Methods for determining the distance to the target using an optical sight. Application of the "thousandth" formula in shooting practice How to determine the distance when shooting
The range to the target by its angular magnitude is determined when firing from a standstill and from a stop. For this, sights are used. small arms... In addition, calculations can be made according to the formula:
Where D- range to the target (object), m;
H (W)- height (width) of the target (object), m;
1000 - constant value;
Have- the angle at which the target (object) is visible, in thousandths.
Determination of the range using the sighting devices of small arms is carried out by comparing the apparent dimensions of the target with the covering size of the front sight or the slot of the sight. In this case, the weapon is held in the accepted firing position.
For example, if, when firing from an AK assault rifle, the visible width of the machine gun (0.75 m) is equal to the width of the front sight, then the range to the target is 250 m;
if the machine gun seems to be 2 times narrower than the front sight, the range to it is 500 m. Similarly, you can use the slot of the weapon sight.
To determine the distance to a target (object) by calculation using formula (1), it is necessary to know the height or width of this target (object) and its angular value.
Example. Determine the range to the enemy tank if its width of 3.5 m is visible at an angle of 5 thousandths (0-05).
Decision. According to the formula (1)
The angular magnitude of the target (object) is measured using optical instruments (binoculars, periscope, etc.), and in the absence of them - using the fingers of the hand and improvised items.
When measuring angular values with the help of improvised items, they must be held in front of yourself at a distance of 50 cm from the eye.
Then one millimeter division of the ruler will correspond to 2 thousandths of the range (2 etc.). This follows from formula (2), which can be written in the following form:
,(2)
Example. Measure the angular value of the tree with a ruler if, when it is 50 cm away from the eye (L = 500 mm), the height (B) corresponds to 25 mm.
Decision. According to the formula (2)
The angular values of the fist and fingers when they are 50 cm away from the manhole, shown in Fig. 1 are average, so every sergeant and soldier should clarify and remember them.
Fig. 1. Price in thousandths of the fist and fingers.
Even if you have nothing to do with shooting, sometimes you need find out the distance to any object. This can be done using a goniometric reticle, which is supplied with some models of binoculars, scopes and monoculars. But, for example, in my monocular there is no such grid. What to do?
Instead of a binocular scale, you can use the standard ruler scale found on many compasses in the same way. 
The difference will be that the division of the binoculars scale is equal to 5 thousandths, and one millimeter of the scale of the ruler located 50 cm from the eye should be counted as 2 thousandths.
The calculation formula is the same.
D = (B x 1000) / Y
- D is the distance to the object;
- B is the known height or width of the item in meters;
- 1000 - constant value;
- Y is the angular apparent size of the object in thousandths.
let's consider determining the distance to an object using a ruler with a specific example.
Let's say you come to some settlement and see a house. The standard door height is 2 meters. We look at the door through the ruler scale, holding it in a bent hand in front of us about 50 cm.
The door on the ruler scale is 12 millimeters. As we remember, 1 millimeter is equal to 2 thousandths. That is, the door is 12 x 2 = 24 thousandths. The known door height (2 meters) is multiplied by 1000 and divided by 24 thousandths. We get 83.3 meters to the building. As you can see, everything is pretty simple.
In a camping trip, travel 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 or other obstacle, in determining the height of a tree, in calculating the remaining path to the final destination. In these cases, the thousandth will help.
In military practice, where in calculations it is constantly necessary to use the ratios between angular and linear quantities, instead of the degree system of measures, an artillery (linear) system is used. Simpler and more convenient for fast approximate calculations. The artillerymen take the central angle of a circle constricted by an arc equal to 1/6000 of the circumference as a unit of angular measures.
This angle is called the division of the goniometer, as it is used in all artillery goniometers. Sometimes this angle is called the thousandth. This name is explained by the fact that the length of the arc of such an angle along the circumference is approximately equal to a thousandth of its radius. This is a very important circumstance.
Therefore, when observing the objects around us, we are, as it were, in the center of concentric circles, the radii of which are equal to the distances to the objects. And the measure of the central angles will be linear segments equal to a thousandth of the distance to objects. So, if a house 5 meters long is located at a distance of 1000 meters from the observer, then it fits into the central angle equal to five thousandths. Such an angle is written on paper like this: 0-05, and reads - zero, zero five.
If the length of the fence is 100 meters, then it fits into the central corner equal to 100 thousandths, one large division of the goniometer. This angle is written down on paper as follows: 1-00 thousandth, and it reads - one, zero. From these examples it can be seen that corners allow very quickly and easily through the simplest arithmetic operations switch from angular measurements to linear measurements and vice versa.
