Scaling online calculator. Scale and methods for calculating it using an online calculator. How to find out the map scale

The easiest way to determine the scale is to read the indicating inscription in the drawing stamp. Any drawing must contain information about the scale of the product or structure. If the object is large, then use reducing scale and designate it as 1:10 or 1: 5,000. This means that the real size of the object is 10 or 5,000 times smaller than in the drawing. Therefore, in order to find out what the actual height or length of an object is, you need to multiply the drawing value by the second number in the scale indication.
The same scaling is applied to a geographic map, since the real dimensions of the area are much larger than those displayed on paper.

Step 2

In drawing execution small parts, enjoy increasing scaling so that the image of the object is clear. In this case, the scale in the drawing is designated as 2:1, 4:1, etc. This means that the real size of the object is 2 or 4 times larger than in the drawing. Therefore, in order to find out what the actual height or length of an object is, you need to divide the drawing value by the second number in the scale indication.

Step 3

Sometimes you need to determine the scale yourself. If you have a drawing and the part itself, which is shown in the drawing, then you can take the actual dimensions of the part and compare it with the dimensions in the drawing. When one quantity is divided by another, a ratio is obtained that determines the scale.

Step 4

Measuring a real object can be done with a ruler, tape measure, or caliper. The dimensions of a physical object (part) are taken along the main lengths, i.e. height, width and depth. In the drawing, this corresponds to the values ​​that are determined by extreme points products and are marked with a two-headed arrow. It does not matter how complex the product configuration is.

For example (according to the standard Google service help), longitude, in one of the formats of the maps.google.ru service, is 41.40338° east longitude. In practice, in decimal fractions of geodetic degrees, five decimal places are enough, which corresponds to the maximum possible actual accuracy (up to several meters horizontally) of conventional satellite navigation devices intended for civilian users.
Then, the sequence of calculations is:
40338 / 100,000 = X / 60
X = (40338 * 60) / 100,000 ~ 24.2028 (from the proportion we find the numerator of the right fraction).
Whole minutes: 24"

2028 / 10,000 = X / 60
X = (2028 * 60) / 10,000 ~ 12.17
Seconds: 12.17"

Result: 41.40338° = 41° 24" 12.17" (forty-one degrees, twenty-four minutes, twelve point seven seconds).

Latitude is recalculated in the same sequence.

Google supports various angular data formats.

Examples of how to do it right

Abbreviated forms for recording geographic coordinates (north latitude, east longitude):

Degrees and, separated by a space, minutes with their decimals:
41 24.2028, 2 10.4418

Decimal degrees:
41.40338, 2.17403

The full form of writing an angle (degrees, minutes, seconds with their decimals):
41° 24" 12.1674", 2° 10" 26.508"

A simplified degree-minute version, which Google may be able to recognize if two pairs of numbers (integer degrees and minutes) separated by a comma are typed into the search bar:
41 24, 2 10

The Googlemap service has an online converter for converting coordinates and converting them into the required format.

Online maps of various Internet services make it possible to set and receive location coordinates with an accuracy of six decimal places of degrees, after the decimal point, that is, up to a meter. This is enough to work together with modern car navigators and built-in mobile devices(smartphones, tablets and other gadgets) by receivers of signals from the satellite global positioning system GLONASS (Russia), GPS (USA) and Beidou (China). Navigation devices for “civilian” users have a single measurement error of up to several meters (in the horizontal plane on the earth’s surface). Electronic digital data may vary significantly. Vector maps have significant advantages over raster formats: the ability to automatically search for information (by the name of a settlement, the characteristics of a geographical object) and quickly update to the current version, good readability when zooming in/out, layering thematic layers, obtaining a three-dimensional three-dimensional image, the ability overlaying scanned copies from paper materials, for example from Soviet topographic tablets.

