Topic 7. Measurement of distances and areas on topographic maps

7.1. Measurement and postponus distance on the map

To measure the distance on the map, a millimeter or large-scale ruler, a circular meter, and for measuring the lines of lines - Kurvimeter is used.

7.1.1. Measurement of distances with millimeter line

Millimeter ruler measure the distance between specified points On the map with an accuracy of 0.1 cm. The resulting number of centimeters multiply by the value of the named scale. For flat terrain, the result will correspond to the distance on the ground in meters or kilometers.
Example. On the map scale 1: 50 000 (in 1 cm - 500 m.) The distance between two points is 3.4 cm. Determine the distance between these points.
Decision. Named scale: 1 cm 500 m. The location distance between the points will be 3.4 × 500 \u003d 1700 m..
At the corners of the inclination of the earth's surface, more than 10º must enter the appropriate amendment (see below).

7.1.2. Measurement of distances with a circular meter

When measuring the distance in a straight line, the circular needle is installed on the endpoints, then, without changing the circular solution, the distance is counted according to a linear or transverse scale. In the case when the circulation solution exceeds the length of a linear or transverse scale, an integer number of kilometers is determined by the squares of the coordinate grid, and the residue is the usual order along the scale.

Fig. 7.1. Measurement of distances with a circulatory-measuring meter.

For length loan line Sequentially measured the length of each link, and then summarize their values. Such lines are measured also by increasing the circulat solution.
Example. To measure the length of the broken ABCD. (Fig. 7.2, but), Circle's legs first put on the point BUT and IN. Then rotating the circus around the point IN. move rear leg From the point BUT exactly IN", lying on the continuation of the direct Sun..
Front leg from point IN Turn in point FROM. As a result, a circular solution is obtained In "S.=AU+Sun.. Moving in the same way the rear feet of the circulation from the point IN" exactly FROM"and the front of FROM in D.. Circular solution is obtained
With "d \u003d in" C + Cd, the length of which is determined by a transverse or linear scale.

Fig. 7.2. Line length measurement: aBCD's broken; b - curve1b1c1;
B "C" - auxiliary points

Long curves segments Measure the chord of the circular steps (see Fig. 7.2, b). A circular step equal to an integer number of hundreds or tens of meters is installed using a transverse or linear scale. When the circular legs are permutable along the measured line in directions shown in Fig. 7.2, B arrows, say steps. The total length of the line A 1 C 1 is made of a segment A 1 in 1 equal to the step of step multiplied by the number of steps, and the residue in 1 s 1 measured by cross or linear scale.

7.1.3. Measuring distance Kurvimmeter

Curves segments are measured by mechanical (Fig. 7.3) or electronic (Fig. 7.4) Kryvimimer.

Fig. 7.3. Kurvimeter mechanical

First, rotating the wheel with the hand, set the arrow to zero division, then rolled the wheel on the measured line. The countdown on the dial against the end of the arrow (in centimeters) is multiplied by the magnitude of the map scale and get the distance on the ground. Digital Kurvimeter (Fig. 7.4.) - This is a high-precision, user-friendly instrument. Kurvimeter includes architectural and engineering functions and has a convenient display for reading information. This device can handle metric and Anglo-American (feet, inches, etc.) values, which allows you to work with any cards and drawings. You can enter the most frequently used type of measurement, and the device will automatically translate large-scale measurements.

Fig. 7.4. Kurvimeter digital (electronic)

To improve the accuracy and reliability of the results, it is recommended to conduct all measurements twice - in direct and reverse directions. In the case of minor differences in the measured data for the final result, the arithmetic value of the measured values \u200b\u200bis taken.
The accuracy of measurement of the distances in the specified methods using a linear scale is 0.5 - 1.0 mm on a map scale. The same thing, but using a transverse scale is 0.2 - 0.3 mm by 10 cm of the line length.

7.1.4. Recalculation of horizontal injections to inclined range

It should be remembered that as a result of measuring distances by cards, the lengths of horizontal projections of lines (D) are obtained, and not the length of the lines on the earth's surface (s) (Fig. 7.5).

Fig. 7.5. Inclined range ( S.) and horizontal injections ( d.)

