On the world map hemisses the greatest distortion has. In what parts of the world map distortion are the largest? Earth Bark is a more young in the area
Objectives and objectives of studying the topic:
Give an idea of \u200b\u200bdistortion on maps and types of distortion:
Form an idea of \u200b\u200bdistortion in lengths;
- form an idea of \u200b\u200bdistortion in the squares;
- form an idea of \u200b\u200bdistortion in the corners;
- form an idea of \u200b\u200bdistortion in forms;
The result of mastering the topic:
The surface of the ellipsoid (or ball) cannot be deployed to the plane while maintaining the likeness of all outlines. If the surface of the globe (the earth's ellipsoid model), cutting on the strips according to meridians (or parallel), deploy to the plane, ruptures or overlaps will occur in the cartographic image, and by removing from the equator (or from the middle meridian) they will increase. As a consequence, it is necessary to stretch or compress the strips to fill the gaps in meridians or parallel.
As a result of stretching or compression in the cartographic image, distortions arise in lengthm. (MJ) , squares p.Cornersw. and forms k.. In this regard, the scale of the card, which characterizes the degree of decrease in objects when moving from nature to the image, does not remain constant: it changes from point to point and even at one point in different directions. Therefore, it should be distinguished dS Main Scale , equal to a given scale, in which a decrease in the earth's ellipsoid occurs.
The main scale shows the total degree of reduction adopted for this card.On the maps always signs the main scale.
In all other places Maps scales will differ from the main one, they will be larger or smaller, these scales are called private and denote the letter DS 1.
Under the scale in cartography, the attitude of an infinitely small segment taken on the map, to the corresponding segment on it on the earth's ellipsoid (globe). It all depends on what is taken as a basis when building a projection - a globe or an ellipsoid.
The smaller the scale changes within the site, the more perfect will be a cartographic projection.
To perform cartographic works you need to know distribution On the map values \u200b\u200bof private scales so that you can make amendments to the measurement results.
Private scales are calculated by special formulas. Analysis calculations of private scales shows that among them there is one direction with the greatest scale , and another - with the smallest.
Gallest The scale expressed in the principle of the main scale is denoted by the letter " but", but least - Letter « in" .
The directions of the greatest and smallest scale are called the main directions . The main directions only then coincide with the meridians and parallels, when the meridians and parallels intersect under straight corners.
In such cases Scale by meridians denote the letter « m » , and in parallel - Letter « n » .
Private-scale ratio to the main characterizes length distortion m. (MJ).
In other words, the value m. (MJ) There is the ratio of the length of an infinitely small segment on the map to the length of the infinitely small segment of it on the surface of the ellipsoid or ball.
m.(MJ) \u003d dS 1.
Distortion of space.
Distortion of Square p. It is defined as the attitude of infinitely small areas on the map to infinitely small squares on an ellipsoid or a bowl:
p \u003d. dP 1.
Projections in which there are no distortions of the area are called isometric.
While creating physical and geographical and socio-economic cards can be saved the faithful ratio of space. In such cases, it is beneficial to apply equal and arbitrary (equalization) projections.
In the equalization projections of the area distortion 2-3 times less than in the equilibonal.
For political maps The world is desirable to preserve the correctness of the ratio of the areas of individual states, without distorting the external contour of the state. In this case, it is beneficial to apply an equalization projection.
The projection of the Mercator for such cards is not suitable, as areas are very distorted in it
Angle distortion. Take an angle U on the surface of the globe (Fig. 5), which on the map is depicted by an angle u ′ .
Each side of the corner on the globe forms an angle α with a meridian, which is called azimuth. On the map, this azimuth is depicted by an angle α ′.
In the cartography, two types of angular distortions were adopted: distortion of direction and distortion of angles.
A. ′
α α ′
0 U 0 ′
U. ′
In B. ′
Fig.5. Distortion of corners
The difference between azimuth side of the corner on the map α ′ and azimuth side of the corner on the globe called distortion of direction .
