What does a scale of 1 to 10,000 mean? Scales of topographic maps and plans
Instructions
Look carefully at the map and find the kilometer grid that should be marked on it. The sides of the grid squares correspond to a certain quantity; you can find out this quantity by the signatures on the exits of the stack line at the edge of the card frame. For example, the distance between two adjacent grid lines is 1 km. Measure this distance with a ruler. Let's say you get 2 cm. Thus, the scale of the map is 500 m in 1 cm or 1:50000.
The second way to determine the scale is by the map nomenclature. Carefully review the card details. The nomenclature is an alphanumeric sheet of the card. Any scale series has its own specific value, from which a specialist can easily determine the scale of the map. For example, the nomenclature designation M-35 scale 1:1000000; M-35-XI indicates a scale of 1:200000; M-35-18-A-6-1 – scale 1:10000, etc. Of course, to determine the scale in this way it is necessary to have an understanding of nomenclature designations and certain experience handling topographic maps.
The third way to determine the map scale is by known distances. Find pictures of kilometer markers on highways. Measure the distance from one pillar to another on the map. You will immediately recognize the scale of the map (the number of centimeters of the map will correspond to one kilometer of terrain).
On maps at a scale of 1:200000, the distances between settlements in kilometers are indicated on the roads. In this case, measure the distance in centimeters from one settlement to another, and divide the signed number of kilometers by the distance expressed in centimeters. Thus, you have obtained the map scale, that is, the number of kilometers in one centimeter.
If you are in an area shown on a map, determine its scale based on the measured distances. To do this, measure the distance between the objects on the map.
Also use knowledge of the length of the meridian arc. One minute along the meridian is equal to approximately 2 km, or more precisely – 1.85 km. On the side of the map frame there are signatures of degrees and minutes, each minute is highlighted with a checker. If, say, the length of one minute is 3.7 cm, then the map scale will be 1:50000 (one centimeter on the map is equal to 0.5 km on the ground).
Sources:
- How to determine scale
- Scale accuracy Lengths of lines on the ground corresponding to
In practical applications, scale, as a rule, establishes the ratio of the size of a graphic image of an object to the natural size of the object itself. Any product drawn must be drawn exactly to scale. Determining the scale on a given map or drawing is an important task. Moreover, the scale can be presented in the image in numerical form or graphically. In the latter case we speak of a linear scale.
You will need
- Measuring ruler
Instructions
If a specific area is given, you can find the scale using landmarks with known distances. Kilometer posts are usually located along the roads. Find them on and, using a ruler or centimeter divisions, measure the distance between the nearest depicted pillars.
Translate the natural meaning. Write down the ratio of the resulting values as 2:100000, where 2 - in your case will be equal to the number of measured centimeters on the map, and 100000 - the number of centimeters in 1 kilometer between pillars on the ground.
Bring the resulting ratio to the type of scale. To do this, you need to get the ratio of how many centimeters on the ground correspond to one centimeter on the map. To do this, divide the expression 2:100000 by the first number. Get 1:50000 - this is the scale of your map. It means that 1 centimeter on the map corresponds to 0.5 kilometers on the ground.
If there are no landmarks on the map with a pre-known distance, independently measure the distance between the objects marked on the map directly on the depicted area. Next, take measurements on the map in centimeters. Then perform the scale calculation as described above.
When writing a scale for magnification, the unit is expressed for the size of a natural object. But the first number still corresponds to the distance on the drawing or map. In this case, the scale will look like this: 20:1.
Images of large objects can be obtained on paper or any other medium only in a reduced form. This primarily concerns various cards terrain. The map scale is the ratio of the length of a line drawn between two points on a plan or map to the same distance on the ground. Knowing the scale is necessary in order to measure distances on a map.
Instructions
Usually, any card or is indicated in its legend - the accompanying explanatory text. The scale can be depicted in the form of a scale or text, which indicates how many meters or kilometers on the ground is equal to 1 cm of distance plotted along a given scale. Scale 1: 50000, which means that 1 cm plotted on this map is equal to 500 meters or 0.5 km in reality. The larger the scale, the smaller the number indicated in its numerator. Topographic maps at a scale of 1:10000 and larger are considered classified information.
