Ballistic coefficient
[4][5] Here are several methods to compute i or Cd: where: If n is unknown, it may be estimated as: where: or A drag coefficient can also be calculated mathematically: where: or From standard physics as applied to "G" models: where: This formula is for calculating the ballistic coefficient within the small arms shooting community, but is redundant with Cb,projectile: where: In 1537, Niccolò Tartaglia performed test firing to determine the maximum angle and range for a shot.
He showed that drag on shot increases proportionately with the density of the air (or the fluid), cross sectional area, and the square of the speed.
[14][15][16] In 1718, John Keill challenged the Continental Mathematica, "To find the curve that a projectile may describe in the air, on behalf of the simplest assumption of gravity, and the density of the medium uniform, on the other hand, in the duplicate ratio of the velocity of the resistance".
In his book published that same year "New Principles of Gunnery", he uses numerical integration from Euler's method and found that air resistance varies as the square of the velocity, but insisted that it changes at the speed of sound.
[17][9][18] In 1753, Leonhard Euler showed how theoretical trajectories might be calculated using his method as applied to the Bernoulli equation, but only for resistance varying as the square of the velocity.
[20] Many countries and their militaries carried out test firings from the mid eighteenth century on using large ordnance to determine the drag characteristics of each individual projectile.
Using his ballistic tables along with Bashforth's tables from the 1870 report, Mayevski created an analytical math formula that calculated the air resistances of a projectile in terms of log A and the value n. Although Mayevski's math used a differing approach than Bashforth, the resulting calculation of air resistance was the same.
He found that the angle of departure is sufficiently small to allow for air density to remain the same and was able to reduce the ballistics tables to easily tabulated quadrants giving distance, time, inclination and altitude of the projectile.
The British Royal Artillery results were very similar to those of Mayevski's and extended their tables to 5,000 ft/s (1,524 m/s) within the 8th restricted zone changing the n value from 1.55 to 1.67.
Thereafter, the Type 1 standard projectile was renamed by Ballistics Section of Aberdeen Proving Grounds in Maryland, USA as G1 after the Commission d'Experience de Gâvre.
This misconception may be explained by Colonel Ingalls in the 1886 publication, Exterior Ballistics in the Plan Fire; page 15, In the following tables the first and second columns give the velocities and corresponding resistance, in pounds, to an elongated one inch in diameter and having an ogival head of one and a half calibers.
They were deduced from Bashforth's experiments by Professor A. G. Greenhill, and are taken from his papers published in the Proceedings of the Royal Artillery Institution, Number 2, Volume XIII.
Cb is commonly found within commercial publications to be carried out to 3 decimal points as few sporting, small arms projectiles rise to the level of 1.00 for a ballistic coefficient.
What differs is retardation factors found through testing of actual projectiles that are similar in shape to the standard project reference.
Another method of determining trajectory and ballistic coefficient was developed and published by Wallace H. Coxe and Edgar Beugless of DuPont in 1936.
But the U.S. Army Ordnance Corps continued using the Siacci method into the middle of the 20th century for direct (flat-fire) tank gunnery.
The development of the electromechanical analog computer contributed to the calculation of aerial bombing trajectories during World War II.
After World War II the advent of the silicon semiconductor based digital computer made it possible to create trajectories for the guided missiles/bombs, intercontinental ballistic missiles and space vehicles.
[9][22] Between World War I and II the U.S. Army Ballistics research laboratories at Aberdeen Proving Grounds, Maryland, USA developed the standard models for G2, G5, G6.
Also, the newer methodology proposed by Dr. Arthur Pejsa and the use of the G7 model used by Mr. Bryan Litz, ballistic engineer for Berger Bullets, LLC for calculating boat tailed spitzer rifle bullet trajectories and 6 Dof model based software have improved the prediction of flat-fire trajectories.
[citation needed] For the precise establishment of BCs (or perhaps the scientifically better expressed drag coefficients), Doppler radar-measurements are required.
Weibel 1000e or Infinition BR-1001 Doppler radars are used by governments, professional ballisticians, defense forces, and a few ammunition manufacturers to obtain exact real-world data on the flight behavior of projectiles of interest.
[citation needed] Doppler radar measurement results for a lathe turned monolithic solid .50 BMG very-low-drag bullet (Lost River J40 13.0 millimetres (0.510 in), 50.1 grams (773 gr) monolithic solid bullet / twist rate 1:380 millimetres (15 in)) look like this: The initial rise in the BC value is attributed to a projectile's always present yaw and precession out of the bore.
The 6 and 6.5 have relatively light recoil compared to high BC bullets of greater caliber and tend to be shot by the winner in matches where accuracy is key.
Examples include the 6mm PPC, 6mm Norma BR, 6×47mm SM, 6.5×55mm Swedish Mauser, 6.5×47mm Lapua, 6.5 Creedmoor, 6.5 Grendel, .260 Remington, and the 6.5-284.
The .30-06 Springfield and .308 Winchester cartridges also offer several high-BC loads, although the bullet weights are on the heavy side for the available case capacity, and thus are velocity limited by the maximum allowable pressure.
[citation needed] In the larger caliber category, the .338 Lapua Magnum and the .50 BMG are popular with very high BC bullets for shooting beyond 1,000 meters.
[69] However, in the past decade or so, it has been shown that ballistic coefficient measurements by independent parties can often be more accurate than manufacturer specifications.
A very high ballistic coefficient vehicle would lose velocity very slowly and would impact the Earth's surface at higher speeds.
[75] In general, reentry vehicles carrying human beings or other sensitive payloads back to Earth from space have high drag and a correspondingly low ballistic coefficient (less than approx.
