It makes no sense to make the same calculations several times if the original data does not change. A rounded log with a diameter of 20 cm and a length of 6 meters will always have the same volume, regardless of who and in which city conducts the count. Only the formula V=πr²l gives the correct answer. Therefore, the volume of one OCB will always be V=3.14×(0.1)²×6=0.1884 m³. In practice, in order to exclude the moment of carrying out standard calculations, cubes are used. Such useful and informative tables are created for various types of lumber. They help to save time and find out the cubic capacity of round timber, boards, CBM, and timber.
The name of this building guide is due to the fact that the volume as a physical quantity is measured in cubic meters (or cubic meters). For a simpler explanation, they say "cubature", respectively, the table was called "cubature". This is an ordered matrix, which contains data on the volume of one product for various initial parameters. The base column contains sections, and the row contains the length (molding) of the material. The user only needs to find the number located in the cell at their intersection.
Let's consider a specific example - a cubic yard of roundwood. It was approved in 1975, is called GOST 2708-75, the main parameters are diameter (in cm) and length (in meters). Using the table is very simple: for example, you need to determine the V of one log having Ø20 cm with a length of 5 m. At the intersection of the corresponding row and column, we find the number 0.19 m³. A similar cube for round timber exists according to another standard - ISO 4480-83. Reference books are very detailed in increments of 0.1 m, as well as more general, where the length is taken in 0.5 m.
little secrets
The very use of the cube is not difficult, but the main nuance is the correct data. Round wood is not a cylinder, but a truncated cone, in which the lower and upper cuts are different. One of them can be 26 cm, and the other - 18. The table assumes an unambiguous answer for a particular section.
Various sources suggest doing it in two ways: calculate the average value and take the volume from the reference book for it, or take the size of the upper cut as the main section. But if the tables were compiled according to certain standards, then they must be used in accordance with the accompanying instructions. For a cubature GOST 2708-75, the diameter of the upper saw cut of the log is taken. Why is the raw data moment so important? Because with a length of 5 meters for Ø18 cm we get 0.156 m³, and for Ø26 cm - 0.32 m³, which is actually 2 times more.
Another nuance is the correct cubes. If complex formulas for truncated cones were used in the GOST 2708-75 table, calculations were carried out, and the results were rounded to thousandths, then modern companies that make up their own cubes allow themselves “liberties”. For example, instead of 0.156 m³, there is already the number 0.16 m³. Often, frankly erroneous cubic meters are posted on Internet sites, in which the volume of a log 5 meters long with Ø18 cm is indicated not 0.156 m³, but 0.165 m³. If an enterprise uses such directories, selling roundwood to consumers, then it makes a profit, in fact deceiving customers. After all, the difference in 1 product is significant: 0.165-0.156=0.009 or almost 0.01 m³.
The main problem of round timber is a different section. Sellers offer to resolve issues with calculations in the following ways:
- calculation of the volume of each unit and summation of the obtained values;
- storage method;
- finding the average diameter;
- method based on the density of the wood.
1. It must be said right away that the first of the indicated options gives the correct results. Only the calculation of the volume of each log and the subsequent addition of the numbers ensures that the buyer will pay for the timber that he will receive from the company. If the length is the same, then it is enough to find the cross-sectional areas of all the trunks, add them up, and then multiply by the length (in meters).
2. Warehousing method.
It is assumed that the stored round timber occupies a part of the space that has the shape of a rectangular parallelepiped. In this case, the total volume is found by multiplying the length, width and height of the figure. Given that there are voids between the stacked trunks, 20% is subtracted from the resulting cubic capacity.
Minus - the acceptance as an indisputable fact that the tree occupies 80% of the total space. After all, it may well happen that the bars are folded inaccurately, thereby the percentage of voids is much greater.
3. Density based method.
In this case, you need to know the mass of the forest and the density of the wood. The cubature is easily found by dividing the first number by the second. But the result will be very inaccurate, since a tree of the same species has a different density. The indicator depends on the degree of maturity and humidity.
4. Average method.
If the trunks of harvested trees are almost the same in appearance, then any 3 of them are chosen. Measure the diameters, and then find the average value. Further, according to the cubature, the parameter for 1 product is determined and multiplied by the required amount. Let the results show: 25, 27, 26 cm, then the average is Ø26 cm, since (25 + 26 + 27) / 3 = 26 cm.
