The ballistic coefficient jsb (abbreviated as BC) of a body is a measure of its ability to overcome air resistance in flight. It is inversely proportional to negative acceleration: a larger number indicates less negative acceleration, and the projectile's resistance is directly proportional to its mass.
Little story
In 1537, Niccolo Tartaglia conducted several test shots to determine the maximum angle and range of a bullet. Tartaglia concluded that the angle is 45 degrees. The mathematician noted that the trajectory of the shot is constantly bending.
In 1636, Galileo Galilei published his results in “Dialogues on Two New Sciences”. He found that a falling body has constant acceleration. This allowed Galileo to show that the trajectory of the bullet was a curve.
Around 1665, Isaac Newton discovered the law of air resistance. In his experiments, Newton used air and liquids. He showed that resistance to a shot increases in proportion to the density of air (or liquid), cross-sectional area, and bullet weight. Newton's experiments were carried out only at low speeds - up to about 260 m / s (853 ft / s).
In 1718, John Keel challenged Continental Mathematics. He wanted to find a curve that a projectile could describe in the air. This problem suggests that air resistance increases exponentially to the velocity of the projectile. Keel could not find a solution to this difficult task. But Johann Bernoulli undertook to solve this difficult problem and soon afterwards found an equation. He realized that air resistance varies as "any power" of speed. This proof later became known as the Bernoulli equation. That it is the forerunner of the concept of "standard projectile".
Historical inventions
In 1742, Benjamin Robins created a ballistic pendulum. It was a simple mechanical device that could measure the speed of a projectile. Robins reported bullet speeds from 1,400 ft / s (427 m / s) to 1,700 ft / s (518 m / s). In his book The New Principles of Shooting, published in the same year, he used numerical integration using the Euler method and found that air resistance "varies as the square of the projectile’s flight speed."
In 1753, Leonard Euler showed how theoretical trajectories can be calculated using the Bernoulli equation. But this theory can only be used for resistance, changing like a square of speed.
In 1844, the electro-ballistic chronograph was invented. In 1867, this device showed the flight time of a bullet accurate to one tenth of a second.
Test run
Since the mid-18th century, test shots have been conducted in many countries and their armed forces using large ammunition to determine the resistance characteristics of each individual projectile. These individual test experiments were recorded in extensive ballistic tables.
Serious tests were carried out in England (the test was Francis Bashfort, the experiment itself was carried out at the Woolwich bogs in 1864). The projectile has reached speeds of up to 2800 m / s. Friedrich Krupp in 1930 (Germany) continued testing.
The shells themselves were solid, slightly convex, the tip had a conical shape. Their sizes ranged from 75 mm (0.3 inches) with a weight of 3 kg (6.6 pounds) to 254 mm (10 inches) with a weight of 187 kg (412.3 pounds).
Methods and standard projectile
Until the 1860s, many military men used the calculus method to correctly determine the trajectory of a projectile. This method, which was suitable for calculating only one path, was performed manually. To make the calculations much easier and faster, research has begun on creating a model of theoretical resistance. Research has led to a significant simplification of experimental processing. It was the concept of a "standard projectile." Ballistic tables were compiled for a fictitious projectile with a given weight and shape, specific dimensions and a certain caliber. This simplified the calculation of the ballistic coefficient of a standard projectile, which could move in the atmosphere according to a mathematical formula.
Ballistic coefficient table
The aforementioned ballistic tables usually include such functions: air density, projectile flight time in the range, range, degree of projectile departure from a given trajectory, weight and diameter. These indicators facilitate the calculation of ballistic formulas, which are needed in order to calculate the initial velocity of the projectile in the range and flight path.
1870 Bashforth barrels fired a projectile at a speed of 2800 m / s. For calculations, Maevsky used the Bashfort and Krupp tables, which included up to 6 zones with limited access. The scientist conceived the seventh restricted area and extended the Bashfort trunks to 1100 m / s (3.609 ft / s). Mayevsky converted the data from imperial units to metric (currently SI units).