ω = α′ - α
The difference between the value of the corner U ′ on the map and the value of u on the globe called distortion of the corner those.
2Ω \u003d U '- U
Angle distortion is expressed in magnitude 2Ω. Because the angle consists of two directions, each of which has a distortion ω .
Projections in which there are no distortions of angles are called equifricular.
Distortion of forms is directly related to the distortions of the corners (specific values w. corresponds to certain values k. ) and characterizes the deformation of figures on the map relative to the corresponding figures on the ground.
Distortion of form They will be the greater, the more scope will differ in the main directions.
As form distortion measures take the coefficient k. .
k \u003d a / in
where but and in - The greatest and smallest scale at this point.
Distortions on geographical maps The larger than the more depicted territory, and within one distortion map increase with the removal from the center to the edges of the card, and the rate of increment changes in different directions.
In order to clearly imagine the nature of distortion in different parts of the card, often use the so-called ellipse distortion.
If we take on the globe of the circle of infinite-small size, then during the transition to the card due to stretching or compression, this circle will distort similarly to the outlines of geographic objects and takes the form of an ellipse. This ellipse is called ellipse distortion or indicatorussia teasso.
The size and degree of exhaustion of this ellipse compared to the circle reflect all types of distortion inherent in the map in this place. View and sizes Ellipses of unequal in different projections and even at different points of the same projection.
The greatest scale in the ellipse distortion coincides with the direction of the large axis of the ellipse, and the smallest - with the direction of the small axis. These directions are called the main directions .
Ellipse distortion on maps is not depicted. They enjoy in mathematical cartography to clarify the magnitude and nature of distortion in some kind of projection.
The directions of the ellipse axes may coincide with the meridians and parallels, and in some cases the axis of the ellipse can occupy relative to the meridians and parallels an arbitrary position.
Determination of distortions for a number of card points and subsequent conduct on them isokol -lines connecting points with the same distortion values \u200b\u200bgives a visual picture of distortion distribution and allows you to take into account distortion when using the card. To determine distortion within the map, you can enjoy special tables or amokol schemes. Ishocol can be for corners, areas, length or shapes.
Whatever the way it is not to deploy the earth's surface to the plane, it will necessarily be broken and overlapping, which in turn leads to stretching and compression.
But on the map at the same time there will be places in which there will be no compression and stretching.
Lines or points on a geographic map, in which there are no distortions and maintains the main scale of the card, call lines or points of zero distortion (LNI and ENT) .
As the distortion is removed from them increase.
Questions for repetition and fixing material
1. What is the cause of cartographic distortions?
2. What types of distortions occur when moving from the surface
Ellipsoid to the plane?
3. Explain what point and the zero distortion line?
4. On what scalle maps remains constant?
5. How to determine the presence and magnitude of the distortion in certain places of the map?
6. What is the Tisso Indicator?
7. What is the destination of the ellipse of distortion?
8. What is isozol and what are their appointment?
Date: 24.10.2015
Cartographic projection - Mathematical method of image of the globe (ellipsoid) on the plane.
For designing a spherical surface on the plane Used auxiliary surfaces.
By sight The auxiliary cartographic surface of the projection is divided into:
Cylindrical 1. (the auxiliary surface is the side surface of the cylinder), conical 2 (side surface of the cone), azimuthal 3. (The plane called picture).
Also highlight Polyconic
pseudo-cylindrical conditional
and other projections.
By orientation Auxiliary projection figures are divided into:
- normal (in which the axis of the cylinder or cone coincides with the axis of the Earth model, and the art plane is perpendicular to it);
- transverse (in which the axis of the cylinder or cone is perpendicular to the axis of the earth model, and the picture plane or parallel to it);
- obliquewhere the axis of the auxiliary figure is in an intermediate position between the pole and the equator.