Given the disadvantages of the considered methods, the only correct way to calculate the cubature can be considered to be the volume of each log using the cubature GOST 2708-75 or ISO 4480-83 and summing up the data obtained.
For many builders, the topic of calculating the number of logs in a cube is familiar. But for an unprepared person, this may seem not only very distant, but also incomprehensible. And very often there are disagreements between the builders themselves, as well as between the builders and the customer about how many logs should be in a cube.
In order to deal with this problem, a mathematical method is usually used, which in a few minutes can give a clear answer about how many logs are needed for a certain number of cubic meters.
As a rule, rounded logs are used in the construction of wooden buildings. But this material may differ in size, that is, in length and diameter. The unit of measurement is taken to be centimeters. There are one million centimeters in one cubic meter. Thus, first you need to decide on the size of the logs.
In order to measure the size of the logs, you will need a regular centimeter tape measure. All logs, as a rule, should initially be of the same size, and later, depending on the project, they are sawn into the necessary elements.
So, having measured the size of the log with a tape measure, we get the values \u200b\u200bof the length and diameter in centimeters. For example, let's try to calculate how many logs are needed for one cubic meter if the logs are six meters long and eighteen centimeters in diameter.
The following formula is required for the calculation:
Volume = Pi * Radius * Radius * Length.
Six meters in this case equals six hundred centimeters. Pi is always 3.14. We get the radius by dividing the diameter by two. Thus, our formula takes the following form: Volume \u003d 3.14 * (18: 2) * (18: 2) * 600 \u003d 3.14 * 9 * 9 * 600 \u003d 152604 centimeters. To convert to cubic meters, divide the resulting number by one million: 152604: 1000000 = 0.1526. This result tells us that one log of this size will take up only 0.15 with a small cubic meter.
Now you need to figure out how many logs are in a meter. This is our main task. To do this, we will divide one cubic meter by the result of our calculations - 0.1526. It turns out: Quantity = 1: 0.1526 = 6.55 logs. It turns out that for one cubic meter we need to take about seven logs of a given size.
If we consider logs of a larger diameter, for example, twenty-four centimeters, then the calculation results will be different:
Volume = 3.14 * 12 * 12 * 600 = 271296 cubic centimeters = 0.2713 cubic meters.
This means that in one cubic meter there will be: 1: 0.2713 \u003d 3.69 logs. In this case, there will be fewer logs in one cubic meter.
To calculate the number of logs per cubic meter, a very simple formula is used, which allows you to calculate the result in a matter of minutes. For calculations, of course, it is better to arm yourself with a tape measure and a calculator.
In the industrial harvesting of roundwood, it is quite difficult to determine its cubic capacity. To accurately calculate the volume of each log, you can use the truncated cone volume formula, which takes into account the main diameters of both cuts and the length of the log itself.
Round wood is very convenient and practical for building houses, baths and other residential and non-residential premises.
In fact, the cubic size of the roundwood is not calculated in such a complicated way. It is accepted all over the world to count it in a faster way. Special tables are used for this.
How to calculate the cubic capacity of a single tree without additional measurements?
A few years ago, to calculate the volume of a single tree, they used the product of the arithmetic mean of the areas of saw cuts and the length of the tree. With the help of a meter (reminiscent of an ordinary caliper), the diameter of the tree in its middle part was determined. Then it was multiplied by 3 and the cross-sectional area was obtained.
Further, the resulting number was multiplied by the length of the workpiece, and a volumetric result was obtained. This method of calculation is inaccurate, since the thickness of the bark is not taken into account. The number Pi was taken with a large deviation from the real one, and the formula in its distorted form gave large errors.
The formula itself looks like this: the diameter of a rounded log is divided by 2 and squared, then multiplied by Pi and the length of the log.
Even if we measure the thickness of the bark and take this into account to determine the diameter of the tree itself, then deviations from these indicators will be inaccurate, although with a smaller error. More accurate calculations showed that the actual deviations in the calculations of the cubature of a round log with primitive measurements have a certain dependence on the parameters of the tree, which was taken into account when compiling the corresponding tables to determine the volumetric parameter. Let's try to figure out how to calculate the cubic capacity of the forest. This will require:
- roulette;
- the corresponding calculation tables, where there is a final cubature.
