With the help of a topographic map, you can solve a lot of practical tasks without leaving the area. According to the topographic map, it is possible to determine: the scale of this card, the distance between any local objects, the size of any area, steepness of the skates, the height of any point of the terrain, the mutual exceeding points, the visibility of the points, the number of trees in the forest, the amount of water in the river and much more.
Usually on each topographic map gives a linear, numerical and textual scale. But how to be, if for this or another reason it did not turn out? Experienced specialist appearance The topographic map can immediately call its scale. If you can not do this, you should resort to the following methods.
Determination of the scale of the topographic map by kilometer grid.
Its side corresponds to a certain number of centimeters. If this distance is 2 cm, then the scale of the card is 1 cm - 500 meters, that is, 1: 50,000. If 4 cm, then the scale of the card will respectively, 1: 25,000.
Determining the scale of the topographic map by the length of the arc meridian.
In order to use this method, it is necessary to firmly remember that one minute by meridian is approximately 2 km (more precisely 1.85). The signatures of degrees and minutes are on the map, and in addition, each minute is highlighted with a checkered. For example, in Figure below, the length of one minute is approximately 4 cm. This means that the scale of this card will be 1:50,000.
To determine between two points, first measure this distance on the map, and then using a numerical or linear map scale, determine the actual value of this distance on the ground. If you want to determine the distance not in a straight line, but on a winding road, use special instrument - Kurvieme.
This is a device for measuring the length of the curves of lines. The base of the Kurvimeter serves wheels, the length of the circle of which is known. The wheel rotation is transmitted to an arrow rotating around a circular scale. Knowing the number of wheel speeds, rolling through the measured line, is easy to determine its length.
How to measure the area along the topographic map.
Measuring area with a geometric way.
The measured area is divided into a network of triangles, squares, trapezoids whose areas are calculated according to known formulas. The sum of the areas of famous figures will give total areaconcluded in the contour.
Square measurement with square mesh.
It is very convenient to determine the area with a millimeter grid that is applied to transparent paper or film. This mesh is applied on the circuit of the map and calculate the number of square millimeters. Knowing what is 1 mm2 topographic map on the ground (for a scale of 1: 100,000 - 1 mm2 is equal to hectare, that is 100 x 100 m), it is easy to determine the area on the map.
The distance between horizontals, the so-called pinch, shows the steepness of the skate. The main methods for determining the steepness of the skates along the topographic map are as follows.
How to determine the steepness of the skates on the scale of the tracks of the topographic map.
Usually, the drawing is placed in the field of the topographic map to determine the steepness of the skates on the fields of the topographic map. Along the lower base of this scale, numbers are indicated that indicate the rolling rods in degrees. On the perpendicular to the base, the corresponding magnitudes of the inclusion of the map are postponed.
In the left part of the embedding scale is constructed for the main height of the section, in the right - with a five-time height of the cross section. To determine the steepness of the skate, for example, between points a-in, It is necessary to take a circulation of this distance and postpone on the scale of embarrassment and read the steering wheel - 3.5 degrees.
If it is necessary to determine the slope of the skate between the horizontals thickened N-M, then this distance should be postponed on the right scale and the steepness of the skate in this case will be equal to 10 degrees.
How to determine the steepness of the scope by calculation.
Having measured according to the locking of D and knowing the height of the cross section H, the steepness of the skate can be determined by the formula: a \u003d h / d. Where a is the steepness of the skate in degrees, D is the distance between two adjacent horizontals in millimeters.
How to determine the steepness of the rod using a ruler or eye.
On Soviet cards standard height The cross sections for each scale is established such that the embedding of 1 cm corresponds to the steepness of about 1 degree. From the above formula, it can be seen that how many times the locking is less than one centimeter, the steepness of the skate is so many times more than one degree. It follows that the embedding of 1 mm corresponds to the steepness of 10 degrees, the embedding of 2 mm is 5 degrees, the embedding of 5 mm is 2 degrees and so on.
Based on the book "Map and Compass - My Friends".
Klimenko A.I.
The ratio of the genuine value of the object to the magnitude of its image. A person is not able to portray large objects, for example, a house, in a natural value, therefore, when you see a large object in the picture, drawing, layout, and so on, a person reduces the value of the object several times: in two, five, ten, a hundred, thousands etc. The number indicating how many times the depicted object is reduced, there is a scale. Scale applies when the micromyr image is image. A person cannot portray a living cage, which is considered in the microscope, in a natural value and therefore increases the value of its image several times. The number indicating how many times an increase or decrease in a real phenomenon during its image is defined as a scale.
Scale in geodesy, cartography and design
Scale Shows how many times each line applied to the card or drawing, less or more of its valid sizes. There are three types of scale: numerical, named, graphic.
Scale on maps and plans can be represented numerically or graphically.
Numerical scale They are recorded in the form of a fraction, in the numerator of which is a unit, and in the denominator - the degree of reducing the projection. For example, the scale of 1: 5,000 shows that 1 cm on the plan corresponds to 5,000 cm (50 m) on the ground.
The scale is larger to the scale that the denominator is less. For example, scale 1: 1 000 larger than scale 1:25,000.