The main forms of representing the values ​​of geographic coordinates with an accuracy of a few meters:
degrees with hundred thousandths (YY.YYYYY°)
degrees, minutes with thousandths (GG° MM.MMM")
degrees, minutes, seconds with tenths (GG° MM" CC.S")


This number of decimal places (“five-three-one”) corresponds to the order of the maximum possible actual accuracy of a single measurement of conventional GPS navigators, during their normal operation, under acceptable conditions (good location of satellites in the sky, good level of satellite signal, etc.). d.) With repeated measurements at a point rigidly fixed by a device, the positioning accuracy, theoretically, should increase due to the collection of statistics to determine the mathematical average from a cloud of numerical values. But this does not make much sense if the original satellite signal is software modified, and there is an artificial error in the coordinates, which operators increase for ordinary consumers, for example, in wartime, and for other reasons. In such cases, in selective access mode for civilian users, data distortions appear - the coordinate grid can be significantly shifted relative to the true position. The “walking of the grid” occurs along a random or specified trajectory, within a horizontal radius or arbitrary volume of space specified by the system operator.

When specifying the coordinates of the search area, for example, if a tourist group is lost on the route, for search and rescue operations, the duty officer is informed of the estimated location of the missing, in the form of numbers:
GG° MM" CC" northern latitude, GG° MM" CC" eastern longitude

If it is not possible to find out the coordinates of the lost, in this case, the rescuers are explained in detail - where to look, how to get there, where, best, to get through. Geographical landmarks are transmitted as the reference is detailed, from largest to smallest, narrowing the radius, speeding up the search.

For correct presentation and correct calculations, it is necessary to accurately indicate the coordinate system used for mobile positioning. Used in practice:
WGS-84 (worldwide, on which all GPS navigators work),
"Pulkovo-42" (SK-42, used on old military maps of Soviet times),
MSK (any local coordinate system).

To convert a reference to another coordinate system, you can use special converters by installing the selected program on Personal Computer or on a smartphone (mobile applications can be downloaded for free from services Google Play or Android Market).

On any geographical map you can see something like this: “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

  • Tape measure or surveying compass
  • Ruler

Instructions

1. If you have a plan on which various objects are depicted fairly accurately, and you need to find out at what scale this plan was made, start with measurements. Select an object 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 the roulette loop to it. Drive the 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 measuring on the territory. Let's say it turns out that a barn 5 meters long on the plan occupies 2.5 cm. Convert meters to centimeters. That is, it turns out that 2.5 cm contains 500 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 accurately, take several measurements. Let's say, measure the shed on the site and the distance from the gate to the pond. Plans are different, and the dimensions of one or another object may be drawn unsatisfactorily correctly. If there are discrepancies, do another freeze. Correct the image of the object, the one that does not correspond to the other two, on the plan.

Scale is a numerical designation of parameters related to real objects that are impossible to depict in natural size. Their layouts are used in the figure.

Instructions

1. The scale is written using several methods, say, numerically - 1: 1000000. The ratio of sizes can also be indicated in this form: 1 cm 10 km is a named scale. Linear method display is shown as a line with divisions.

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 character of the territory; a sparsely populated area, say, is easier to depict. Maps come in large, medium and small scale. Large-scale maps are when 1 cm is from 100 to 2000 meters, medium-scale - 1 cm is up to 10 km, small-scale - 1 cm is more than 10 km.

3. Scale is also important in photography. With the help of lenses, photographers change sizes from very small to very large. The methodology for scale metamorphosis depends on the specifics of the survey. If these are small objects, say, insects, the scale increases, if they are huge, it decreases.

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

5. Firms are differentiated by the scale of their activities. There are, say, territorial organizations, and there are also federal ones. People are different in scale. True, not from a physical point of view, there is a psychological concept of “figure scale”. This means human qualities, set goals and results of activities.

Video on the topic

Note!
The size of a reduced object is relative to its natural size. The distance between objects can be changed to 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 impossible to analyze the distances and sizes of objects.

