Volume of the tree trunk

When constructing, as well as in various kinds of everyday questions, it is sometimes necessary to determine the volume of the tree trunk, to calculate how many cubic meters of wood it contains, and at the same time weigh it. It turns out that this task is not as simple as it seems; There is no exact solution, but only an approximate evaluation. Even for a tree trunk, which has been felled and peeled from the branches, the task is far from easy. The fact is that the tree trunk, the most smooth and thin, does not represent a cylinder, a full cone, a truncated cone, or any other geometric body whose volume we can calculate by the formula. Therefore, a more or less accurate calculation of the volume of a tree trunk can only be done by means of higher mathematics. In practice, however, approximate volume calculations are used, which are obtained with an accuracy sufficient for many practical purposes.

When constructing, as well as in various kinds of everyday questions, it is sometimes necessary to determine the volume of the tree trunk, to calculate how many cubic meters of wood it contains, and at the same time weigh it

The volume of the tree trunk is more or less close to either the volume of the truncated cone, or - for the trunk of the tree with the vertex end - to the volume of the full cone, or, finally - for short logs - to the volume of the cylinder. But can not we find a formula for the volume that would be right for all three named bodies?..

Such a formula exists and is called the Simpson formula. To do this, you need four dimensions - the length of the trunk and the area of the three bases of the tree: the lower frame, the top and the middle of the length. Measurement of the lower and upper diameters is very simple; Direct definition of the average diameter without special adaptation is rather inconvenient. But the difficulty can be circumvented if we measure the circumference of the trunk with a string and divide its length by the number pi in order to obtain a diameter. The final formula looks like this:

V = h/6*(b1 + 4*b2 + b3),

where h is the length of the trunk, b1, b2, b3 - the areas of the lower, middle and upper bases, respectively.

But how to determine the volume of the trunk of a tree on the vine? Without climbing on it, only the diameter of its lower part is accessible to measurements. In this case, we will have to be satisfied with a very approximate evaluation. To do this, use a special table of numbers that show how much the volume of the tree trunk is from the volume of the cylinder of the same height and diameter measured at the height of the adult's chest, 130 centimeters. This, of course, is only an approximate estimate, before not too deviating from the true result: up to 2% in the direction of exaggeration and up to 10% in the direction of understatement.

From here we can estimate the weight of the tree on the vine. Let, for example, you stand near a fir tree, the height of which you determined at 28 meters, and the circumference of the trunk at chest height was equal to 120 centimeters. Then the area of the corresponding circle is 1131 square centimeters, or 0,113 square meters, and the trunk volume is 0,5õ0,113õ28 = 1,58 cub. meter. Assuming that 1 cu. meter fresh spruce wood weighs an average of 650 kilograms, we find that 1,58 cubic meters should weigh more than a ton.

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