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2-Dimensional Figures: Definition, Area & Example

What is a two-dimensional figure in math? Maybe the term 2D sounds familiar and makes you think of a video game, like Tetris, or a movie. This concept is similar to the understanding of 2D that we have in math. Two-dimensional (2D) figures are shapes formed by closed lines in a plane, and they have two dimensions: length and width. As they do not exist in three-dimensional (3D) space, these shapes do not have depth.

Definition of 2-dimensional figures

Two-dimensional figures are the flat plane shapes or figures that have two dimensions (length and width) in the same plane.

For example, if we drew three lines on a 2D plane surface, like a piece of paper, we could obtain a triangle, which is an example of a 2D shape. We just need one plane to show these 2D figures, as they do not have depth. In math, there are as many 2D shapes as you can imagine, as you just have to link one line with another in a plane.

These lines that form the shapes are called the sides of the plane figure. All sides do not have to be connected, as we can distinguish between closed shapes or open shapes, depending on whether they form vertices or not. We will mainly focus on closed shapes, as they are the most common in math.

Examples of 2-dimensional figures, StudySmarter Originals

Examples of 2-dimensional figures

Now, think about the popular game, Tetris, which is played in 2D. All of the shapes we can see in this game are two-dimensional figures that have lengths and widths. In Tetris, there are numerous two-dimensional shapes, but in math, there are four distinguished two-dimensional figures we work often with:

• Triangle
• Square
• Rectangle
• Circle

Let’s consider each of these four two-dimensional shapes in more detail.

Triangle

As a 2D shape, the triangle consists of three sides and three vertices. The summation of all the internal angles in a triangle is equal to 180º. We can distinguish between different types of triangles depending on whether the sides are equal or not. We can also distinguish types of triangles by the angles they form with one another.

For example, the triangles with all sides of the same length are called equilateral triangles, while if they have just two equal sides, they are called isosceles triangles. If none of the sides are the same length, the triangle is called a scalene triangle. On the other hand, an example of a triangle classified by its internal angles is a right triangle, which has an angle of 90º.

Different triangles, StudySmarter Originals

Square

As 2-dimensional figures, squares are formed by four equal sides with four vertices. All of the internal angles formed by the vertices are equal to 90º. We can label a 2D shape as a square only if all four sides are of the same length.

Square, StudySmarter Originals

Rectangle

These shapes are formed by four sides, with each side equal only to its opposite side. Therefore, both of these two pairs have the same length between them. In a rectangle, all internal angles formed by the vertices are equal to 90º, like in the square. If all the sides’ lengths were equal as well, the 2-dimensional figure would be a square.

Illustration of a rectangle, StudySmarter Originals

Circle

In a 2D plane, the circle consists of points that are all equally distanced with respect to one point in the shape’s center. This means that it has no vertices. In other words, we can also understand a circle as a uniquely curved line that is equally distanced from the center at all of its points.

The distance from the circle’s points to its center is called the radius. Also, if we measure from one point of the circle to another, passing through the circle’s center, the distance is called the diameter. The diameter is always twice the length of the radius.

Circle, StudySmarter Originals

There are more two-dimensional shapes in math that we can classify based on aspects like the number of sides and vertices as well as their structure.

Perimeter of a 2-dimensional figure

In math, the perimeter of a 2D figure is the total sum of the length of all of its sides. Therefore, if the sides of the plane figure are expressed in the length unit of meters, for example, the perimeter of the shape is also expressed with meters. We can express the perimeter with the following formula:

P=a1+a2+a3+…+an=∑ani=1n

In the perimeter formula, the terms a1+a2+a3 (and so on) represent the different sides in the two-dimensional figure. In the second part of the equation is a symbol (∑) which indicates that all these side lengths should be summed up.

Perimeter of a triangle

Let’s take a look at the 2D shapes with the lowest number of sides: the triangles. The triangle has three sides; therefore, the perimeter of the triangle is equal to the sum of those three sides. Let’s take a look at an example of the perimeter calculation below.