We can talk about a fixed scale only when there is a print of the map on paper. In the event that the card is given in electronic form, its scale depends on the image magnification factor.
If for some reason the map scale is not indicated, there is no border design or legend, then it can be determined using the GoogleEarth or YandexMap geoinformation mapping servers, turning them on in the “Hybrid” mode, which allows you to simultaneously see a digitized image of the area along with the satellite photographic base - roads, city boundaries, free-standing buildings.
Determine the geographic location of the area depicted on the map. Select two characteristic points on it that can be easily identified from a satellite image of the area. Usually, it is convenient to use intersections of highways or improved highways for this purpose.
Find these two points using a satellite image of the area. Use the Ruler tool to measure the distance between them. When you activate the tool, a sign appears where the distance between the two points you specify on the satellite image will automatically be displayed. Set the units of measurement that are convenient for you – meters, kilometers.
Divide the result by satellite images distance by the number of centimeters measured on the map. You will get the scale value of this map.
Video on the topic
The scale shows how many times the map reduces the actual terrain depicted on it. Only knowing this value can you plot real distances on a map or terrain diagram. You can find out the scale by the markings on the map. If there is none, calculate it using the parallel lines.
Betuganov Astemir
Project Manager:
Shopagova Alla Sergeevna
Institution:
MCOU "Secondary School No. 27" Nalchik
In the presented research paper in mathematics on the topic "Scale and its application" I will try to find out at what scale it will be convenient to place objects on an A4 sheet. Working on a research project about scale will help me consolidate my knowledge in mathematics.
In my mathematics research project "Scale and Its Applications" I will need to clarify and compare the mathematical calculations with the data obtained.
During research work in mathematics about scale and its application, I hope that the scales that I set will allow me to arrange objects on an A4 landscape sheet.
Also, in the practical part of my work, I will consider and mathematically solve interesting problems involving distance and scale.
Introduction
Main part
1. Definition of scale.
2. Solving interesting problems at scale.
Conclusions
Applications.
Introduction
In mathematics lessons in the 6th grade, we covered this interesting topic, from which we learned how, using a scale, you can find a distance on the ground, knowing the length of the segment on the map corresponding to this distance on the ground, and vice versa.
When drawing images of objects on paper, we are most often forced to change their actual sizes: large objects have to be depicted in a reduced form, and small ones have to be enlarged.
Areas of the earth's surface are depicted on paper in a reduced form. An example of such an image is any map or plan. Small details are shown enlarged in the drawings.
But a drawing, map or plan should give an idea of the actual dimensions of objects. Therefore, a special entry is made on drawings and maps showing the ratio of the length of a segment on a map or drawing to its actual length.
The topic of my research project in mathematics is " Scale and its application».
Project goal: find out at what scale it will be convenient to place objects on an A4 sheet.
Project objectives:
- consolidate school knowledge in mathematics;
- clarify whether mathematical calculations are comparable with the data obtained.
Hypothesis: It is most effective to draw patterns at 1:10, apartment layout at 1:100; house passport 1:1000; city map 1:10000; area map 1:100000.
Expected result: The scales I have specified will allow me to place objects on a landscape sheet.
Equipment:
ruler, pencil, compass, calculator, map.
sheet A 4, ruler, pencil.
Definition of scale
Scale is a fraction where the numerator is one, and the denominator is a number that shows how many times the distance on the terrain plan is reduced than on the ground.
For example: 1:1000 (one thousandth) means that all distances on the ground are reduced by a thousand times. How larger number in the denominator of the fraction, the greater the decrease and the greater the coverage of the territory.
- numerical, expressed in numbers 1:1000;
- named, is expressed in words, that is, cm is converted to m: 1cm is 10m, 10m is the scale value;
- linear, knowing the scale, we can determine the distances.
Let's look at the map. The scale is indicated at the top (1: 500,000). They say that the map was made on a scale of one five hundred thousandth. This means that 1 cm on the map corresponds to 500,000 cm on the ground. This means that a 1 cm segment on the map corresponds to a 5 km segment on the ground.
And if I take a segment 3 cm long on the map, then on the ground it will be a segment 15 km long.