People often encounter the need to imagine the real dimensions of an object depicted in a drawing 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, you need to calculate the exact distance between two cities. In order to cope with the task, you need to know how to translate the scale.

You will need

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

Instructions

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

2. Other scales are also used in drawing. 1:2 means that the part in the drawing should be two times smaller than 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. A very small object can be drawn, say, on a scale of 4:1, 10:1, etc. If you see a similar designation in front of you, it means that the object in the picture is four or ten times larger than it actually is.

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

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

5. Occasionally there is a need to change the scale of a three-dimensional object. For example, during a labor lesson, a teacher may give an assignment to make a part shown in a technical drawing on a certain scale. You need to find out how much material is required for this. The thesis of the translation 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 for solving it depends on the shape of a particular part. The number that indicates the scale is cubed, and then multiplied by the volume of the part calculated from the drawing data.

Helpful advice
You can try to draw a simple plan yourself, setting yourself a certain scale. Let's say a scale of 1:10 for a room plan is absolutely fine. Measure the length of the walls and large objects, determine their relative position and draw a plan in exact accordance with the data obtained.

Note!
The smaller the denominator of the fraction in which it is written, the larger the scale. 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 is no peg at hand, press the tape measure firmly against the wall of the object. It is more comfortable to measure each person on the ground - say, along the bottom of the wall.


Enlarging or reducing an image on paper is characterized by scale. On a geographic map, the image of the area is represented by a reduction scale.

Numerical scale map is expressed by the ratio of 1 to a number showing how many times the real segment has been reduced.

Most geographic maps are made on a scale of 1:20,000,000 or 1:25,000,000. This scale means that 1 cm on the map corresponds to 20,000,000 cm = 200 km or 25,000,000 cm = 25 km on the ground, since in scale records, the dimensions of the map and terrain units must match.

If the map shows a scale of 1:20,000,000, then by measuring the distance between points in centimeters and multiplying it by 20,000,000, you will get the real distance between points in centimeters.

To simplify calculations, you can immediately convert the scale to kilometers or meters on the ground.

For example, the distance between city A and city B was 3.5 cm on the map, map scale 1:25,000,000.

Solution:
1) 25,000,000 cm = 250 km
2) 3.5 * 250 = 875 (km)

In addition to the numerical scale, the map can also show linear scale.

The first square on the left shows the scale (1 cm on the map is equal to 200 m on the ground). By attaching a ruler to the map, we immediately determine from it how many meters this segment will be on the ground.

Scale is the ratio of 2 linear dimensions, which is used when creating drawings and models and allows you to show large objects in a reduced form, and small ones in an enlarged form. In other words, this is the ratio of the length of a segment on the map to the true length on the ground. Different practical situations may require you to know how to find the scale.

When does it become necessary to define scale?

How to find scale

This mainly happens in the following situations:

  • when using a card;
  • when making a drawing;
  • in the manufacture of models of various objects.

Types of scale

A numerical scale should be understood as a scale expressed as a fraction.

Its numerator is one, and its denominator is a number showing how many times the image is smaller than the real object.

A linear scale is a measuring stick that you can see on maps. This segment is divided into equal parts, labeled with the values ​​of distances commensurate with them on real terrain. A linear scale is convenient because it provides the ability to measure and plot distances on plans and maps.

A named scale is a verbal description of what distance one centimeter actually corresponds to on a map.

For example, there are 100,000 centimeters in one kilometer. In this case, the numerical scale would look like this: 1:100000.

How to find the map scale?

Take, for example, a school atlas and look at any page of it.

At the bottom you can see a ruler that indicates what distance on real terrain corresponds to one centimeter on your map.

The scale in atlases is usually indicated in centimeters, which will need to be converted to kilometers.

For example, when you see the inscription 1:9,500,000, you will understand that 95 kilometers of real terrain corresponds to only 1 cm of the map.