Isosceles triangle with side lengths, StudySmarter Originals

In the picture above, we have an isosceles triangle in 2D. This type of triangle has two sides of the same length and a third side with a different length. If we compute the perimeter of this 2D figure, we obtain:

P=a+b+c= 3m+3m+1m=7m

Perimeter of squares and rectangles

Even though a triangle, a square, and a rectangle are not the same, we can still calculate their perimeters with the same formula given above. And if we have any other 2D figure, this process of summing up all sides remains the same as well.

For squares and rectangles, we have to sum up four sides to calculate the perimeter. The perimeter of the square is a+a+a+a, where a is the side length of all four sides. The perimeter of a rectangle is a+a+b+b, where a and b are the two different side lengths of the equal opposite pairs. Let’s see some examples.

Eva has a whiteboard that measures 46 cm by 60 cm. what is the perimeter of this board?

Solution: Two different side lengths are given, and we know that a whiteboard has four sides. So, the figure will be a rectangle. The perimeter of this rectangle =46+46+60+60=212cm

Find the perimeter of the given figure.

2D square figure, StudySmarter Originals

Solution: The perimeter of the above square figure is:

Perimeter=a+a+a+a=25+25+25+25=100cm

Perimeter of a circle

Now you may be wondering, «But what about the circle?» Calculating a circle’s perimeter of course cannot be done with side lengths! We defined the circle as a 2D shape formed by points that are all equally distanced from the center. To calculate the perimeter of a circle in 2D (also called the circumference), we use a different formula:

P= 2πr

In this formula, r is equal to the radius of the circle and π is the number pi, which has a fixed value. From this formula, we see that the perimeter of a circle is proportional to its radius. So, if we increase the radius of a circle, we also increase its perimeter.

The diameter of a circle is given as 14 cm. What is the perimeter or circumference of this circle?

Circle with diameter, StudySmarter Originals

Solution: The circle’s diameter was given as d=14cm.To calculate the perimeter, we need to find the radius. And we know that the diameter is twice the length of the radius.

⇒d=2r⇒r=d2=142=7cm

So, the perimeter of a circle is:

P=2πr=2×π×7=44cm

Hence, the perimeter of the circle is 44 cm.

Area of 2-dimensional figures

In math, the area of a two-dimensional figure is the quantity of surface delimited by the perimeter of a figure in a plane. In other words, the area in 2D is the space inside the lines we use to draw a figure. We use square units to describe area, like square meters (m2) or square feet (ft2).

Now, take a look out from your computer at the floor of the room. Imagine the walls as lines of a shape in 2D. The surface of the floor you are observing is its area because it is the space inside the perimeter (in this case, the room’s walls).

Depending on two-dimensional figure and its shape, we have different formulas to compute area.

Area of a triangle

Starting again with the 2D shape with the lowest number of vertices, the area of the triangle is calculated with the following math formula:

A=12bh

Isosceles triangle with base and height, StudySmarter Originals

The area of the triangle depends on the base b of the triangle and its height h, which is the distance from the middle of the base to the opposite vertex. The base of the triangle does not need to be its shortest side: it can be any side. However, we then need to measure the height from the side chosen as the base to the opposite vertex.

A triangle has a base of 13 inches and a height of 6 inches. What is the area of this triangle?

Solution: Here, base b=13inches and height h=6inches. So the area is:

A=12×b×h=12×13×6=13×3=39

So, the area of the given triangle is 39 inches2.

Area of squares and rectangles

The area measurement for the square and the rectangle are the same, but we will describe the area of the rectangle first, as it is more general with this math formula:

A=bh

In this case, b is one side and h is another side with a different value. This area computation works for any 2D figure with four sides that are parallel to each other, called a parallelogram. Therefore, it also works for the square, but as all the sides have the same length in a square, we can also calculate its area as:

A=b2=b×b

Where b is the length of any side.