Graphic scope divided into linear and transverse. Linear scale - This is a graphic scale in the form of a large-scale ruler separated by equal parts. Cross scale - This is a graphic scale in the form of a nomogram, the construction of which is based on the proportionality of segments of parallel straight lines crossing the side of the angle. The scale is used for more accurate measurements of the lines on the plans. The transverse scale is used as follows: Put the length of the length on the bottom line of the transverse scale in such a way that one end (right) is for the whole division of OM, and the left went out of 0. If the left leg falls between the tent divisions of the left segment (from 0), then We raise both legs of the meter upwards until the left leg falls to the intersection of anyone transuned and any horizontal line. At the same time, the right leg of the meter should be on the same horizontal line. The smallest CD \u003d 0.2 mm, and accuracy - 0.1.
Scale accuracy - This is a segment of the horizontal lines of the line corresponding to 0.1 mm on the plan. The value of 0.1 mm to determine the accuracy of the scale is made due to the fact that it is a minimum stretch 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. At this scale, 1 cm on the plan corresponds to 10,000 cm (100 m) on the ground, 1 mm - 1,000 cm (10 m), 0.1 mm - 100 cm (1 m).
The scales of images in the drawings should be chosen from the following row:
When designing general Plans large objects allowed to apply 1: 2,000; 1: 5,000; 1:10 000; 1:20 000; 1:25 000; 1:50 000.
In the necessary cases, it is allowed to apply the scale of Zoom (100N): 1, where N is an integer.
Scale in the photo
Some photographers measure the scale as an object sizes ratio to the size of its image on paper, screen or other media. The correct method of scale definition depends on the context in which the image is used.
Scale is important when calculating the depth of the sharply depicted space. Photographers are available a very wide range of scales - from almost infinitely small (for example, when shooting celestial bodies) to very large (without using special optics, it is possible to obtain scale of about 10: 1).
The scale number indicating how many times is reduced or increased real dimensions in the drawing.
Notes
Wikimedia Foundation. 2010.
Synonyms:- PRIMEBASE.
- Baidou
Watch what is "scale" in other dictionaries:
SCALE - (Masstaq, from him. Mass measure). 1) Merilo, a linear measure, adopted in the drawings in a reduced form. 2) In artillery: a copper line with the designation on it to caliber guns, shells and consumer measures in artillery. Vocabulary foreign words … Dictionary of foreign words of the Russian language
Scale - - The ratio of the length of this line depicted in the drawing, plan or map, to its length in nature. [Dictionary of main terms required in designing, construction and operation road roads.] Scale is an attitude ... ... Encyclopedia Terms, Definitions and Explanations of Building Materials
scale - Cm … Synonym dictionary
Scale - The ratio of linear dimensions depicted on the map, aerial photograph and so on the subject to its dimensions in nature. There is a scale of reducing and increasing, it can be expressed by a numerical attitude (numerical scale) or depicted graphically ... ... Sea dictionary
SCALE - [ASH] (or scale), scale, husband. (it. Masstab). 1. The ratio of reduced distances and sizes on the map and drawing to valid. Geographical map of large scale. Scale 10 miles in inches. In ten-minute scale. 2. Measure. In the Big … Dictionary Ushakova
scale 1: 1 - Full scale - [A.S.Goldberg. English Russian energy dictionary. 2006] Topics Energy as a whole Synonyms Full scale en Full Scale ... Technical translator directory
SCALE - (it. MA? STAB) Lenten length ratio in drawing, plan or map to the length of the corresponding line in nature. Indicated in the form of a fraction, the numerator of which equal to unity, and a denominator of the number showing the degree of reduction of lines (eg, 1: 100 ... ... Big Encyclopedic Dictionary
Scale - (it. Maβstab; from MAβ measure and stab stick * a. Scale; N. Maβstab, Skala; F. Echelle; and. Escala) Line length ratio in drawing, plan, card, subject model to the length of the corresponding line in nature. HA geogr. Maps are distinguished by the main M. ... ... Geological Encyclopedia
SCALE - (from him. MA? STAB) English. Scale; it. MA? Stab. 1. The ratio of the linear dimensions of the object shown in the drawing, plan, the map to its size in nature. 2. Sizes, relative magnitude of h. L. (eg, price scale). Antinazi. Encyclopedia Sociology ... Encyclopedia of sociology
The final result of topographic-geodesic works are drawings ground surface, Numeric data for the preparation of digital location models, etc. The material presented in an ordered form. Drawings can be compiled on paper based, presented in electronic form or as a computer database. Traditional forms of drawings are: map, Plan, Profile.
As an image on paper, i.e. On the plane of the entire earth's surface or significant areas, it is impossible to avoid image distortions due to the curvature of the depicted surface, since with any method of designing the plane there are distortions in the lengths of the lines and corners between them.
Reduced earth curvature influence, flat image of the whole earth surface or a significant part of it, built according to certain mathematical laws, is called card .
Depending on the appointment of the map, a certain cartographic projection is selected when it is created, i.e. Mathematical location design law on a plane.
The orthogonal projection of small areas of the terrain (up to 20 × 20 km) on the level surface can be considered flat, neglecting the curvature ground. A reduced image of such a projection on paper will be without distortion caused by curvature land, and a similar area of \u200b\u200bterrain.
