Since ancient times, mankind has been trying to achieve victory in a collision with the enemy at the maximum possible distance, so as not to destroy their own soldiers. Slings, bows, crossbows, then guns, now rockets, shells and bombs - all of them need an accurate calculation of the ballistic trajectory. And if it was possible to visually track the point of contact with the old military “equipment”, which allowed them to study and shoot more accurately next time, then in the modern world the destination point is usually so remote that it is simply impossible to make out without it.
What is a ballistic trajectory
This is the path that an object overcomes. He must have a certain initial speed. It is affected by air resistance and gravity, which eliminates the possibility of movement in a straight line. Even in space, such a trajectory will be distorted under the influence of the gravity of various objects, although not as significantly as on our planet. If you do not take into account the resistance of air masses, then most of all such a process of movement will resemble an ellipse.
Another option is hyperbole. And only in some cases will it be a parabola or a circle (upon reaching the second and first space velocity, respectively). In most cases, such calculations are carried out for missiles. They usually fly in the upper atmosphere, where the influence of air is minimal. As a result, most often the ballistic trajectory still resembles an ellipse. Depending on many factors, such as speed, mass, type of atmosphere, temperature, planet rotation, and so on, individual parts of the path can take many different forms.
Ballistic trajectory calculation
In order to understand exactly where the released body will fall, differential equations and the method of numerical integration are used. The ballistic trajectory equation depends on many variables, but there is also a universal option that does not provide the necessary accuracy, but is quite sufficient for an example.
y = x-tgѲ 0 -gx 2 / 2V 0 2 -Cos 2 Ѳ 0, where:
- y is the maximum height above the ground.
- X is the distance from the start point to the moment when the body reaches the highest point.
- Ѳ 0 - throw angle.
- V 0 is the initial velocity.
Thanks to this formula, it becomes possible to describe a ballistic flight path in an airless space. It will turn out in the form of a parabola, which is typical for most variants of free movement in similar conditions and in the presence of gravity. The following characteristic features of such a trajectory can be distinguished:
- The most optimal elevation angle for the maximum distance is 45 degrees.
- The object has the same speed of movement both during launch and at the time of landing.
- The throw angle is identical to the angle at which the drop will occur.
- The object reaches the top of the trajectory in exactly the same time, after which it then falls down.
In the vast majority of calculations of this kind, it is customary to neglect the resistance of air masses and some other factors. If we take them into account, then the formula will come out too complicated, and the error is not so large as to significantly affect the effectiveness of the hit.
Differences from the floor
By this name is understood another variant of the path of the object. The flat and ballistic trajectory are somewhat different concepts, although the general principle is the same. In fact, this type of movement implies the maximum possible movement in the horizontal plane. And throughout the path the object retains sufficient acceleration. A ballistic version of the movement is needed to travel long distances. For example, a flat trajectory is most important for a bullet. She should fly straight straight for as long as possible and break through everything that gets in her way. On the other hand, a rocket or a shell from a cannon inflicts maximum damage at the very end of the movement, as they gain the highest possible speed. In the interval of their movement, they are not so crushing.
Modern use
The ballistic trajectory is most often used in the military sphere. Missiles, shells, bullets and so on - they all fly far, and for an accurate shot you need to take into account many variables. In addition, the space program is also based on ballistics. Without it, it’s impossible to launch a rocket so that it ultimately does not fall to the ground, but makes several rounds of the planet (or even breaks away from it and goes further into space). In general, almost everything that can fly (regardless of how it does) is somehow connected with the ballistic trajectory.
Conclusion
The ability to calculate all the elements and run any object in the right place is extremely important in modern times. Even if we do not take the armed forces, which traditionally need such capabilities more than anyone else, there will still be many completely civilian applications.