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Peculiarities .
How much does a board cube weigh?Technology for calculating the volume of a single log
First you need to use a tape measure to measure the length of the tree and its diameter on the cut in the upper part (excluding the bark). After that, let's look at the tabular parameters: at the intersection of the line, where the length of the tree is indicated, and the column indicating the corresponding diameter, we find the volume of the measured body. Everything is simple and reliable.
Such calculations also cannot be called absolutely accurate, since the features in which the forest was grown and the shape of the trunk were not taken into account. But it is customary not to pay attention to such trifles with large volumes of workpieces.
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Calculation of volume of cubic capacity of stockpiled timber
With industrial volumes of harvesting round logs, other methods and tabular data are used. In essence, a round forest in a stored state has the shape of a rectangular parallelepiped. Calculations of its volume are familiar to everyone from school. But it is impossible to use this method, since the dimensions of the voids between the logs will not be taken into account. By the way, they also directly depend on the diameter of the logs, which can be calculated mathematically.
Through numerous calculations, the coefficient was determined, with the help of which a special table was compiled. It works similarly to the previously described table, with the only difference that the volume of the mentioned parallelepiped and the average thickness of the upper cut are taken into account. The cubic capacity of the forest can be calculated with great accuracy.
But one cannot hope for good accuracy of calculations with inaccurate stacking of forest products. This procedure is not used in the warehouse storage of timber, since in this case the volume that the round timber occupies directly in the warehouse is estimated.
It is very easy to calculate the cubic capacity after preliminary weighing the forest.
Next, you need to calculate the volume by dividing the mass of the forest by the density, which corresponds to the type of wood. Such a calculation cannot be considered ideal either, since the forest in different degrees of maturity has a deviation in density. The humidity of the wood can also play a special role here.
Construction works require the solution of many different issues, among which the most important task is the selection and purchase of lumber. It is not difficult to calculate how many linear meters of boards and timber will be needed during the construction process. That's just the price of commercial wood is indicated for 1 cubic meter, and this often causes difficulties for novice home craftsmen. The ability to correctly select and calculate the amount of edged or unedged lumber in a cube will save money and avoid a situation where, after completion of construction work, a pile of unused boards remains on the site.
Classification and characteristics of lumber
The very name "lumber" suggests that this type of construction raw material is obtained by longitudinal sawing of tree trunks on circular or band saws. For the production of boards and timber, several sawing methods are used:
- tangential (in a circle),
- radial.
Tangential sawing involves the movement of the saw tangentially to the annual rings of the tree, which reduces the amount of waste, and hence the cost of building materials. The boards obtained in this way have a beautiful, pronounced pattern, therefore they are often used for finishing purposes. Disadvantages of circular sawing include the wood's tendency to shrink and swell, and a significant difference in texture as the cutting tool approaches the center of the log.
In the sawmill industry, several methods of sawing the trunk are used.
With radial sawing, the cutting line passes through the core of the tree, so the output of boards will be less and their price will be higher. However, if it is necessary to obtain high quality wood, this method is used. This is due to the fact that, compared with the tangential method, radial sawing boards have halved swelling and shrinkage rates. In addition to the sawing methods discussed above, a mixed method is also used, which combines the advantages of the first two.
The concept of lumber actually includes not only the traditional molding, which is most often seen in the construction markets. A complete list of products that are obtained when sawing logs includes:
- board;
- beam;
- bar;
- lagging;
- croaker.
The last two types of lumber are waste, which absolutely does not prevent them from being used for certain types of construction work, as well as for finishing purposes.
Boards
Boards include rectangular lumber with a thickness of not more than 100 mm and a width to thickness ratio of at least 2:1. Depending on the degree of processing, the board can be edged and unedged. The first is a finished product without bark and with evenly sawn edges, while the second is a "semi-finished product" taken directly from the saw frame.
The edged board has even edges and a constant width along the entire length of the lumber
Most often in construction boards of such standard sizes are used:
- thickness - 25 mm, 40 mm, 50 mm, 60 mm;
- width - from 75 to 275 mm with gradation through 25 mm;
- length - from 1 m to 6.5 mm in 250 mm increments.
Boards of other sizes can be obtained by cutting or planing standard lumber, as well as by making an individual order for sawing round timber.
