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Calculation of the cubic capacity of a round log. How to correctly calculate the cubic capacity of roundwood: instructions for making calculations. The simplest calculation is carried out according to the formula = P * R2 * N, where

To build a house, bath or other wooden building with your own hands, you need to know how to calculate the cubic capacity of a log. This will allow you to purchase exactly as much building material as is required for the upcoming work, so you can properly plan your budget and save a certain amount of money.

The volume of round timber is measured in cubic meters. At the design stage of a future building, it must be taken into account that the diameter of the logs used for the construction external walls home may be different. Its value depends on the air temperature in the region during the cold season. So, if in winter the temperature does not fall below -22 ° C, then round timber with a cross section of 150 mm can be used. In severe frosts, for a comfortable stay in the house, it is necessary to choose a thicker building material. At the same time, their cubic capacity will also depend on the section of the logs.

apply a mathematical formula;
use a cube.

The formula for calculating the volume of logs

The algorithm for calculating the cubic capacity of logs is quite simple and understandable even for a novice master. First, according to the existing project, the total amount of timber is calculated. Then the cubature of one element is calculated, after which the obtained values are multiplied among themselves.

If we consider a log from a geometric point of view, then it looks like a cylinder. Therefore, to calculate its cubature, you can use the formula for calculating the volume of a cylinder: V = π * r² * l, where: V is the volume; π is a mathematical constant equal to 3.14; r is the radius of the round timber; l is the length of the log.

As an example, consider a situation where it is necessary to calculate the cubic capacity of timber for the construction of a 6x12x2.4 m bath. It is planned to use logs 300 cm long and 15 cm in diameter as a building material. First you need to find out the total amount of round timber. For laying one row around the perimeter of the future building, you will need: 6/3 + 12/3 = 6 logs. To drive the height of the walls, you should prepare: 240/15 = 16 pcs. Summing up the obtained values, we find out that for the construction of a bath it is necessary to buy: 16 * 6 \u003d 96 logs. The volume of one element will be equal to: 3.14x(0.15/2)²x3 = 0.0529 m³. For the given example, the total cubic capacity of the required timber will be equal to: 0.0529 * 96 = 5.08 m³.

The above algorithm can only be applied when construction material meets the following requirements:

logs are cylindrical;
their length and diameter are the same.

If during the construction process it is necessary to use round timber, in which the dimensions of the butt and top are different (truncated cone), then the standard formula for calculating the volume of a cylinder will not give a true result. In this case, the following formula must be applied: V = (π/400000)*l*, where d is the tip diameter; D - butt diameter; a is the round timber contraction factor. Its value depends on the length and cross section of the butt. The values of the coefficient a are presented in the table.

Using a cubature

The volume of timber is strictly regulated by GOST 2708-75 and is a matrix in which the volumes of round timber are inscribed, depending on its geometric parameters. This table consists of rows and columns. The former contain information about the cross section of the product, and the latter about its length.

The table is very easy to use and significantly reduces the time of calculations. For example, you need to calculate the volume of a log with a length of 5 m and a diameter of 25 cm. At the intersection of the corresponding column and row is the number 0.295 m³.

The volume of timber of different diameters

If everything is more or less clear with logs of the same size, then with round logs of different cross-sections, the buyer may experience certain difficulties. In this case, the volume can be calculated in several ways:

calculate the cubature of each element, after which the obtained values are summed up;
calculate the amount of space occupied;
find the average diameter of the log and use it to carry out further calculations.

To obtain the most accurate results, it is necessary to use the first method, but it is the most laborious and can take a lot of time. However, in this case, you can be sure that you will buy exactly as much building material as you need to perform certain tasks.

The second method assumes that the material occupies a space of a certain size, which has the shape of a parallelepiped. It can be the body of a truck, part of a warehouse, etc. Since voids form between the logs during folding, the actual volume of wood should be reduced by approximately 20%.

The calculation algorithm is as follows:

the dimensions of the parallelepiped filled with round timber are calculated (length, width and height);
the available values are multiplied among themselves;
the resulting value is multiplied by the coefficient of hollowness, that is, by 0.8, which will be the final result.

This method is the simplest and fastest, so it is used quite often.

