With the help of a topographic map, you can solve a lot of practical problems without leaving the area. According to the topographic map, you can determine: the scale of this map, the distance between any local objects, the size of any area, the steepness of the slopes, the heights of any points in the terrain, the mutual excess of points, the visibility of points, the number of trees in the forest, the amount of water in the river, and much more.
Typically, each topographic map is given a linear, numerical and textual scale. But what if, for one reason or another, it was not there? Experienced specialist in outward appearance topographic map can immediately tell its scale. If you cannot do this, then you should resort to the following methods.
Determination of the scale of the topographic map on the kilometer grid.
Its side corresponds to a certain number of centimeters. If this distance is 2 cm, then the scale of the 1 cm map is 500 meters, that is, 1: 50,000. If 4 cm, then the scale of the map will accordingly be 1: 25,000.
Determination of the scale of the topographic map along the length of the meridian arc.
In order to use this method, one must firmly remember that one minute along the meridian is approximately 2 km (more precisely 1.85). The degrees and minutes are labeled on the map, and in addition, each minute is marked with a checkerboard. So, for example, in the picture below, the length of one minute is approximately 4 cm. This means that the scale of this map will be 1:50 000.
To determine between two points, first measure this distance on the map, and then, using the numerical or linear scale of the map, determine the actual value of this distance on the ground. If you need to determine the distance not in a straight line, but along a winding road, use special device- with a curvimeter.
It is a device for measuring the length of curved lines. The base of the curvimeter is a wheel, the circumference of which is known. The rotation of the wheel is transmitted to the arrow turning on a circular scale. Knowing the number of revolutions of the wheel rolling along the measured line, it is easy to determine its length.
How to measure area from a topographic map.
Measuring area in a geometric way.
The measured area is divided into a network of triangles, squares, trapezoids, the areas of which are calculated using well-known formulas. The sum of the areas of the known figures gives total area enclosed in a contour.
Measuring area using a grid of squares.
It is very convenient to determine the area using a millimeter grid, which is applied to transparent paper or film. Such a grid is applied to the outline of the map and the number of square millimeters is counted. Knowing what is equal to 1 mm2 of a topographic map on the ground (for a scale of 1: 100,000 - 1 mm2 is equal to a hectare, that is, 100 X 100 m), it is easy to determine the area on the map.
The distance between the contours, the so-called inception, shows the steepness of the slope. The main methods for determining the steepness of the slopes on a topographic map are as follows.
How to determine the steepness of the slopes on the scale of the topographic map.
Usually, to determine the steepness of the slopes, a drawing is placed in the fields of a topographic map - a scale of laying. Along the lower base of this scale, numbers are indicated that indicate the steepness of the slopes in degrees. On the perpendiculars to the base, the corresponding values of the foundations are plotted on the map scale.
On the left, the scale is plotted for the main section height, on the right, for a fivefold section height. To determine the steepness of the slope, for example, between dots a-b, it is necessary to take this distance with a compass and put it on the scale of laying and read the steepness of the slope - 3.5 degrees.
If it is required to determine the steepness of the slope between the thickened n-m horizontals, then this distance must be postponed on the right scale and the steepness of the slope in this case will be equal to 10 degrees.
How to determine the steepness of the slopes by calculation.
Having measured the location d on the map and knowing the height of the section h, the steepness of the slope a can be determined by the formula: a = h / d. Where a is the steepness of the slope in degrees, d is the distance between two adjacent contours in millimeters.
How to determine the steepness of the slopes using a ruler or by eye.
On Soviet maps standard height the cross-section for each scale is set such that a slope of about 1 degree corresponds to a depth of 1 cm. From the above formula, it can be seen that how many times the laying is less than one centimeter, how many times the steepness of the slope is more than one degree. It follows that a slope of 10 degrees corresponds to a 1 mm setting, a 2 mm setting - 5 degrees, a 5 mm setting - 2 degrees, and so on.
Based on the book "Map and Compass - My Friends".
Klimenko A.I.
The ratio of the natural size of an object to the size of its image. A person is not able to depict large objects, for example, a house, in full size, therefore, when depicting a large object in a drawing, drawing, layout, and so on, a person reduces the size of the object several times: two, five, ten, one hundred, one thousand etc. The number showing how many times the depicted object is reduced is the scale. The scale is also used when depicting the microcosm. A person cannot depict a living cell, which he examines through a microscope, in full size and therefore increases the size of its image several times. The number showing how many times the increase or decrease of a real phenomenon is made when it is depicted, is defined as a scale.
