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Ballistic coefficient
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In ballistics, the ballistic coefficient (BC) of a body is a measure of its ability to overcome air resistance in flight.[1] It is inversely proportional to the negative acceleration: a high number indicates a low negative acceleration--the drag on the projectile is small in proportion to its mass.
Contents
[hide]
1 Formulae
1.1 General
1.2 Ballistics
1.3 Commercial Use
2 History
2.1 Background
2.2 Test Firing
2.3 Methods and the Standard Projectile
2.3.1 The Bashforth Method
2.3.2 The Mayevski/Siacci Method
2.3.3 The Ballistic Tables
2.3.4 The G Model
3 Differing mathematical models and bullet ballistic coefficients
3.1 The transient nature of bullet ballistic coefficients
3.2 General trends
3.3 Information sources
4 Satellites and reentry vehicles
5 See also
6 References
7 External links
Formulae[edit]
General[edit]
B C P h y s i c s = M C d ⋅ A = ρ ⋅ ℓ C d {\displaystyle BC_{Physics}={\frac {M}{C_{d}\cdot A}}={\frac {\rho \cdot \ell }{C_{d}}}}
Where:
BCPhysics = ballistic coefficient as used in physics and engineering
M = mass
A = cross-sectional area
Cd = drag coefficient
ρ {\displaystyle \rho } = density
𝓁 = characteristic body length
Ballistics[edit]
The formula for calculating the ballistic coefficient for small and large arms projectiles only is as follows:
B C P r o j e c t i l e = m d 2 ⋅ i {\displaystyle BC_{Projectile}={\frac {m}{d^{2}\cdot i}}} [2]
Where:
BCProjectile = ballistic coefficient as used in point mass trajectory from the Siacci method (less than 20 degrees).[3]
m = mass of bullet
d = measured cross section (diameter) of projectile
i = Coefficient of form
The Coefficient of form (i) can be derived by 6 methods and applied differently depending on the trajectory models used: G Model, Beugless/Coxe; 3 Sky Screen; 4 Sky Screen; Target Zeroing; Doppler radar.[4][5]
Here are several methods to compute i or Cd:
i = 2 n ⋅ 4 n − 1 n {\displaystyle i={\frac {2}{n}}\cdot {\sqrt {\frac {4n-1}{n}}}} [6][7][8]
Where:
i = Coefficient of form.
n = number of calibers of the projectile's ogive.
Where n is unknown:
n = ( 4 ⋅ ℓ 2 + 1 ) 4 {\displaystyle n={\frac {(4\cdot \ell ^{2}+1)}{4}}} [9]
Where:
n = number of calibers of the projectile's ogive.
𝓁 = length of the head (ogive) in number of calibers.
or
A drag coefficient can also be calculated mathematically:
C d = 8 ρ ⋅ v 2 ⋅ π ⋅ d 2 {\displaystyle C_{d}={\frac {8}{\rho \cdot v^{2}\cdot \pi \cdot d^{2}}}} [10]
Where:
Cd = drag coefficient.
ρ {\displaystyle \rho } = density of the projectile.
v = projectile velocity at range.
π (pi) ≈ 3.14159
d = measured cross section (diameter) of projectile
or
From standard physics as applied to “G” models:
i = C p C G {\displaystyle i={\frac {C_{p}}{C_{G}}}} [11]
Where:
i = Coefficient of form.
CG = drag coefficient of 1.00 from any “G” model, reference drawing, projectile.[12]
Cp = drag coefficient of the actual test projectile at range.
Commercial Use[edit]
This formula is for calculating the ballistic coefficient within the smalls arms shooting community, but is redundant with BCProjectile:
B C S m a l l a r m s = S D i {\displaystyle BC_{Smallarms}={\frac {SD}{i}}} [13]
Where:
BCSmallarms = Ballistic coefficient
SD = Sectional density
i = Coefficient of form (form factor [14])
History[edit]
Background[edit]
In 1537, Niccolò Tartaglia did some test firing to determine the maximum angle and range for a shot. His conclusion was near 45 degrees. He noted that the shot trajectory was continuously curved.[11]
In 1636, Galileo Galilei published results in "Dialogues Concerning Two New Sciences". He found that a falling body had a constant acceleration. This allowed Galileo to show that a bullet's trajectory was a curve.[15][11]
Circa 1665, Sir Isaac Newton derived the law of air resistance. Newton's experiments on drag were through air and fluids. 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.[11] Newton’s experiments were only at low velocities to about 260 m/s (853 ft/s).[16][17][18]
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”. This challenge supposes that air resistance increases exponentially to the velocity of a projectile.[verification needed] Keill gave no solution for his challenge. Johann Bernoulli[clarification needed The Bernouilli equation is credited to Jacob Bernouilli] took up this challenge and soon thereafter solved the problem and air resistance varied as “any power”[verification needed] of velocity;[clarification needed It is said above that air resistance was supposed to increase exponentially with velocity.] known as the Bernoulli equation.[verification needed] This is the precursor to the concept of the “standard projectile”.[19]
In 1742, Benjamin Robins invented the ballistic pendulum. This was a simple mechanical device that could measure a projectile's velocity. Robins reported muzzle velocities ranging from 1,400 ft/s (427 m/s) to 1,700 ft/s (518 m/s). 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.[20][11][21]
In 1753, Leonhard Euler showed how a 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.[22]
In 1844, the Electro-ballistic chronograph was invented and by 1867 the electro-ballistic chronograph was accurate to within one ten millionth of a second.[23]
Test Firing[edit]
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. These individual test firings were logged and reported in extensive ballistics tables.[24][25]
Of the test firing, most notably were: Francis Bashforth at Woolwich Marshes & Shoeburyness, England (1864-1889) with velocities to 2,800 ft/s (853 m/s) and M. Krupp (1865–1880) of Friedrich Krupp AG at Meppen, Germany, Friedrich Krupp AG continued these test firings to 1930; to a lesser extent General Nikolai V. Mayevski, then a Colonel (1868–1869) at St. Petersburg, Russia; the Commission d'Experience de Gâvre (1873 to 1889) at Le Gâvre, France with velocities to 1,830 m/s (6,004 ft/s) and The British Royal Artillery (1904–1906).[26][27][28][11][29]
The test projectiles (shot) used, vary from spherical, spheroidal, ogival; being hollow, solid and cored in design with the elongated ogival-headed projectiles having 1, 1½, 2 and 3 caliber radii. These projectiles varied in size from, 75 mm (3.0 in) at 3 kg (6.6 lb) to 254 mm (10.0 in) at 187 kg (412.3 lb) [30][31][32]
Methods and the Standard Projectile[edit]
Many militaries up until the 1860s used calculus to compute projectile trajectory. The numerical computations necessary to calculate just a single trajectory was lengthy, tedious and done by hand. So, investigations to develop a theoretical drag model began. The investigations led to a major simplification in the experimental treatment of drag. This was the concept of a “standard projectile”. The ballistic tables are made up for a factitious projectile being defined as: "a factitious weight and with a specific shape and specific dimensions in a ratio of calibers." This simplifies calculation for the ballistic coefficient of a standard model projectile, which could mathematically move through the standard atmosphere with the same ability as any actual projectile could move through the actual atmosphere.[33][34][11]
The Bashforth Method[edit]
In 1870, Bashforth publishes a report containing his ballistic tables. Bashforth found that the drag of his test projectiles varied with the square of velocity (v2) from 830 ft/s (253 m/s) to 430 ft/s (131 m/s) and with the cube of velocity (v3) from 1,000 ft/s (305 m/s) to 830 ft/s (253 m/s). As of his 1880 report, he found that drag varied by v6 from 1,100 ft/s (335 m/s) to 1,040 ft/s (317 m/s). Bashforth used rifled guns of 3 in (76 mm), 5 in (127 mm), 7 in (178 mm) and 9 in (229 mm); smooth-bore guns of similar caliber for firing spherical shot and howitzers propelled elongated projectiles having an ogival-head of 1½ caliber radius.[35][36][37]