I downloaded a map of the Kabardino-Balkarian Republic from the Internet. Map of the republic with a scale of 1:10000, that is, 1 cm 100 meters, and the scale of the surrounding area is 1:100000 in 1 cm 1 kilometer. I immediately found my native village using it.
So, scale (German. Massstab, lit. " measuring stick»: Maß « measure», Stab « stick") - in general, the ratio of two linear dimensions.
In many areas of practical application scale is the ratio of the image size to the size of the depicted object .
The concept of scale is most common in geodesy, cartography and design - 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 life-size, and 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, a thousand and so on again. The number showing how many times the depicted object is reduced is the scale.
Scale is also used when depicting the microworld. A person cannot depict a living cell, which he examines through a microscope, in its natural size and therefore increases the size of its image several times.
The number showing how many times the real phenomenon is increased or decreased when depicting it is defined as scale.
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 determining scale depends on the context in which the image is being used.
Conclusions
Compared my assumptions put forward in my hypothesis with inscriptions on patterns, maps and technical plans of the house and apartment. It turned out that in some places I was mistaken 10 and even 100 times.
- patterns are most effectively drawn at 1:10;
- apartment layout 1:100;
- house passport 1:1000;
- city map 1:10000;
- area map 1:100000.
In fact, the apartment plan is usually taken at a scale of 1:200; the scale of the maps turned out to be exactly the same as in the original, but they are located on as many as 6 landscape sheets!
So once again, I am convinced that before making assumptions, you need to recalculate several times.
Thus, we formed the concept of scale, map, drawing, and practiced solving problems for calculating the length of a segment on the ground and on the map.
Solving scale problems
Task 1. The distance between the two cities is 400 km. Find the length of the segment connecting these cities on a map made at a scale of 1:5000000.
Solution:
400km = 400000m = 40000000cm
40000000: 5000000 = 40: 5 = 8 (cm)
Task 2. The distance from Moscow to St. Petersburg in a straight line is approximately 635 km from center to center. The length of the route along the highway is 700 km.
How many times must this distance be reduced so that it can be depicted on a slide as a segment 14 cm long?
Solution:
700km = 700000m = 70000000cm
70000000cm: 14cm = 5000000(times)
The frames of maps of derived scales are constructed by dividing the base sheet along the lines of parallels and meridians into several equal parts, i.e. The layout of sheets is always based on a geographic coordinate grid. We consider the following scales of maps and plans to be standard:
Layout scheme and nomenclature of topographic maps of derivative scales for the main one Russian Federation SK-42 coordinate systems:
| Scale |
Base sheet |
divided into |
Designation |
Frame size |
| 1: 1 000 000
|
N-37 |
4 x 6 degrees |
||
| 1: 500 000
|
1: 1 000 000
|
4 sheets (A, B, C, D) |
N-37-B |
2 x 3 degrees |
| 1: 200 000
|
1: 1 000 000
|
36 sheets (I-XXXVI) |
N-37-XXIII |
40" x 60" |
| 1: 100 000
|
1: 1 000 000
|
144 sheets (1-144) |
N-37-89 |
20" x 30" |
| 1: 50 000
|
1: 100 000
|
4 sheets (A, B, C, D) |
N-37-44-B |
10" x 15" |
| 1: 25 000
|
1: 100 000
|
16 sheets (a,b,c,d) |
N-37-114-GB |
5" x 7" 30" |
| 1: 10 000
|
1: 100 000
|
64 sheets (1,2,3,4) |
N-37-78-Bv-3 |
2" 30" x 3" 45" |
Topographic maps at a scale of 1: 200,000 and smaller are open to us; for a scale of 1: 100,000 the order of use is defined - for official use; all larger scales of topographic maps are closed.