We have a tablecloth of size 70 inches by 70 inches. What is its area?

Solution: Here, both sides are the same length, so it is a square with length b=70inches. The area of the square tablecloth is:

A=b2=(70)2=4900

The area of the table cloth is 4900 inches2.

Area of a circle

Lastly, we have the area of the circle. As with the perimeter, its area also depends on the radius. The area of a circle can be calculated with the following equation:

A=πr2

Again, the r corresponds to the radius of the circle, and π is the number pi. From the formula, we see that if we make the radius bigger and bigger, the area of the circle also grows (in this case, by the power of two).

For example, you could see how this relationship works in real life in a garden. Imagine you attach a rope to some point and spin it in circles around that point. This motion would describe the shape of a 2D circle. If you moved the spinning rope further away from its center point, increasing the radius of the circle, you would see that the area of the spinning rope is now bigger.

Find the area of a circle with radius r=5.2cm and round it to the nearest tenth.

Solution: The area of the circle is:

A=πr2=3.14×5.22=3.14×5.2×5.2=84.9056≈84.9cm2

Further representations of 2-dimensional figures

We have previously seen some 2D shapes such as the triangle, the square, the rectangle, and the circle. But an infinite number of figures exist that you could describe. In general, we classify two-dimensional figures by their number of sides and vertices as well as their internal angles (formed by the vertices).

If we increased a rectangle’s sides by one, it would have five sides, making it a pentagon. With six sides, it’d be a hexagon, and so on.

Polygons with different numbers of sides, StudySmarter Originals

There are also different types of four-sided two-dimensional figures. Apart from the rectangle and the square, if a 2D shape has at least two equal sides and its angles are not 90º, it is a rhombus, with a shape similar to a diamond.

Rhombus, StudySmarter Originals

There are a lot of different 2D shapes, with regular sides, irregular sides, equal angles, etc. Now you just have to use some imagination and try to search for examples of them!

2 Dimensional Figures — Key takeaways

• In math, two-dimensional figures consist of figures with two dimensions: length and width. They are also called polygons.
• We can classify two-dimensional figures by the number of sides and vertices, the sides’ lengths, and the internal angles they form.
• Some of the most-used shapes in math are the triangle, the square, the rectangle, and the circle.
• The circle consists of points that are all equally distanced with respect to one point in the shape’s center. This means it has no vertices.
• The perimeter is the sum of all side lengths of the shape. For the circle, it is directly proportional to its radius.
• The area of the figure is the 2D surface delimited by its sides. Depending on the figure, we use different math formulas to compute its area.
• There are shapes with five sides called pentagons, six sides called hexagons, and more. Also, there are more examples of shapes with four sides, such as the rhombus.

2D

In geometry, a dimension can be defined as the minimum number of coordinates necessary to specify a point within a mathematical space. Based on this definition, a two-dimensional object is an object in which a point on the object can be specified using 2 coordinates; in other words, the object has 2 separate dimensions that can be measured, as opposed to a 1D object such as a line, where only one dimension can be measured.

A two-dimensional (2D) object is often described as having length and width, but no depth/thickness. 2D objects are also referred to as 2D shapes, 2D figures, plane figures, and more. The study of 2D objects is also referred to as plane geometry, and as the name suggests, plane geometry deals with objects that lie entirely within one plane.

Types of 2D objects

There are many different types of 2D objects. Two broad categories of 2D objects are polygons and curved shapes.

Polygons

Polygons are a type of closed (all the segments form a closed boundary) shape formed by a finite number of straight line segments. A square, hexagon, and pentagon are a few examples of polygons.

All of the above are formed only using straight line segments: a square has 4, a hexagon has 6, and a pentagon has 5. In general an n-gon is made up of n line segments, or sides. Polygons can be further distinguished into many different categories.