Bashforth uses b as the variable for ballistic coefficient. When b is equal to or less than v2, then b is equal to P for the drag of a projectile. It would be found that air does not deflect off the front of a projectile in the same direction, when there are of differing shapes. This prompted the introduction of a second factor to b, the coefficient of form (i). This is particularly true at high velocities, greater than 830 ft/s (253 m/s). Hence, Bashforth introduced the “undetermined multiplier” of any power called the k {\displaystyle k} factor that compensate for this unknown effects of drag above 830 ft/s (253 m/s); k > i {\displaystyle k>i} . Bashforth then integrated k {\displaystyle k} and i {\displaystyle i} as K v {\displaystyle K_{v}} .[38][39][40][41]
Although Bashforth did not conceive the “restricted zone”, he showed mathematically there were 5 restricted zones. Bashforth did not propose a standard projectile, but was well aware of the concept.[42]
The Mayevski/Siacci Method[edit]
In 1872, General Mayevski published his report Trité Balistique Extérieure, which included the Mayevski model. 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 calculations of air resistance was the same. Mayevski proposed the restricted zone concept and found there to be 6 restricted zones for projectiles.[43][44][45][11][46]
Circa 1886, General Mayevski published the results from a discussion of experiments made by M. Krupp (1880). Though the ogival-headed projectiles used varied greatly in caliber, they had essentially the same proportions as the standard projectile, being mostly 3 caliber in length, with an ogive of 2 calibers radius. Giving the standard projectile dimensionally as 10 cm (3.9 in) and 1 kg (2.2 lb).[47][48][49]
In 1880, Colonel Francesco Siacci published his work “Balistica”. Siacci found as did those who came before him that the resistance and density of the air becomes greater and greater as a projectile displaced the air at higher and higher velocities.[50]
Siacci's method was for flat-fire trajectories with angles of departure of less than 20 degrees. 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. Using Bashforth's k and Mayevski's tables, Siacci created a 4 zone model. Siacci used Mayevski's standard projectile. From this method and standard projectile, Siacci formulated a shortcut.[51][11][52]
Siacci found that within a low velocity restricted zone, projectiles of similar shape, and velocity in the same air density behave similar; δ w d 2 {\displaystyle {\tfrac {\delta w}{d^{2}}}} or δ C {\displaystyle {\tfrac {\delta }{C}}} . Siacci used the variable C {\displaystyle C} for ballistic coefficient. Meaning, air density is the generally the same for flat-fire trajectories, thus sectional density is equal to the ballistic coefficient and air density can be dropped. Then as the velocity rises to Bashforth's k {\displaystyle k} for high velocity when C {\displaystyle C} requires the introduction of i {\displaystyle i} . Following within today's currently used ballistic trajectory tables for an average ballistic coeficient: m d 2 ⋅ p 0 p {\displaystyle {\tfrac {m}{d^{2}}}\cdot {\tfrac {p_{0}}{p}}} would equal m d 2 i {\displaystyle {\tfrac {m}{d^{2}i}}} equals S D i {\displaystyle {\tfrac {SD}{i}}} as B C {\displaystyle BC} .[53][54]
Siacci wrote that within any restricted zone, C being the same for two or more projectiles, the trajectories differences will be minor. Therefore, C agrees with an average curve, and this average curve applies for all projectiles. Therefore, a single trajectory can be computed for the standard projectile without having to resort to tedious calculus methods, and then a trajectory for any actual bullet with known C can be computed from the standard trajectory with just simple algebra.[55][11]
The Ballistic Tables[edit]
The aforementioned ballistics tables are generally: functions, air density, projectile time at range, range, degree of projectile departure, weight and diameter to facilitate the calculation of ballistic formulae. These formulae produce the projectile velocity at range, drag and trajectories. The modern day commercially published ballistic tables or software computed ballistics tables for small arms, sporting ammunition are exterior ballistic, trajectory tables.[56][57][58]
The 1870 Bashforth tables were to 2,800 ft/s (853 m/s). Mayevski, using his tables, supplemented by the Bashforth tables (to 6 restricted zones) and the Krupp tables. Mayevski conceived a 7th restricted zone and extended the Bashforth tables to 1,100 m/s (3,609 ft/s). Mayevski converted Bashforth's data from Imperial units of measure to metric units of measure (now in SI units of measure). In 1884, James Ingalls published his tables in the U.S. Army Artillery Circular M using the Mayevski tables. Ingalls extended Mayevski's ballistics tables to 5,000 ft/s (1,524 m/s) within an 8th restricted zone, but still with the same n value (1.55) as Mayevski's 7th restricted zone. Ingalls, converted Mayevski's results back to Imperial units. 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. These ballistic tables were published in 1909 and almost identical to those of Ingalls. In 1971 the Sierra Bullet company calculated their ballistic tables to 9 restricted zones but only within 4,400 ft/s (1,341 m/s).[59][11][60]
The G Model[edit]
In 1881, the Commission d'Experience de Gâvre did a comprehensive survey of data available from their tests as well as other countries. After adopting a standard atmospheric condition for the drag data the Gavre drag function was adopted. This drag function was known as the Gavre function and the standard projectile adopted was the Type 1 projectile. 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. For practical purposes the subscript 1 in G1 is generally written in normal font size as G1.[11][61]
The general form for the calculations of trajectory adopted for the G model is the Siacci method. The standard model projectile is a "fictitious projectile" used as the mathematical basis for the calculation of actual projectile's trajectory when an initial velocity is known. The G1 model projectile adopted is in dimensionless measures of 2 caliber radius ogival-head and 3.28 caliber in length. By calculation this leaves the body length 1.96 caliber and head, 1.32 caliber long.[62][11]
Over the years there has been some confusion[citation needed] as to adopted size, weight and radius ogival-head of the G1 standard projectile. 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, No 2, Vol. XIII. Further it is discussed that said projectile's weight was one pound.[63]
For the purposes of mathematical convenience for any standard projectile (G) the BC is 1.00. Where as the projectile's sectional density (SD) is dimensionless with a mass of 1 divided by the square of the diameter of 1 caliber equaling an SD of 1. Then the standard projectile is assigned a coefficient of form of 1. Following that B C = S D i = 1 1 = 1.00 {\displaystyle BC={\tfrac {SD}{i}}={\tfrac {1}{1}}=1.00} . BC, as a general rule, within flat-fire trajectory, is carried out to 2 decimal points. BC 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.[64]
When using the Siacci method for different G models, the formula used to compute the trajectories is the same. What differs is retardation factors found through testing of actual projectiles that are similar in shape to the standard project reference. This creates slightly different set of retardation factors between differing G models. When the correct G model retardation factors are applied within the Siacci mathematical formula for the same G model BC, a corrected trajectory can be calculated for any G model.