So, for example, if there is a tree next to a house located from the observer at a distance of D-1500 meters (D - range) and the angle between them fits in fifty-five thousandths - Y = 0-55 (Y - angle) and you need to determine the distance from at home to the tree - B (B - distance), then the formula for determining the linear dimensions follows from the proportion B: D = Y: 1000.
H = D x Y / 1000 = 1500 x 55/1000 = 82.5 meters.
From the same proportion, you can derive the formula for the thousandth and to determine the distance to objects.
D = 1000 x V / Y
Let's solve a simple example of determining the distance through the thousandth formula - you see a man at the 6-meter-high pillar. It is required to determine the distance to it. First, we determine in which corner the height of the column fits. Let us assume that the height of the pillar fits into the angle Y = 0-05 (five thousandths). Then, using the formula for determining the range, we get: L = 1000 x 6/5 = 1200 meters.
Using the above two formulas allows you to quickly and accurately determine any linear and angular values on the ground.
There are ratios between the divisions of the goniometer (in thousandths) and the usual degree system of angular measures: one thousandth of 0-01 is equal to 3.6 ′ (minutes), and the large division of the goniometer (1-00) = 6 degrees. These ratios allow, if necessary, to carry out the transition from one measurement system to another.
Angles on the ground can be measured using field binoculars, a ruler, and improvised objects. 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 a small one - 0-05 thousandths.
To measure the angle between two directions, it is necessary, looking through binoculars, 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 (enemy machine gun) is located to the left of the road at an angle of 0-30.
The vertical scale is used when determining vertical angles. In the case of their large sizes, you can also use the horizontal scale by turning the binoculars vertically. If absent, angles can be measured with a regular ruler with millimeter divisions. If you hold such a ruler in front of you at a distance of 50 cm from your eyes, then one 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 setting the ruler exactly 50 cm from the eye. This can be achieved by tying a thread to a ruler and biting it with your teeth at a distance of 50 cm. Using a 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 (box, pencil), the size of which is known in millimeters, and therefore in thousandths. Such a measurement is taken out at a distance of 50 cm from the eye and, by comparison, the desired angle value is determined by it.
Based on the book "Map and Compass - My Friends".
Klimenko A.I.
We often hear that shooters simply do not know how to determine the distance to the target (target) at which they need to shoot. And this despite the fact that an optical sight is installed on a rifle, or a gun (carbine). In general, the topic of scopes is very common in questions on forums and in letters from readers. The main issues are reticle and distance to the object of observation. Which reticle is best for long range shooting? Why big ones? Because at a distance of 10 to 20 m it is easier to use a collimator sight. I decided to organize some information about optics and distance.
A simple method for determining the distance to an object
In the picture below you can see the reticle Rangefinder, or as it is popularly called - "crossbow net". Scopes with this type of reticle have become very popular among owners of weapons with telescopic sights. A convenient scale for calculating distances and at the same time auxiliary crosshairs allow you to very accurately calculate the distance to the target, making certain adjustments. The figure clearly shows how you can determine the distance to the target using the example of a 4x32 optical sight.
Visual determination of the distance to the target using an optical sight
(Rangefinder reticle, or crossbow reticle)
It should be noted that the adjustment and preliminary calibration of each sight must be carried out separately. This should be done as follows:
- take a "standard" with a vertical and horizontal size of 50 cm (for example, a cardboard box),
- set the magnification of the sight to 4 (if you have a scope with variable magnification) and look at the "standard" through the telescopic sight from a distance of 30 m. Usually at this distance, 0.5 meters of width is placed between the curves at the level of the central crosshair.
If the “standard” does not fit between the curves or, on the contrary, is much smaller, then you need to change the distance to the target until you achieve the desired result. Remember this distance, or best of all, make a note to yourself so that later, when necessary, you can quickly calculate the distance to the target.
In the same way, we find the distances corresponding to all other reticle marks on the reticle. After that, you can already start targeting the sight. "Why not the other way around?" - you ask. Yes, because it is easier to aim the scope at already known distances. Now, looking at the object of the hunt through a telescopic sight, you will know the exact distance to the target.
Such sights can be mounted on pneumatic and firearms.
For an approximate determination of the distance, a sniper or shooter can use the following also simplest methods.
Eye measuring method for determining the distance to the target
To hit the target with the first shot, you need to know the distance to it. This is necessary to correctly determine the value of corrections for crosswind, air temperature, Atmosphere pressure and, most importantly, to set the correct sight and aiming point selection.