Scale in surveying, cartography and design
Scale shows how many times each line, plotted on a map or drawing, is less or more than its actual size. There are three types of scale: numerical, named, graphic.
The scales on maps and plans can be represented numerically or graphically.
Numerical scale written in the form of a fraction, in the numerator of which there is one, and in the denominator - the degree of reduction of the projection. For example, a scale of 1: 5,000 shows that 1 cm on the plan corresponds to 5,000 cm (50 m) on the ground.
The larger is the scale with the smaller denominator. For example, a scale of 1: 1,000 is larger than a scale of 1: 25,000.
Graphic scales are subdivided into linear and transverse. Linear scale is a graphic scale in the form of a scale bar divided into equal parts. Transverse scale is a graphical scale in the form of a nomogram, the construction of which is based on the proportionality of the segments of parallel straight lines intersecting the sides of the corner. The transverse scale is used for more accurate measurements of the lengths of lines on plans. The transverse scale is used as follows: measure the length on the lower line of the transverse scale so that one end (right) is on the whole division OM, and the left goes beyond 0. If the left leg falls between tenth divisions of the left segment (from 0), then raise both legs of the meter up until the left leg hits the intersection of some transvensal and some horizontal line. In this case, the right leg of the meter should be on the same horizontal line. The smallest CP = 0.2 mm, and the accuracy is 0.1.
Scale accuracy- this is a segment of the horizontal space of the line, corresponding to 0.1 mm on the plan. The value of 0.1 mm for determining the accuracy of the scale is taken 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 scale of images in drawings should be selected from the following range:
When designing master plans large objects are allowed to use a scale of 1: 2,000; 1: 5,000; 1:10 000; 1:20 000; 1:25 000; 1:50 000.
In necessary cases, it is allowed to use the magnification scales (100n): 1, where n is an integer.
Scale in photography
Some photographers measure scale as the ratio of the size of an object to the size of its image on paper, screen, or other media. The correct technique for scaling depends on the context in which the image is used.
Scale is important when calculating depth of field. A very wide range of scales is available to photographers - from almost infinitely small (for example, when photographing celestial bodies) to very large (without using special optics, it is possible to obtain scales of the order of 10: 1).
Scale is a number showing how many times the actual dimensions in the drawing are reduced or increased.
Notes (edit)
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Synonyms:- PrimeBase
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See what "Scale" is in other dictionaries:
SCALE- (German Masstaq, from German Mass measure). 1) a measure, a linear measure, taken in the drawings in a reduced form. 2) in artillery: a copper ruler with the designation on it of the caliber of guns, shells and the most common measures in artillery. Dictionary foreign words … Dictionary of foreign words of the Russian language
Scale- - the ratio of the length of a given line, shown in a drawing, plan or map, to its length in kind. [Glossary of basic terms required for design, construction and operation highways.] Scale is a ratio ... ... Encyclopedia of terms, definitions and explanations of building materials
scale- Cm … Synonym dictionary
Scale- the ratio of the linear dimensions of the object depicted on the map, aerial photograph, etc. to its dimensions in nature. Distinguish between the scale of reduction and increase, can be expressed by a numerical ratio (numerical scale) or depicted graphically ... ... Marine Dictionary
SCALE- [ash] (or scale), scale, husband. (German Masstab). 1. The ratio of reduced distances and dimensions on the map and drawing to the actual ones. Large scale geographic map. Scale 10 versts in inch. On a ten-verst scale. 2. Measure. In the Big … Dictionary Ushakova
scale 1: 1- full scale - [A.S. Goldberg. The English Russian Energy Dictionary. 2006] Topics energy in general Synonyms full scale EN full scale ... Technical translator's guide
SCALE- (German Ma? stab) the ratio of the length of a line in a drawing, plan or map to the length of the corresponding line in nature. It is denoted as a fraction, the numerator of which is is equal to one, and the denominator is a number indicating the degree of reduction in line lengths (eg, 1: 100 ... ... Big Encyclopedic Dictionary
Scale- (German Maβstab; from Maβ measure and Stab stick * a. scale; n. Maβstab, Skala; f. echelle; and. escala) the ratio of the length of a line in a drawing, plan, map, subject model to the length of the corresponding line in nature. Ha geogr. maps distinguish between the main M. ... ... Geological encyclopedia
SCALE- (from German Ma? stab) eng. scale; German Ma? Stab. 1. The ratio of the linear dimensions of the object shown in the drawing, plan, map to its dimensions in nature. 2. Size, relative size h. L. (e.g. price scale). Antinazi. Encyclopedia of Sociology ... Encyclopedia of Sociology
The end result of topographic and geodetic works are drawings earth surface, numerical data for the compilation of digital terrain models, etc. material presented in an ordered manner. Drawings can be drawn up on paper backing presented in electronic form or in the form of a computer database. The traditional forms of drawings are: map, plan, profile.