Curved shapes

Curved objects are another type of 2D object. They may or may not be closed objects, and not all of their «sides» need to be curved to be considered a curved object. The circle, ellipse, and other objects below are just a few examples.

Regardless of the type of object (curved, polygon, etc.), to be classified as a 2D object, the object must lie entirely within one plane and can only be measured in 2 different dimensions. When a third dimension exists, we are instead dealing with 3D objects and what is referred to as solid geometry.

Coordinate geometry

Coordinate geometry, also referred to as analytic geometry or Cartesian geometry is the study of geometry in the context of a coordinate system. In two dimensions, a Cartesian coordinate system is referred to as a rectangular (or orthogonal) coordinate system. It is comprised of two perpendicular number lines referred to as axes such that both axes share the same unit of length. The position of a point in the coordinate plane is given by an ordered pair of numbers (x1, y1), where x1 indicates horizontal position and y1 indicates vertical position, as shown in the figure below.

Coordinate geometry enables us to define shapes numerically, which in turn allows us to use other mathematical concepts such as algebra to formulate equations that we can use to study shapes and solve problems. For example, the distance formula can be used to determine the lengths of the sides of a shape if the points at the vertices of the shape are known.

Other dimensions

In geometry, we usually consider 0-dimensional, 1-dimensional, 2-dimensional, and 3-dimensional space.

0D

A point is a 0D object; it has no dimensions, only a position in space.

Of course, a point on a page (like the one above) does have some dimension, since for practical purposes, we have to use something to represent 0D.

1D

A one-dimensional object only has 1 dimension. Usually, this dimension is length. A line, ray, or line segment, are all examples of 1D objects. Only one coordinate (3) is necessary to specify the position of point A on the number line below.

3D

A cube is a 3D object; it has length, width, and height. The dotted lines represent the 3 dimensions of the cube, which shows that 3 coordinates are necessary to specify the position of point A within the cube.

Three-dimensional modeling in the modern world / Sudo Null IT News

Today I will tell you about what 3D modeling is, how it happens, where it is used and what it is eaten with. This article is primarily aimed at those who have only vaguely heard what 3D modeling is, or are just trying their hand at it. Therefore, I will explain the maximum «on the fingers.»

I myself am a technical specialist and have been working with 3D models for more than 10 years, I have worked in more than 10 different programs of different classes and purposes, as well as in various industries. In this regard, a certain helicopter view of this industry has accumulated, with which I would like to share with you.

3D modeling has firmly entered our lives, partially or completely restructuring some types of business. Every industry that 3D modeling has brought change to has its own set of standards and unspoken rules. But even within the same industry, the number of software packages can be so numerous that it can be very difficult for a beginner to figure out and navigate where to start. Therefore, for starters, let’s look at what types of 3D modeling are and where they are used.

There are 3 major industries that today can not be imagined without the use of three-dimensional models. They are:

• Entertainment
• Medicine (surgery)
• Industry

The first one we encounter almost every day. These are films, animation and 90% of computer games. All virtual worlds and characters are created using the same principle — polygonal modeling .

These triangles and quadrangles are called polygons.

The more polygons per model area, the more accurate the model. However, this does not mean that if the model contains few polygons (low poly), then this is a bad model, and the person’s hands are not from there. The same cannot be said about the fact that if the model has Over999999 polygons (High poly), then this is cool. It all depends on the destination. If, for example, we are talking about massive multiplayer, then imagine what it will be like for your computer when you need to process 200 characters around if they are all high poly?

Polygon modeling occurs by manipulating polygons in space. Pulling, rotating, moving, etc.

A pioneer in this industry is Autodesk (known to many for its AutoCAD product, but more on that later).
The Autodesk 3Ds Max and Autodesk Maya products have become the de facto industry standard. And as a 15-year-old teenager, I started my acquaintance with 3D models with 3Ds Max.

