Since ancient times, humanity has tried to achieve victory in a collision with the enemy at the maximum possible distance, so as not to destroy their own warriors. Slings, bows, crossbows, then guns, now rockets, projectiles and bombs - they all need an accurate calculation of the ballistic trajectory. And if with the old military "equipment" it was possible to track the point of impact visually, which made it possible to study and shoot more accurately next time, then in the modern world the destination point is usually so far away that it is simply impossible to see it without additional devices.
What is a ballistic trajectory
This is the path that some object overcomes. It must have a certain initial speed. It is affected by air resistance and gravity, which excludes 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 it will be a parabola or a circle (upon reaching the second and first space velocityrespectively). In most cases, such calculations are carried out for missiles. They tend to 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, rotation of the planet, and so on, individual parts of the path can take on a variety of forms.
Calculate ballistic trajectory
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 certain universal version that does not give the required accuracy, but is quite sufficient for an example.
y=x-tgѲ0-gx2/2V0 2-Cos2Ѳ0, where:
- y is the maximum height above the ground.
- X is the distance from the starting point to the moment when the body reaches the highest point.
- Ѳ0 – throwing angle.
- V0 – initial speed.
Thanks to this formula, it becomes possible to describe the ballistic flight trajectory in airless space. It will turn out in the form of a parabola, which is typical for most options for free movement in such conditions and in the presence of gravity. The following characteristic features of such a trajectory can be distinguished:
- The most optimal elevation angle forthe maximum distance is 45 degrees.
- The object has the same speed of movement both at the time of launch and at the moment of landing.
- The throw angle is the same as the fall angle.
- 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 they are taken into account, then the formula will turn out to be too complicated, and the error is not so large as to significantly affect the effectiveness of the hit.
Differences from the flat one
This name means another variant of the object's path. Flat and ballistic trajectory are somewhat different concepts, although the general principle is the same for them. In fact, this type of movement implies the maximum possible movement in the horizontal plane. And throughout the path, the object maintains sufficient acceleration. The ballistic version of the movement is necessary for moving over long distances. For example, flat trajectory is most important for a bullet. She must fly straight enough for as long as possible and punch through everything that gets in her way. On the other hand, a rocket or a projectile from a cannon inflicts maximum damage precisely at the end of the movement, as it gains the maximum possible speed. In between their movement, they are not so crushing.
Modern use
Ballisticthe trajectory is most often used in the military sphere. Rockets, projectiles, 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 is impossible to accurately launch a rocket so that it ultimately does not fall to the ground, but makes several turns around 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 it) is somehow connected with a ballistic trajectory.
Conclusion
The ability to calculate all the elements and launch any object in the right place is extremely important in modern times. Even if you do not take the military, which traditionally needs such capabilities more than anyone else, there will still be many quite civilian applications.