The ability to quickly and accurately determine the distance to stationary, moving, as well as to emerging targets is one of the main conditions for the successful work of a sniper. 
Fig. Proportional perception of the target by the sniper with the PSO-1 sight reticle to develop automatic skills in determining the range
The main, the simplest and fastest, the most accessible to a sniper in any conditions of a combat situation. However, a sufficiently accurate eye is not acquired immediately, it is developed through systematic training carried out in a variety of terrain conditions, at different times of the year and day. To develop your eye, you need to exercise more often in evaluating distances by eye, with the obligatory check of them in steps and on a map or in some other way.
First of all, it is necessary to learn to mentally imagine and confidently distinguish on any terrain several of the most convenient distance standards. You should start your workout with short distances (10, 50, 100 m). Having mastered these distances well, you can go sequentially to large (200, 400, 800 m) up to the maximum range of actual fire sniper rifle... Having studied and fixed these standards in visual memory, one can easily compare with them and evaluate other distances.
In the process of such training, the main attention should be paid to taking into account the side effects that affect the accuracy of the eye method for determining distances:
1. Larger objects seem closer to smaller ones at the same distance.
2. Objects that are seen more sharply and more distinctly seem to be located closer, therefore:
- objects of bright color (white, yellow, red) seem closer than objects of dark colors (black, brown, blue),
- brightly lit objects appear closer to dimly lit objects at the same distance,
- during fog, rain, at dusk, on cloudy days, when the air is saturated with dust, the observed objects seem farther than on clear sunny days,
- the sharper the difference in the color of objects and the background on which they are visible, the more reduced the distances to these objects seem; for example, in winter, a snowfield brings closer all darker objects on it.
3. The fewer intermediate objects are between the eye and the observed object, the closer this object seems, in particular:
- objects on level ground seem closer,
- especially shortened seem to be the distances defined through vast open water areas, the opposite shore always seems closer than in reality,
- folds of the terrain (ravines, hollows) crossing the measured line, as it were, reduce the distance,
- when observing while lying down, objects appear closer than when observing while standing.
4. When viewed from the bottom up, from the foot of the mountain to the top, objects seem closer, and when viewed from top to bottom - farther.
Visibility of objects at various distances:
| Distance (km) | Thing |
| 0,1 | Human facial features, hands, details of equipment and weapons. Collapsed plaster, architectural decorations, individual building bricks. Shape and color of leaves, bark of tree trunks. Barbed wire threads and personal weapons: pistol, rocket launcher. |
| 0,2 | General facial features, general details of equipment and weapons, headgear shape. Separate logs and planks, broken windows of buildings. Leaves of trees and wire on the supports of the wire fence. Lighted cigarettes at night. |
| 0,3 | Oval of a person's face, coloring of clothes. Building details: cornices, platbands, drainpipes. Light infantry weapons: rifle, assault rifle, light machine gun. |
| 0,4 | Headwear, clothes, shoes. Living figure in general outline... Bindings of frames in the windows of buildings. Heavy infantry weapons: AGS, mortar, heavy machine gun. |
| 0,5-0,6 | The contours of a living figure are clear, movements of arms and legs are distinguishable. Large details of buildings: porch, fence, windows, doors. Branches of trees. Wire fence supports. Light artillery: SPG, ZU, BO, heavy mortar. |
| 0,7-0,8 | A living figure is a general outline. The chimneys and attic windows of the buildings are distinguishable. Large branches of trees. Trucks, combat vehicles and tanks standing still. |
| 0,9-1,0 | The outlines of a living figure are difficult to distinguish. Building windows stains. The lower part of the trunk and the general outline of the trees. Telegraph poles. |
| 2,0-4,0 | Small detached houses, railway cars. Lit lanterns at night. |
| 6,0-8,0 | Factory chimneys, clusters of small houses, large detached buildings. At night - lighted headlights. |
| 15,0-18,0 | Large bell towers and large towers. |
Determination of the distance to the target by angular dimensions
Determination of the distance to the target by angular dimensions is possible if the observed linear quantity (height, width or length) of the object to which the distance is determined is known. The method comes down to measuring the angle in thousandths, under which this object is visible.
The thousandth is 1/6000 of the circular horizon, increasing in width in direct proportion to the increase in distance to the reference point, which is the center of the circle. For those who find it difficult to understand, remember that the thousandth is at a distance:
100 m = 10 cm,
200 m = 20 cm,
300 m = 30 cm,
400 m = 40 cm, etc.