If, for example, you know that the distance between your city and the neighboring one is 40 km, then you can simply measure the distance between them on the map with a ruler and determine the ratio.

So, if by measuring you get a distance of 2 cm, you get a scale of 2:40=2:4000000=1:2000000. As you can see, finding the scale is not difficult at all.

Other uses of scale

When making models of airplanes, tanks, ships, cars and other objects, certain scaling standards are used. For example, it could be a scale of 1:24, 1:48, 1:144.

In this case, the manufactured models must be smaller than their prototypes exactly by the specified number of times.

Scaling may be necessary, for example, when enlarging a picture. In this case, the image is divided into cells of a certain size, for example, 0.5 cm. A sheet of paper will also need to be drawn into cells, but already enlarged by the required number of times (for example, the length of their sides can be one and a half centimeters, if the drawing needs to be enlarged 3 times) .

By drawing the contours of the original drawing onto a lined sheet, it will be possible to obtain an image very close to the original.

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Map scale. The scale of topographic maps is the ratio of the length of a line on the map to the length of the horizontal projection of the corresponding terrain line. In flat areas, with small angles of inclination of the physical surface, the horizontal projections of the lines differ very little from the lengths of the lines themselves, and in these cases the ratio of the length of the line on the map to the length of the corresponding terrain line can be considered a scale, i.e.

the degree of reduction in the lengths of lines on the map relative to their length on the ground. The scale is indicated under the southern frame of the map sheet in the form of a ratio of numbers (numerical scale), as well as in the form of named and linear (graphic) scales.

Numerical scale(M) is expressed as a fraction, where the numerator is one, and the denominator is a number indicating the degree of reduction: M = 1/m. So, for example, on a map at a scale of 1:100,000, the lengths are reduced in comparison with their horizontal projections (or with reality) by 100,000 times.

Obviously, the larger the scale denominator, the greater the reduction in lengths, the smaller the image of objects on the map, i.e. the smaller the scale of the map.

Named scale- an explanation indicating the ratio of the lengths of lines on the map and on the ground.

With M = 1:100,000, 1 cm on the map corresponds to 1 km.

Linear scale used to determine the lengths of lines in nature from maps. This is a straight line, divided into equal segments corresponding to the “round” decimal numbers of terrain distances (Fig. 5).

Rice. 5. Designation of scale on a topographic map: a - the base of the linear scale: b - the smallest division of the linear scale; scale accuracy 100 m.

Scale size - 1 km

The segments a laid off to the right of zero are called basis of scale. The distance on the ground corresponding to the base is called the magnitude of the linear scale. To increase the accuracy of determining distances, the leftmost segment of the linear scale is divided into smaller parts, called the smallest divisions of the linear scale.

The distance on the ground expressed by one such division is the accuracy of the linear scale. As can be seen in Figure 5, 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 (with the smallest division of 1 mm) will be 100 m.

The accuracy of measurements on maps and the accuracy of graphical constructions on paper are associated both with the technical capabilities of measurements and with the resolution of human vision. The accuracy of constructions on paper (graphic accuracy) is generally considered to be 0.2 mm.

The resolution of normal vision is close to 0.1 mm.

Ultimate accuracy map scale - a segment on the ground corresponding to 0.1 mm on the scale of a given map. With a map scale of 1:100,000, the maximum accuracy will be 10 m, with a scale of 1:10,000 it will be 1 m.

Obviously, the ability of these maps to depict contours in their actual shape will be very different.

The scale of topographic maps largely determines the selection and detail of the objects depicted on them.

With a decrease in scale, i.e. as its denominator increases, the detail of the image of terrain objects is lost.

To meet the diverse needs of the national economy, science and defense of the country, maps of different scales are needed. A number of standard scales based on the metric decimal system of measures have been developed for state topographic maps of the USSR (Table.