When depicted on paper, i.e. on the plane of the entire earth's surface or its significant sections, it is impossible to avoid image distortions due to the curvature of the displayed surface, since with any method of projection onto a plane, distortions arise in the lengths of the lines and the angles between them.
A reduced, distorted due to the influence of the curvature of the Earth, a flat image of the entire earth's surface or a significant part of it, built according to certain mathematical laws, is called by card .
Depending on the purpose of the map, when creating it, a certain cartographic projection is selected, i.e. mathematical law of terrain projection onto a plane.
The orthogonal projection of small terrain areas (up to 20 × 20 km) onto the level surface can be considered flat, neglecting the curvature of the Earth. A scaled-down image of such a projection on paper will be without distortion caused by the curvature of the Earth, and similar to a site.
In this way, a reduced, similar image on the horizontal plane is comparatively small area the earth's surface is called plan .
A visual representation of the irregularities of the earth's surface is profile , those. reduced image of its vertical section along the selected line.
The plans and maps can depict the situation and relief, or only situation(from French Situation - location).
A set of images on the plan local items natural and artificial(river, forest, bush, land plot, building, street, etc.) is called local situation.
The aggregate of unevenness of the earth's surface of natural origin is called the terrain.
If the plan shows only the boundaries of terrain objects, it is called outline(fig. 3.1, a). If, in addition to the contours, a relief is also applied to the plan, such a plan is called topographic(fig. 3.1, b).
Figure 3.1. Contour (a) and topographic (b) plans.
A map is a drawing on which the surface of the entire Earth or any part of it can be depicted in a generalized and reduced form.
Maps can have various purposes: agricultural, cadastral, economic, political, etc. are the so-called thematic or special maps, they show the contours of the situation and the special load. Maps on which, in addition to the contours of the situation, depicts the relief of the earth's surface, are called general geographic. The general geographic base of the map is a framework for building thematic maps.
For any measurements according to plans and maps, remember that the scale of the plan is the same at all its points, and the scale at all points of the map, as a rule, is different.
The concept of topographic plans and maps.The scale. Scale accuracy.
The concept of the scale of the plan and map.
When drawing up plans, maps, profiles, the results of measuring lines on the ground are reduced by several hundred or thousand times.
The degree of reduction of the horizontal spacing of the terrain lines when depicting them on the plan is called scale.
Under map scale in the general case, the ratio of the length of a line on the map to its length on the reference surface is understood. Depending on the cartographic projection, the images on the map in different places have different levels of distortion, so the scale of the map is not the same. For maps drawn on a small scale, the medium scale is usually labeled.
The scale expressed as a number in the form of a simple fraction is called numerical... Its numerator is one, and the denominator is a round number, for example, 1/500, 1/1000 or 1: 500, 1: 1000. The scale 1: 500 shows that the horizontal distance of the terrain line is reduced on the plan by 500 times and one unit of length on the plan, map or profile corresponds to 500 such units on the terrain, i.e. one centimeter on a plan, map or profile corresponds to 500 cm or 5 m on the ground.
The numerical scale is signed on plans, maps or profiles in their lower part, accompanied by an explanatory inscription, for example, "1 centimeter 5 m", since it is convenient to express the length of the terrain lines in meters. To determine the number of meters on the ground in one centimeter of the plan (map), it is necessary to discard the last two zeros at the denominator of the numerical scale, for example, 1 cm of a plan of 1: 2000 scale corresponds to 20m on the ground.
In order to show more details on the plan (map), they must be drawn up on a larger scale. How less denominator numerical scale, the larger the scale, and the scale with a large denominator is considered small. Large scales include: 1: 500, 1: 1000, 1: 2000, 1: 5000; to the average - 1:10 000, 1:25 000, 1:50 000; to small ones - 1: 100,000, 1: 200,000, 1: 500,000, 1: 1,000,000 and smaller.
Plans and maps in Russia are created on an accepted scale, forming a strictly defined system called large-scale series... The scale range is set in such a way that it meets all the conditions of consumers and it is possible to easily move from one scale to another.