Another method of determining trajectory and ballistic coefficient was developed and published by Wallace H. Coxe and Edgar Beugless of DuPont in 1936. This method is by shape comparison an logarithmic scale as drawn on 10 charts. The method estimates the ballistic coefficient related to the drag model of the Ingalls tables. When matching an actual projectile against the drawn caliber radii of Chart No. 1, it will provide i and by using Chart No. 2, C can be quickly calculated. Coxe and Beugless used the variable C for ballistic coefficient.[65][11]
The Siacci method was abandoned by the end of the World War I for artillery fire. 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.[11][66]
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. In 1965, Winchester Western published a set of ballistics tables for G1, G5, G6 and GL. In 1971 Sierra Bullet Company retested all their bullets and concluded that the G5 model was not the best model for their boat tail bullets and started using the G1 model. This was fortunate, as the entire commercial sporting and firearms industries had based their calculations on the G1 model. The G1 model and Mayevski/Siacci Method continue to be the industry standard today. This benefit allows for comparison of all ballistic tables for trajectory within the commercial sporting and firearms industry.[11][67]
In recent years there have been vast advancements in the calculation of flat-fire trajectories with the advent of Doppler radar and the personal computer and handheld computing devices. Also, the newer methodology proposed by Dr. Arthur Pejsa and the use of the G7 model used by Mr. Brian 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.[11][68][69]
Differing mathematical models and bullet ballistic coefficients[edit]
G1 shape standard projectile. All measurements in calibers/diameters.
G7 shape standard projectile. All measurements in calibers/diameters.
Wind drift calculations for rifle bullets of differing G1 BCs fired with a muzzle velocity of 2,950 ft/s (900 m/s) in a 10 mph (16 km/h) crosswind.[70]
Energy calculations for 9.1 grams (140 gr) rifle bullets of differing G1 BCs fired with a muzzle velocity of 2,950 feet per second (900 m/s).[71]
Most ballistic mathematical models and hence tables or software take for granted that one specific drag function correctly describes the drag and hence the flight characteristics of a bullet related to its ballistic coefficient. Those models do not differentiate between wadcutter, flat-based, spitzer, boat-tail, very-low-drag, etc. bullet types or shapes. They assume one invariable drag function as indicated by the published BC. Several different drag curve models optimized for several standard projectile shapes are available, however.
The resulting drag curve models for several standard projectile shapes or types are referred to as:
G1 or Ingalls (flatbase with 2 caliber (blunt) nose ogive - by far the most popular)[72]
G2 (Aberdeen J projectile)
G5 (short 7.5° boat-tail, 6.19 calibers long tangent ogive)
G6 (flatbase, 6 calibers long secant ogive)
G7 (long 7.5° boat-tail, 10 calibers tangent ogive, preferred by some manufacturers for very-low-drag bullets[73])
G8 (flatbase, 10 calibers long secant ogive)
GL (blunt lead nose)
Since these standard projectile shapes differ significantly the Gx BC will also differ significantly from the Gy BC for an identical bullet.[74] To illustrate this the bullet manufacturer Berger has published the G1 and G7 BCs for most of their target, tactical, varmint and hunting bullets.[75] Other bullet manufacturers like Lapua and Nosler also published the G1 and G7 BCs for most of their target bullets.[76][77] How much a projectile deviates from the applied reference projectile is mathematically expressed by the form factor (i). The applied reference projectile shape always has a form factor (i) of exactly 1. When a particular projectile has a sub 1 form factor (i) this indicates that the particular projectile exhibits lower drag than the applied reference projectile shape. A form factor (i) greater than 1 indicates the particular projectile exhibits more drag than the applied reference projectile shape.[78] In general the G1 model yields comparatively high BC values and is often used by the sporting ammunition industry.
The transient nature of bullet ballistic coefficients[edit]
Variations in BC claims for exactly the same projectiles can be explained by differences in the ambient air density used to compute specific values or differing range-speed measurements on which the stated G1 BC averages are based. Also, the BC changes during a projectile's flight, and stated BCs are always averages for particular range-speed regimes. Further explanation about the variable nature of a projectile's G1 BC during flight can be found at the external ballistics article. The external ballistics article implies that knowing how a BC was determined is almost as important as knowing the stated BC value itself.
For the precise establishment of BCs (or perhaps the scientifically better expressed drag coefficients), Doppler radar-measurements are required. The normal shooting or aerodynamics enthusiast, however, has no access to such expensive professional measurement devices. 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.
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:
Range (m)
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
Ballistic coefficient (G1)
1.040 1.051 1.057 1.063 1.064 1.067 1.068 1.068 1.068 1.066 1.064 1.060 1.056 1.050 1.042 1.032
The initial rise in the BC value is attributed to a projectile's always present yaw and precession out of the bore. The test results were obtained from many shots, not just a single shot. The bullet was assigned 1.062 for its BC number by the bullet's manufacturer, Lost River Ballistic Technologies.
Measurements on other bullets can give totally different results. How different speed regimes affect several 8.6 mm (.338 in calibre) rifle bullets made by the Finnish ammunition manufacturer Lapua can be seen in the .338 Lapua Magnum product brochure which states Doppler radar established BC data.[79]
General trends[edit]
Sporting bullets, with a calibre d ranging from 4.4 to 12.7 millimetres (0.172 to 0.50 in), have BCs in the range 0.12 to slightly over 1.00. Those bullets with the higher BCs are the most aerodynamic, and those with low BCs are the least. Very-low-drag bullets with BCs ≥ 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.[80]
Ammunition makers often offer several bullet weights and types for a given cartridge. Heavy-for-caliber pointed (spitzer) bullets with a boattail design have BCs at the higher end of the normal range, whereas lighter bullets with square tails and blunt noses have lower BCs. The 6 mm and 6.5 mm cartridges are probably the most well known for having high BCs and are often used in long range target matches of 300 m (328 yd) – 1,000 m (1,094 yd). 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, 6x47mm SM, 6.5×55mm Swedish Mauser, 6.5×47mm Lapua, 6.5 Creedmoor, 6.5 Grendel, .260 Remington, and the 6.5-284. The 6.5 mm is also a popular hunting caliber in Europe.