What do we get as an output by making such a model? We get visual IMAGE . Gamers sometimes say «I fell through textures» in a game. In fact, you are falling through the polygons that these textures are applied to. And the fall into infinity occurs precisely because there is nothing behind the image. Basically, the resulting images are used for RENDER (final rendering of the image), in the game / in the movie / for the desktop image.

Actually, I once tried to “blind” something to make a cool render (then it was much more difficult).
Speaking of modeling. There is such a direction as 3D-sculpting. In essence, the same polygonal modeling, but aimed at creating mostly complex biological organisms. It uses other polygon manipulation tools. The process itself is more like chasing than 3D modeling.

If a polygonal model is made in the form of a closed volume, such as the same sculptures, then thanks to modern 3D printing technology (which can chew through almost any shape), they can be brought to life.

In fact, this is the only way for polygonal 3D models to get into the real world. From the above, we can conclude that polygonal modeling is needed exclusively for creative people (artists, designers, sculptors). But this is not clear. So, for example, another major area of ​​application of 3D models is medicine , namely, surgery. It is possible to grow a prosthesis of a bone instead of a fragmented one. For example, the lower jaw for a turtle.

I have no medical education and I have never modeled anything for medicine, but given the nature of the forms of the model, I am sure that polygonal modeling is used there. Medicine has now stepped very far, and as the following video shows, you can fix almost everything (if you had money).

Of course, using polygonal modeling, it is possible to build all these restoring and reinforcing elements, but it is impossible to control the necessary gaps, sections, take into account the physical properties of the material and manufacturing technology (especially the shoulder joint). For such products, industrial design methods are used.

Correctly they are called: CAD (Computer-Aided Design) or in English CAD (Computer-Aided Design) . This is a fundamentally different type of modeling. That’s what I’ve been doing for 8 years now. And it is about him that I will tell you in the future. How is this method different from polygonal? The fact that there are no polygons. All forms are integral and are built according to the principle profile + direction.

The base type is solid modeling . From the name you can understand that if we cut the body, inside it not will be empty. Solid modeling is available in any CAD system. It is great for designing frames, gears, engines, buildings, airplanes, cars, and anything that comes out of industrial production. But in it (unlike polygonal modeling) it is impossible to make a model of a package with products from a supermarket, a copy of a neighbor’s dog or crumpled things on a chair.

The purpose of this method is to obtain not only a visual image, but also measurable and operational information about the future product.

CAD is an accurate tool and when working with CAD, you must first imagine the topology of the model in your head. This is the algorithm of actions that forms the shape of the model. Here, just by topology, you can distinguish an experienced specialist from a crooked one. Not always conceived topology and shape complexity can be implemented in a solid state, and then an integral part of industrial design comes to our aid — surface modeling .

Topology in surfaces is 10 times more important than in solid modeling. Incorrect topology — the collapse of the model. (I remind you that this article is a review and for beginners, I do not paint the nuances here). Mastering the topology of surfaces at a high level, closes 70% of issues in industrial modeling. But it takes a lot of practice and constant practice. In the end, the surfaces are still closed into a solid model.

Over time comes the understanding of the most convenient method for modeling a particular product. There are a lot of life hacks here, and each specialist has his own.

IMPORTANT: using CAD without specialized education is not productive! I myself have seen many times how creative people, or jacks of all trades, tried to design. Yes, of course they modeled something, but it was all “a spherical horse in a vacuum”.
When modeling in CAD, in addition to topology, it is necessary to have design skills. Know the properties of materials and production technology. Without this, it’s the same as hammering nails with a pillow, or ironing with a vacuum cleaner.

In CAD we get the electronic-geometric model of product .

(I remind you that with polygonal modeling we get a visual image)

From it you can:

• Make drawings
• It can be used to write a program for CNC machines,
• It can be parameterized (this is when changing 1 parameter you can change the model without alteration)
• Strength and other calculations can be carried out.
• It can also be sent for 3D printing (and the quality will be better)
• Make a render.