|
|
This figure shows the division of a sheet of scale 1: 1,000,000 On 4 sheets of scale 1: 500,000 (A, B, C, D), For 36 sheets of scale 1:200,000 (indicated by Roman numerals), and For 144 sheets, scale 1:100,000 (indicated by Arabic numerals). |
|
 |
This figure shows the division of a sheet of scale 1: 100,000: For 4 sheets of scale 1: 50,000 Scale sheet division 1: 50,000 Scale sheet division 1: 25,000 Three-digit numbers from 1 to 256 show division into sheets of scale 1: 5,000, but maps of this scale are very rare in practice. |
|
|
|
|
|
Although the frames of all topographic maps have boundaries along a geographic grid, on the topographic map sheets themselves, starting from a scale of 1: 200,000 and for all maps larger, it is no longer geographical, but a rectangular, so-called kilometer grid with a step of 4000 m for a scale of 1: 200,000 and up to 1000 m for a scale of 1: 10,000, which is a display of the rectangular Gauss-Kruger coordinate system.
On the standard SK-42 topographic maps there is complete information about the coordinates of the sheet both in the geographic coordinate system and in the rectangular Gauss-Kruger coordinate system. The fragment of the topographic map below shows a corner with information about its coordinates and explains how to understand it correctly. This is a sheet of topographic map at a scale of 1: 200,000 with the nomenclature number N-38-XXII, made in the SK-42 coordinate system.
 |
| Topographic map angle 1: 200,000 and coordinate information: |
| at the very corner of the sheet the geographical coordinates of this corner are written, 46° 00" east longitude and 54° 00" north latitude; At the top frame, the numbers 48, 52, 56, 60 are the kilometer grid coordinates, and together with the small number 85 next to 60 they show the exact Y coordinate value of this vertical line in the rectangular Gauss-Kruger coordinate system, equal to 8,560,000 m; that is, this map is from zone 8, and the coordinate of the line is 60 km east of the middle meridian of the zone; In the right frame, the numbers 76, 80, 84 are also kilometer grid coordinates, and together with the small number 59 next to 80 they show the exact X coordinate value of this horizontal line in the rectangular Gauss-Kruger coordinate system, equal to 5,980,000 m; is the distance to that line from the equator. |
Transverse scale, unlike a linear scale, allows you to measure and transfer lines to a map or plan with greater accuracy.
Usually the transverse scale is drawn on a metal plate, but it can also be drawn on paper.
Start of construction transverse scale similar to constructing a linear scale.
The two outer perpendiculars are divided into 10 equal parts and lines parallel to the base of the scale are drawn through the resulting points.
The upper left base, as well as the lower left base, is divided into 10 equal parts.
The division points of the upper left base and the lower left base are connected by inclined lines as shown in the figure. These slanted lines are called transversals.
Near the transversals, mark divisions that are equal to a hundredth of the base of the scale (100 m / 100 = 1 m).
The picture shows transverse scale with a base of 2 cm corresponding to a numerical scale of 1:5000 (2 cm * 5000 = 10000 cm = 100 m).
Thus, the transverse scale allows you to measure and plot lines on a map or plan with an accuracy of one hundredth of the base of the scale (1 m for a numerical scale of 1:5000).
Transverse scale used as follows:
1). into the measuring compass solution, take a segment from a map or plan, the length of which must be determined;
2). apply the compass to the transverse scale so that its right needle is on the zero or other perpendicular to the right of zero, and the left needle is on the same horizontal line with the right needle;
3). sum up the readings along the perpendiculars on the right and left needles of the compass to the right and left of the zero perpendicular.
In the figure, the lengths of the measured segments according to the 1:5000 scale plan are 252 meters and 477 meters.
Map scale is the ratio of the length of a segment on the map to its actual length on the ground.
Scale ( from German - measure and Stab - stick) - the ratio of the length of a segment on a map, plan, aerial or satellite image to its actual length on the ground.
Numerical scale - a scale expressed as a fraction, where the numerator is one, and the denominator is a number indicating how many times the image is reduced.
Named (verbal) scale - type of scale, verbal indication of what distance on the ground corresponds to 1 cm on a map, plan, photograph.
Linear scale - an auxiliary measuring ruler applied to maps to facilitate the measurement of distances.
A named scale is expressed by named numbers denoting the lengths of mutually corresponding segments on the map and in nature.
For example, there are 5 kilometers in 1 centimeter (5 kilometers in 1 cm). Numerical scale is a scale expressed as a fraction in which: the numerator is equal to one, and the denominator is equal to a number showing how many times the linear dimensions on the map are reduced. The following are the numerical scales of the maps and the corresponding named scales.
