us have seen this designation at the bottom of a topographic map or area plan. The numerical scale of the map has the following form (for example): 1:100,000. This means that the real length of the segment on the ground is 100,000 times greater than its length on this map.
A named scale is used when you need to know what the map scale is. It is also quite often indicated on geographical maps. It looks like this: 1 cm - 1 km.
Linear scale is already a graphic type of scale. It is a ruler, which is divided into columns of appropriate sizes. The photo above shows this type of scale.
Transverse scale is a more sophisticated version of the graphical view. It is used for the most accurate measurements and can be found on more serious maps.
How to use the map scale correctly? Suppose you need to use a specific map to find out the real distance between villages A and B. In this case, you are given the following scale: 1 cm - 0.5 km (or 1:50,000). To do this, you need to take a regular ruler and measure the distance between two points on the map. Then the resulting value (suppose this is a segment 5 centimeters long) should be multiplied by 0.5 km, according to the scale of our map. Thus, we will get the correct answer: the distance between village A and village B is 2.5 kilometers.
Types of maps (by scale)
Scale is one of the criteria for classifying geographic maps. So, according to him, all cards are divided into:
- small-scale (scale up to 1:1,000,000);
- medium-scale (from 1:1,000,000 to 1:200,000);
- large-scale (from 1:200,000 and more).
Of course, on large-scale maps the terrain is more detailed: individual streets or even buildings can be shown here. The larger the scale of the map, the more terrain objects can be depicted on it.
Small-scale geographic maps, as a rule, are used to depict hemispheres and continents, medium-scale - for states and their parts, large-scale - for individual, small areas. Military personnel, local historians, and tourists are very familiar with large-scale maps.
Cartographic generalization
No matter how detailed the map is, it still will not be able to display absolutely all the objects and details that are present in a given area. This is precisely the essence of the concept of “cartographic generalization”.
The word generalis can be translated from Latin as “generalized.” Generalization is the process of selecting those geographical objects that will be depicted on a specific map. Moreover, this process is objective, expedient and scientifically sound.
To understand what generalization is, it is enough to remember the cards that you probably held in your hands. So, on the map of Eurasia you are unlikely to find the city of Cherepovets. But it will definitely be marked on the map of the Vologda region.
Cartographic generalization helps to make the map of the highest quality, functional, and easy to read. Of course, it directly depends on the scale.
Finally
So what is scale? This value shows how reduced the image is compared to the actual size of the imaged object. This concept is most widespread in cartography and geography. There are several types of scales: numerical, named, linear and transverse.
The concept of cartographic generalization is closely related to the term “scale”. This process allows surveyors to select important geographic features and display them on a geographic map.
Scale is the ratio of the actual dimensions of an object to the image or model of the object.
The geographic scale helps determine how many times all real dimensions on the map have been reduced - the area of the territory, individual objects, the length of rivers, roads, etc.
In ancient times, scale was not known, so objects were placed on the map at an arbitrary distance from each other. Using such a map, a person could not determine whether it would take 2 days, 2 weeks or 2 months to get to the desired place.
The first cartographer to use scale in drawing up a map was Anaximander of Miletus, an ancient Greek scientist (VI – V centuries BC), who coined the term “law” and proposed the first formulation of the law of conservation.
Depending on the scale, maps are conventionally divided into:
— small-scale (survey) - less than 1:1,000,000;
- medium-scale (survey-topographic) - from 1:200,000 to 1:1,000,000;
- large-scale (topographic) - from 1:10,000 to 1:100,000.
Scales up to 1:5,000 are used primarily in drawing up topographic plans.
Type of scale: graphic, numerical, named scales
In legends of geographical maps, graphic (also known as linear) and numerical scales are used; they rarely resort to named ones.
Numerical scale
To write it, fractions are used, in which the numerators are 1 cm (unless otherwise stated), and the denominators are numbers showing how many times the indicator is reduced. For example, a scale of 1:25,000 demonstrates that 1 cm of map corresponds to 25,000 cm (250 m) of terrain.
The smaller the denominator, the larger the scale: 1:1000 is larger than 1:5,000, because in the first case, 10 m “fits” in 1 cm of the map, and in the second - 50 m. Maps with a large scale are more detailed and meaningful, but they can be used for small areas of the area.
Linear (graphic) scale
A linear or graphic scale is especially convenient and makes it possible to find out distances and sizes without calculations and conversions of lengths from scale to real. A linear scale looks like a ruler with divisions - small and large, each of which is labeled with the corresponding metric value. The main division is usually a 2 cm segment for which the scaling size is indicated, for example - 100 m, 500 m, etc. 