Cartographic distortions - This is a violation of the geometric properties of the earth's surface objects (lengths of lines, corners, shapes and squares) when they are displayed on the map.
The smaller the scale of the card, the more distortion. On large-scale distortion maps is insignificant.
Select four types of distortion on maps: length, square, corners and form objects. Each projection is characterized by their distortion.
By the nature of distortion, cartographic projections are divided into:
- equifricularin which the corners and forms of objects are stored, but the lengths and square are distorted;
- isometricin which the area is stored, but the corners and forms of objects are substantially changed;
- arbitrary, in which distortion of lengths, squares and corners, but they are distributed on the map evenly. Among them, the rivopromizes of the projections are highlighted, in which there are no distortions of length or by parallel, or in meridians.
Lines and points of zero distortion - lines, along which and points in which there are no distortions, because here when designing a spherical surface to the plane, an auxiliary surface (cylinder, cone or picture plane) were tangent To the ball.
Scaleshown on the maps save only on lines and at points of zero distortion. It is called the main thing.
In all other parts of the map, the scale differs from the main thing and is called partial. It requires special calculations to determine.
To determine the character and magnitude of the distortion on the map, you need to compare the degree mesh of the map and the globe.
On globe All parallels are at the same distance from each other, everything meridians are equal to each other and intersect with parallels at right angles. Therefore, all the cells of the degree mesh between adjacent parallels have the same dimensions and shape, and the cells between the meridians are expanding and increase from the poles to the equator.
To determine the magnitude of the distortion, the ellipses of distortion are also analyzed - ellipseed figures formed as a result of distortion in a certain projection of circles conducted on the globe of the same scale as the map.
In an equally projection The ellipses of distortion have a circle form, the value of which increases depending on the distance from the points and the zero distortion lines.
In an isometric projection Ellipses of distortion have the form of ellipses whose areas are the same (the length of one axis increases, and the second is reduced).
In an equalization projection Ellipses of distortion have the form of ellipses with the same length of one of the axes.
Basic signs of distortion on the map
- If the distance between the parallels is the same, this indicates that the distances in meridians are not distorted (equal exposure in meridians).
- Distances are not distorted by parallel if the radii parallels on the map correspond to the radius parallels on the globe.
- Square is not distorted if the cells created by meridians and parallels from the equator are squares, and their diagonals intersect at right angles.
- The lengths of the parallel are distorted, if the lengths of the meridians are not distorted.
- Distorted lengths in meridians, if the lengths are not distorted along the parallels.
The nature of the distortion in the main groups of cartographic projections
| Cartographic projections | Distortions |
| Equifricular | Keep the corners, distort the area and length of lines. |
| Isometric | Keep areas, distort the angles and forms. |
| Equipment | In one direction there are a permanent scale of lengths, distortions of corners and areas are in equilibrium. |
| Arbitrary | Distort the corners and squares. |
| Cylindrical | There are no distortion along the equator line, and according to the degree of approach to poles - increase. |
| Conical | Distortion is missing along the cone and globe touch parenches. |
| Azimuth | Distortion is absent in the central part of the map. |
1. Distortions are the less, the smaller part of the surface of the globe is shown on the map. Topographic maps covering very small sections of the earth's surface, on which the bulge of the Earth is not noticeable, give the most accurate images.
2. In different parts of the same map scale different. Scale at points or on zero distortion lines are called the main scale. It is usually indicated on the maps. When the zero distortion from the points or the zero distortions, the map scale is increasingly different from the main one. Only on topographic maps indicated on them is valid for all parts of them.
3. The smallest distortions on the maps - in their midblars, with the removal of the distortion cards to the edges (frame) increases.