In this way, reduced, similar image on the plane of horizontal injections is relatively small plot The earth's surface is called plan .
Visual image of the irregularities of the earth's surface is profile , those. reduced image of its vertical cut by the selected line.
On plans and maps there may be a situation and relief, or only situation (from Franz. Situation - location).
Collapse of images on the plan local items natural and artificial origin (river, forest, shrub, land, building, street, etc.), called situation situation.
A combination of irregularities of the earth's surface of natural origin is called terrain.
If only the boundaries of objects are depicted on the plan, it is called contour(Fig. 3.1, but). If, except for the contours, the relief is applied to the plan, such a plan is called topographic(Fig. 3.1, b.).
Fig.3.1. Contour (a) and topographic (b) plans.
The card is called a drawing, on which the surface of the entire Earth can be depicted or any part of it in a generalized and reduced form.
Maps may have various appointment: Agricultural, Cadastral, Economic, Political, etc. - these are the so-called thematic or specialcards, they show the contours of the situation and a special load. Maps on which, in addition to the contours of the situation, is depicted terrestrial surface, called outcast.The outcast base of the map is a framework for building thematic maps.
With any measurements according to the plans and cards, it should be remembered that the scale of the plan in all its points is the same, and the scale in all points of the card is usually different.
The concept of topographic plans and maps.Scale. Scale accuracy.
The concept of the scale of the plan and card.
When drawing up plans, cards, profiles, the results of measurement of lines on the ground are reduced by several hundred or thousands of times.
The degree of reduction of horizontal principles of terrain lines during the image of them on the plan is called scale.
Under map scale In general, it is understood as the ratio of the length of the line on the map to its length on the nature of the attitudes. Depending on the cartographic projection of the image on the map in different places have different in the magnitude of the distortion, therefore the scale of the map of the neodynaks. For maps drawn up in a small scale, an average scale is usually signed.
Scale, pronounced in the form of a simple fraction called numerical. It has a numeral equal to one, and the denominator is a circular number, for example, 1/500, 1/1000 or 1: 500, 1: 1000. Scale 1: 500 shows that the horizontal injure line of the area is reduced on the plan 500 times and one unit of length on the plan, the map or profile corresponds to 500 such units, i.e. One centimeter on the plan, the map or profile corresponds to 500 cm or 5 m on the ground.
The numerical scale sign on the plans, maps or profiles in their lower part, accompanying an explanatory inscription, for example, "in 1 centimeter 5 m", as the length of the terrain lines are conveniently expressed in meters. To determine the number of meters on the ground in one centimeter of the Plan (Maps), it is necessary for a denominator of a numerical scale to discard the last two zero, for example, 1 cm scale plan 1: 2000 corresponds to 20m on the ground.
To show more details on the plan (map), they should be on a larger scale. Than less denominator Numerical scale, the scale is larger, and the scale with a large denominator is considered small. Close-up are: 1: 500, 1: 1000, 1: 2000, 1: 5000; to average - 1:10 000, 1:25 000, 1:50 000; To small - 1: 100,000, 1: 200,000, 1: 500,000, 1: 1 000 000 and smaller.
Plans and maps in Russia are created in the accepted scale forming a strictly defined system called large-scale near. The large-scale row is set with such a calculation so that it satisfies all the conditions of consumers and the ability to easily move from one scale to another.
Knowing numerical scale, easily length of terrain lines translate into length lines on the plan (map) and vice versa. Such a translation is associated with calculations, so not to make such calculations, use scale (nomogram) graphically built. This scale is called linear scale (Fig. 3.2).
Fig. 3.2. Numerical and linear scales.
A linear scale is a graph in the form of a stretch of a straight horizontal line, on which equal segments are sequentially postponed. basescale. The base of scale corresponds to an integer number of tens or hundreds of meters on the ground. To increase the accuracy of measurements, the leftmost base is divided into smaller segments.
The beginning of the account is zero (0) - the total point of the first and second base base. The remaining segments are signed according to a numerical scale. If the base base is 2 cm, then such a linear scale is called normal. In fig. 3.1 Normal linear scale is constructed for numerical 1: 10,000 (1 cm - 100 m, and 2 cm - 200 m).
Linear scale measurements are usually produced circular meter(Fig.3.3), which must be adjusted well before work. When measuring the circus should be kept by one hand, tilting it a few of themselves so that both the needles of the needle are clearly visible at the same time.
Fig. 3.3. Determination of a linear scale distance.
When measuring the distances, the circular solution is installed at points A and B on the plan, and then the circular is applied to the linear scale so that its left leg came to the left of zero, and the right thing stood exactly on one of the divisions to the right from zero. The determined distance will be equal to the amount of samples at both ends of the needles of the circulation, i.e. 100 + 86 \u003d 186m. At the same time, the tenths of the shallow divisions are determined by the "eye".