Knowing the numerical scale, it is easy to translate the lengths of the terrain lines into the lengths of the lines on the plan (map) and vice versa. Such a translation is associated with calculations, therefore, in order not to perform such calculations, use scale(nomogram) graphically constructed. This scale is called linear scale(fig. 3.2).
Rice. 3.2. Numerical and linear scales.
The linear scale is a graph in the form of a segment of a straight horizontal line, on which equal segments are successively plotted, called basis scale. The base of the scale corresponds to an integer number of tens or hundreds of meters on the ground. To improve the measurement accuracy, the leftmost base is divided into smaller segments.
The counting start is zero (0) - the common point of the first and second scale bases. The rest of the segments are signed in accordance with the value of the numerical scale. If the base of the scale is 2 cm, then such a linear scale is called normal... In fig. 3.1 normal linear scale is built for a numerical 1: 10000 (1 cm - 100 m, and 2 cm - 200 m).
Linear measurements are usually made caliper(fig 3.3), which must be well adjusted before operation. When measuring, the compass should be held with one hand, tilting it slightly away from you so that both points of the needles are clearly visible at the same time.
Rice. 3.3. Determination of distances on a linear scale.
When measuring distances, the compass solution is set at points A and B on the plan, and then the compass is applied to a linear scale so that its left leg is to the left of zero, and the right leg is exactly on one of the divisions to the right of zero. The determined distance will be equal to the sum of the readings at both ends of the compass needles, i.e. 100 + 86 = 186m. In this case, tenths of small divisions are determined "by eye".
When performing cartometric work on plans (maps), the main elements of graphic construction are the pinch points of the compass needle and the line. The pin is a very small circle. The physiological property of the human eye is such that when viewed from a distance of 25-30 cm two adjacent points (pricks) they merge into one if the distance between them is less than 0.1 mm (according to research by the Department of Geodesy of the State University of Education - 0.08 mm). This is due to the critical angle of human vision, equal to 1 ¢. The value of 0.1 mm is taken as the limiting graphic accuracy measurements on the map, i.e. is the minimum value that can be seen with the naked eye and felt when measured with a compass.
When performing survey work, the measure of the accuracy of the work, along with the value of 0.1 mm, is the distance corresponding to this value on the ground, called extreme accuracy of scale. This is the maximum accuracy with which the distance can be determined according to a given plan (map). It should be borne in mind that due to the accumulation of inevitable errors in technological process making a plan (map) the practical accuracy of the result of measuring distances according to plans (maps) is much coarser than the maximum graphic accuracy and can reach 1 mm.
The ultimate scale accuracy is easy to calculate by dividing the denominator of a numerical scale by 10,000. For example, a scale accuracy of 1: 5,000 is 0.5m. It is necessary to know the magnitude of the scale accuracy when choosing the scale of the survey and when determining which terrain objects should not be filmed, since they will not be displayed at this scale.
For example, a land plot with a size of 10x10 m on maps of scales 1: 50,000, 1: 100,000 and 1: 200,000 will be depicted as a point, and with a plan (map) scale of 1: 5000, 1: 10,000, 1: 25,000, will have dimensions, respectively, 2.0x2.0 mm, 1.0x1.0mm, 0.4x0.4mm, i.e. the larger the denominator of the numerical scale, the less detail of the plan and, conversely, the smaller the denominator of the numerical scale, the greater the detail.
Construction of a transverse scale, its accuracy. Measuring the lengths of lines on the plan.
To improve the accuracy of measuring distances on the plan (map), so as not to measure the value of the segment "by eye", use a scale transverse scale, which can be plotted as follows.
Rice. 3.4. Normal transverse scale.
On a horizontal line KL(Figure 3.4) lay the base of a scale equal to 2 cm several times.Lines perpendicular to KL... First foundation KS divided into ten equal parts. Extreme perpendiculars KM and LN divided into ten equal parts and through divisions on perpendiculars, lines are drawn parallel to the base KL. The MV segment is also divided into 10 equal parts. Wherein C connect to point A, and the rest of the oblique lines, called transversals are carried out in parallel. As a result of graphic constructions, the so-called lateral scale... Section a 1 b 1 called smallest division transverse scale.
If the number of divisions at the base of the scale n, the number of divisions on the perpendicular m, then the smallest division of the transverse scale a 1 b 1 will be equal to:
a 1 b 1 = KS/nm . (3.1)
Example... If KS= 2 cm, n = 10, m= 10, then a 1 b 1= 2 cm / 10x10 = 0.02cm,
which at a scale of 1:10 000 corresponds to 2 m, a 2 b 2- 4 m, etc., AB- 20 m.