Distortion on the hemisphere cards. To find out which distortions turned on the hemispheres on the map, it is necessary to compare the degree grid of the globe and the map mesh map. On the globe, all meridians have the same length, which corresponds to reality. On the map of hemispheres the length of meridians is different. The average meridian is depicted straight line, the rest - curved. The further the meridians are located from the average, the more they are curved, and the extreme form a semi-rareness and almost one and a half times longer than the average meridian parallels on the globe are depicted in the form of circles parallel to each other. On the map hemispheres Equator - straight line, and parallels - arcs, and the distance between adjacent parallels of the unequal and increase to the edges of the card.
Let's see what is the location of the meridians and parallels on the hemispheres map and how it is reflected in the objects depicted. On the globe section of the earth's surface (ocean or sushi) near the equator, having a length of 10 ° in latitude, everywhere has a figure similar to a square. On the map of the hemispheres these sections on different longitudes have different figures. In the center they have a form close to the square, as well as on the globe, and to the edge of the map, their form changes greatly. In this case, the segments of the meridians are lengthened, and the segments of the equator are shortened
From all this it follows that distances that are the same on the globe (land), in different places of the card are depicted by segments of different lengths, i.e., the scale of the map of the neodynaks in different parts. So it turns out the difference in the cartographic image.
The scale specified on the maps is accurate not for the entire card, but only for its specific parts. Therefore, it is impossible to use it when measuring distances and areas. On the map, the semisses scale corresponds to the indicated only at the central point, namely at the point of intersection of the equator and the average meridian. This is a point of zero distortion. In all other parts of the map, the scale is greater than or less specified on it. On other maps may not point, but the line of zero distortion.
Distortion on world maps. On world distortion maps, the largest, since they are depicted the surface at once. For example, on a globe of 1 ° longitude at 60 ° C. sh. and Yu. sh. It is 55.8 km, i.e., two times less than at the equator. On the world map, this distance is only 1.5 times. 1 ° longitude 80 ° C. sh. and Yu. sh. For less than the equator, already 6.5 times, and on the world map only 2 times. The scale specified on these world maps is stored in parallel to 45 ° C. sh. and Yu. sh. According to the parallels lying from them towards the equator, it is less, and in the side of the poles - more. And to the poles he increases rapidly. Therefore, in the northern and southern parts of our world maps, geographicals are noticeably stretched from west to east. In terms of meridians, the scale indicated on world maps is stored only in the center - at the intersection of the average meridian and equator. With the removal in all directions the scale of lengths in meridians increases. Therefore, the length of the segments of meridians between parallels increases.
1. Explain why the globe is called the volume model of the Earth.
The globe almost completely repeats the formus of the Earth, the position of objects and its surface.
How does the form of the globe differ from the real form of the Earth?
Globus - a ball, the land is also surrounded by the poles.
2. Set which two hemispheres at the same time there is a boy depicted in this photo.
West and East
3. Determine what kind of coverage of territory includes the submitted maps. Using the Atlas, bring examples of cards of each type.
1 - Cards of countries (physical map of Russia).
2 - world maps (political map of the world, physical map of the world)
4. Place the parallels from the longest to the shortest.
45 ° Yu.Sh. 25 ° S.Sh., 0 ° sh., 70 ° Yu.Sh., 30 ° Yu.Sh. 60 ° C.SM 20 ° S.Sh.
0 20 S.Sh. 25 S.Sh. 30 S.Sh. 45 Yu.Sh. 60 S.Sh. 70 Yu.Sh.
5. In the picture, the ships of the Russian Antarctic Expedition "East" and "Mirny" are depicted at noon off the coast of Peter I (68 ° Yu.Sh.). Determine in which direction ships are moving.
In the southern hemisphere at noon, the sun bends to the north, as the ship floats towards the sun, he floats to the north.
6. Give examples of cards from your atlas, made in such ways that are shown in the drawings.
7. Determine in which parts of these cards the image of the Earth is distorted most. Explain why.
On the world map. Length is less than the equator. The smaller the scale, the greater the distortion.
8. Determine which from the figures depicted:
a) only parallels;
b) only meridians;
c) degree grid.