When performing cardmetric work on the plans (maps), the main elements of the graphic construction are the docks of the circulation needles and the line. Nabol is a mug of very small diameter. The physiological property of the human eye is such that when viewed from a distance of 25-30 cm, two nearby points (Naskov) are merged into one if the distance between them is less than 0.1 mm (according to the studies of the GUZE geodesy and 0.08 mm). This is associated with a critical angle of view of a person equal to 1 ¢. The value of 0.1 mm is accepted for the limit graphic accuracymeasurements on the map, i.e. It is such a minimum value that can be seen with the naked eye and feel when measuring the circular.
When performing removal work, the measure of accuracy of work along with a value of 0.1 mm is the corresponding distance in the area called this magnitude limit accuracy scale. This is the maximum accuracy with which the distance on this plan (map) can be determined. It should be borne in mind that due to the accumulation of inevitable errors in technological process Manufacturing Plan (Maps) The practical accuracy of the measurement measurement of distances according to the plans (cards) is significantly roughening limit graphics accuracy and can reach 1mm.
The maximum scale accuracy is easy to calculate, dividing the numerical scale denominator to 10,000. For example, the accuracy of 1: 5,000 is 0.5 m. It is necessary to know the magnitude of the accuracy scale. When you select the shooting scale and when determining which area objects should not be removed, as they are not depicted on this scale.
For example, a land plot of 10x10 m on the scales of 1: 50,000, 1: 100 000 and 1: 200,000 will be pictures in the form of a point, and with a plan scale (cards) 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 way the plan is smaller and, on the contrary, the smaller the denominator of the numerical scale, the detail is greater.
Connecting a transverse scale, its accuracy. Measurement of lines on the plan.
To increase the accuracy of measurement distance on the plan (map), so as not to measure the magnitude of the segment "to the eye", use the scale transverse Scale that can be constructed as follows.
Fig. 3.4. Normal transverse scale.
On the horizontal direct Kl (Fig. 3.4) Delay several times the scale of scale equal to 2 cm. Through the obtained points carry lines perpendicular to Kl. The first base Ks.divide ten equal parts. Extreme perpendicular KM and LN.deliver to ten equal parts and through divisions on perpendicular lines, parallel bases Kl. MV segments are also divided into 10 equal parts. Wherein C. Connect with a point BUT, and the remaining inclined lines, called transversalare carried out in parallel. As a result, graphic constructions are obtained, the so-called cross scale. Section a 1 B 1 called the smallest division transverse scale.
If the number of scale base divisions n., number of divisions on perpendicular M, then the smallest division of transverse scale a 1 B 1 It will be:
a 1 B 1 = Ks./nm. . (3.1)
Example. If a Ks. \u003d 2 cm, n. = 10, m. \u003d 10, then a 1 B 1 \u003d 2 cm / 10x10 \u003d 0.02cm,
that 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 the almost value of all its divisions can be calculated for any numerical scale.
A transverse scale is usually engraved on special metal rules called large-scale as well as on geodesic transport.
On such large-scale rules, the sequence numbers of small and large divisions are usually indicated, so for each specific scale of the plan, it is necessary to pre-determine which value in meters corresponds to the smallest division of scale and other divisions.
The transverse scale is as follows. Let it be necessary to postpone on the plan (map) of the scale 1: 10,000 line of 246 m (Fig. 3.3). Under the basis of a scale equal to 2 cm, one division of the right of zero will correspond to 200 m, on the left - 20 m. The smallest division according to formula (3.1) - 2 m. Put the right leg of the meter to divide 200 (sequence number 1), and The second leg is left from zero to the second division (because one division corresponds to 20 m), which will correspond to 240 m.
Then rearring the meter up so that the left leg of the meter went to the inclined line (transverse), and the right - vertical to the third horizontal line on which there is a segment 3 in 3 The corresponding 6m and receive the total length of the line 246 m. \u200b\u200bThe resulting solution of the meter is postponed on the plan (map).
To determine the length of the line on the plan, they take an appropriate solution of the meter and applied to a transverse scale so that its right leg coincided with the division to the right of zero, and the second - was within the left of the zero of the base. Then count the number of meters. If the left leg of the meter does not coincide with the division on the base, then the meter solution moves upwards to the coincidence with the transversal, and both legs must lie on one horizontal line. After that, count the length of the horizontal location of the area. If the length of the line exceeds the length of the transverse scale, it is measured or postponed in parts.
With the help of a normal transverse scale, you can postpone and measure the distances with an accuracy of 0.2 mm, which corresponds to one cell of the base. If the position of the circular legs between the horizontal lines of the scale of scales to evaluate the eye, then the distances can be counted up to 0.1 mm.
Scale - This is the ratio of the length of the segment on the map, plan, or drawing to the real length of the real length on the ground.
Scale shows: How many times each line. applied to the card, reduced in relation to her valid sizes On the terrain.
Reducing the image is a need, we rarely think about it, however, we also rarely depict the items in the natural value. As a rule, so that they fit on a sheet of paper, they have to be reduced, less often - you have to increase. It is especially important for the image of the earth's surface, because to depict her one in one is completely impossible.
Is any reduced image possessing a scale? Of course not. The scale of the scale is not applicable, even if the drawing is very high-quality. In any case, the artist will make distortion in the depicted object, and from the definition of scale we see that each (!) The line of our image is reduced relative to the real object equally. Therefore, the image on the scale can be performed at least in the presence of measuring instruments (at least ruler). As a maximum - using computing equipment.