The actual distance on the inclined surface can be calculated by the formula:

where d. - Length horizontal line projection S.;
α - The angle of inclination of the earth's surface.

The length of the line on topographic surface can be determined using a table (tab.7.1) relative values \u200b\u200bof the amendments to the length of horizontal injections (in%) .

Table 7.1.

Terms of use Table

1. In the first line of the table (0 tens), the relative values \u200b\u200bof the amendments at the angles of inclination from 0 ° to 9 ° are given, in the second - from 10 ° to 19 °, in the third - from 20 ° to 29 °, in the fourth - from 30 ° up to 39 °.
2. To determine the absolute value of the amendment, it is necessary:
a) in the table over the angle of inclination to find the relative amount of the correction (if the angle of the topographic surface is set not in an integer number of degrees, then the relative amount of the amendment is necessary to find interpolating between the tables);
b) Calculate the absolute value of the correction to the length of horizontal injections (i.e. this length is multiplied by the relative amount of the amendment and the resulting product is divided by 100).
3. To determine the length of the line on the topographic surface, it is necessary to add the calculated absolute value of the amendment to the length of the horizontal injection.

Example. The topographic map is defined the length of horizontal injections of 1735 m., Topographic surface inclination angle - 7 ° 15 '. The table relative values \u200b\u200bof the amendments are shown for entire degrees. Consequently, for 7 ° 15 "It is necessary to determine the nearest large and closest smaller magnitude to one degree - 8º and 7º:
for 8 ° relative magnitude of the amendment 0.98%;
for 7 ° 0.75%;
Difference of table values \u200b\u200bin 1º (60 ') 0.23%;
The difference between the specified angle of inclination of the earth's surface is 7 ° 15 "and the nearest smaller tabular value of 7º is 15."
We compile proportions and find a relative amount of amendment for 15 ":

For 60 'the amendment is 0.23%;
For 15 'amendment is h.%
h.% = = 0,0575 ≈ 0,06%

The relative magnitude of the correction for an angle of inclination 7 ° 15 "
0,75%+0,06% = 0,81%
Then it is necessary to determine the absolute value of the amendment:
= 14.05 m "14 m.
The length of the inclined line on the topographic surface will be:
1735 m + 14 m \u003d 1749 m.

At low angles of tilt (less than 4 ° - 5 °), the difference in the length of the inclined line and its horizontal projection is very small and may not be taken into account.

7.2. Measurement of space on cards

Definition of areas of sites by topographic cards Based on the geometric dependence between the shape area and its linear elements. The scale of the square is equal to the square of linear scale.
If the sides of the rectangle on the map are reduced in n. Once, the area of \u200b\u200bthis figure will decrease in n. 2 times. For map scale 1:10 000 (in 1 cm 100 m) The scale of the area will be equal to (1: 10 000) 2 or 1 cm 2 will be 100 m × 100 m \u003d 10 000 m 2 or 1 hectare, and on the map of scale 1 : 1 000 000 in 1 cm 2 - 100 km 2.
Graphic, analytical and instrumental methods are used to measure the area of \u200b\u200bmaps. The use of a particular measurement method is due to the shape of the measured area specified by the accuracy of the measurement results required by the speed of receiving the data and the presence of the necessary devices.

7.2.1. Measurement of the area of \u200b\u200bthe area with rectilinear boundaries

When measuring the area of \u200b\u200bthe site with rectilinear borders The plot is divided into simple geometric figuresThe area of \u200b\u200beach of them is measured by the geometric method and, summing up the area of \u200b\u200bindividual sections, calculated based on the scale of the card, receive the total area of \u200b\u200bthe object.

7.2.2. Measurement of the area of \u200b\u200bthe area with a curvilinear circuit

Object C. curvilinear contour They are 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 are mutually compensated for each other (Fig. 7.6). The measurement results will be at some extent approximate.

Fig. 7.6. Hinding the curvilinear boundaries of the site and
breakdown its square on simple geometric shapes

7.2.3. Measuring area area with complex configuration

Measuring areas of sites, having a complex incorrect configuration more often produced with the help of pallets and plan meters, which gives the most accurate results. Grid pallet It is a transparent plate with square grid (Fig. 9.9).