In 1884, James Ingalls introduced his trunks in the U.S. Army Artillery Circular using Mayevsky tables. Ingolls expanded ballistic shafts to 5,000 m / s, which were within the eighth restricted zone, but still with the same value n (1.55) as the 7th restricted Mayevsky zone. Up to the end, improved ballistic tables were published in 1909. In 1971, Sierra Bullet calculated its ballistic tables for 9 restricted areas, but only within 4,400 feet per second (1,341 m / s). This zone has destructive power. Imagine a shell weighing 2 kg flying at a speed of 1341 m / s.
Mayevsky Method
We already mentioned this surname a bit, but let's look at what kind of method this person came up with. In 1872, Maevsky published a report by Trité Balistique Extérieure. Using his ballistic tables along with the Bashfort tables from the 1870 report, Maevsky created an analytical mathematical formula that calculated the air resistance for the projectile in terms of log A and n values. Although the scientist took a different approach to mathematics than Bashfort, the calculated calculations of air resistance were the same. Mayevsky proposed the concept of a restricted zone. In the study, he discovered the sixth zone.
Around 1886, the general published the results of a discussion of the experiments of M. Krupp (1880). Despite the fact that the shells used were very different in caliber, they had basically the same proportions as the standard shell, 3 meters long and 2 meters radius.
Siacci method
In 1880, Colonel Francesco Siacci published his work Balistica. Ciacci suggested that resistance and air density become greater as the projectile speed increases.
The Siacci method was intended for trajectories with a flat fire with deviation angles of less than 20 degrees. He found that such a small angle does not allow air density to have a constant value. Using the tables of Bashfort and Majewski, Ciacci created a 4-zone model. Francesco used a standard shell, which was created by General Mayevsky.
Ballistic coefficient of a bullet
The ballistic coefficient of a bullet (BC) is basically a measure of how the bullet is rationalized, that is, how well it cuts through the air. Mathematically, this is the ratio of the specific density of a bullet to its shape factor. Ballistic coefficient is, in fact, a measure of air resistance. The higher the number, the lower the resistance, and the more efficient the bullet penetrates the air.
Another value is BC. The indicator determines the trajectory and drift of the wind when other factors are equal. BC changes with the shape of the bullet and the speed with which it moves. Spitzer, which means “directional,” is a more effective form than “round nose” or “flat point”. At the other end of the bullet, the tail of the boat (or conical heel) reduces air resistance compared to a flat base. Both increase BC bullets.
Bullet range
Of course, each bullet is different and has its own speed and range. A shot from a rifle at an angle of about 30 degrees will give the largest flight distance. This is a really good angle as an approximation to optimal performance. Many speculate that 45 degrees is the best angle, but it is not. The laws of physics and all natural forces that can interfere with an accurate shot affect the bullet.
After the bullet leaves the barrel, gravity and air resistance begin to work against the starting energy of the muzzle wave, and destructive force develops. There are other factors, but these two have the greatest impact. As soon as the bullet leaves the barrel, it begins to lose horizontal energy due to air resistance. Some people will tell you that the bullet rises when it leaves the barrel, but this is only true if the barrel was placed at an angle when fired, which often happens. If you shoot horizontally to the ground and simultaneously throw the bullet up, both shells will hit the ground almost at the same time (minus the slight differential caused by the curvature of the earth and a slight drop in vertical acceleration).
If you aim a weapon at an angle of about 30 degrees, the bullet will fly much farther than many people think, and even a low-energy weapon like a gun will send the bullet more than one mile away. A projectile from a high-powered rifle can cover about 3 miles in 6-7 seconds, so in no case can you shoot into the air.
Ballistic coefficient of pneumatic bullets
Pneumatic bullets were not created to hit the target, but in order to stop the target or cause minor physical harm. In this regard, most bullets for airguns are made of lead, since this material is very soft, light and gives the projectile a small initial speed. The most common
types of bullets (calibers) are 4.5 mm and 5.5. Of course, larger-caliber ones were created - 12.7 mm. When firing a shot from such pneumatics and such a bullet, one must already think about the safety of outsiders. For example, ball-shaped bullets are made for an entertaining game. In most cases, this type of shell is coated with copper or zinc to avoid corrosion.