Unedged board has a lower cost, but without finishing, its scope is limited
The parameters of lumber used in construction are standardized and determined according to the current GOST 8486–86 for softwood and GOST 2695–83 for hardwood.
bar
Timber is called lumber, the cross section of which is a square with sides of at least 100 mm. The size of the beam in the diameter is unified and can vary from 100 to 250 mm in increments of 25 mm. The standard defines the length of products of this type from 2 to 9 m, but most often square-section lumber with a length of no more than 6 m is used. to sleepers.
The beam is an ideal material for the construction of frames and other wooden structures.
The bar differs from the bar considered above only in that its cross section does not exceed 100x100 mm. The typical length of the bar is also 6 m, and the size in diameter ranges from 40 mm to 90 mm in 10 mm increments. To simplify the classification, bars are often referred to as a rail, in which the cross section has a rectangular shape, and the ratio of thickness to width is at least 1:2. The standard range of edges of softwood slats looks like this: 16, 19, 22, 25, 32, 40, 44, 50, 60, 75 mm. For hardwood lumber, products of increased width are additionally provided, and the product line itself looks like this: 19, 22, 25, 32, 40, 45, 50, 60, 70, 80, 90, 100 mm.
A variety of bars and slats allow you to strengthen and make any wooden structure as stable as possible
Obapol and croaker
Obapol represents the very first cut of round timber, in which the outer surface remains untreated. Unlike obapol, the croaker can have a cut on half of the second side or an alternation of processed and unprocessed sections from the side of the bark. The value of obapol and slab in construction is secondary, since the unaesthetic appearance and reduced performance characteristics make it possible to use this type of lumber only for auxiliary purposes. Most often, slab and obapol are used as a fastening material, as well as for the manufacture of formwork, crates or flooring for scaffolding. This material is also interesting as a decorative material for decorating walls, fences and other vertical structures.
Despite external unsightliness, slab and obapol are widely used for secondary construction tasks.
Technology for calculating the number of boards in a cube
On the wood market, both edged lumber and unedged boards are presented, along the edges of which there is a wane. Depending on the type of wood products, several methods are used to determine the cubic capacity.
How to find out the number of edged lumber in a cube
The algorithm for determining the cubature of lumber is based on the formula known to every student for finding the volume of a rectangular parallelepiped. In order to find out the cubature of one board (V) in a cube. m, it is necessary to find the product of its length (a) by the width (b) and thickness (h) in meters V=a×b×h.
The desired figure will make it easy to calculate how many boards of this type will fit in one cubic meter of lumber. For this, 1 cu. m of lumber is divided by the volume of one product. For example, if you need to find out the cubic capacity of one board with parameters 6000x200x25 mm, then by substituting these numbers into the formula, we get V = 6x0.2x0.025 = 0.03 cubic meters. m. Therefore, in one cubic meter there will be 1 / 0.03 = 33.3 of such products.
The grooved board has a groove on one side and a ridge on the other. Since both of these elements are approximately equal to each other, their parameters can be neglected. That is why the size of tongue-and-groove lumber in diameter is measured without taking into account the locking part.
In the case of boards that have the same dimensions, the calculation can be simplified by substituting the dimensions of the lumber stack into the formula. Of course, at the same time, its laying should be as dense as possible, otherwise the gaps between the individual elements will affect the accuracy of the calculations. Given that the cost of individual types of wood reaches tens of thousands of rubles, such an error can result in a pretty penny.
To simplify the calculations, you can use special tables that allow you to quickly determine the cubic capacity or the amount of wood in 1 cubic meter. m lumber.
Table: the number of edged boards in 1 cu. m lumber standard length
| Board size, mm | The number of boards 6 m long in 1 cu. m | The volume of one board, cube. m |
| 25x100 | 66,6 | 0.015 |
| 25x150 | 44,4 | 0.022 |
| 25x200 | 33,3 | 0.03 |
| 40x100 | 62,5 | 0.024 |
| 40x150 | 41,6 | 0.036 |
| 40x200 | 31,2 | 0.048 |
| 50x100 | 33,3 | 0.03 |
| 50x150 | 22,2 | 0.045 |
| 50x200 | 16,6 | 0.06 |
| 50x250 | 13,3 | 0.075 |
The cubature of timber of standard sizes can also be determined using the table below.