Table 1. Scales of topographic maps of the USSR
Numerical scale Card name 1 cm on the map corresponds to a distance on the ground 1 cm2 on the map corresponds to an area on the ground
1:5 000 Five thousandth 50 m 0.25 ha
1:10 000 Ten-thousandth 100 m 1 ha
1:25 000 Twenty-five thousandth 250 m 6.25 ha
1:50 000 Fifty thousandth 500 m 25 hectares
1:100 000 One hundred thousandth 1 km 1 km2
1:200 000 Two hundred thousandth 2 km 4 km2
1:500 000 Five hundred thousandth 5 km 25 km2
1:1 000 000 Millionth 10 km 100 km2

In the complex of cards named in table.

1, there are actual topographic maps of scales 1:5000-1:200,000 and survey topographic maps of scales 1:500,000 and 1:1,000,000. The latter are inferior in accuracy and detail to the depiction of the area, but individual sheets cover significant territories, and these maps are used for general familiarization with the area and for orientation when moving at high speed.

Measuring distances and areas using maps.

When measuring distances on maps, it should be remembered that the result is the length of horizontal projections of lines, and not the length of lines on the earth's surface. However, at small angles of inclination, the difference in the length of the inclined line and its horizontal projection is very small and may not be taken into account. So, for example, at an inclination angle of 2°, the horizontal projection is shorter than the line itself by 0.0006, and at 5° - by 0.0004 of its length.

When measuring from distance maps in mountainous areas, the actual distance on an inclined surface can be calculated

according to the formula S = d·cos α, where d is the length of the horizontal projection of the line S, α is the angle of inclination.

Inclination angles can be measured from a topographic map using the method indicated in §11. Corrections to the lengths of inclined lines are also given in the tables.

Rice. 6. Position of the measuring compass when measuring distances on a map using a linear scale

To determine the length of a straight line segment between two points, a given segment is taken from the map into a compass-measuring solution, transferred to the linear scale of the map (as indicated in Figure 6) and the length of the line is obtained, expressed in land measures (meters or kilometers).

In a similar way, measure the lengths of broken lines by taking each segment separately into a compass solution and then summing their lengths. Measuring distances along curved lines (along roads, borders, rivers, etc.)

etc.) are more complex and less accurate. Very smooth curves are measured as broken lines, having first been divided into straight segments. Winding lines are measured with a small constant opening of a compass, rearranging it (“walking”) along all the bends of the line. Obviously, finely sinuous lines should be measured with a very small compass opening (2-4 mm).

Knowing what length the compass opening corresponds to on the ground, and counting the number of its installations along the entire line, determine its total length. For these measurements, a micrometer or spring compass is used, the opening of which is adjusted by a screw passed through the legs of the compass.

7. Curvimeter

It should be borne in mind that any measurements are inevitably accompanied by errors (errors). According to their origin, errors are divided into gross errors (arising due to the inattention of the person making the measurements), systematic errors (due to errors in measuring instruments, etc.), random errors that cannot be fully taken into account (their reasons are not clear).

Obviously, the true value of the measured quantity remains unknown due to the influence of measurement errors. Therefore, its most probable value is determined. This value is the arithmetic average of all individual measurements x - (a1+a2+ …+аn):n=∑a/n, where x is the most probable value of the measured value, a1, a2…an are the results of individual measurements; 2 is the sign of the sum, n is the number of dimensions.

The more measurements, the closer the probable value is to the true value of A. If we assume that the value of A is known, then the difference between this value and the measurement of a will give the true measurement error Δ=A-a.

The ratio of the measurement error of any quantity A to its value is called relative error -. This error is expressed as a proper fraction, where the denominator is the fraction of the error from the measured value, i.e. Δ/A = 1/(A:Δ).

So, for example, when measuring the lengths of curves with a curvimeter, a measurement error of the order of 1-2% occurs, i.e. it will be 1/100 - 1/50 of the length of the measured line. Thus, when measuring a line 10 cm long, a relative error of 1-2 mm is possible.