Fig. 7.7. Square grid pallet

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, so in order to increase the accuracy of measurements, labels with small squares are used (with a side 2 - 5 mm). Before working on this map, the area of \u200b\u200bone cell is determined.
The area of \u200b\u200bthe plot is calculated by the formula:

Where: but -square side expressed on the map scale;
n. - the number of squares in the limits of the circuit of the measured section

To increase the accuracy, the area is determined several times with an arbitrary permutation of the palette used in any position, including with a turn relative to its initial position. For the final value of the area, the average arithmetic is taken from the measurement results.

In addition to the mesh beans, point and parallel palets are used, which are transparent plates with stamped dots or lines. The 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. 7.8).

Fig. 7.8. Pallet

The weight of each point is equal to the price of the division of the palette. The area of \u200b\u200bthe measured area is determined by counting the number of points inside the contour, and multiply this amount by weight point.
On the parallel palette, equidate parallel straight lines are depricted (Fig. 7.9). The measured area, when applied to it, the palettes will be divided into a number of trapezions with the same height h.. The segments of parallel lines inside the contour (in the middle between the lines) are the average lines of trapez. To determine the area of \u200b\u200bthe site using this palette, it is necessary to multiply all measured medium lines to multiply between parallel lines of the Palest h.(taking into account scale).

P \u003d H.∑ l.

Fig. 7.9. Pallet consisting of a system
Parallel lines

Measure squares of significant areas made by cards using planimeter .

Fig. 7.10. Polar Planometer

The plan meter is used to determine the area mechanically. Wide distribution has a polar plan meter (Fig. 7.10). It consists of two levers - pole and water-based. Determination of the contour area plan meter comes down to the following actions. Signing the pole and installing the oscillating lever at the starting point of the contour, take countdown. Then the bypass spire is gently leading along the contour until the starting point and take the second countdown. The difference of samples will give the contour area in the divisions of the planimeter. Knowing the absolute price of the basement of the planimeter, the contour area is determined.
The development of equipment contributes to the creation of new devices that increase productivity when calculating areas, in particular - use modern devices, among which - electronic plan meters .

Fig. 7.11. Electronic plan meter

7.2.4. Calculation of the area of \u200b\u200bthe polygon by coordinates of its vertices
(analytical method)

This method Allows you to determine the area of \u200b\u200bthe plot of any configuration, i.e. With any number of vertices whose coordinates ( x, Y.) Known. At the same time, the numbering of the vertices should be made along the clockwise arrow.
As can be seen from fig. 7.12, Square S. polygon 1-2-3-4 can be considered as the difference in space S "figures 1U-1-2-3-3uand S "figures 1Y-1-4-3-3
S \u003d S "- S".

Fig. 7.12. To calculate the area of \u200b\u200bthe polygon by coordinates.

In turn, each of the squares S "and S "it is the sum of the scene of the trapezes, the parallel sides of which are the abscissions of the corresponding vertices of the polygon, and altitudes - the difference of the ordinate of the same vertices, i.e.
S " \u003d pl. 1U-1-2-2-2 + pl. 2,2-3-3,
S "\u003d PL 1U-1-4-4U + PL. 4U-4-3-3U
or:

2s " = (x 1+ x 2)(w. 2 – w. 1) + (X 2.+ x. 3 ) (w. 3 - u 2)
2 S." = (x 1+ x 4)(w. 4 – w. 1) + (x 4.+ x 3)(w. 3 - w. 4).
In this way,
2s = (x 1.+ x 2)(w. 2 – w. 1) + (X 2.+ x. 3 ) (w. 3 - u 2) - (x 1.+ x 4)(w. 4 – w. 1) - (x 4.+ x 3)(w. 3 - w. 4).

Opening brackets, get
2s = x 1 u 2 – x 1 u 4 + x 2 U. 3 - x. 2 in 1 + x 3 y 4 - x 3 u 2 + x 4. In 1. - x 4 W. 3

From here
2s = x 1 (y 2 - w. 4) + x 2 (y 3 - in 1) + x 3 (y 4 - w. 2 ) + x 4 (in 1. - w. 3 ) (7.1)
2s = y 1 (x 4 - h. 2) + y 2 (x 1 - h. 3 )+ y 3 (x 2 - h. 4 )+ y 4 (x 3 - x 1) (7.2)

Submit expressions (7.1) and (7.2) in general, noted by i.serial number ( i. = 1, 2, ..., p)the tops of the polygon:
2s = (7.3)
2s = (7.4)

Hence, the doubled area of \u200b\u200bthe polygon is equal to either the amount of the works of each abscissa to the difference in the order of the subsequent and previous vertices of the polygon, or the amount of the products of each ordinate to the difference between the abscissa of the previous and subsequent vertices of the polygon.