In the United States, hunting cartridges such as the .25-06 Remington (a 6.35 mm caliber), the .270 Winchester (a 6.8 mm caliber), and the .284 Winchester (a 7 mm caliber) are used when high BCs and moderate recoil are desired. The .30-06 Springfield and .308 Winchester cartridges also offer several high-BC loads, although the bullet weights are on the heavy side.
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. Newer chamberings in the larger caliber category are the .375 and .408 Cheyenne Tactical and the .416 Barrett.
Information sources[edit]
For many years, bullet manufacturers were the main source of ballistic coefficients for use in trajectory calculations.[81] 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.[82][83][84] Since ballistic coefficients depend on the specific firearm and other conditions that vary, it is notable that methods have been developed for individual users to measure their own ballistic coefficients.[85]
Satellites and reentry vehicles[edit]
Satellites in Low Earth Orbit (LEO) with high ballistic coefficients experience smaller perturbations to their orbits due to atmospheric drag.
The ballistic coefficient of an atmospheric reentry vehicle has a significant effect on its behavior. A very high ballistic coefficient vehicle would lose velocity very slowly and would impact the Earth's surface at higher speeds. In contrast, a low ballistic coefficient would reach subsonic speeds before reaching the ground.
In general, reentry vehicles that carry human beings back to Earth from space have high drag and a correspondingly low ballistic coefficient. Vehicles that carry nuclear weapons launched by an intercontinental ballistic missile (ICBM), by contrast, have a high ballistic coefficient, which enables them to travel rapidly from space to a target on land. That makes the weapon less affected by crosswinds or other weather phenomena, and harder to track, intercept, or otherwise defend against.
See also[edit]
External ballistics - The behavior of a projectile in flight.
Trajectory of a projectile
References[edit]
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Jump up ^ Cline, Donna (2002). Exterior Ballistics Explained, Trajectories, Part 3 "Atmosphere". Lattie Stone Ballistics. p. 39.
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Jump up ^ Pejsa, Arthur, New Exact Small Arms Ballistics: The Source Book for Riflemen, 2008; p. 29, Kenwood Publishing ISBN 978-0974990262
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Jump up ^ Pejsa, Arthur, Modern Practical Ballistics 2nd Edition, 1991; p. 6, Kenwood Publishing ISBN 978-0961277635
Jump up ^ Bashforth, Francis, A revised account of the experiments made with the Bashforth chronograph..., 1890; pg 6, Cambridge at the University Press
Jump up ^ Bashforth, Francis, A revised account of the experiments made with the Bashforth chronograph..., 1890; p. 13, Cambridge at the University Press
Jump up ^ Bashforth, Francis, A revised account of the experiments made with the Bashforth chronograph..., 1890; pp. 5–11, Cambridge at the University Press
Jump up ^ Cline, Donna, Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient, 2002; p. 39, Lattie Stone Ballistics
Jump up ^ Bashforth, Francis; Reports on experiments made with the Bashforth chronograph..., 1878-1879; p. Protest, 1, H.M Stationary Office, Harrison & Sons, London
Jump up ^ Bashforth, Francis, A revised account of the experiments made with the Bashforth chronograph..., 1890; pp. 13, 135, Cambridge at the University Press
Jump up ^ Ingalls, James M., Exterior Ballistics in the Plan Fire, 1886; pp. 18,19, D. Van Nostrand Publisher
Jump up ^ Cline, Donna, Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient, 2002; p. 39–40, Lattie Stone Ballistics
Jump up ^ Bashforth, Francis; Reports on experiments made with the Bashforth chronograph..., 1878-1879; pp. 3–4, H.M Majesty's Stationery Office, Harrison & Sons, London
Jump up ^ Bashforth, Francis, A revised account of the experiments made with the Bashforth chronograph..., 1890; pp. 36, 135, Cambridge at the University Press
Jump up ^ Ingalls, James M., Exterior Ballistics in the Plan Fire, 1886; p. 19, D. Van Nostrand Publisher
Jump up ^ Ingalls, James M., Exterior Ballistics in the Plan Fire, 1886; p. 8, D. Van Nostrand Publisher
Jump up ^ Coast Artillery School Press, Reference Notes for Use in the Course in Gunnery and Ammunition, 1917; p. 12, Coast Artillery School, ASIN:B00E0UERI2
Jump up ^ Bashforth, Francis; Reports on experiments made with the Bashforth chronograph..., 1878-1879; p. 4, H.M Majesty's Stationery Office, Harrison & Sons, London
Jump up ^ Bashforth, Francis, A revised account of the experiments made with the Bashforth chronograph..., 1890; pp. 135–136, Cambridge at the University Press
Jump up ^ Ingalls, James M., Exterior Ballistics in the Plan Fire, 1886; p. 19, D. Van Nostrand Publisher
Jump up ^ Bashforth, Francis; Reports on experiments made with the Bashforth chronograph..., 1878-1879; pp. 3,5–6, H.M Majesty's Stationery Office, Harrison & Sons, London
Jump up ^ Bashforth, Francis, A revised account of the experiments made with the Bashforth chronograph..., 1890; p. 1, Cambridge at the University Press
Jump up ^ Ingalls, James M., Exterior Ballistics in the Plan Fire, 1886; pp. 7–8, 31, 136, D. Van Nostrand Publisher
Jump up ^ [1]
Jump up ^ Bashforth, Francis; Reports on experiments made with the Bashforth chronograph..., 1878-1879; pp. 5–6, H.M Majesty's Stationery Office, Harrison & Sons, London
Jump up ^ Bashforth, Francis, A revised account of the experiments made with the Bashforth chronograph..., 1890; pg pgvii, Cambridge at the University Press
Jump up ^ Ingalls, James M., Exterior Ballistics in the Plan Fire, 1886; pg14,18-31, D. Van Nostrand Publisher
Jump up ^ Mayevski, Nikolai V, Trité Balistique Extérieure , 1872; pp. 58, 133 of the Schedules, Gauthier-Villars, Printer Bookseller office longitudes of the Polytechnic School, (Translated from French )