Since the base of the transverse scale is chosen equal to 2 cm, then practically the value of all its divisions in meters can be calculated for any numerical scale.
The transverse scale is usually engraved on special metal rulers called large-scale, as well as on a geodesic protractor.
Such scale bars usually indicate the ordinal numbers of small and large divisions, therefore, for each specific scale of the plan, it is necessary to first determine which value in meters corresponds to the smallest division of the scale and other divisions.
The transverse scale is used as follows. Let it be required to put on a plan (map) of a scale of 1: 10000 a line 246 m long (Fig. 3.3). With a scale base of 2 cm, one division to the right of zero will correspond to 200 m, to the left - 20 m. The smallest division according to formula (3.1) is 2 m. The right foot of the meter is placed at division with mark 200 (serial number 1), and the second leg - to the left of zero by the second division (since one division corresponds to 20 m), which will correspond to 240 m.
Then, rearranging the meter up so that the left leg of the meter goes along an inclined line (transversal), and the right leg goes along the vertical to the third horizontal line, on which there is a segment a 3 in 3 corresponding to 6 m and the total length of the line is 246 m. With the resulting solution of the meter, the distance is plotted on the plan (map).
To determine the length of the line on the plan, take the appropriate meter solution and apply it to the transverse scale so that its right leg coincides with the division to the right of zero, and the second is within the base left of zero. Then the number of meters is counted. If the left leg of the meter does not coincide with the division on the base, then the solution of the meter is moved up until it coincides with the transversal, while both legs should lie on the same horizontal line. After that, the length of the horizontal distance of the terrain line is counted. If the length of the line exceeds the length of the transverse scale, then it is measured or set aside in parts.
Using the normal transverse scale, distances can be plotted and measured with an accuracy of 0.2 mm, which corresponds to one hundredth of the base. If the position of the legs of the compass between the horizontal lines of the scale is assessed by eye, then the distances can be measured with an accuracy of 0.1 mm.
Scale is the ratio of the length of a line segment on a map, plan or drawing to its corresponding real length on the ground.
The scale shows: how many times each line. plotted on the map, reduced in relation to its actual size on the ground.
Reducing the image is a necessity, we rarely think about it, however, we also rarely depict objects in full size. As a rule, in order for them to fit on a sheet of paper, they have to be reduced, less often they have to be increased. This is especially true for the image of the earth's surface, because it is completely impossible to depict it one to one.
Does any thumbnail image have a scale? Of course not. The scale is not applicable to the drawing, even if the drawing is of very high quality. In any case, the artist will distort the depicted object, and from the definition of the scale, we see that each (!) Line of our image is equally reduced in relation to the real object. Therefore, the image to scale can be performed at least if there is measuring instruments(at least rulers). As a maximum - with the use of computer technology.
How is scale recorded?
Scale is an attitude. The ratio involves the process of division, which means that the scale is a mathematical fraction, in which there is a numerator and a denominator. In the numerator of the fraction, the length of the segment in the image is written, and in the denominator, the length of the real displayed segment.
Suppose the image is made (although this is impossible for a map) on a one-to-one scale - the length of the depicted segment coincides with the length of the depicted one.
The scale is written as 1: 1
If the image is reduced by 3 times, then the scale will be written as 1: 3
A decrease of 100,000 times is written as 1: 100,000
What does it mean?
If the scale is 1 to 1, then 1 centimeter of our image corresponds to 1 real centimeter of the depicted surface, and if 1: 100,000, then 1 centimeter of the image corresponds to 100,000 centimeters. And one meter of the image? 1 meter will then correspond to 100,000 meters. Note that whatever the selected length on the map, the actual length will be greater - in our case, 100,000 times. If the scale is 1: 1000 - then a thousand; 1:30 million - thirty million.
Translation
When we say that one centimeter of the map corresponds to thirty million centimeters, no one will understand anything. So, you need to translate this astronomical number into something understandable. We know that there are 100 centimeters in 1 meter. This means that you can convert centimeters to meters. We divide 30,000,000 centimeters by 100 and we get 300,000 meters. It is also not very convenient, which means that it is necessary to translate further. Remember that there are 1000 meters in 1 kilometer. We divide 300,000 meters by 1000. It turns out 300 kilometers. This means that one centimeter of a map with a scale of 1:30 000 000 contains 300 kilometers, and this can already be imagined.