An intermediate computing control is to satisfy the conditions:
\u003d 0 or \u003d 0

The values \u200b\u200bof coordinates and their differences are usually rounded up to tenth meters, and works to whole square meters.
Complex formulas for the settlement area can be easily solved using spreadsheets. MicrosoftXL. . An example for a polygon (polygon) of 5 points is given in Tables 7.2, 7.3.
Table 7.2 Introduce the initial data and formulas.

Table 7.2.

Table 7.3 shows the computing results.

Table 7.3.

7.3. Eye measurements on the map

In the practice of kartometric works are widely used eyemerimswhich give approximate results. However, the skill is easy to determine on a map of distance, directions, square, slope and other characteristics of objects contributes to mastering the skills of the correct understanding of the cartographic image. The accuracy of the eye definitions increases with the acquisition of experience. Eyemerish skills warn gross miscalculations in measurements.
For determining linear objects The card should be hovering with the magnitude of these objects with segments of kilometer mesh or linear scale divisions.
For determining squares of objects As a peculiar palette, kilometer mesh squares are used. Each square of the scale mesh is 1:10,000 - 1:50,000 on the ground corresponds to 1 km 2 (100 hectares), the scale of 1: 100,000 - 4 km 2, 1: 200 000 - 16 km 2.
The accuracy of quantitative definitions on the map, with the development of the character, is 10-15% of the measured value.

Questions and tasks for self-control

Explain the measurement order on the map of the straight line.

Explain the measurement order on the map of the broken line.

Explain the measurement order on the winding line curve with the meter circulator.

Explain the measurement order on the winding line curve by Kurvimeter.

How can I use the length of the linear object on the topographic map?

Which area on the ground corresponds to one square of the coordinate mesh map scale 1:25 000?

Instruction

Go to Google search engine and click on the word "cards", which is in the top of the search engine. With the right side you will see the card, and with the left two buttons: "Routes" and "My Places". Click on "Routes". Under it, two windows "A" and "B" will appear, that is, the initial and end point of the reference. Full, you are in Ufa, and you need to find out how much time will take the road to Perm. In this case, in the window "A" enter "Ufa", and in the window "B" - "Perm". Click on the button under the window "Routes". The map will appear the track, and under the windows "A" and "B", how many kilometers from one city to another, and how much time you need to spend to get to the car. If you are interested Walk, click on the button with a pedestrian image, which is located above the windows "A" and "B". The service will restructure the route and automatically calculate distance And the expected time on the road.

In the case when it is necessary distance From point "A" to "in", located in a single paragraph, should be operated according to the scheme described above. The difference consists of only the fact that the title of the area needs to be added the street and, perhaps, the house number through the comma. (For example, "A": Moscow, Tverskaya 5 and "B": Moscow, Colored Boulevard, 3).

There are situations when you are interested distance Between objects "directly": through fields, forests and rivers. In this case, click on the gear ring icon in upper corner pages. In the resulting detailed menu, select Google Laboratory and turn on the Distance Measurement Tool, save the changes. A ruler appeared in the upper left corner of the card, click on it. Mark on the reference, and then the end point. A red line will appear between these points on the map, and the breakdown will be shown on the panel on the left side.

Helpful advice

You can choose one of two units of measurements: kilometers or miles;
- by pressing a few points on the map, you can determine the distance between many points;
- If you enter the service using your profile, Google cards will remember your settings in Google Map Lab.

Sources:

• measure the distance on the map

Going into the summer tourist journey on foot, by car or kayak, it is advisable to know in advance that the distance that will be needed to overcome. To measure length Ways, do not do without a card. But on the map it is easy to determine the direct distance between two objects. And how to be, for example, with measuring the length of the winding water route?

