To have an opportunity to try to obtain a victory in battles at the maximum distance, people invented at first onions, and then — guns and shells. In the ancient time it was possible to trace a hit point easily visually. Today the target of rockets will defend so far what to get to it without additional devices will turn out hardly.
Features of motion of bodies including shells after force from the outside stops acting on them, such science as external ballistics studies. Experts of this area make various schemes and tables, developing optimal variants for firing.
Ballistic trajectory
The object moving on certain coordinates is affected, as we know, by the following forces:
- the device setting it in motion at the initial stage;
- air resistance force;
That is rectilinear the movement, for example, the bullet or a shell cannot be anyway. That trajectory on which such objects after start move and is called ballistic. This way can look as a parabola, a circle, a hyperbole or an ellipse.
The first two types of trajectories are reached respectively at the 2nd and first cosmic speeds. Experts carry out calculations for movement on such trajectories for ballistic missiles.
If the body moves as a result of operation of any device, ballistic its trajectory cannot be considered. In this case it treats dynamic or aviation. For example, the plane on a ballistic trajectory will fly only if his pilot switches off engines.
Ballistic missiles intercontinental
Such rockets move on a special ballistic trajectory. At first they move vertically up. So happens over a short period of time. Further the control system develops an object towards the purpose.
Design of MBR have multistage. Thanks to it, such rocket can reach even the target located in other hemisphere of Earth. After fuel burning out the used step of MBR separates, and in the same second following is connected. At achievement certain heights and speeds the rocket of this version directs to the earth, to the planned purpose.
Sites of the ballistic movement
Trajectories of movement of bullets, rockets or shells can be divided conditionally on:
- departure point — point of counting;
- the weapon horizon — the site at a departure point crossed by an object at start-up and completion of the movement;
- the eminence — the line which is conditionally continuing the horizon forming the vertical plane;
- trajectory top — the point located in the middle between the purpose and the place of start;
- aiming — the line of aiming between a target and a point of release;
- angle of sight — a conditional corner between a target and the horizon of weapon.
Properties of a trajectory
Under the influence of gravity and atmospheric resistance the speed of the started object begins to decrease gradually. As a result also height of its flight falls. Trajectories of the movement of the released bodies divide generally into three types:
- interfaced;
- nastilny;
In the first case at unequal trajectories the flying range of a body remains invariable. If in a trajectory the corner of the eminence exceeds a corner of the largest range — the way will be called hinged, otherwise — nastilny.
As calculation is carried out: the simplified formula
To define, where exactly on the earth the rocket will explode, experts make calculations with use of a technique of integration and the differential equations. Similar calculations usually differ in complexity and hits yield the most exact results.
For calculations of a ballistic trajectory of rockets also the simplified technique can sometimes be used. Air on atmosphere border, as we know, rarefied. And therefore its resistance for ballistic missiles can sometimes not be considered. The simplified formula of calculation of a ballistic trajectory as follows looks:
- y=x-tgѲ0-gx2/2V02-Cos2Ѳ0, where:
x \the distance from a departure point to top of a way, y is top of a trajectory, v0 is speed at start, Ѳ0 — the angle of start. The way of an object in this case represents a parabola. Such trajectory is called vacuum.
If air resistance when flying a ballistic missile it is considered, formulas will turn out very difficult. To carry out such long calculations often is inexpedient as the error arising because of influence of the atmosphere in the rarefied air is insignificant and does not play a special role.
More difficult methods of calculations
Besides vacuum, when performing various calculations the experts can define trajectories:
- material point;
- solid body.
In the first case, besides gravity, are considered:
- curvature of the Earth's surface;
- air resistance (front);
- speed of rotation of the planet.
With use of this more difficult technique the trajectory of the movement of artillery shells can be described, for example.
When calculating a way of moving of a solid body to attention not only the front air resistance, but also other aerodynamic forces is accepted. In flight the shell often moves not only progressively, but also with rotation. By this technique, for example, the way of the missiles launched at right angle to a movement trajectory in air of the high-speed plane can pay off.
The operated shells
If an object is also operated, calculations become even more difficult. In this case the targeting equations are added to formulas of the movement of a solid body, in addition.
It allows to correct a trajectory in case of, for example, change of draft, turn of a wheel and so forth. That is gradually to reduce a deviation of a way of the movement of an object from settlement.
Purpose of performance of calculations
Most often calculations of ballistic trajectories are made for rockets and shells when conducting fighting. Their main objective at the same time is definition of the location of a system of weapon so that the target could be hit as fast as possible and precisely.
Delivery of a shell to a target after carrying out calculations is carried out usually in two steps:
- the fighting position is defined so that the purpose was not further delivery radius;
- aiming is carried out and firing is made.
In the course of aiming, exact coordinates of a target, such, for example, as an azimuth, the range and the eminence are defined. If the purpose is dynamic, its coordinates are calculated taking into account the movement of the released shell.
This targeting when firing is stored in electronic bases today. The special computer software automatically sends weapon to the situation necessary for defeat of the purposes warheads.
Calculations also of this sort can be made also in astronautics. Calculations of near-earth and interplanetary trajectories, taking into account the movement of Earth and the purpose, for example, of the Moon or Mars, at start of spacecrafts are carried out, of course, only on computers with use of various difficult programs.