I think this is enough for you. We sorted out:

• 2 main types of modeling.
• Dismantled the application areas.
• Analyzed the capabilities of each method and its purpose.
• Discussed the basic types of modeling in CAD and some of the nuances.

Hope you enjoyed!

Ministry of Construction and Housing Policy of the UR

April 10, 2017 Trud newspaper

Chemical weapons destroyed irrevocably

Nikolai Ivanov

9015 6 Russia has once again demonstrated to the world that it remains a high-tech power

Russia is completing the destruction of its stockpiles of chemical weapons (CW). The corresponding federal target program is being implemented in an exemplary manner, overcoming all the difficulties that arose on this difficult and dangerous path, which began twenty years ago (in 19On the 97th, our country ratified the international Convention on the Prohibition of the Development, Production, Stockpiling and Use of Chemical Weapons and on Their Destruction). There were many problems: lack of funding, especially in the 1990s, lack of special technologies, trained personnel, industrial capacities, distrust and protests of the population of the regions where chemical weapons are stored, a crisis in industry and the construction industry…

Everything was successfully overcome. Seven high-tech facilities for the destruction of chemical weapons have been created, unique technologies that have no analogues in the world have been developed, which in practice have confirmed high efficiency, reliability and safety, and professional personnel have been trained. The local population has completely changed its attitude towards the chemical disarmament program, not only because there are no more threatening arsenals of weapons of mass destruction in the regions, but also because many social infrastructure facilities have been built there, high-tech enterprises have appeared that should provide people with work for many years to come.

What the staff of the Federal Directorate for the Safe Storage and Destruction of Chemical Weapons (Federal Directorate) is working on today, we are talking with its creator and permanent head Doctor of Technical Sciences, professor, multiple winner of the Russian Federation Government Prize in Science and Technology, holder of many orders, honorary citizen of the regions in which chemical weapons were stored and destroyed, Colonel General Valery Kapashin.

— Valery Petrovich, how many chemical warfare agents are left for the Federal Administration team to destroy and how much time will it take?

— As of April 2017, about 1,000 tons of chemical warfare agents remain in warehouses, all of them are located at one facility in the village of Kizner of the Udmurt Republic. Of the 40,000 tons of chemical agents available in our country, almost 39,000 tons have been safely destroyed by now. Six out of seven facilities completely destroyed their stocks of chemical weapons. At the Kizner facility, 5,744 tons of OM were stored, after putting it into operation, 4,744 tons were destroyed here in three years. We have been ordered not to reduce the rate of destruction, so that the complete completion of the destruction of chemical weapons in the Russian Federation will occur at the end of the current 2017. Mikhail Babich, Chairman of the State Commission for Chemical Disarmament, recently reported this to Russian President Vladimir Putin. With the commissioning of the last two production buildings at the Kizner facility in May and July, there will be no technical, financial, organizational or other unresolved issues to complete the combat mission assigned to us by the Supreme Commander of the country. And we will fulfill it with honor and, I want to emphasize especially, safely!

— This event will undoubtedly cause a wide resonance: Russia has once again demonstrated to the whole world that it remains a high-tech power. Are you interested in the further fate of the facilities created for the destruction of chemical weapons, because these are modern enterprises equipped with the latest technology and technology?

— They will be re-profiled and used to organize new enterprises on their production base. This was originally stipulated in the federal target program «Destruction of stockpiles of chemical weapons in the Russian Federation» (Program). By the way, investors were quickly found for our facilities, having learned about their high potential. In the city of Pochep, Bryansk region, on the basis of the facility for the destruction of chemical weapons, it is planned to expand the production of medical preparations, in the village. Leonidovka, Penza region — production of building and finishing materials, facility capacity in the village. Maradykovsky Kirov region liked «Rosatom». There are applicants for objects in the city of Shchuchye, Kurgan Region, in the city of Kambarka, Udmurt Republic, pos. Mountain Saratov region. However, beforehand, a set of works must be completed everywhere to eliminate the consequences of the activities of storage facilities and facilities for the destruction of chemical weapons. In other words, the territories where chemical warfare agents were stored, the workshops in which they were destroyed, the technological lines through which they were transported, must be brought to a guaranteed safe state. Something will have to be disassembled and subjected to degassing, something will be processed on the spot, and then garbage and the resulting waste will be collected and stored.