How is the scale written?
Scale is an attitude. The relationship implies the division process, which means, the scale is a mathematical fraction in which there is a numerator and denominator. In a numerator, the fraction is recorded in the length of the segment on the image, and in the denominator - the length of the real depicted segment.
Suppose the image is made (at least for the map it is impossible) on the scale of one to one - the length of the depicted section coincides with the length of the depicted.
Scale is written as 1: 1
If the image is reduced 3 times, the scale will be written as 1: 3
The decrease of 100,000 times is written as 1: 100,000
What does it mean?
If the scale is 1 to 1, it means 1 centimeter of our image corresponds to 1 real centimeter of the surface of the surface, and if 1: 100,000, which means 1 centimeter of the image corresponds to 100,000 centimeters. And one image meter? 1 meter will then correspond to 100,000 meters. Note that whatever the selected length on the map, the real length will be greater - in our case 100,000 times. If the scale is 1: 1000 - then in a thousand; 1:30 000 000 - thirty million.
Transfer
When we say that one centimeter of the card corresponds to thirty million centimeters, no one will understand anything. So, it is necessary to translate this astronomical number into something clear. We know that 1 meter is 100 centimeters. So, you can translate centimeters to meters. 30,000,000 centimeters divide by 100 and get 300,000 meters. Also is not too convenient, it means that you need to translate further. Remember that 1 kilometer 1000 meters. We divide 300,000 meters per 1000. It turned out 300 kilometers. It means that in one centimeter map scale 1:30 000 000 contains 300 kilometers, and this can already be submitted.
There is a simple I. reliable way Transfer centimeters to kilometers - ultimately we divided the number 100,000 (first at 100, and then 1000), so you can simply mentally close 5 zeros and translate much faster, but you need to remember that it is only suitable for translating centimeters to kilometers And only then when zeros are enough. For a scale of 1:50,000, we will be enough to stay on meters.
Speed \u200b\u200bspecies
That scale that is written in the form of a fraction through the sign ":" called numerical. Examples of numerical scale: 1: 1000 1: 1000 000 1: 250 000
Regularly in order not to perform all the time to perform the transfer of a numerical scale on maps (especially school) indicate named scale. It shows what distance is contained in 1 centimeter of the map and 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 line. It is convenient, because if it is possible, using the circus meter or ruler to measure the distance on the map, attach it to a linear scale and get the result corresponding to the real distance.
Types of cards on scale
Key a distinctive feature Maps from the picture is the presence of scale. Map without scale is not a map. All cartographic works are customary to classify according to the scale in which they are completed.
- Small-scale (world maps or mainland - their scale smaller 1: 1000 000)
- Medium-scale (maps of countries, large islands - from 1: 100,000 to 1: 1000 000)
- Large-scale (maps of small states, regions, cities - less than 1: 100,000)
Remember: the larger the scale, the less placed on the card. The fact is that the scale is a fraction, and the smaller the denomoter of the fraction, the larger.
Increase or decrease the image on paper is characterized scale. On the geographic map, the image of the area is represented by a decrease scale.
Numerical scale The maps are expressed by the ratio of 1 to the number indicating how many times the reducing the real segment is made.
Most geographic maps 1:20 000 000 or 1:25,000,000 are made to 1:20,000,000. Such a scale indicates that 1cm on the map corresponds to 20,000,000 cm \u003d 200 km or 25,000,000 cm \u003d 25 km on the ground, since the size of the scale is dimension Units of the card and the area must coincide.
If a scale of 1:20,000,000 is marked on the map, then measuring the distance between points in centimeters and multiplying it to 20,000,000, you will get the real distance between points in centimeters.
To simplify calculations, it is possible to properly translate into kilometers or meters on the ground.
For example, the distance between the city A and the city of B was 3.5 cm on the map, the scale of the card 1:25,000,000.
Decision:
1) 25 000 000 cm \u003d 250 km
2) 3.5 * 250 \u003d 875 (km)
In addition to a numerical scale on the map can be given linear scale.
The first square on the left shows the scale (1 cm on the map is 200 m on the ground). Applying a ruler to the map, we immediately define on 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 in the consolidated one. In other words, this is the ratio of the length of the segment on the map to the true length of the area. Different practical situations May require knowledge of how to find a scale.
When does the need to determine the scale?
How to find scale
This is mainly happening in the following situations:
- when using the card;
- when performing a drawing;
- in the manufacture of models of various objects.
Speed \u200b\u200bspecies
Under the numerical scale should be understood the scale expressed by the fraction.
Its numerator is a unit, and the denominator is the number indicating how many times the image is less than a real object.
Linear scale is a measuring line that you can see on the maps. This segment is divided into equal parts signed by the values \u200b\u200bof the distance among them in real areas. It is convenient for a linear scale by ensuring the ability to measure and build distances on the plans and maps.
A named scale is a verbal description of how much the distance in reality corresponds to one centimeter on the map.
For example, one kilometer is 100,000 centimeters. In this case, the numerical scale would look like this: 1: 100000.
How to find a map scale?
Take, for example, school atlas and take a look at any of its page.