The average method can be used when the cross section of all logs is almost the same. In this case, 3-5 elements are selected from the total amount of timber. After that, the diameter of each of the selected round timber is calculated and the average value is determined. Further, according to the formula or cube, the volume for one element is calculated, and then the result is multiplied by the number of logs required.

Conclusion on the topic

To date, there are several ways to calculate the cubic capacity of logs. All of them have a small error, which must be taken into account when buying timber. The most accurate method is considered to be the determination of the volume of each element with further multiplication of the obtained values, and the fastest is the calculation of the cubic capacity of the space occupied.

Method two: formula

This calculation method is most suitable for timber that is approximately the same in length and has a diameter similar to each other. The following formula is used for calculations: π *R*L, where π is equal to 3.14, R is the radius of the log, and L is its length.

Tip: building materials in the form of logs, of course, have a similar diameter, but still, they are slightly different from each other. And in order to get the most accurate result, it is necessary to measure the volume of any three units from the batch - according to the above formula. And then these parameters are summed up and divided by 3. We have an average number. We multiply the figures obtained by the number of logs at our disposal and get the volume.

Method three: tables

This technique is used by craftsmen quite often in determining the volume of logs necessary for the construction of the calculation. These are ready-made tables, which show the already calculated figures that have been developed empirically. So, we measure the diameter of the log and its length, substitute these values in the table (see below) and get what we are looking for at the intersection of the columns.

Also, in order to correctly calculate these values, a cube is used according to GOST 2708-75, where, according to generally accepted construction conditions, the required numbers are also indicated, depending on the 2 initial ones: the length and diameter of the log.

For example, here are the following tables:

And for calculations, they use an online kubaturnik, for example, of the following plan: http://www.enerteh.ru/news/kubaturnik.html

Calculation algorithm example

The algorithm for obtaining data is practically simple to implement. For example:

According to the drawing of the premises, we consider the total amount of lumber (round timber) that will be used in the construction of the planned building.
When determining the quantity, we take into account the required (or desired) thickness of timber (that is, their diameter).
We measure the average volume of the log. Knowing the total amount that is available, we get the final volume of round timber, which is necessary for construction. We calculate the approximate volume of a log using the formula (see above) or according to the table.

Building material is often not perfectly round

To use this algorithm, it is necessary that round lumber meet certain criteria:

the shape should be conditionally cylindrical;
logs should be approximately the same length and diameter.

The matter becomes more complicated if it is necessary to calculate the cubic capacity of building materials of various formats. Therefore, the methods for calculating the cubic capacity for rounded and unprocessed logs are somewhat different.

For industrial preparation roundwood 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 for warehousing timber, since in this case the volume occupied by the round timber 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.

The cubic capacity of a log is the volume of wood material, measured in cubic meters. This value is used in the construction of wooden log cabins to calculate the amount of roundwood. It is important to determine the cubic capacity when selling firewood, where payment is provided for each cubic meter of wood. How to calculate the volume of round cylindrical lumber correctly?

It is necessary to know the cubic capacity of a tree when buying this building material, since payment is made for each cubic meter.

There are several ways to roughly estimate the cubic capacity of roundwood or firewood. All developed methods use data from measurements of geometric dimensions and mathematical calculations. A tape measure is traditionally used to measure building values.

Calculation of the cubic capacity of the occupied space

The easiest way is to define a cubic rectangular space in which the beam is folded. Such a place can be a dump truck body or a barn. You can also calculate the geometric dimensions of the woodpile if it is folded in the form of a neat rectangle.

Since the spatial cubature is not completely filled with wood, the determined value is reduced by the void factor. In construction calculations, it is considered that the coefficient of voids is 0.8. That is, 20% of the space is occupied by air voids, and 80% by wood.

The cubic size is defined as follows:

The length, width and height of a rectangular space are measured.
The obtained values are multiplied among themselves, the value of the volume is obtained.
The resulting value is multiplied by a factor of 0.8, which takes into account the approximate number of voids between round logs.
The resulting value is taken as the desired volume of the log.

This method is used to calculate the cubic capacity of round timber or boards of various sizes, firewood.