— Speaking of waste, many citizens are concerned about their future fate. First, what is this waste? Where and how will they be stored? Are they dangerous for the local population and the environment? What is their total mass? Is it possible, in principle, to use waste from destroyed chemical weapons somewhere?…

— As the organizer and leader of the chemical disarmament process in the Russian Federation from the first kilograms of chemical weapons, I declare with all responsibility: there is no danger to the population and the environment in the places of storage of waste from the destruction of chemical weapons. There is no danger from the chemical composition of the waste: these substances belong to the III and IV hazard classes, like the same fuels and lubricants, household chemicals, mineral fertilizers or ordinary table salt. There is no danger from the fact that they will be taken away by someone or washed away by precipitation, dispelled by winds. All waste is packaged in special waterproofing containers and stored in closed landfills, to which there is no free access. I want to especially emphasize that it is impossible to use these wastes for the preparation of chemical warfare agents, chemical weapons have been irretrievably destroyed.

— Are these landfills currently under protection and will they be protected in the future?

— Yes. And while we continue to destroy the remnants of chemical weapons at the Kizner facility in the Udmurt Republic, process the reaction masses, while we carry out work to eliminate the consequences of the activities of the facilities, in general, as long as the Federal Directorate exists, we will protect the waste landfills. There is no doubt that the state, together with the regional authorities, will find a solution to this issue even after the mission of the Federal Office is completed.

— How long can waste from the destruction of chemical warfare agents be stored?

— No time limit set. Packed in special containers and sheltered from snow, rain, sunlight and winds, these wastes can be stored for decades.

— Are there technologies for their processing and use?

— The question is not quite the right one, the task of the Federal Office is the safe destruction of chemical weapons, which we are scrupulously and responsibly working on. How the waste will be used is not up to us. However, as a specialist, I see no problems here. These wastes can and should be used. And scientists have already proposed several technologies, including, for example, obtaining ultra-pure arsenic from lewisite waste. Over time, of course, other technologies will be offered. So the waste will not interfere with anyone, there is no threat from them either, they can lie down until their time.

— Valery Petrovich, tell us in more detail what is the waste from the destruction of chemical agents?

— Warfare agents are highly toxic lethal chemical compounds. They were destroyed with the help of special degassing reagents, which required 3-4 times more mass than the destroyed agents. During degassing (passage of the neutralization reaction), a non-toxic substance was formed, the so-called reaction mass (RM). However, the reaction masses could still contain minor residues of OM, so PM was subjected to heat treatment in special furnaces. When exposed to high temperatures, the reaction masses completely decomposed with the formation of off-gases and a solid. Gaseous wastes were passed through special absorbent filters, and in the end only solid wastes remained in the form of various salts. In other words, wastes from the destruction of OM are dry salts.

During the destruction of chemical weapons, waste of III and IV hazard classes (low and moderate hazard) accumulated at the facilities, which, I repeat, will still be generated in the future when performing work to eliminate the consequences of the activity and bring the facilities to a safe state. All waste is subject to disposal at special landfills, the construction of which we completed last year. The technology for storing waste from the destruction of chemical weapons completely excludes their contact with the environment.

— And how much waste from the processing of organic matter did you get?