There is a simple and reliable way converting centimeters to kilometers - in the end we divided the number by 100,000 (first by 100, and then by 1000), so you can simply mentally close 5 zeros and translate much faster, but you need to remember that this is only suitable for converting centimeters to kilometers and only when there are enough zeros. For a scale of 1:50 000, it will be enough for us to stop at meters.
Scale views
The scale that is written as a fraction through the sign ":" is called numerical... Numerical scale examples: 1: 1000 1: 1000 000 1: 250 000
Regularly, so that you do not have to carry out a translation of a numerical scale all the time on maps (especially school ones) indicate named scale. It shows what distance is contained in 1 centimeter of the map and is recorded: 1 cm 1 m; 1 cm 10 km; 1 cm 2.5 km, respectively.
Sometimes a linear scale is added under the map in the form of a measuring ruler. This is convenient, because if it is available, you can, using a compass-meter or a ruler, measure the distance on the map, apply it to a linear scale and get a result corresponding to the real distance.
Types of maps by scale
Key distinctive feature the map from the figure is the presence of a scale. A map without a scale is not a map. All cartographic works are usually classified according to the scale in which they were performed.
- Small-scale (maps of the world or continents - their scale is smaller than 1: 1000,000)
- Medium-scale (maps of countries, large islands - from 1: 100,000 to 1: 1,000,000)
- Large-scale (maps of small states, regions, cities - less than 1: 100,000)
Remember: the larger the scale, the less it fits on the map. The fact is that the scale is a fraction, and the smaller the denominator of the fraction, the larger it is.
Enlarging or reducing an image on paper is characterized by scale... On a geographic map, the image of the terrain is represented by a scale of reduction.
Numerical scale the map is expressed by the ratio of 1 to the number showing how many times the real segment has been reduced.
Majority geographic maps made on a scale of 1:20 000 000 or 1:25 000 000. This scale suggests 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 the scale record the dimension map and terrain units must match.
If the scale is 1: 20,000,000 on the map, 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, the scale of the map is 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). Having applied 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 that is used when creating drawings and models and allows you to show large objects in a reduced form, and small objects in enlarged form. In other words, it is the ratio of the length of the line 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 determine the scale?
How to find the scale
This mainly happens in the following situations:
- when using the card;
- when executing a drawing;
- in the manufacture of models of various objects.
Scale views
The numerical scale should be understood as the scale expressed as a fraction.
Its numerator is one, and the denominator is a number that shows how many times the image is smaller than the real object.
A linear scale is a ruler that you can see on maps. This segment is divided into equal parts, signed with the values of distances commensurate with them on real terrain. The linear scale is convenient in that it provides the ability to measure and plot distances on plans and maps.
A named scale is a verbal description of how much distance in reality corresponds to one centimeter on a map.
For example, one kilometer is 100,000 centimeters. In this case, the numerical scale would look like this: 1: 100000.
How do I find the scale of the map?
Take a school atlas, for example, and take a look at any page of it.
At the bottom, you can see a ruler that indicates what distance in real terrain corresponds to one centimeter on your map.
Scale in atlases is usually indicated in centimeters, which will need to be converted to kilometers.
For example, seeing 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 gap between them on the map with a ruler and determine the ratio.
So, if by measuring you got a distance of 2 cm, then you get a scale of 2: 40 = 2: 4000000 = 1: 2000000. As you can see, finding the scale is not difficult at all.
Other use cases for scale
When making models of aircraft, tanks, ships, cars, and other objects, certain scaling standards are used. For example, it can be a scale of 1:24, 1:48, 1: 144.
In this case, the manufactured models must be smaller than their prototypes precisely by the specified number of times.
Scaling may be needed, for example, when enlarging a picture. In this case, the image is divided into cells of a certain size, for example, 0.5 cm. The sheet of paper will also need to be drawn into cells, but already enlarged in required number times (for example, the lengths of their sides can be one and a half centimeters if the drawing needs to be enlarged 3 times).
By putting the contours of the original drawing on the lined sheet, it will be possible to get an image very close to the original.
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Map scale... The scale topographic maps is called the ratio of the length of the line on the map to the length of the horizontal projection of the corresponding line of the terrain. On flat territories, with small corners the slope 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 line of the terrain 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 below the southern border of the map sheet as a ratio of numbers (numerical scale), as well as in the form of named and linear (graphical) 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 a factor of 100,000.
Obviously, the larger the scale denominator, the greater the decrease 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 the lines on the map and on the ground.