Jump up ^ Cline, Donna, Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient, 2002; p. 40, Lattie Stone Ballistics
Jump up ^ Ingalls, James M., Exterior Ballistics in the Plan Fire, 1886; p. 19, D. Van Nostrand Publisher
Jump up ^ Mayevski, Nikolai V, Trité Balistique Extérieure , 1872; p. 58, Gauthier-Villars, Printer Bookseller office longitudes of the Polytechnic School, (Translated from French )
Jump up ^ Siacci, Francesco,Balistica; Second edition entirely recast , 1888; p. 7, Torino F.Casanova, Publisher bookseller Via Academy of Sciences, (Translated from Italian and Latin)
Jump up ^ Siacci, Francesco,Balistica; Second edition entirely recast , 1888; pg3, Torino F.Casanova, Publisher bookseller Via Academy of Sciences, (Translated from Italian and Latin)
Jump up ^ Siacci, Francesco, Balistica; Second edition entirely recast , 1888; pg5,8, Torino F.Casanova, Publisher bookseller Via Academy of Sciences, (Translated from Italian and Latin)
Jump up ^ Cline, Donna, Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient, 2002; p. 39, Lattie Stone Ballistics
Jump up ^ Siacci, Francesco,Balistica; Second edition entirely recast , 1888; p. 4, Torino F.Casanova, Publisher bookseller Via Academy of Sciences, (Translated from Italian and Latin)
Jump up ^ Cline, Donna, Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient, 2002; p. 42, Lattie Stone Ballistics
Jump up ^ Siacci, Francesco,Balistica; Second edition entirely recast , 1888; p. 5, Torino F.Casanova, Publisher bookseller Via Academy of Sciences, (Translated from Italian and Latin)
Jump up ^ Bashforth, Francis; Reports on experiments made with the Bashforth chronograph..., 1878-1879; H.M Stationary Office, Harrison & Sons, London
Jump up ^ Bashforth, Francis, A revised account of the experiments made with the Bashforth chronograph..., 1890; Cambridge at the University Press
Jump up ^ Mayevski, Nikolai V, Trité Balistique Extérieure , 1872; p. i of the Schedules, Gauthier-Villars, Printer Bookseller office longitudes of the Polytechnic School, (Translated from French )
Jump up ^ Ingalls, James M., Exterior Ballistics in the Plan Fire, 1886; p. 19, D. Van Nostrand Publisher
Jump up ^ Cline, Donna, Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient, 2002; p. 40, Lattie Stone Ballistics
Jump up ^ Cline, Donna, Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient, 2002; pg 40, Lattie Stone Ballistics
Jump up ^ Coast Artillery School Press, Reference Notes for Use in the Course in Gunnery and Ammunition, 1917; p. 12, Coast Artillery School, ASIN:B00E0UERI2
Jump up ^ Ingalls, James M., Exterior Ballistics in the Plan Fire, 1886; p. 15, D. Van Nostrand Publisher
Jump up ^ Coast Artillery School Press, Reference Notes for Use in the Course in Gunnery and Ammunition, 1917; p. 12, Coast Artillery School, ASIN:B00E0UERI2
Jump up ^ Coxe, Wallace H. and Bugless, Edgar, Exterior Balistics Charts, 1936; p. Charts 1, 2 Ballistic Engineers of the Burnside Laboratory, of E.I. Du Pont De Nemours & Company Inc., Wilmington, Delaware
Jump up ^ Cline, Donna, Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient, 2002; p. 39, Lattie Stone Ballistics
Jump up ^ Cline, Donna, Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient, 2002; p. 42, Lattie Stone Ballistics
Jump up ^ Pejsa, Arthur, Modern Practical Ballistics 2nd Edition, 1991; Kenwood Publishing ISBN 978-0961277635
Jump up ^ Berger Bullets Reloading Manual 1st Edition 2012; Berger Bullets LLC; p161, ISBN 978-0-615-63762-4
Jump up ^ JBM Ballistics online trajectory calculator
Jump up ^ JBM ballistics online trajectory calculator
Jump up ^ Exterior Ballistics and Ballistic Coefficients
Jump up ^ A Better Ballistic Coefficient by Bryan Litz, Ballistician Berger Bullets Archived 2009-08-02 at the Wayback Machine.
Jump up ^ Ballistic Coefficient Basics
Jump up ^ Berger Bullets Technical Specifications
Jump up ^ Lapua bullets technical information Archived 2012-02-17 at the Wayback Machine.
Jump up ^ Nosler AccuBond Longe Range technical information
Jump up ^ Form Factors: A Useful Analysis Tool by Bryan Litz, Chief Ballistician Berger Bullets
Jump up ^ .338 Lapua Magnum product brochure Archived September 27, 2011, at the Wayback Machine.
Jump up ^ LM Class Bullets, very high BC bullets for windy long ranges. Archived February 19, 2008, at the Wayback Machine.
Jump up ^ McDonald, William and Algren, Ted. Sierra Loading Manual, 5th ed., Section 2.5. Examples of Ballistic Coefficient Measurements, 2003.
Jump up ^ Litz, Bryan. Applied Ballistics for Long Range Shooting. Cedar Springs, MI : Applied Ballistics, LLC, 2009a, 2nd Edition, 2011.
Jump up ^ Emily Bohnenkamp, Bradford Hackert, Maurice Motley, and Michael Courtney, Comparing Advertised Ballistic Coefficients with Independent Measurements, DTIC, 2012. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA554683
Jump up ^ Alex Halloran, Colton Huntsman, Chad Demers, and Michael Courtney, More Inaccurate Specifications of Ballistic Coefficients, DTIC, 2012. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA555975
Jump up ^ Courtney, Elya, Collin Morris, and Michael Courtney. "Accurate Measurements of Free Flight Drag Coefficients with Amateur Doppler Radar." Cornell University Library (2016). https://arxiv.org/ftp/arxiv/papers/1608/1608.06500.pdf
External links[edit]
Aerospace Corporation Definition
Chuck Hawks Article on Ballistic Coefficient
Ballistic Coefficient Tables
Exterior Ballistics.com
How do bullets fly? The ballistic coefficient (bc) by Ruprecht Nennstiel, Wiesbaden, Germany
Ballistic Coefficients - Explained
Ballistic calculators
Retrieved from "https://en.wikipedia.org/w/index.php?title=Ballistic_coefficient&oldid=826699582"
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text:
iPad Pro
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
iPad Pro
12.9" iPad Pro in Gold
Developer
Apple Inc.