— This is not difficult to calculate. If for guaranteed and effective destruction of toxic substances, 3-4 times more reagents were required by mass, then out of 40 thousand tons of available agents, 3-4 times more waste was obtained. There is also waste of building materials (concrete, brick, mineral wool, as well as aluminum oxide and some others) that are generated during the dismantling of some building structures and waste of ferrous (cases of destroyed chemical munitions) and non-ferrous metals. The latter, after undergoing thermal decontamination, are not sent to the disposal site, but will be used as recyclable materials at metallurgical enterprises.

— What do waste disposal sites look like at chemical weapons storage and destruction facilities?

— These landfills are specialized, they are built according to exclusive, specially developed projects. A separate and protected area of ​​about 10 hectares is located near the industrial zone of the facility. About a dozen specially equipped covered storage facilities, a two-section control and regulation pond for collecting rain and melt water and several control wells, as well as a waste repacking plant have been built there.

The landfill has a metal fence with a security alarm. There are two gates to enter the site.

Ground structures were erected for waste disposal, consisting of compartments isolated from each other with dimensions of 12 by 36 m each and a height (along the bottom of floor slabs) of 3.2 and 5.0 m. The structures are made of prefabricated concrete and monolithic reinforced concrete structures.

In order to comply with the regulatory requirements to ensure a height of at least 2 m from the groundwater level (at its highest rise) to the lower level of the disposed waste, the structures are built on sand bedding with a layer of 2.0-2.5 m. base, which increases their environmental reliability.

In order to increase tightness and prevent waste from entering the ground in each compartment, the floors have a two-layer waterproofing of hydroisol on hot bituminous mastic over a cold bituminous primer. Waterproofing is also installed on the walls to a height of 300 mm and covered with flat asbestos-cement sheets on hot bituminous mastic, thus ensuring the creation of an impervious sump and eliminating the possibility of contamination of ground and surface water.

— All in accordance with modern environmental requirements.

— Waste is currently packed in steel drums with polyethylene liners. When laid down for long-term storage, some of them will be repacked from barrels into flexible containers. Such wastes include: a mixture of sodium salts, a free-flowing mixture of salts, waste from the thermal destruction of RM and wastewater, melted salts, spent aluminum oxide. Certain types of waste are sent for burial in steel barrels with a volume of 200 liters and 216.5 liters. Such wastes include: ash and slag from solid waste incineration, scale from metal roasting, and some others.

Ventilation pipes are installed in the walls of each storage compartment. After filling the compartment with waste, the end openings are tightly sealed with brickwork, and the ventilation pipes are closed with plugs. To ensure control of the state of the air environment inside the compartment filled with waste and covered by a compartment, a device for introducing control devices is embedded in each branch pipe. Through this device, air samples can be taken from the compartment using a portable sampler.

— During the waste storage process, will air quality be monitored not only near the storage facilities, but also in the compartments themselves?

— No chemical reactions can take place there, any specialist will tell you, however, air condition control is provided. This is another guarantee of security. Continuous monitoring will allow monitoring the state of the environment, confirming compliance with environmental safety requirements.

The capacity of the landfills makes it possible to completely bury all the received waste. Their storage will not lead to violation of hygiene standards and deterioration of the sanitary and epidemiological situation.

— The local population should not have concerns for their safety and the safety of the environment, the issue of waste storage is as well thought out as the entire chemical weapons destruction program. I would like to return to the beginning of our conversation so that you can tell us in more detail about the work to eliminate the consequences of the activities of facilities and prepare them for re-profiling. How long will it take, from what sources will funding come, what types of specific work will be done?

— A new targeted federal program «Liquidation of the consequences of the activities of storage facilities and facilities for the destruction of chemical weapons» has been developed, which has passed almost all approvals and is being approved by the Government of the Russian Federation. So the financing of these works will come from the federal budget. By the way, without waiting for the adoption of the new program, we have already launched preparations for the liquidation of the consequences of activities at all the facilities that have completed the destruction of chemical weapons and have begun some liquidation work that does not require capital investments.

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