The scale of the plan is the same at all points.
The map scale at each point has its own particular value, depending on the latitude and longitude of the given point. Therefore, its strict numerical characteristic is a partial scale - the ratio of the length of an infinitesimal segment D/ on the map to the length of the corresponding infinitesimal segment on the surface of the ellipsoid of the globe. However, for practical measurements on a map, its main scale is used.
Forms of expression of scale
The designation of scale on maps and plans has three forms: numerical, named and linear scales.The numerical scale is expressed as a fraction in which the numerator is one, and the denominator M is a number showing how many times the dimensions on the map or plan are reduced (1: M)
In Russia for topographic maps Standard numerical scales are accepted:
For special purposes, topographic maps are also created at scales of 1: 5,000 and 1: 2,000.
Main scales topographic plans in Russia are:
1:5000, 1:2000, 1:1000 and 1:500.
However, in land management practice, land use plans are most often drawn up at scales of 1: 10,000 and 1:25,000, and sometimes 1: 50,000.
When comparing different numerical scales, the smaller one is the one with the larger denominator M, and, conversely, the smaller the denominator M, the larger the scale of the plan or map.
Thus, a scale of 1: 10,000 is larger than a scale of 1: 100,000, and a scale of 1: 50,000 is smaller than a scale of 1: 10,000.
Named scale
Since the lengths of lines on the ground are usually measured in meters, and on maps and plans - in centimeters, it is convenient to express the scales in verbal form, for example:There are 50 meters in one centimeter. This corresponds to a numerical scale of 1: 5000. Since 1 meter is equal to 100 centimeters, the number of meters of terrain contained in 1 cm of a map or plan is easily determined by dividing the denominator of the numerical scale by 100.
Linear scale
It is a graph in the form of a straight line segment, divided into equal parts with signed values of the corresponding lengths of terrain lines. Linear scale allows you to measure or plot distances on maps and plans without calculations.Scale accuracy
The maximum possibility of measuring and constructing segments on maps and plans is limited to 0.01 cm. The corresponding number of meters of terrain on the scale of a map or plan represents the maximum graphic accuracy of a given scale. Since the accuracy of the scale expresses the length of the horizontal location of the terrain line in meters, then to determine it, the denominator of the numerical scale should be divided by 10,000 (1 m contains 10,000 segments of 0.01 cm). So, for a map of scale 1: 25,000, the scale accuracy is 2.5 m; for map 1: 100,000- 10 m, etc.Scales of topographic maps
| Numerical scale cards | Name cards | 1 cm on the map corresponds on terrain distance | 1 cm 2 on the map corresponds on the ground area |
| 1: 5 000 1: 1 000 000 | Five thousandth Ten-thousandth Twenty-five thousandth Fifty thousandth One hundred thousandth Two hundred thousandth Five hundred thousandth, Or half a millionth Millionth | 50 m 10 km | 0.25 ha 100 km 2 |
Below are the numerical scales of the maps and the corresponding named scales:
Scale 1: 100,000
1 cm on the map - 1000 m (1 km) on the ground
10 cm on the map - 10,000 m (10 km) on the ground
Scale 1:10000
1 cm on the map - 100 m (0.1 km) on the ground
10 cm on the map - 1000m (1 km) on the ground
Scale 1:5000
1 cm on the map - 50 m (0.05 km) on the ground
10 cm on the map – 500 m (0.5 km) on the ground
Scale 1:2000
1 cm on the map – 20 m (0.02 km) on the ground
10 cm on the map – 200 m (0.2 km) on the ground
Scale 1:1000
1 cm on the map – 1000 cm (10 m) on the ground
10 cm on the map – 100 m on the ground
Scale 1:500
1 cm on the map – 5 m on the ground
10 cm on the map – 50 m on the ground
Scale 1:200
1 cm on the map – 2 m (200 cm) on the ground
10 cm on the map – 20 m (0.2 km) on the ground
Scale 1:100
1 cm on the map – 1 m (100 cm) on the ground
10 cm on the map – 10 m (0.01 km) on the ground