With M = 1: 100,000, 1 cm on the map corresponds to 1 km.
Linear scale serves 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 the terrain distances (Fig. 5).
Rice. 5. Designation of the scale on the topographic map: a - the base of the linear scale: b - the smallest division of the linear scale; scale accuracy 100 m.
Scale value - 1 km
The segments a, laid down to the right of zero, are called basis of scale... The distance on the ground corresponding to the base is called linear scale... To improve the accuracy of determining the distances, the leftmost segment of the linear scale is divided into smaller parts in, called the smallest divisions of the linear scale.
The distance on the ground, expressed in one such division, is the accuracy of the linear scale. As can be seen in Figure 5, with a numerical scale of the map 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 related to both technical capabilities measurements, and with the resolution of human vision. The accuracy of constructions on paper (graphic accuracy) is considered to be equal to 0.2 mm.
The resolution of normal vision is close to 0.1 mm.
Ultimate accuracy map scale - a segment on the terrain corresponding to 0.1 mm in the scale of this map. At a map scale of 1: 100,000, the ultimate accuracy will be 10 m, at a scale of 1:10 000 it will be equal to 1 m.
Obviously, the possibilities of depicting contours on these maps in their actual outlines will be very different.
The scale of topographic maps largely determines the selection and detail of the objects depicted on them.
Scaling down, i.e. with an increase in its denominator, the detail of the image of terrain objects is lost.
To meet the varied needs of the national economy, science and defense of the country, maps of different scales are needed. For the state topographic maps of the USSR, a number of standard scales have been developed based on the metric decimal system measures (tab.
| Table 1. Scales of topographic maps of the USSR | |||
| Numerical scale | Card name | 1 cm on the map corresponds to the distance on the ground | 1 cm2 on the map corresponds to the area of the area |
| 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 ha |
| 1:100 000 | One hundred thousandth | 0.6 miles | 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 actually topographic maps of scales 1: 5000-1: 200,000 and survey-topographic maps of scales 1: 500,000 and 1: 1,000,000. maps are used for general acquaintance with the terrain, for orientation when driving at high speed.
Measuring distances and areas from maps.
When measuring distances from maps, remember that the result is the lengths of the horizontal projections of the lines, and not the lengths of the 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 angle of inclination of 2 °, the horizontal projection is shorter than the line itself by 0.0006, and at 5 ° - by 0.0004 of its length.
When measured from distance maps in mountainous areas, the actual distance on an incline 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.
The angles of inclination can be measured from the topographic map by the method specified in §11. Corrections to the lengths of slanted lines are also given in the tables.
Rice. 6. The position of the caliper when measuring distances on the 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 the solution of the measuring compass, 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, the lengths of the broken lines are measured by taking each segment separately into the compass solution and then summing their lengths. Distance measurements along curved lines (roads, borders, rivers, etc.)
are more complex and less accurate. Very smooth curves are measured as broken lines, pre-divided into straight line segments. Winding lines are measured with a small constant solution 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 solution (2-4 mm).
Knowing what length the compass solution corresponds to on the ground, and calculating the number of its installations along the entire line, determine its total length. For these measurements, a micrometer or a spring compass is used, the solution of which is regulated 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). By their origin, errors are subdivided into gross blunders (arising from the carelessness 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 value 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 +… + an): n = ∑a / n, where x is the most probable value of the measured value, a1, a2… an are the results of individual measurements; 2 - sum sign, n - number of measurements.
The more measurements, the closer the most probable value to the true value 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 the relative error -. This error is expressed as a correct 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 with a length of 10 cm, there may be a relative error of 1-2 mm.
This value on different scales gives different mistakes in the lengths of the measured lines. So, on a map with a scale of 1: 10,000, 2 mm corresponds to 20 m, and on a map of a scale of 1: 1,000,000 it will be 200 m.
Hence it follows that more accurate results measurements are obtained using large-scale maps.
Determination of areas plots on topographic maps is based on the geometric relationship between the area of a figure and its linear elements.
Area scale equal to square linear scale. If the sides of the rectangle on the map are reduced by n times, then the area of this figure will decrease by n2 times.
For a map with a scale of 1:10 000 (1 cm - 100 m), the scale of areas will be (1:10 000) 2 or 1 cm2- (100 m) 2, i.e. in 1 cm2 - 1 ha, and on a map with a scale of 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 measured area, the specified accuracy of the measurement results, the required speed of data acquisition and the availability of the necessary instruments.