To use a graphic scale, a compass opening equal to the segment being measured is applied to the scale bar and the distance between objects, the length of the desired section, etc. is immediately found out.
Named scale
The named scale differs from others in that it spells out in words how many meters or kilometers there are in 1 cm. For example: 1 cm - 250 m; 1 cm - 5 km.
Where to look for scale on the map?
To find out the scale of a geographic map, you need to look at the corners of the map or its legend. A legend is a list of symbols with their explanation.
Very often, maps show all 3 types of scales so that each person can figure out how many times the real distances are reduced on the map.
Numerical scale standards
The following numerical scale standards have been adopted in the Russian Federation:
1:10 000
1:25 000
1:50 000
1:100 000
1:200 000
1:300 000
1:500 000
1:1 000 000
There are also maps with a scale of 1:2,000, 1:5,000. They are used for special tasks, because Such large scales are the area of application of topographic plans.
There are overview geographic maps with an incredibly small scale, for example - 1:1,000,000,000 (one in a trillion). It was created in 2010 by scientists at Ghent University in Belgium using CMOS semiconductor technology. on this map is 40 micrometers long - 0.04 mm, about half the thickness of a human hair. 
And the “Map of Industrialization of the USSR” from the St. Petersburg Geological Exploration Museum is famous not only for its huge scale - 1:1,500,000, but also... for its beauty. It was made for the 20th anniversary of the October Revolution in 1937 from 50,000 fragments, including Ural jasper for land, lapis lazuli for water, amazonite for lowlands. Map length - 6 m, height - 4.5 m, weight - about 3.5 tons. At the Paris World Exhibition of 1937, the map was awarded the Grand Prix, and in New York - a gold medal.
The position line of the aircraft is the geometric location of points of possible location on the earth's surface, determined by the constancy of the measured value.
Orthodrome is the shortest distance between two points along the arc of a great circle. Orthodrome intersects the meridians at different angles. The point at which the orthodrome intersects the meridian at right angles and reaches the greatest latitude is called the vertex point V.
A loxodrome is a line crossing the meridians at a constant angle.
Line of equal azimuths (bearings) - a line at each point of which a constant point of bearing is under the same true bearing.
A line of equal distances is a line in which all points are equidistant from some fixed point. On the globe, lrr is the circumference of a small circle.
A line of equal differences in distances (hyperbola) is a line at each point of which the difference in distances to two fixed points is a constant value.
13.Cartographic projections. Nature of distortion. Method of construction.
KP is a method of depicting the surface of the earth (globe) in a reduced size on a plane.
According to the nature of the distortion, they are divided into:
1)conformal, or conformal - angles and directions are transmitted without distortion
2) equal in size - areas without distortion 3) equidistant - the partial scale in one of the main directions is constant and = 1 4) arbitrary (world map)
According to the method of construction, CPs are divided into: cylindrical, azimuthal, conical, polyconical, multifaceted, arbitrary or conditional
Conical - radio navigation scale maps are made in a conformal conic projection on a secant cone.
Cards from Jepesen are designed in the lambertian equiangular conic. The cards are used for international flights. Available for lower and upper space, scales are 5; 7.5; 10;20; 30;40; 48;60 nautical miles in 1 inch.
The map scale is shown on the edge. The maps contain information about routes, minimum altitudes, dangerous and restricted areas, and radio data. Units of measurement, direction in degrees from the magnetic meridian, distance in nautical miles, altitude in feet, time Greenwich mean.
14.Main and private scale of the map.
MAP SCALE: the ratio of the length of a segment on a map (globe) to the corresponding segment on the surface of the Earth. There are main and private scales.
MAIN SCALE (M = S g. / S g.) – the degree of general reduction of the Earth when projected onto a plane. (M)
The size of the entire map is not constant. There are partial, numerical, graphic, linear.
PARTIAL scale (µ = dSк / dSз) – the ratio of a small segment on the map at a given point and in a given direction to the corresponding segment on Earth. The directions where (µ) are maximum and minimum are called principal. On navigation maps they usually coincide with meridians and parallels. Ch.M. in the direction of the meridian – m; parallels – n.
INCREASE IN SCALE (C) – the ratio of the private scale to the main one: C = µ/M.
LENGTH DISTORTION (V) – deviation of the scale increase from unity: V = C – 1. Relative length distortion in percent: V = 100 (C – 1).
DIRECTIONAL DISTORTION - the difference between the angle on the Earth's surface in the direction of the largest scale and the corresponding angle on the map: ω = arсsin [(m-n)/(m+n)].
AREA DISTORTION (p) – the ratio of the area of an infinitely small area on the map to
the corresponding area on the globe on the main scale: p = mn m - µ along the meridian; n – (hm)µ- along the parallel.