Table: the amount of timber in 1 cu. m lumber
| Beam size, mm | The number of products with a length of 6 m in 1 cu. m | Volume of 1 bar, cu. m |
| 100x100 | 16.6 | 0.06 |
| 100x150 | 11.1 | 0.09 |
| 100x200 | 8.3 | 0.12 |
| 150x150 | 7.4 | 0.135 |
| 150x200 | 5.5 | 0.18 |
| 150x300 | 3.7 | 0.27 |
| 200x200 | 4.1 | 0.24 |
Very often it is required to determine the surface area (floor or wall) that can be covered with a board of one thickness or another with a volume of 1 cubic meter. m. To do this, you can use the formula S \u003d 1 / h, where h is the thickness of the lumber. So, one cubic meter of a 40 mm board will be enough to equip S = 1 / 0.04 = 25 square meters. m floor. To facilitate the process of calculating the area allows a table called a cubature. It contains data on the cross-section of boards, their number in 1 cu. m and the desired area that they can cover.
Method for calculating the cubature of an unedged board
Unedged lumber is not trimmed at the edges, so not only the size in the diameter of individual products varies, but also the width of different parts of one board. In this regard, it is possible to calculate the volume of a stack of raw lumber only approximately. The same applies to calculating the cubic capacity of a separate unedged lumber, although the error in this case will be much smaller.
So, to calculate the cubature of an unedged board, there are two constants - thickness and length, and one variable - width. To avoid complex calculations using differential algebra methods, the last parameter is simply averaged. To do this, the board is measured in several places and the arithmetic mean is found. For example, for a board with a diameter at the base of 400 mm, a width of 350 mm in the middle and 280 in the top, the calculated value will be (430 + 340 + 260) / 3 = 343 mm. Further calculations are carried out in exactly the same way as for edged lumber.
Most often, the width of an unedged board is determined only on the basis of measurements along the edges of the lumber. It should be noted that the accuracy of calculations directly depends on the number of measurements, therefore, in critical cases, their number is increased.
If it is required to find out the cubic capacity of a package of unedged wood, then the products are stacked on top of each other in such a way that the following conditions are met:
- stacks must be aligned along the front end;
- boards in a stack should not overlap;
- it is not allowed to change the width of the package along the entire length of the lumber;
- the protrusion of the outermost products beyond the stack should not exceed 100 mm.
By measuring the height, length and width of a package of unedged wood with a tape measure, the approximate cubic capacity is determined using the formula V=a×b×h. To find out a more accurate value, the result is multiplied by the stacking factor, which can be found in special tables.
16.06.2014 17:04
After all the ideas for the implementation of the construction of the house have been worked out and the final version of the construction of the house from round logs has been selected, the question arises of how much such a house will cost you. To determine the cost of building a log house from rounded logs, you need to know how many cubes of logs are in this log house. In this article, we will try to explain in detail how to calculate the cubic capacity for the construction of rounded logs.
Calculation of the cubic capacity of rounded logs
The simplest way to calculate is by the formula - pr² . H
Π — 3,14
r² - round log radius squared
N - round log length
We substitute the data in the formula:
3.14 *(0.11 m)²* 6m= 0.228 m3
So, we got how many cubes are in one rounded log with a diameter of 220mm. Next, you need to calculate how many logs in your house and multiply the resulting amount by the cubic capacity of one log (0.228 m3). It is easy to calculate the number of logs in the wall, but initially you need to determine for yourself how high the floor will be.
How to calculate the cubic capacity of the forest
It is also necessary to add 7% to the resulting height by shrinkage if the log is of natural moisture.
For example, the height of the first floor is 2.9 meters. The height of one log of 220 mm, minus the lunar groove, will be - 190.5 mm. Next, we divide the floor height of 2.9m by the thickness of the log without a groove - 0.19m, having previously translated all the numbers into meters.
2.9: 0.19 = 15.26 pieces. We received the required number of logs with a diameter of 220mm in order to build a floor with a height of 2.9 meters. It is necessary not to forget and add 7% to the shrinkage of the house. A total of 16 crowns will be obtained. Now, in order to find out the total floor volume of a 6x6 house, 16 crowns high, you need to perform the following calculation:
16 (crowns) * 4 (walls) * 0.228 (volume of one log) \u003d 14.6 m3 of a log. Now, in order to find out the cost of a log for the entire log house, it is necessary to multiply the number of cubes received by the price of a log for one cube. The cost of one meter of a cubic rounded log can be found here.