Manufacturer
Foxconn (under contract)
Product family
iPad
Type
Tablet computer
Release date
November 11, 2015 (12.9-inch 1G model)
March 31, 2016 (9.7-inch model)
June 13, 2017 (12.9 2G and 10.5-inch models)
Introductory price
12.9-inch model:
$799 USD (32 GB WiFi only)
9.7-inch model:
$599 USD (32 GB WiFi only)
10.5-inch model:
$649 USD (64 GB WiFi only)
Discontinued
June 5, 2017 (12.9-inch 1G and 9.7-inch)
Operating system
Original: iOS 9.1 (12.9-inch 1G model)
iOS 9.3 (9.7-inch model)
iOS 10.3.2 (10.5-inch and 12.9-inch 2G model)
Current: iOS 11.4, released May 29, 2018 (2018-05-29)
System-on-chip used
12.9-inch 1G and 9.7-inch: Apple A9X with 64-bit architecture and Apple M9 motion co-processor
12.9-inch 2G and 10.5-inch: Apple A10X with 64-bit architecture and Apple M10 motion co-processor
CPU
12.9-inch 1G: 2.26 GHz dual-core 64-bit ARMv8-A[1]
9.7-inch: 2.16 GHz dual-core 64-bit
12.9 inch 2G and 10.5 inch: 2.39 GHz hexa-core 64-bit
Memory
12.9-inch: 4 GB LPDDR4 SDRAM[1]
9.7-inch: 2 GB LPDDR4 SDRAM
10.5-inch: 4 GB LPDDR4 SDRAM
Storage
12.9-inch 1G:
32(WiFi only), 128 or 256 GB flash memory [2]
9.7-inch:
32, 128 or 256 GB flash memory[2]
12.9-inch 2G and 10.5-inch: 64, 256 or 512 GB flash memory[2]
Display
12.9-inch:
2732×2048 px (264 PPI) (IPS panel) (5.5 megapixels), 12.9 in (327.8 mm) diagonal, 4:3[2]
9.7-inch:
2048×1536 px (264 PPI) (IPS panel) (3.1 megapixels), 9.7 in (246.3 mm) diagonal, 4:3[2]
10.5-inch:
2224×1668 px (264 PPI) (IPS Panel), 10.5 in diagonal, 4:3[2]
Graphics
12-core PowerVR Series 7XT[3]
Sound
Four speakers, adjusting sound to device orientation
Input
Multi-touch screen, headset controls and ambient light sensors, 3-axis accelerometer, 3-axis gyroscope, digital compass, dual microphone, Bosch Sensortec BMP280 barometer
Camera
12.9-inch 1G: 1.2 megapixels 720p front-facing and 8 megapixels rear-facing[2]
9.7-inch: 5 megapixels 720p front-facing and 12 megapixels 4K rear-facing[2]
12.9-inch 2G and 10.5-inch: 7 megapixels 1080p front-facing and 12 megapixels 4K rear-facing[2]
Connectivity
Wi-Fi and Wi-Fi + Cellular:
Wi-Fi 802.11 a/b/g/n/ac; dual channel (2.4 GHz and 5 GHz); HT80 with MIMO[2]
Bluetooth 4.2[2]
Wi-Fi + Cellular:
GPS & GLONASS[2]
GSM
UMTS / HSDPA
850, 900, 1700, 1900, 2100 MHz[2]
GSM / EDGE
850, 900, 1800, 1900 MHz[2]
CDMA
CDMA/EV-DO Rev. A and B.
800, 1900 MHz[2]
12.9-inch Wi-Fi + Cellular:
LTE
Multiple bands
1, 2, 3, 4, 5, 7, 8, 13, 17, 18, 19, 20, 25, 26, 28, 29 and TD-LTE 38, 39, 40, 41[2]
9.7-inch Wi-Fi + Cellular:
LTE Advanced
Multiple bands
1, 2, 3, 4, 5, 7, 8, 12, 13, 17, 18, 19, 20, 25, 26, 27, 28, 29, 30 and TD-LTE 38, 39, 40, 41[2]
Power
12.9-inch: 3.77 V 38.8 W·h (10,307 mA·h)[4]
9.7-inch: 3.82 V 27.91 W·h (7,306 mA·h)[5]
10.5-inch: 3.77 V 30.8 W·h (8,134 mA·h)[6]
Online services
App Store, Apple Music, iTunes Store, iBookstore, iCloud, Game Center
Dimensions
12.9-inch:
305.7 mm (12.04 in) (h)
220.6 mm (8.69 in) (w)
6.9 mm (0.27 in) (d)
9.7-inch:
240 mm (9.4 in) (h)
169.5 mm (6.67 in) (w)
6.1 mm (0.24 in) (d)
10.5-inch:
250.6 mm (9.87 in) (h)
174.1 mm (6.85 in) (w)
6.1 mm (0.24 in) (d)
Weight
12.9-inch Wi-Fi: 713 g (1.572 lb)
12.9-inch Wi-Fi + Cellular: 723 g (1.594 lb)
9.7-inch Wi-Fi: 437 g (0.963 lb)
9.7-inch Wi-Fi + Cellular: 444 g (0.979 lb)
10.5-inch WiFi: 469 g (1.034 lb)
10.5-inch WiFi + Cellular:
477 g (1.052 lb)
Related articles
Apple Pencil, Apple A9X, Apple A10X
Website
www.apple.com/ipad-pro/
This article is part of a series on the
iPad
1st · 2 · 3rd · 4th · Air · Air 2 · 2017 · 2018
(5th) (6th)
Mini
1st
2
3
4
Pro
1st
2nd
List of iPad models
v
t
e
The iPad Pro family is a line of iPad tablet computers designed, developed, and marketed by Apple Inc., that runs the iOS mobile operating system. It is currently available in two screen sizes, 10.5-inch (27 cm) and 12.9-inch (33 cm),[7] each with three options for internal storage capacities: 64, 256, or 512 GB; the 512 GB configuration making iPad Pro the first iOS device to offer that storage size.
The first iPad Pro, the 12.9-inch version, was announced on September 9, 2015,[8] and released on November 11, 2015.[9] It is larger than all previous iPad models and the first iPad tablet to feature LPDDR4 RAM.[1] The 12.9-inch tablet was later followed by the smaller 9.7-inch version, which was announced on March 21, 2016, and released on March 31 that same year.[10]
On June 5, 2017, a second generation of iPad Pro was announced, which features A10X Fusion processors, with basic storage of 64 GB, and optional 512 GB. Upgraded displays include a new 10.5-inch version to replace the 9.7-inch model, while the 12.9-inch version was refreshed.[11] Following this announcement, the first generation iPad Pros, both 9.7 and 12.9 inch, were discontinued.
Contents
[hide]
1 First generation
2 Second generation
3 Accessories
3.1 Smart Keyboard
3.2 Apple Pencil
4 Reception
4.1 General reviews
4.2 First generation reviews
4.3 Second generation reviews
5 Model comparison
6 Timeline
7 See also
8 References
9 External links
First generation[edit]
The 12.9-inch version of the iPad Pro was announced during an Apple Special Event on September 9, 2015. It was released on November 11, 2015 with gold, silver, and space gray color options. Prices ranging from US $799.99 to $1,229.99 based on storage size and cellular connectivity. On March 21, 2016, the 9.7 inch version of the iPad Pro was announced at an Apple keynote with an additional rose gold color option. The 9.7 inch version also introduced the ability to choose base 32GB Model with Cellular + WiFi option. (Previously, Cellular + WiFi option was only available on 128GB iPad Pro models.) The 9.7 inch model is priced from $599 to $1,129 depending on the configuration. It was released on March 31, 2016.