At the bottom you can see a ruler on which it is indicated how much the distance on the real area corresponds to one centimeter on your card.
The scale in atlases is usually indicated in centimeters to be translated into kilometers.
For example, seeing the inscription 1: 9,500,000, you will understand that 95 kilometers of real locality corresponds to only 1 cm card.
If, for example, you know that the distance between your city and the neighboring is 40 km, then you can simply measure the range between them on the map and determine the ratio.
So, if by measuring you received a distance of 2 cm, then you get the scale 2: 40 \u003d 2: 4000000 \u003d 1: 2000000. As you can see, find the scale is completely simple.
Other occasion use cases
In the manufacture of models of aircraft, tanks, ships, cars and other objects, certain scaling standards are used. For example, it may be scale 1:24, 1:48, 1: 144.
At the same time, the manufactured models must be less than their prototypes in the specified number of times.
Scaling may need, for example, with an increase in any pattern. In this case, the image is divided into cells of a certain size, for example, 0.5 cm. The paper sheet will need to be alleged on the cells, but already enlarged in neighborhood Once (example, the lengths of their parties can be one and a half centimeters if the drawing needs to be increased 3 times).
Applying the contours of the original drawing to the discharge sheet, you can get an image, very close to the original.
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Scale card. Scale topographic maps It is called the ratio of the line length on the map to the length of the horizontal projection of the corresponding area line. On flat territories, with small corners The tilt of the physical surface, the horizontal projections of the lines are very little different from the lengths of the lines themselves, and in these cases can be considered the scale of the line length ratio on the map to the length of the corresponding area line, i.e.
the degree of reduction of length lines on the map relative to their length on the ground. The scale is indicated under the southern frame of the card sheet in the form of the ratio of numbers (numerical scale), as well as in the form of a named and linear (graphic) scale.
Numerical scale (M) It is expressed by the fraction, where in the numerator unit, and in the denominator the number indicating the degree of reduction: M \u003d 1 / m. For example, on the map on a scale of 1: 100000, lengths are reduced relatively to their horizontal projections (or with reality) 100,000 times.
Obviously, the larger the value of the scale, the greater the reduction in lengths, the smaller the image of objects on the map, i.e. The smaller the scale of the card.
Named scale - Explanation, indicating the ratio of lines on the map and on the ground.
At m \u003d 1: 100 000 1 cm on the map corresponds to 1 km.
Linear scale It serves to determine the lengths of the lines in nature. This is a straight line, divided into equal segments, corresponding to the "round" decimal number of area distances (Fig. 5).
Fig. 5. Designation of the scale on topographic map: a - linear base: B - the smallest division of linear scale; Scale accuracy 100 m.
Squeege size - 1 km
Segments A, postponed to the right of zero, are called base base. The location of the ground is called linear magnitude. To increase the accuracy of determining the distance of the extreme left, the linear scale segment is divided into smaller parts in, called the smallest linear scale divisions.
The distance on the ground expressed in one such division is the accuracy of a linear scale. As can be seen in Figure 5, with a numerical map of the card 1: 100 000 and the base of the linear scale in 1 cm The magnitude of the scale will be 1 km, and the accuracy of the scale (with the smallest division of 1 mm) - 100 m.
Accuracy of measurements on the cards and the accuracy of graphic buildings on paper are connected with technical capabilities measurements and with the resolution of human vision. The accuracy of construction on paper (graphic accuracy) is considered to be 0.2 mm.
The resolution of normal vision is close to 0.1 mm.
Limit accuracy The scale of the card is a segment on the ground, corresponding to 0.1 mm on the scale of this card. With the scale of the card 1: 100 000, the limit accuracy will be 10 m, with a scale of 1:10,000, it will be equal to 1 m.
Obviously, the possibilities of the image on these circuit cards in their actual outlines will be quite different.
The scale of topographic maps largely determine the selection and detail of the objects depicted on them.
With a decrease in scale, i.e. With an increase in its denominator, the detail of the image of the objects is lost.
To meet the diverse needs of the sectors of the national economy, science and defense of the countries, maps of different scales are required. For state topographic maps of the USSR, a number of standard scales based on metric decimal system measures (Table.
| Table 1. Scales of topographic maps of the USSR | |||
| Numerical scale | Map title | 1 cm on the map corresponds to the area distance | 1 cm2 on the map according to the area of \u200b\u200bthe square |
| 1:5 000 | Five thousand | 50 M. | 0.25 g |
| 1:10 000 | Ten thousand | 100 meters | 1 g |
| 1:25 000 | Twenty pyattyanya | 250 meters | 6.25 hectares |
| 1:50 000 | Fifty thousand | 500 meters | 25 g |
| 1:100 000 | Stomasky | 1 km | 1 km2 |
| 1:200 000 | Two-hundredth thousand | 2 km | 4 km2. |
| 1:500 000 | Five hundred dollar | 5 km | 25 km2. |
| 1:1 000 000 | Millionna | 10 km | 100 km2. |
In the complex of maps named in Table.
1, allocate topographic maps of scale 1: 5000-1: 200,000 and overview and topographic maps of scale 1: 500 000 and 1: 1 000 000. The latter are inferior and details of the area of \u200b\u200bthe area, but individual sheets cover significant territories, and these Maps use for general familiarization with the area for orienting when driving at high speed.