This value on different scales gives different errors in the lengths of the measured lines. So, on a map of scale 1:10,000, 2 mm corresponds to 20 m, and on a map of scale 1:1,000,000 it will be 200 m.

It follows that more accurate measurement results are obtained when using large-scale maps.

Definition of areas plots on topographic maps is based on the geometric relationship between the area of ​​the 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 a factor of n, then the area of ​​this figure will decrease by a factor of n2.

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 cm2 - (100 m)2, i.e. in 1 cm2 - 1 hectare, and on a map of scale 1:1,000,000 in 1 cm2 - 100 km2.

To measure areas on maps, graphical and instrumental methods are used. The use of one or another measurement method is dictated 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.

8. Straightening the curved boundaries of the site and dividing its area into simple ones geometric figures: dots indicate cut-off areas, hatching indicates attached areas

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

Plan scale

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. 8). The measurement results will be somewhat approximate.

Rice. 9. Square grid palette placed on the measured figure. Area of ​​the plot P=a2n, a - side of the square, expressed on the map scale; n - number of squares falling within the contour of the measured area

Measuring the areas of areas with complex irregular configurations is often done using palettes and planimeters, which gives the most accurate results.

The grid palette (Fig. 9) is a transparent plate (made of plastic, organic glass or tracing paper) with an engraved or drawn grid of squares. 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 in land measures, i.e.

the price of dividing the palette.

Rice. 10. Dot palette - a modified square palette. Р=a2n

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.

10). 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.

11. A palette consisting of a system of parallel lines. The area of ​​the figure is equal to the sum of the lengths of the segments (middle dotted lines) cut off by the contour of the area, multiplied by the distance between the lines of the palette.

Equally spaced parallel lines are engraved on the parallel palette. The measured area will be divided into a number of trapezoids with the same height when the palette is applied to it (Fig. 11). The parallel line segments inside the contour in the middle between the lines are the midlines of the trapezoids. Having measured all the middle lines, multiply their sum by the length of the gap between the lines and obtain the area of ​​the entire area (taking into account the areal scale).

The areas of significant areas are measured from maps using a planimeter.

The most common is the polar planimeter, which is not very difficult to operate. However, the theory of this device is quite complex and is discussed in geodesy manuals.

12. Polar planimeter

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How to find out the map scale

A topographic map is a projection of a real ground mathematical model onto a plane in reduced form.

The amount of relief image decreases and is called the denominator of the scale. In other words, the scale of a map is the ratio of the distance between two objects measured along it to the distance between the same objects measured on the ground. Knowing the scale of the map, you can always calculate the actual size and distance between objects located on the earth's surface.

instructions

  • An indispensable condition for the publication of any topographic map or graph is a sign of its scale, without which it loses its meaning and becomes simply beautiful picture. Usually the scale of the map is indicated in its description - legends or taken to the border. You can indicate it in the head, as well as with explanatory notes. Sometimes popular schematic diagrams write the scale directly on the map itself. Look closely at the map and look for "Criterion 1:" or "M 1:".
  • If the map is cropped and there is no border treatment, you can specify the desired scale on another map of the same area whose scale is known.

    Find a pair of identical characteristic points in the field on both maps. These may be structures or industrial building, road intersections, characteristic characteristics areas that are reflected on one and the other map. Measure the distance between them on both charts and calculate the ratio between the scales—the number of times the desired scale is smaller or larger than the one listed for the other card.

  • Keep in mind that the scale is usually an integer multiple of 100 or 1000.

    If you get a scale value, it's not the result of measurement error, so the scale of your map brings that value.

  • If there is no other card, high technology will be available. Use one of the map services available in Yandex or Google.

    Finding distance on a map

    Their database is converted into flat images, mainly maps. Find them in the area shown on your map of unknown magnitude and in the two locations you have chosen as a feature.

    Use the Ruler tool to determine the distance between these points in the spatial images in the selected units. If you know the distance on the map and the distance in the field, specify the map scale and convert it to an integer greater than 100 or 1000.

