Among the main characteristics of maps of the area most often distinguish this. This is scale accuracy . In the article we will analyze what this concept hides in itself. We also consider what is the scale in general, describe its main varieties. Let us examine how the concept of "graphic accuracy" is associated with the subject of our conversation.
What is it?
The scale is an important refinement, showing how much each line that was drawn on the drawing, plan, is smaller or larger than the actual size of the object that it depicts. Such refinements are presented on drawing documents and maps both numerically and graphically.
The scale of plans, the accuracy of scale - concepts that can be found in a wide variety of areas:
- Cartography.
- Design.
- Geodesy.
- The photo.
- Modeling.
- Programming.
- Maths.
- Film technology.
Some of these applications, their features, we will consider during the article.
Scale accuracy
And now the definition of a key concept. Scale accuracy is part of the horizontal line that will mean 0.1 mm in the drawing. Why is this value chosen?
0.1 mm here is adopted due to the fact that this is the smallest segment that can distinguish the human eye in the image without the use of special equipment, tools, instruments.
We give a concrete example. Given 1: 10000. The scale accuracy will be, respectively, 1 m. We will analyze in more detail:
- 1 cm on a plan or image is 10,000 cm (or 100 m) in real terrain.
- 1 mm in the image is 1,000 cm (or 10 m).
- 0.1 mm is 100 cm (or 1 m) in real terrain.
Thus, it is easy to determine the ultimate accuracy of the scale. This is the distance of the real surface, equal to 0.1 mm on the map - the minimum distance that a person can distinguish.
Graphic accuracy
Now let's get acquainted with the graphic accuracy of the scale. This is another significant feature when using plans and maps.
Graphic accuracy is associated with the resolution of "and" the human eye. In turn, it makes up βG.β Hence, Ξ = u.
That is, if the angle "and" between the vectors at the two points "B" and "L" when viewed by an observer with a normal level of vision is "G" or more, then they will be perceived as two points. If this angle to the concept of resolution is less than "G", then "L" and "B" will be perceived by a person as one point.
It is best to get acquainted with the definition of scale accuracy with a specific example. Suppose a person examines a map from the best distance "b" equal to 35 cm. The value of G = and. Now you need to determine the smallest distance (that is, graphic accuracy) between "B" and "L", at which they will still be perceived by the observer as two different points. Here is the calculation:
1 - is! - 1/3438 x 350 mm = 0.1 mm.
1/3438 is the value of the angle u = G, which in this case is expressed in radians (3438 'is the number of minutes in radians).
Thus, the output value of 0.1 mm is the graphic accuracy of the plan or map.
Relationship of concepts
Now let's see how the above term is related to the main one. The accuracy of the scale is, as we recall, the distance on the surface of the Earth, which is 0.1 mm on the document.
You can derive the formula:
T = gM = 0.1 M mm.
Decipher its elements:
- T - scale accuracy.
- M is the denominator of scale.
- g = 0.1 mm - graphic accuracy.
From this we can derive a related interpretation. Scale accuracy is the graphic accuracy that is expressed in the scale of a map or plan. And what is the result? Graphic accuracy will appear as a constant (0.1 mm) for all existing scales.
Accordingly, the accuracy of the scale will begin to change with him. It will be the higher, the larger the compiler has chosen the scale.
And now we will deal with the features of such a characteristic as scale in various fields of application.
Design, surveying and cartography
We are aware of what accuracy means "500" scale - 1: 500. Let us now consider what varieties of it are characteristic of the field of design, cartography, and geodesy:
- Numerical scale. The indicator is prescribed as a fraction. In its numerator there will be a unit, and in the denominator - some degree of reduction in projection on the map. For example, let's take a scale of 1: 5,000. It means that 1 cm on the plan, on the map, is 5,000 cm (or 50 m) in real terrain. Accordingly, there will be a larger scale that differs by a smaller denominator. So, 1: 1,000 will be larger than 1:20,000.
- Named scale. The map maker prescribes on the document what distance in real terrain is 1 cm on the plan. Here is an example: "In 1 centimeter - 1000 kilometers." Or briefly: "1 cm = 100 km."
- Graphic scale. In turn, it will be divided into transverse and linear. We will analyze them separately.
Varieties of the graphic category
What is the accuracy of the scale - the transverse scale? Let's get acquainted with the characteristics:
- Linear. Such a graphic scale on the map is presented in the form of a ruler, which will be divided into real parts.