Measurement of distances and areas on maps.
When measuring distances on maps, it should be remembered that the result of horizontal projections of lines is obtained, and not the length of the lines on the earth's surface. However, at low 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. 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 its length.
When measuring the distances in the mountainous areas, the actual distance on the inclined surface can be calculated
according to the formula S \u003d D · Cos α, where D is the length of the horizontal projection of the line S, α is the angle of inclination.
Tilt angles can be measured by the topographic map by the method specified in §11. The adjustments in the length of the inclined lines are also given in the tables.
Fig. 6. Position of the Circular Meter when measuring distances on the map using a linear scale
To determine the length of the length of the line between two points into the solution of the circular meter, the specified segment is taken from the card, transferred to a linear scale of the card (as indicated in Figure 6) and receive the length of the line expressed in the accommodation measures (meters or kilometers).
Similarly, the lengths of the broken lines are measured, taking into a circular solution each segment separately and then summing their lengths. Measurements of distances on curve lines (on roads, borders, rivers, etc.
p.) More complex and less accurate. Very smooth curves are measured as broken, smashing pre-for rectilinear segments. The winding lines are measured by a small constant circulature solution, rearranged it ("Stepping") in all curves of the line. It is obvious that fine-cutting lines should be measured with a very small circulation solution (2-4 mm).
Knowing what length on the area corresponds to a circular solution, and calculating the number of its installations throughout the line, determine its total length. With these measurements, a microzer meter or spring circular is used, the solution of which is controlled by a screw pasted through the feet of the circulation.
7. Kurvimeter
It should be borne in mind that any measurements are inevitably accompanied by errors (errors). By their origin, the error is divided into coarse blunders (arise due to the inattention of the person producing measurement), systematic errors (due to the errors of measuring devices, etc.), random errors that cannot be fully taken into account (the reasons are not clear).
It is obvious that the true meaning of the measured value due to the influence of measurement errors remains unknown. Therefore, they determine its likely meaning. This value is an arithmetic average of all individual measurements x - (A1 + A2 + ... + An): n \u003d σa / n, where X is the likely value of the measured value, A1, A2 ... AN - the results of individual measurements; 2 - Sign of the amount, N is the number of measurements.
The more measurements, the closer the most likely value to the true value of A. If we assume that the value A is known, then the difference between this value and the measurement A will give a true measurement error Δ \u003d a-a.
The ratio of the error of measuring any value A to its value is called relative error -. This error is expressed in the form of proper fract, where in the denominator - the proportion of errors from the measured value, i.e. Δ / a \u003d 1 / (A: Δ).
For example, when measuring the lengths of the curves, the crossmeter occurs error of measurements of about 1-2%, i.e. it will be 1/100 - 1/50 part of the length of the measured line. Thus, when measuring a line of 10 cm long, a relative error is possible 1-2 mm.
This value in different scales gives different errors In the lengths of the measured lines. So, on the map scale 1:10 000 2 mm corresponds to 20 m, and on the map of scale 1: 1 000 000 This will be 200 m.
Hence it follows that more accurate results Measurements are obtained when using large maps.
Definition of space Plots on topographic maps is based on the geometric relationship between the shape area and its linear elements.
Scale space equal to square linear scale. If the sides of the rectangle on the map are reduced in n times, then the area of \u200b\u200bthis figure will decrease in P2 times.
For map scale 1:10 000 (1 cm - 100 m) The scale of the area will be equal to (1:10,000) 2 or 1 cm2- (100 m) 2, i.e. In 1 cm2 - 1 hectare, and on the map of scale 1: 1 000 000 in 1 cm2 - 100 km2.
Graphic and instrumental methods are used to measure the area of \u200b\u200bthe cards. The use of a particular measurement method is dictated by the form of a measured area, a given accuracy of measurement results required by the speed of receiving data and the presence of the necessary devices.
8. Hindering the curvilinear boundaries of the site and breakdown its area to simple geometric figures: points indicated cut-off areas, hatching - sequential sections
When measuring the area of \u200b\u200bthe area with rectilinear boundaries, a plot is divided into simple geometric shapes, measure the area of \u200b\u200beach of them with a geometric method and, summing up the area of \u200b\u200bindividual sections, calculated taking into account the scale of the map, receive the total area of \u200b\u200bthe object.
Scale plan
The object with the curvilinear contour is divided into geometric shapes, pre-hidden boundaries with such a calculation so that the sum of the cut-off areas and the amount of excess to the mutually compensated each other (Fig. 8). The measurement results will be somewhat close.
Fig. 9. Square grid pallet superimposed on the measured figure. The area of \u200b\u200bthe P \u003d A2N area, A - the side of the square, expressed on the map scale; n - the number of squares in the limits of the circuit of the measured site
Measuring areas of areas having a complex incorrect configuration are more often produced using pallets and plan meters, which gives the most accurate results.