You will need

• Terrain map, Circul, Paper strip, Kurvimeter

Instruction

Reception First: Using a Circular. Install the circulat solution suitable for measuring the length, otherwise it is pitchable. The step will depend on how the wind is to be measured. Usually, the circular step should not exceed one centimeter.

Place one leg of the circulation in the starting point of the measured path length, the second needle in the direction of movement. Consistently turn the circular around each of the needles (will resemble steps along the route). The length of the intended path will be equal to the number of "steps", multiplied by the circulation step, taking into account the scale of the map. The residue is less than the circular step, you can measure linearly, that is, in a straight line.

The second method involves the presence of a conventional paper strip. Put the paper strip on the edge and align the route line. In those places where the line bends properly bend and strip paper. After that remains to be measured length The resulting segment of the path through the strip, of course, again, taking into account the scale of the map. This method is suitable only to measure the length of small segments of the path.

Scale card. The scale of 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 area line. In the flat areas, with small angles of the tilt of the physical surface, the horizontal projections of the lines differ very little from the lengths of the lines themselves, and in these cases can be considered the scale of the line length 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: 100,000 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 numbers 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. scale scale - 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 scale of the card 1: 100 000 and the basis of a linear scale in 1 cm The magnitude of the scale will be 1 km, and the accuracy of the scale (with the smallest division in 1 mm) - 100 m. Accuracy of measurements by cards and accuracy of graphic buildings on paper are associated 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 maximum accuracy will be 10 m, with a 1:10,000 scale, it will be equal to 1 m. It is obvious that the possibilities of the image on these circuits 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 industries national economyThe science and defense of the country requires maps of different scales. For state topographic maps of the USSR, a number of standard scales based on the metric decimal system of measures have been developed (Table 1).

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 separate sheets Encompasses significant territories, and these cards use for general familiarization with the locality, 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.) are 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.

Fig. 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 - (a 1 + a 2 + ... + a n): n \u003d σa / n, where X is the likely value of the measured value, A 1, A 2 ... 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 crushedwhere 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 at 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. It follows that more accurate measurement results are obtained when using large-scale cards.

Definition of space Plots on topographic maps is based on the geometric relationship between the shape area and its linear elements. The scale of the square is equal to the square of 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 cm 2 - (100 m) 2, i.e. 1 cm 2 - 1 hectare, and on the map of scale 1: 1 000 000 per 1 cm 2 - 100 km 2.

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.

Fig. 8. Hindering the curvilinear boundaries of the site and breakdown its area to simple geometric shapes: dots marked the cut-off areas, hatching - the 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. 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 A 2 N, 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. Grid pallet (Fig. 9) is a transparent plate (from plastic, organic glass or tracing) with a stamped or drawn square mesh. 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 a 2 n

In addition to the grid pools, point and parallel palets are used, which are transparent plates with stamped dots or lines. The points are put in one of the corners of the mesh pale cells 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.

Fig. 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. P \u003d rσl

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 is the Polar Player, work with which is not a great difficulty. However, the theory of this device is quite complex and is considered in geodesy manuals.

Very often, users face a situation where you need to calculate the distance of the path. However, how and with how to do it? The first thing comes to mind is a navigator capable of determining the distance. However, the problem is that the navigator works only with a car expense, and if you are located, for example, in the park and want to find out how many kilometers it is necessary to go through the desert areas, such a "solution" of the problem will not solve it at all.

However, we would not write an article if we had no trump card in the sleeve: we are talking about maps. The application is updated every day and complemented by new chips, to say exactly when it became possible to determine the distance, we cannot, but it is probably one of the most useful functions.

In order to find out the distance traveled or planned path, you need:

As the pathway, the distance displayed in the lower left corner will increase. In order to remove the last point, you need to click on the return button, which is located in the upper right corner next to the "Menu" button. By the way, clicking on three menu points, you can completely clean the entire route.

Thus, we learned how to determine the distance of the route of interest.

It is worth noting in general the stable and high-quality work of Google cards. In Play, market there are many similar applications, including maps.me, Yandex.Maps, but for some reason it is the solution from Google, firstly, it's best to fit into the system, bringing your Material-chips, secondly, programmatically implemented on Enough high level. Here you can view the street with the StreetView-Panorama, download offline navigation and so on. In a word, if you are interested in cards - boldly download the official Google decision.