- Transverse. This is a graphic scale presented in the form of a nomogram. Its construction is based on the proportionality of parts of parallel lines that cross the sides of the corner. This scale is applicable for more accurate measurement of the length of lines on the plans. They use it this way: they measure the length on the bottom line of this transverse scale so that the right end is at a whole distance (OM), and the left is behind 0. If the left leg is between tenths, respectively, of the left segment (from 0 ), then the specialist raises both legs of the meter up. Until the left leg of the meter rises already at the intersection of any horizontal line and any transversal. But the right leg should also be on this horizontal line. The minimum CD here is 0.2 mm. Accordingly, the smallest accuracy is 0.1 mm.
A number of scale images in design
We already know what 1: 500 scale accuracy means. But in what cases is the compiler choosing it? Let us examine this question:
- The scale of reduction. Accordingly, they are used in cases where the object needs to be depicted on the plan, the terrain significantly exceeding its area. If the compiler refers to the design of master plans of especially large sizes, then he will find it useful to use the following scales: 1: 2 000, 1: 5 000, 1:10 000, 1:20 000, 1:25 000, 1:50 000.
- Full size. If you want to depict the object on the plan as it is, then turn to the scale of "one to one." Accordingly, 1 cm of real length here will correspond to 1 cm of length on the plan.
- The magnitude of the increase. They are necessary in cases when it is required to depict on the plan too small an object for a detailed acquaintance with its appearance, device.
In the photo
Of course, scale accuracy of 1:10,000 is more associated with cartography. But this also applies to the world of photography. By scale here is meant the ratio of the so-called linear dimensions of the image obtained on an ultra-sensitive matrix or on film to the size of the projection of the corresponding projection zone onto a plane that is perpendicular to the camera.
There are photographers who measure the scale as a ratio of the size of a real object to its size on a screen, photo paper or other medium. But the correct way to determine the scale in a photograph depends only on the context in which the image is used.
In photography, the scale is characterized by important importance in calculating the depth of any sharply depicted object, space. Today, specialists have access to a very wide selection of scale ranges from infinitesimal (used when shooting distant celestial bodies) to very large (without using special optical attachments, for example, today it is possible to get a 10: 1 image).
Here, macro photography is already considered to be on a 1: 1 scale (and, accordingly, larger). But with the proliferation of digital compact cameras, macro photography has also come to be called style when the lens is placed too close to the subject. If we consider the classical definition, then such an interpretation will not be true.
In modeling
For each of the types of poster (or large-scale) modeling, its own scale series are defined. They consist of several scales, characterized by a certain degree of reduction. Interestingly, for each of the types of modeling (railway, automobile, ship modeling, military equipment, aircraft modeling), there are certain historically formed large-scale series that do not intersect with others.
Here the scale is calculated using a simple formula:
L / M = X.
Decrypt:
- L - parameters of the original.
- M - the scale necessary for work.
- X is the desired value.
In programming
In this area, the so-called time scale will be important. Letβs figure out what it is.
In a time-sharing OS, the provision of "real-time" tasks to specific tasks is very important. It differs in that external events are processed without additional delays or omissions. Here another concept will be important - "real time scale". But itβs worthwhile to understand that it has no direct relation to the scale on the maps. This is just a terminological convention.
In film technology
In film technology, the accuracy of the time scale is also important. The latter refers to a quantitative indicator of deceleration or acceleration of movement, which will be equal to the ratio of the projection frame rate to the frequency of the film.
Consider this with a simple example. The projection frame rate when shooting a movie is 24 frames / sec. Filming was carried out at the same time "with a speed" of 72 frames / sec. The time scale in this case will be 1: 3.
And what then, for example, will mean 2: 1? This is twice as fast as the standard course of what is happening on the screen.
In math
In this area, scale refers to the linear relationship of two sizes. Also in many practically applicable areas this will be called the ratio of image size to the actual image size.
In mathematics, scale is the ratio of any distance on the map already to the real distance in real terrain. If you look at an example, this is the same as in cartography. Let's say 1: 100,000,000. So, 1 cm in the image is 100,000 cm in reality. That is, a thousand meters or one kilometer.
Scale is a widely applicable characteristic. This is a standard and integral component in the development of plans, drawings of objects, maps of the area. It is used in the design, in geodesy, cartography, relevant for photography, in film technology, programming and mathematics. It itself is mainly characterized by accuracy - the ratio of the real distance to that adopted on the map.