To perform the calculation for other log diameters, we offer you a number of pre-calculated tables, using which you will surely find answers to your questions.
Article prepared by the company ASK Aegis, which performs log house construction and renders a wide range of construction services in the residential housing market.
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- How to calculate the cubic capacity of a single tree without additional measurements?
- Technology for calculating the volume of a single log
- Calculation of volume of cubic capacity of stockpiled timber
- How to calculate cubic capacity without using tables?
In the industrial harvesting of roundwood, it is quite difficult to determine its cubic capacity. To accurately calculate the volume of each log, you can use the truncated cone volume formula, which takes into account the main diameters of both cuts and the length of the log itself.
Round wood is very convenient and practical for building houses, baths and other residential and non-residential premises.
In fact, the cubic size of the roundwood is not calculated in such a complicated way. It is accepted all over the world to count it in a faster way. Special tables are used for this.
How to calculate the cubic capacity of a single tree without additional measurements?
A cubic meter of timber and a folding cubic meter of roundwood.
A few years ago, to calculate the volume of a single tree, they used the product of the arithmetic mean of the areas of saw cuts and the length of the tree. With the help of a meter (reminiscent of an ordinary caliper), the diameter of the tree in its middle part was determined. Then it was multiplied by 3 and the cross-sectional area was obtained.
Further, the resulting number was multiplied by the length of the workpiece, and a volumetric result was obtained. This method of calculation is inaccurate, since the thickness of the bark is not taken into account. The number Pi was taken with a large deviation from the real one, and the formula in its distorted form gave large errors.
The formula itself looks like this: the diameter of a rounded log is divided by 2 and squared, then multiplied by Pi and the length of the log.
Even if we measure the thickness of the bark and take this into account to determine the diameter of the tree itself, then deviations from these indicators will be inaccurate, although with a smaller error. More accurate calculations showed that the actual deviations in the calculations of the cubature of a round log with primitive measurements have a certain dependence on the parameters of the tree, which was taken into account when compiling the corresponding tables to determine the volumetric parameter. Let's try to figure out how to calculate the cubic capacity of the forest. This will require:
- roulette;
- the corresponding calculation tables, where there is a final cubature.
Technology for calculating the volume of a single log
First you need to use a tape measure to measure the length of the tree and its diameter on the cut in the upper part (excluding the bark). After that, let's look at the tabular parameters: at the intersection of the line, where the length of the tree is indicated, and the column indicating the corresponding diameter, we find the volume of the measured body. Everything is simple and reliable.
Such calculations also cannot be called absolutely accurate, since the features in which the forest was grown and the shape of the trunk were not taken into account. But it is customary not to pay attention to such trifles with large volumes of workpieces.
Calculation of volume of cubic capacity of stockpiled timber
With industrial volumes of harvesting round logs, other methods and tabular data are used. In essence, a round forest in a stored state has the shape of a rectangular parallelepiped. Calculations of its volume are familiar to everyone from school. But it is impossible to use this method, since the dimensions of the voids between the logs will not be taken into account. By the way, they also directly depend on the diameter of the logs, which can be calculated mathematically.
Through numerous calculations, the coefficient was determined, with the help of which a special table was compiled. It works similarly to the previously described table, with the only difference that the volume of the mentioned parallelepiped and the average thickness of the upper cut are taken into account. The cubic capacity of the forest can be calculated with great accuracy.
Types of lumber and their volume.
But one cannot hope for good accuracy of calculations with inaccurate stacking of forest products. This procedure is not used in the warehouse storage of timber, since in this case the volume that the round timber occupies directly in the warehouse is estimated.
It is very easy to calculate the cubic capacity after preliminary weighing the forest.
Cubic round timber table GOST
How to calculate cubic capacity without using tables?
It may be misunderstood that in the timber industry it is impossible to correctly and accurately calculate the cubic capacity of roundwood. But this is not true, since only the primary methods for calculating the volume of roundwood have been considered here. In reality (especially when the timber industry is in the safe hands of specialists), this process is much more complicated.
Later, coefficients and special formulas are applied. This work is difficult, but this is the only way to calculate the cubic capacity of roundwood with a sufficiently high accuracy.