The 9.7-inch iPad Pro, when compared to the iPad Air 2, features a faster CPU, a better camera, and is the first iPad to feature True Tone Flash and Retina Flash. It also had the highest storage for an iPad at the time with a 256 GB storage option and has a True Tone display, which allows the LCD to adapt to ambient lighting to change its color and intensity in different environments.[10]
Both iPad Pro models include the A9X chip and the Apple M9 motion co-processor. The 9.7 inch model, however, has a slightly underclocked CPU (2.16 GHz compared to 2.26 GHz on the 12.9 inch model) and only 2 GB of RAM. A number of features are carried over from the standard iPad, such as Touch ID and the Retina Display. New features include a smart connector for a keyboard and four stereo speakers located in pairs on top and bottom of the device. The 12.9 inch model has a 2732-by-2048 Retina Display at 264 pixels per inch, and the 9.7 inch model has a 2048-by-1536 Retina Display at 264 pixels per inch and features a variable refresh rate, a first for Apple. The 12.9 inch version of the iPad Pro is the first iPad to include 4 GB of RAM.
A customised 12.9 inch iPad Pro was also designed by Jony Ive and submitted to the Time for Design auction. The special edition iPad Pro has an "Edition 1 of 1" label engraved on its back and comes with a custom yellow-gold anodised finish, a blue leather Smart Cover and an orange leather Apple Pencil case cover, all of which are not sold by Apple elsewhere.[12][13]
Second generation[edit]
The second generation of iPad Pro was announced on June 5, 2017 alongside iOS 11 at the 2017 WWDC. The second-generation iPad Pro models, at 10.5-inch and 12.9-inch, have an A10X hexa-core CPU and with a 12-core GPU, supports HDR10 and Dolby Vision content (with iOS 11 or later) with a 120 Hz refresh rate and their True Tone display is 50 percent brighter than the earlier models; both sizes also have a 12-megapixel rear-facing camera with quad-LED True-Tone flash and a 7-megapixel front-facing camera with Retina Flash.[11] They have USB-C connection speeds using Lightning cables, with USB-C fast-charge support.[14] The second generation iPad Pro has the highest storage capacity of iOS devices, up to 512 GB.
Accessories[edit]
There are four accessories made specifically for iPad Pro, all of which are sold separately: a "smart" screen cover; an attachable keyboard, Smart Keyboard; an active bluetooth tracking stylus, Apple Pencil; and a form-fitted silicone case that is compatible with the Smart Keyboard.[15]
Smart Keyboard[edit]
Smart Keyboard docks with iPad Pro using the Smart Connector, a magnetic connection that provides data transfer and power. Smart Keyboard, which doubles as a kickstand, is comparable to that of the competing Microsoft Surface Pro.[16] The design of the Smart Keyboard is similar to the design of the Smart Cover accessory.[17]
Apple Pencil[edit]
Main article: Apple Pencil
IPad Pro and Apple Pencil (in boxes)
Apple Pencil is a precision stylus exclusive to the iPad Pro and the iPad 2018. The accessory is rechargeable via the Lightning port on the tablet itself.[18][19] iPad Pro introduces a new display with increased responsiveness and precision over previous iPad displays with Apple Pencil support added.[20][21] During the keynote, Apple demonstrated drawing, managing publication layout, and document annotation.[22][23][24]
Reception[edit]
General reviews[edit]
The iPad Pro's 9.7-inch version set a record among all currently released tablets tested in color accuracy, screen reflectance, peak brightness, contrast rating in high ambient light, and smallest color variation. However, the iPad Pro 12.9-inch version tested to having better contrast ratio in the dark.[25]
Despite Apple advertising the tablets as PC replacements,[26] most reviewers noted that it still cannot replace a laptop running the Microsoft Windows or macOS desktop operating systems.[27][28] One critic pointed out in a comparative review with the competing Surface Pro that "from a flexibility perspective, there is no denying the Windows 10 advantage for consumers, students, and business users" over iOS.[29]
First generation reviews[edit]
Scott Stein from CNET praised the faster processor and new accessories available. However, he criticized the cost of both the unit and its accessories, while noting its slightly slower processor with less RAM compared to the larger 12.9-inch model.[30] Matt Swider from TechRadar complimented the easy handling, large 256GB configuration and True Tone display, but was upset about the high starting price.[31] Gareth Beavis gave a positive review, commending the expansive screen and audio quality but stated that the battery life could be made longer.[32]
Second generation reviews[edit]
Max Parker from TrustedReviews and Gareth Beavis from TechRadar both praised the 10.5-inch model's high-quality audio and performance, though both critics noted that it was expensive.[33][34]
Reviewing the 12.9 inch second-generation iPad Pro, Lauren Goode of The Verge complimented the quality camera, A10X processor and large screen size but said that the device could have been cheaper.[35]
Model comparison[edit]
Legend:
Discontinued Current
Model
iPad Pro (1st generation)
iPad Pro (2nd generation)
Screen Size
12.9-inch
9.7-inch
12.9-inch
10.5-inch
Image
Initial operating system
iOS 9.1 iOS 9.3 iOS 10.3.2 iOS 10.3.2[36]
Highest supported operating system
iOS 11.3

Model Number[37][38]
A1584 (Wi-Fi)
A1652 (Wi-Fi + Cellular)
A1673 (Wi-Fi)
A1674 or A1675 (Wi-Fi + Cellular)
A1670 (Wi-Fi)
A1671 (Wi-Fi + Cellular)
A1701 (Wi-Fi)
A1709 (Wi-Fi + Cellular)
Announcement date
September 9, 2015 March 21, 2016 June 5, 2017
Release date
November 11, 2015 March 31, 2016 June 13, 2017[39]
Launch price
Wi-Fi models:
32 GB – US$799
128 GB – US$949