The grid pallet (Fig. 9) is a transparent plate (made of plastic, organic glass or tracing) with a bent or stacked mesh square. The palette is applied to the measured circuit and it counts the number of cells and their parts that are inside the contour. The fractions of incomplete squares are evaluated to the eye, therefore, lattices with small squares are used to increase measurement accuracy (with a side of 2-5 mm). Before working on this map, the area of \u200b\u200bone cell in the accommodation measures is determined, i.e.
price fission Paletki.
Fig. 10. Spot pallet - a modified square pallet. P \u003d A2N.
In addition to the grid pools, point and parallel palets are used, which are transparent plates with stamped dots or lines. Points are put in one of the corners of the cells of the grid palette with a known price of division, then the grid lines are removed (Fig.
10). The weight of each point is equal to the price of the patellic division. The area of \u200b\u200bthe measured area is determined by counting the number of points inside the contour, and multiplying this amount by weight point.
11. Pallet consisting of a system of parallel lines. The figure of the figure is equal to the sum of the lengths of the segments (medium dotted), cut by the contour of the site multiplied by the distance between the shell lines.
At the parallel palette, equidate parallel straight lines are loaded. The measured area will be divided into a number of trapezes with the same height when applying a palette (Fig. 11). Segments of parallel lines inside the contour in the middle between the lines are medium lines of the trapez. Having measured all medium lines, they multiply their sum for the length of the gap between the lines and get the area of \u200b\u200bthe entire area (including an area of \u200b\u200bscale).
Measuring the areas of significant areas is made by cards using a plan meter.
The most common polar plan, work with which does not represent great difficulty. However, the theory of this device is quite complex and is considered in geodesy manuals.
12. Polar Planometer
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How to find out the map scale
Topographic map - projection of a real terrestrial mathematical model on a plane in the form. The amount of relief image decreases and is called the denominator of the scale. In other words, the scale of the map is the ratio of the distance between two objects, measured along it, until the distance between the same objects measured on the ground. Knowing the scale of the card, you can always calculate the actual size and distance between objects located on the earth's surface. instructions
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Lesson of geography in grade 6 on the topic "Scale. Species of scale "
The scale of the card is divided into three groups: small-scale (1: 1 000 000, 1: 500,000, 1: 300,000, 1: 200,000); High-scale (1: 100000, 1:50 000, 1:25 000); Large-scale (1: 10000,1: 5000, 1: 2000,2: 1000,1: 500).
Large-scale topographic maps are most accurate and suitable for detailed design.
Small-scale maps are intended: For general study of the area with the general design of the development of the national economy, to take into account the resources of the surface of the Earth and the water space, for the preliminary design of large engineering facilities, for the needs of the country's defense.
Medium-scale cards have more detailed content and more high accuracy; Designed for detailed design in agriculture, road design, trails, power lines, for preliminary development of planning and building rural settlements, To determine the reserves of minerals.
Large-scale maps and plans are compiled for more accurate detailed design (compilation technical projects, irrigation, drainage and landscaping, development of general plans of cities, design engineering networks and communications, etc.).
The more responsible the tasks of shooting, the larger the scale is required, but it is due to high costs, so large-scale shooting should have an engineering rationale.
Card sheets are published in unified system Demands and nomenclature and represent a horizontal projection of a spheroid trapezium - a certain portion of the earth's surface.
The topographic card nomenclature is made to call the designation of its individual sheets (trapezes). The nomenclature of the trapezium is based on a 1: 1000000 scale map list, called an international card.
Species of scale
Scale can write with numbers or words, or portray graphically.
- Numerical.
- Named.
- Graphic.
Numerical scale
Numerical scale sign on the bottom of the plan or card.
For example, the scale "1: 1000" means that all distances are reduced in terms of 1000 times. 1 cm on the plan corresponds to 1000 cm on the ground, or, since 1000 cm \u003d 10 m, 1 cm on the plan corresponds to 10 m on the ground.
Named scale
The named scale of the plan or card is denoted by words.
For example, it can be written "in 1 cm - 10 m".
Linear scale
It is convenient to use the scale depicted in the form of a straight line segment separated by equal parts, usually centimeters (Fig. 15). Such a scale is called linear, it is also shown at the bottom of the card or plan.
Note that when drawing a linear scale, zero put, retreating 1 cm from the left end of the segment, and the first centimeter is divided into five parts (2 mm).
Near each centimeter signed, which distance it corresponds to on the plan.
One centimeter is divided into parts, near which they are written, what distance on the map they correspond. The circular meter 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 scale, you can determine the distances between geographic objects, measure the objects themselves.
If the distance from the road to the river on the plan with a scale of 1: 1000 ("1 cm - 10 m") is 3 cm, it means on the ground it is equal to 30 m.
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Suppose from one object to another 780 m. Show genuine value This distance on paper is impossible, so you have to draw it on the scale. For example, if all distances are depicted 10,000 times smaller than in reality, t.
e. 1 cm on paper will correspond to 10 thousand cm (or 100 m) on the ground. Then, on the 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 the themes:
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Questions to this article:
What is the scale?
What does scale indicate?
What can be measured by scale?
How Veliko Lake, if in captivity with a scale of 1: 2000 ("1 cm - 20 m") its length is 5 cm?
What does scale mean 1: 5000, 1: 50000?
Which one is larger? What scale is more convenient for the plan of the land plot, and what - for a plan of a large city?
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