8. Straightening the curvilinear boundaries of the site and dividing its area into simple geometric figures: dots indicate cut-off areas, hatching - mated areas
When measuring the area of a site with rectilinear boundaries, the site is divided into simple geometric shapes, the area of each of them is measured in a geometric way and, summing up the areas of individual areas calculated taking into account the scale of the map, the total area of the object is obtained.
Scale of the plan
An object with a curvilinear 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 surpluses mutually compensate each other (Fig. 8). The measurement results will be somewhat approximate.
Rice. 9. A square mesh palette overlaid on the figure to be measured. Plot area P = a2n, a - side of the square, expressed in the scale of the map; n is the number of squares that fall within the contour of the measured area
The measurement of the areas of areas with a complex irregular configuration is often performed using pallets 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 measured contour and the number of cells and their parts inside the contour is counted on it. Fractions of incomplete squares are assessed 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 division price of the palette.
Rice. 10. Dot Palette - A modified square palette. P = a2n
In addition to grid pallets, point and parallel pallets 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 division value of 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 point weight.
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 straight lines are engraved on a parallel palette. The area to be measured will be divided into a row of trapezoids with the same height when the palette is placed on it (Fig. 11). The parallel line segments within the outline midway between the lines are the midline of the trapezoid. Having measured all the middle lines, their sum is multiplied by the length of the interval between the lines and the area of the entire site is obtained (taking into account the areal scale).
The measurement of the areas of significant areas is made from maps using a planimeter.
The most common is the polar planimeter, which does not represent great complexity... However, the theory of this instrument is quite complex and is covered in surveying manuals.
12. Polar planimeter
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How to find out the scale of the map
Topographic map is a projection of a real ground mathematical model onto a plane in a reduced form. The amount of embossing is reduced and is called the scale denominator. 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
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Geography lesson in grade 6 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 in the general design of the development of the national economy, for accounting for 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 detailed content and more high precision; intended for detailed design in agriculture, design of roads, routes, power lines, for preliminary development of planning and development of rural settlements, to determine mineral reserves.
Large-scale maps and plans are compiled for more accurate detailed design (drawing up technical projects, irrigation, drainage and greening, development of master plans of cities, design engineering networks and communications, etc.).
The more demanding the survey tasks, the larger the scale required, but this is expensive, so large-scale surveys must have an engineering rationale.
Map sheets are published in unified system razgraphs and nomenclatures and represent a horizontal projection of a spheroidal trapezium - a specific area of the earth's surface.
The nomenclature of topographic maps is usually called the designations of its individual sheets (trapezoids). The nomenclature of trapezoids is based on a map sheet at a scale of 1: 1,000,000, called an international map.
Types of scales
The scale can be written in numbers or words, or displayed graphically.
- Numerical.
- Named.
- Graphic.
Numerical scale
The numerical scale is signed with numbers at the bottom of the plan or map.
For example, the scale "1: 1000" means that on the plan all distances 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 the plan or map is indicated by words.
For example, it can be written "at 1 cm - 10 m".
Linear scale
It is most convenient to use the scale, depicted as a segment of a straight line, 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, 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).
Near each centimeter it is written what distance this corresponds to on the plan.
One centimeter is divided into parts, near which it is written what distance they correspond to on the map. The length of any segment on the plan is measured with a measuring compass or ruler and, applying this segment to a linear scale, its length is determined on the ground.
Applying and using scale
Knowing the scale, you can determine the distances between geographic objects, measure the objects themselves.
If the distance from the road to the river on a plan with a scale of 1: 1000 ("in 1 cm - 10 m") is 3 cm, then on the ground it is equal to 30 m.
Material from the site http://wikiwhat.ru
Suppose, from one object to another 780 m. It is impossible to show this distance in full size on paper, so you have to draw it to scale. For example, if all distances are shown 10,000 times smaller than in reality, i.e.
That is, 1 cm on paper will correspond to 10 thousand cm (or 100 m) on the ground. Then, on a scale, the distance in our example from one object to another will be 7 cm and 8 mm.
Pictures (photos, drawings)
On this page material on topics:
What the numerical scale shows
Geographic scope report
Scale definition 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 be measured with a scale?
How big is the lake, if in captivity with a scale of 1: 2000 ("1 cm - 20 m") its length is 5 cm?
What does the scale 1: 5000, 1: 50,000 mean?
Which one is the larger? What scale is more convenient for a land plot plan, and what scale is more convenient for a large city plan?
Material from the site http://WikiWhat.ru