Knowing the approximate linear dimensions of the target, or the landmark in meters and the angular value of this object, you can determine the distance using the thousandth formula: D = (B x 1000) / Y,
Where D- distance to the target
1000
- a constant unchanged mathematical value that is always present in this formula
Have- the angular magnitude of the target, that is, to put it simply, how many one-thousandth divisions on the scale of an optical sight or other device will take the target
IN is the metric (i.e. in meters) known target width or height.
For example, a target has been detected. It is necessary to determine the distance to it. What are the actions?
1. We measure the angle of the target in thousand.
2. The size of an object located next to the target in meters, multiply by 1000
3. The result obtained is divided by the measured angle in thous.
The metric parameters of some objects are:
| An object | Height (m) | Width (m) |
| 0,25 | 0,20 | |
| 0,25 | 0,25 | |
| Human | 1,7-1,8 | 0,5 |
| Crouching man | 1,5 | 0,5 |
| Motorcyclist | 1,7 | 0,6 |
| Passenger car | 1,5 | 3,8-4,5 |
| Cargo car | 2,0-3,0 | 5,0-6,0 |
| Railway carriage on 4 axles | 3,5-4,0 | 14,0-15,0 |
| Wooden post | 6,0 | - |
| Concrete pillar | 8,0 | - |
| Cottage | 5,0 | - |
| One floor of a multi-storey building | 3,0 | - |
| Factory pipe | 30,0 | - |
The scales of the open sights, optical sights and optical devices in service are calibrated in thousandths and have a graduation price: 
Thus, to determine the distance to an object using optics, it is necessary to place it between the scale divisions of the sight (device) and, having learned its angular value, calculate the distance using the above formula.
Example, you need to determine the distance to the target (chest or growth target), which fits into one small side segment of the scale of the PSO-1 optical sight.
Decision, the width of the chest or growth target (infantryman in full growth) is 0.5 m. According to measurements with the help of PSO-1, the target is closed by one division of the lateral correction scale, i.e. angle of 1 thousandth.
Hence: L = (0.5 x 1000) / 1 = 500m.
Measurement of angles with improvised means
To measure angles with a ruler, you need to hold it in front of you, at a distance of 50 cm from the eye, then one division (1 mm) will correspond to 0-02.
The accuracy of measuring angles in this way depends on the skill in setting the ruler exactly 50 cm from the eye. This can be practiced with a rope (thread) of this length.
To measure angles with improvised objects, you can use your finger, palm, or any small handy object (matchbox, pencil, 7.62 mm sniper cartridge), the dimensions of which are known in millimeters, and therefore in thousandths. To measure the angle, such a measure is also taken out at a distance of 50 cm from the eye, and from it, by comparison, the desired value of the angle is determined.
The angular values of some objects are:
Having acquired skills in measuring angles, one should proceed directly to determining distances from the measured angular dimensions of objects.
Determination of distances by the angular dimensions of objects gives accurate results only if the actual dimensions of the observed objects are well known, and angular measurements are made carefully using measuring instruments (binoculars, stereoscopes).
Preparing binoculars for work
1. Take the binoculars out of the case.
2. Inspect optics and housing.
3. Turning the eyepieces (2), set the required diopter value according to the diopter scale (5).
4. Place the monoculars at the base of the eyes so that there is one field of view.
Measuring range to targets using a binocular reticle
1. Aim the binoculars reticle at the target and determine its angular value.
2. Knowing the height or width of the target, determine the range to the target using the thousandth formula:
where, D is the range to the target,
B is the height or width of the target,
Y is the angular value of the target in thousandths.
Example(fig. 3):
the tank is "placed" between two small divisions, which corresponds to 0-10. The average height of the tank is 2.7 m.We determine the distance to the tank if Y = 0-10, B = 2.7 m
.
The range to the tank is 270 meters.
BINOCULARS NIGHT BN-1
Night binoculars BN-1 are intended for observing the battlefield, studying the terrain and conducting reconnaissance in conditions of natural night illumination.
Specifications BN-1
Identification range at natural night illumination …… 200m.
Magnification 3.2 x.
Field of view 9 ° ± 30.
Battery voltage 8.3-8.8v.
Time of continuous operation of the device (without battery replacement):
At a temperature of + 20 ° C 7h;
At a temperature of 40 g C3 h;
At a temperature of + 40 ° C, 5 h.
Weight of the device:
In the stowed position 3.5kg;
In working position 1.6kg.
