External ballistics
For medium to longer ranges and flight times, besides gravity, air resistance and wind, several intermediate or meso variables described in the external factors paragraph have to be taken into account for small arms.
Meso variables can become significant for firearms users that have to deal with angled shot scenarios or extended ranges, but are seldom relevant at common hunting and target shooting distances.
In the case of ballistic missiles, the altitudes involved have a significant effect as well, with part of the flight taking place in a near-vacuum well above a rotating Earth, steadily moving the target from where it was at launch time.
Projectile/bullet path analysis is of great use to shooters because it allows them to establish ballistic tables that will predict how much vertical elevation and horizontal deflection corrections must be applied to the sight line for shots at various known distances.
[4][5][6] Mathematical models, such as computational fluid dynamics, are used for calculating the effects of drag or air resistance; they are quite complex and not yet completely reliable, but research is ongoing.
Very-low-drag bullets with BC's ≥ 1.10 can be designed and produced on CNC precision lathes out of mono-metal rods, but they often have to be fired from custom made full bore rifles with special barrels.
The resulting fixed drag curve models for several standard projectile shapes or types are referred to as the: How different speed regimes affect .338 calibre rifle bullets can be seen in the .338 Lapua Magnum product brochure which states Doppler radar established G1 BC data.
The relative simplicity however makes that it can be explained to and understood by the general shooting public and hence is also popular amongst ballistic software prediction developers and bullet manufacturers that want to market their products.
[21] Down range velocity measurement data can be provided around key inflection points allowing for more accurate calculations of the projectile retardation rate, very similar to a Mach vs CD table.
A practical downside of the Pejsa model is that accurate projectile specific down range velocity measurements to provide these better predictions can not be easily performed by the vast majority of shooting enthusiasts.
Dr. Pejsa states that he expanded his drop formula in a power series in order to prove that the weighted average retardation coefficient at R / 4 was a good approximation.
The second reference drag curve is adjusted to equal the Siacci/Mayevski retardation rate function at a projectile velocity of 2600 fps (792.5 m/s) using a .30-06 Springfield Cartridge, Ball, Caliber .30 M2 152 grains (9.8 g) rifle spitzer bullet with a slope or deceleration constant factor of 0.5 in the supersonic flight regime.
The empirical test data Pejsa used to determine the exact shape of his chosen reference drag curve and pre-defined mathematical function that returns the retardation coefficient at a given Mach number was provided by the US military for the Cartridge, Ball, Caliber .30 M2 bullet.
The Manges drag law thereby provides a unifying influence with respect to earlier models used to obtain two dimensional closed form solutions to the point-mass equations of motion.
[30] Solids modeling software that determines the projectile parameters of mass, center of gravity, axial and transverse moments of inertia necessary for stability analysis are also readily available, and simple to computer program.
[32] All that is required for the amateur ballistician to investigate the finer analytical details of projectile trajectories, along with bullet nutation and precession behavior, is computer programming determination.
Weibel 1000e or Infinition BR-1001 Doppler radars are used by governments, professional ballisticians, defence forces and a few ammunition manufacturers to obtain real-world data of the flight behavior of projectiles of their interest.
Correctly established state of the art Doppler radar measurements can determine the flight behavior of projectiles as small as airgun pellets in three-dimensional space to within a few millimetres accuracy.
Rocket-assisted projectiles employ a small rocket motor that ignites upon muzzle exit providing additional thrust to overcome aerodynamic drag.
The Sandia National Laboratories announced in January 2012 it has researched and test-fired 4-inch (102 mm) long prototype dart-like, self-guided bullets for small-caliber, smooth-bore firearms that could hit laser-designated targets at distances of more than a mile (about 1,610 meters or 1760 yards).
Testing the predictive qualities of software at (extreme) long ranges is expensive because it consumes ammunition; the actual muzzle velocity of all shots fired must be measured to be able to make statistically dependable statements.
[47][48] In 2015 the US ammunition manufacturer Berger Bullets announced the use of Doppler radar in unison with PRODAS 6 DoF software to generate trajectory solutions.
[49] In 2016 US ammunition manufacturer Hornady announced the use of Doppler radar derived drag data in software utilizing a modified point mass model to generate trajectory solutions.
[57] The amount of aerodynamic jump is dependent on cross wind speed, the gyroscopic stability of the bullet at the muzzle and if the barrel twist is clockwise or anti-clockwise.
Ballistic tables for small calibre projectiles (fired from pistols or rifles) assume a horizontal line of sight between the shooter and target with gravity acting perpendicular to the earth.
The more advanced programs factor in the small effect of gravity on uphill and on downhill shots resulting in slightly differing trajectories at the same vertical angle and range.
Viewed from a non-rotating reference frame (i.e. not one rotating with the Earth) and ignoring the forces of gravity and air resistance, a projectile moves in a straight line.
The maximum practical range[note 4] of all small arms and especially high-powered sniper rifles depends mainly on the aerodynamic or ballistic efficiency of the spin stabilised projectiles used.
The data to calculate these fire control corrections has a long list of variables including:[70] The ambient air density is at its maximum at Arctic sea level conditions.
[note 5] Interesting further reading: Marksmanship Wikibook Here is an example of a ballistic table for a .30 calibre Speer 169 grain (11 g) pointed boat tail match bullet, with a BC of 0.480.
