In a camping trip, traveling, and in other cases, there is often a need to determine the distances to inaccessible objects, measure their length and height. In determining the width of a river or other obstacle, in determining the height of a tree, in calculating the remaining path to the final goal. In these cases, the thousandth.

## Thousandths, thousandths formulas for determining distances and ranges, simplest ways to measure angles on the ground using thousandths.

In military practice, where the calculations constantly have to use the relationships between angular and linear values, instead of a degree system of measures, artillery (linear) is used. More simple and convenient for fast approximate calculations. For a unit of angular measures, gunners take the central angle of a circle pulled together by an arc equal to 1/6000 of the circumference.

This angle is called the division of the goniometer, as it is used in all artillery goniometers. This angle is sometimes called the thousandth. This name is due to the fact that the length of the arc of such an angle around the circumference is approximately one thousandth of its radius. This is a very important circumstance..

Therefore, when observing the objects surrounding us, we are, as it were, in the center of concentric circles whose radii are equal to the distances to the objects. And a measure of the central angles will serve as linear segments equal to a thousandth of the distance to the objects. So, if a house 5 meters long is located at a distance of 1000 meters from the observer, then it fits into a central corner equal to five thousandths. This angle is written on paper like this: 0-05, and zero is read, zero five.

If the fence length is 100 meters, then it fits into the central angle equal to 100 thousandths, one large division of the goniometer. This angle is written on paper like this: 1-00 thousandth, and read one, zero. From these examples it can be seen that the angles allow you to very quickly and easily through the simplest arithmetic operations to switch from angular measurements to linear and vice versa.

So, for example, if a tree is located next to a house located at a distance of D-1,500 meters from the observer (D distance) and the angle between them is fifty-five thousandths Y = 0-55 (Y angle) and you need to determine the distance from the house to the tree B (B distance), then the formula for determining linear dimensions follows from the proportion B: D = Y: 1000.

## H = L x Y / 1000 = 1500 x 55/1000 = 82.5 meters.

From the same proportion one can derive the thousandth formula for determining the distance to objects.

## D = 1000 x V / V

We solve a simple example of determining the distance through the thousandth formula **at a post 6 meters high you see a man. It is required to determine the distance to it.** First, determine the angle in which the column height fits. Assume that the height of the column fits into the angle Y = 0–05 (five thousandths). Then according to the formula for determining the range we get: **D = 1000 x 6/5 = 1200 meters.**

Using the two above formulas allows you to quickly and accurately determine any linear and angular values on the ground.

Between divisions of the goniometer (in thousandths) and the usual degree system of angular measures, there are relations: one thousandth of 0-01 is 3.6&# 8242; (minutes), and a large division of the goniometer (1-00) = 6 degrees. These ratios allow, if necessary, the transition from one measurement system to another.

## The easiest ways to measure angles on the ground using thousandths.

Angles on the ground can be measured using field binoculars, a ruler and improvised items. In the field of view of the binoculars there are two mutually perpendicular goniometric scales for measuring horizontal and vertical angles. The value of one large division of these scales corresponds to 0-10, and small 0-05 thousandths.

To measure the angle between two directions, looking through the binoculars, you need to combine any stroke of the goniometric scale with one of these directions and count the number of divisions to the second direction. So, for example, a separate tree (enemy machine gun) is located to the left of the road at an angle of 0-30.

A vertical scale is used in determining vertical angles. If they are large, you can use the horizontal scale by turning the binoculars vertically. In the absence of a binocular, angles can be measured with a standard ruler with millimeter divisions. If you keep such a ruler in front of you at a distance of 50 cm from the eyes, then one of its division (1 mm) will correspond to an angle of two thousandths (0-02).

The accuracy of measuring angles in this way depends on the skill in making the ruler exactly 50 cm from the eye. This can be achieved by tying the thread to the ruler and biting it with teeth at a distance of 50 cm. Using the ruler, you can measure angles in degrees. In this case, it should be taken out at a distance of 60 cm from the eye. Then 1 cm on the ruler will correspond to an angle of 1 degree.

In the absence of a ruler with divisions, you can use your fingers, palm or any small object (matchbox, pencil), the size of which in millimeters, and therefore in thousandths, is known. Such a measure is taken out at a distance of 50 cm from the eye, and the desired angle is determined from it by comparison.

*Based on the book “Map and Compass My Friends”.*

* Klimenko A.I..*