In shooting, preemption is the distance that a target manages to overcome before the moment a charge hits it. The accuracy of shooting depends on the ability to calculate it correctly. There are people who by nature quite accurately determine the lead when shooting, they intuitively sense where the target will be, and mark it in this place. But most shooters and hunters acquire this skill through lengthy training and the realization of what the lead is and how it is calculated mathematically.

## Basic concepts

First of all, you need to introduce the basic concepts.

- The target path is the imaginary line that the target passes. The trajectory is characterized by the spatial position of the target, its speed and direction of motion (velocity vector).
- Sighting line - a straight line passing through the center of the barrel through the bar of the sight, ideally it will connect the gaze of the shooter and the target at the point of its defeat.
- The angle of encounter with the target (Ξ±) is the angle between the direction of movement of the target at the point of destruction and the sighting line.

## Types of lead

The amount of lead depends on the speed of the target and the time it takes the charge to reach the target. This time, in turn, depends on the distance to the target and the speed of the charge. Three types of lead are distinguished:

- true;
- observable;
- hidden.

## True

True lead is the distance that the target manages to go along its trajectory from the moment of the shot to the moment the charge hits it. This distance depends only on the flight time of the bullet / shot and the speed of the target, calculated by a fairly simple formula:

Y _{and} = V _{M} * t _{s} ,

where Y _{and} is the true lead, V _{M} is the target velocity, t _{s} is the charge flight time.

Calculation example. Target speed 10 m / s. Shooting is carried out from a distance of 50 meters, the average charge speed is 400 m / s, in order to calculate the speed of the charge to the target, it is necessary to divide the distance by the charge speed, it turns out t _{s} = 50/400 = 0.125 s. Find the true lead:

At _{and} = 10 * 0.125 = 1.25 meters.

## Observed

But the true lead value visually coincides with what the shooter sees, only in one case: if the target moves strictly perpendicular to the aim line, that is, the angle Ξ± is 90 Β°. Naturally, such conditions rarely occur, in most cases the target moves at an indirect angle with respect to the shooter's gaze, so the observed lead is a kind of projection of the true distance the target will move.

The observed lead is determined not only by the flight time of the charge and the speed of the target, but also in many ways by the angle of encounter with the target (Ξ±). The smaller this angle, the smaller the observed lead value. At an angle Ξ± = 0 Β°, the target will fly away strictly from the arrow or fly towards it, that is, it will be impossible to take a lead with lead. The observed lead is calculated by the formula:

Y _{n} = Y _{and} * sin (Ξ±),

where Y _{n} is the observed lead, Y _{and} is the true lead, Ξ± is the angle of encounter with the target.

Calculation example. Take the true lead from the previous example and assume that the target moves away from the shooter at an angle of 45 Β° with respect to his view (aim line), then the observed lead will be equal to:

At _{n} = 1.25 * sin (45 Β°) = 1.25 * 0.707 = 0.88 meters.

## Hidden

There is another type of lead - this is hidden, which is hardly relevant for hunters and idle shooting enthusiasts. Its value is negligible, respectively, the effect on the calculation of the distance traveled by the target from the shot to the hit is negligible. The latent lead is made up of the time the gunpowder burns during firing (approximately 0.003 seconds) and the time the charge takes to travel through the barrel (approximately 0.004 seconds), that is, in total it is 0.007 seconds.

Such a short time is taken into account only by professional shooters at competitions of the level of olympiads and world championships, where even miserable nuances that can affect the result are important.