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Calculation of the volume of individual logs

Figure 1. Measurement of two perpendicular diameters in the section of a bar

If the roundwood is characterized by the same length of logs and a close diameter, then you can calculate the volume of selectively 3 beams, reduce them to the average calculated value and multiply it by the number log material. In this case, the calculations are performed as follows:

Choose any 3 beams.
Measure their diameter and length. For ease of calculation, measurements should be taken in meters.
Calculate the cubic space occupied by each of the round timber using the formula:

where Pi is a number equal to 3.14,

R is the radius equal to half of the measured diameter,

L is the length of the beam.

The obtained values of 3 cubic meters of roundwood will be close to each other. They must be added and the sum divided by 3. Thus, we get the value of the average volume of one log.
Next, we multiply the resulting average value by the number of blanks in the machine or storage.

Since logs of similar diameters and standardized lengths are used for construction, this method is widely used to estimate the cubic capacity of scaffolding.

If the shape of the beam is slightly pressed down, its cut in section will not be round, but slightly oval. How then to determine the value of the diameter? To do this, measure the size of 2 perpendicular diameters in the cross section of the beam: the largest and smallest. Next, the measured values are summed up and divided by 2. The resulting value will be the average diameter used in the calculations (Fig. 1).

Round wood is a cylinder by mathematical standards. The volume of a cylinder is calculated as the area of its circumference multiplied by the length of the cylinder itself (read logs).

where: number Pi- 3,14159265358979; R- radius of the circle; H- the length of the cylinder. But since the comparison of a log with a cylinder is purely conditional, in real calculations the diameter of the log is measured at its midpoint. Naturally, without bark. We were taught from school that the area of a circle is calculated: as the number Pi (3.14159) multiplied by the radius of the circle squared. Or another option, this is again the number Pi multiplied by the diameter of the circle to the fourth degree. These are purely theoretical calculations of the volume (cubic capacity) of one single log. And if we are talking about large volumes of timber, the so-called stacks of timber, where there are hundreds of cubes of round timber? In this case, of course, no one will calculate the m3 of each log. To simplify the work of storekeepers, standardizers, technologists and other employees of woodworking enterprises, who, on duty, have to measure wood, use a round wood cube. This is nothing more than tables approved by GOST, containing calculations of the volume of round wood, depending on the thickness of its top. Experienced lumberjacks and woodworkers poke the wood in 2 cm increments, usually in even sizes. It is worth noting that specialists who constantly deal with the forest can, by eye, with great accuracy, determine the diameter of a log without the use of rulers or tape measures. And then there are already mathematical calculations of the points of the forest:

so many logs of this diameter,
so many different diameters
etc.

After that, the values of the log volume of each diameter are taken from the forest cubature and multiplied by the number of linear meters.

For example, a log with a diameter of 20 mm has a volume of 0.23 m3, and there were 100 such logs 6 m long in a stack. Thus, the result is obtained, based on the cubic capacity of lumber: V = 0.23m3 * 100pcs = 23 m3 - i.e. the stack will be 23 m3 with a top diameter of 20 mm.

Similarly, the volume of logs of other diameters is calculated using the values of the roundwood cube of 6 meters in length.

Table-cubature roundwood

Part I - the length of the log of the measured forest, ranging from 4 to 8.5 linear meters.

Diameter/cm	Length/m
Diameter/cm

Part II - the length of the log of the measured forest ranging from 9 to 13.5 linear meters.

Diameter/cm	Length/m
Diameter/cm

Converting a storage cubic meter of wood into a dense one

Timber stored in piles in open areas is counted in cubic meters (m3). This is the so-called warehouse cubic meter of timber, measured with all the voids and gaps between the logs.

In fact, the storage m3 is the measurements of the stack in terms of external dimensions: width, height and length. When selling round lumber, such a concept as a dense cubic meter of wood is used. What it is? It can be imagined as a stack of timber without voids and any gaps between the logs. That is, like a solid volume of wood. How is the volume of round timber converted into a dense cubic meter? A stack of wood, sorted by length, is measured by external dimensions. The values are multiplied and the warehouse m3 is obtained. Next, a special conversion factor is used (see table). As a result of multiplying the obtained volume of the storage cubic capacity by the coefficient from the table, the value of the dense cube of the forest * is obtained.