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Geography lesson in 6th grade on the topic “Scale. Types of scale"

By scale, maps are divided into three groups: small-scale (1:1,000,000, 1:500,000, 1:300,000, 1:200,000); medium-scale (1:100000, 1:50,000, 1:25,000); large-scale (1:10000,1:5000, 1:2000,1:1000,1:500).

Large-scale topographic maps are the most accurate and suitable for detailed design.

Small-scale maps are intended: for a general study of the area during the general design of the development of the national economy, for taking into account the resources of the earth's surface and water space, for the preliminary design of large engineering facilities, for the needs of the country's defense.

Medium-scale maps have more detail and higher accuracy; intended for detailed design in agriculture, design of roads, routes, power lines, for preliminary development of planning and rural development settlements, to determine mineral reserves.

Large-scale maps and plans are compiled for more accurate detailed design (drawing up technical projects, irrigation, drainage and landscaping, development of master plans for cities, design utility networks and communications, etc.).

The more important the survey task, the larger the scale required, but this is associated with high costs, so large-scale surveys must have an engineering justification.

Sheets of maps are published in a unified system of layout and nomenclature and represent a horizontal projection of a spheroidal trapezoid - a certain area of ​​the earth's surface.

The nomenclature of topographic maps is usually called the designation of its individual sheets (trapezoids). The nomenclature of trapezoids is based on a sheet of map at a scale of 1:1000000, called the international map.

Types of scales

The scale can be written in numbers or words, or depicted graphically.

  • Numerical.
  • Named.
  • Graphic.

Numerical scale

The numerical scale is signed with numbers at the bottom of the plan or map.

For example, a scale of “1: 1000” means that all distances on the plan are reduced by 1000 times. 1 cm on the plan corresponds to 1000 cm on the ground, or, since 1000 cm = 10 m, 1 cm on the plan corresponds to 10 m on the ground.

Named scale

The named scale of a plan or map is denoted in words.

For example, it may be written “1 cm - 10 m”.

Linear scale

It is most convenient to use a scale depicted as a straight line segment divided into equal parts, usually centimeters (Fig. 15). This scale is called linear and is also shown at the bottom of the map or plan.

Please note that when drawing a linear scale, the zero is set, retreating 1 cm from the left end of the segment, and the first centimeter is divided into five parts (2 mm each).

Next to each centimeter there is a sign indicating what distance it corresponds to on the plan.

One centimeter is divided into parts, next to which it is written what distance on the map they correspond to. Using a measuring compass or ruler, measure the length of any segment on the plan and, applying this segment to a linear scale, determine its length on the ground.

Application and use of scale

Knowing the scale, you can determine the distances between geographical objects and measure the objects themselves.

If the distance from the road to the river on a plan with a scale of 1: 1000 (“1 cm - 10 m”) is 3 cm, then on the ground it is 30 m.

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Let’s assume that from one object to another there are 780 m. It is impossible to show this distance in full size on paper, so you will have to draw it to scale. For example, if all distances are depicted 10,000 times smaller than in reality, i.e.

e. 1 cm on paper will correspond to 10 thousand cm (or 100 m) on the ground. Then, to scale, the distance in our example from one object to another will be equal to 7 cm and 8 mm.

Pictures (photos, drawings)


On this page there is material on the following topics:

  • What does the numerical scale show?

  • Report geographical scope

  • Scale definition of koroikr

  • Scale 1: 10 abstract

  • Causes of the revolution in Europe 1848-184

Questions for this article:

  • What is scale?

  • What does the scale show?

  • What can you measure with a scale?

  • How big is the lake if on a film with a scale of 1: 2000 (“1 cm - 20 m”) its length is 5 cm?

  • What does scale 1:5000, 1:50000 mean?

    Which one is larger? Which scale is more convenient for a land plot plan, and which for a large city plan?

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