256 GB – US$1,099
Wi-Fi + Cellular models:
128 GB – US$1,079
256 GB – US$1,229
Wi-Fi models:
32 GB – US$599
128 GB – US$749
256 GB – US$899
Wi-Fi + Cellular models:
32 GB – US$729
128 GB – US$879
256 GB – US$1,029
Wi-Fi models:
64 GB – US$799
256 GB – US$899
512 GB – US$1,099
Wi-Fi + Cellular models:
64 GB – US$929
256 GB – US$1,029
512 GB – US$1,229
Wi-Fi models:
64 GB – US$649
256 GB – US$749
512 GB – US$949
Wi-Fi + Cellular models:
64 GB – US$779
256 GB – US$879
512 GB – US$1,079
SoC
Apple A9X Apple A10X Fusion
Motion coprocessor
Apple M9 Apple M10
CPU
2.26 GHz dual-core Apple Twister[1] 2.26 GHz dual-core Apple Twister (underclocked to 2.16 GHz) ~2.36 GHz hexa-core Apple Fusion (3× Hurricane + 3× Zephyr)[40]
GPU
12-core PowerVR Series 7XT[3]
Memory
4 GB LPDDR4 RAM[1] 2 GB LPDDR4 RAM 4GB LPDDR4 RAM[41]
Display
12.9 inches (330 mm) [diagonal] multi-touch display with LED backlighting
and an oleophobic, fingerprint and scratch-resistant coating, Fully laminated display, Antireflective coating 9.7 inches (250 mm) [diagonal] multi-touch display with LED backlighting
and an oleophobic and scratch-resistant coating, Wide color display, True Tone display,
Fully laminated display, Antireflective coating
12.9 inches (330 mm) [diagonal] multi-touch display with LED backlighting
and an oleophobic and scratch-resistant coating, Wide color display, True Tone display,
Fully laminated display, Antireflective coating, ProMotion display (120 Hertz refresh rate)
10.5 inches (270 mm) [diagonal] multi-touch display with LED backlighting
and an oleophobic and scratch-resistant coating, Wide color display, True Tone display,
Fully laminated display, Antireflective coating, ProMotion display (120 Hertz refresh rate)
2732-by-2048 pixel resolution 264 ppi (Retina Display) 2048-by-1536 pixel resolution at 264 ppi (Retina Display) 2732-by-2048 pixel resolution at 264 ppi (Retina Display) 2224-by-1668 pixel resolution at 264 ppi (Retina Display)
Camera
iSight
8 MP, ƒ/2.4 aperture, HDR for photos, Autofocus, five-element lens, Hybrid IR filter,
Backside illumination, Face Detection, Exposure control, Panorama (up to 43 MP), Burst mode, Tap to focus, Photo geotagging, Timer mode, Video Recording, 1080p video recording (30 fps), Slo-mo video support for 720p at 120 fps, Time-lapse video, Video image stabilization, 3× digital zoom, Video geotagging
12 MP, ƒ/2.2 aperture, Auto HDR for photos, five-element lens, Hybrid IR filter, Backside illumination, Autofocus with Focus Pixels, Improved face detection, Exposure control, Panorama (up to 63 MP), Burst mode,
Tap to focus, Photo geotagging, Timer mode, Video Recording, Cinematic video stabilization, 4K video recording (30 fps), 1080p HD video recording at 30 fps or 60 fps, Slo-mo video support for 1080p at 120 fps and 720p at 240 fps, Time-lapse video, 3× digital zoom, Live Photos, True Tone LED flash, Sapphire crystal lens cover, Improved local tone mapping, Improved noise reduction, Video geotagging
12 MP, ƒ/1.8 aperture, Auto HDR for photos, Autofocus with Focus Pixels, six-element lens, Hybrid IR filter, Backside illumination,Improved face detection, Exposure control, Panorama (up to 63 MP), Burst mode, Tap to focus,
Photo and video geotagging, Timer mode, Video Recording, Cinematic video stabilization, 4K video recording (30 fps), 1080p HD video recording at 30fps or 60fps, Slo-mo video support for 1080p at 120 fps and 720p at 240 fps, Time-lapse video, 3× digital zoom, True Tone LED flash, Sapphire crystal lens cover, Improved local tone mapping, Improved noise reduction
FaceTime
1.2 MP, ƒ/2.2 aperture, 720p HD video recording, Auto HDR for photos and videos, Backside illumination, Exposure control, Burst mode, Timer mode and Face Detection 5 MP, ƒ/2.2 aperture, 720p HD video recording, Retina Flash, Auto HDR for photos and videos, Backside illumination, Exposure control, Burst mode, Timer mode and Face Detection 7 MP ƒ/2.2 aperture, 1080p HD video recording, Auto HDR for photos and videos, Backside illumination, Exposure control, Burst mode, Timer mode and Face Detection
Wireless
Wi-Fi
Wi-Fi (802.11a/b/g/n/ac); dual channel (2.4 GHz and 5 GHz); HT80 with MIMO
Bluetooth 4.2 technology
Wi-Fi + Cellular
Above plus:
UMTS/HSPA/HSPA+/DC-HSDPA (850, 900, 1700/2100, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz), CDMA EV-DO Rev. A and Rev. B (800, 1900 MHz), LTE (Bands 1, 2, 3, 4, 5, 7, 8, 13, 17, 18, 19, 20, 25, 26, 28, 29, 38, 39, 40, 41), Data only, Includes Apple SIM (U.S., UK, and Germany only)
Above plus:
UMTS/HSPA/HSPA+/DC-HSDPA (850, 900, 1700/2100, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz), CDMA EV-DO Rev. A and Rev. B (800, 1900 MHz), LTE Advanced (Bands 1, 2, 3, 4, 5, 7, 8, 12, 13, 17, 18, 19, 20, 25, 26, 27, 28, 29, 30, 38, 39, 40, 41), Data only, Embedded Apple SIM
Geolocation
Wi-Fi
Wi-Fi
Apple location databases
iBeacon microlocation
Wi-Fi + Cellular
Above plus:
Assisted GPS
GLONASS
Cellular network
Environmental sensors
Accelerometer
Gyroscope
Ambient light sensor
Magnetometer
Barometer
Battery
3.77 V 38.8 W·h (10307mA·h) rechargeable lithium‐polymer battery[4] 3.82 V 27.91 W·h (7306mA·h) rechargeable lithium‐polymer battery[42] 3.77 V 41 W·h (10875mA·h) rechargeable lithium‐polymer battery[43] 3.77 V 30.8 W·h (8134mA·h) rechargeable lithium‐polymer battery[41]
Dimensions
305.7 mm (12.04 in) (h)
220.6 mm (8.69 in) (w)
6.9 mm (0.27 in) (d)
240 mm (9.4 in) (h)
169.5 mm (6.67 in) (w)
6.1 mm (0.24 in) (d)
305.7 mm (12.04 in) (h)
220.6 mm (8.69 in) (w)
6.9 mm (0.27 in) (d)
250.6 mm (9.87 in) (h)
174.1 mm (6.85 in) (w)
6.1 mm (0.24 in) (d)
Weight
Wi-Fi model: 710 g (1.57 lb)
Wi-Fi + Cellular model: 720 g (1.59 lb)
Wi-Fi: 437 g (0.963 lb)
Wi-Fi + Cellular: 444 g (0.979 lb)
Wi-Fi model: 677 g (1.493 lb)
Wi-Fi + Cellular model: 692 g (1.526 lb)
Wi-Fi: 469 g (1.034 lb)
Wi-Fi + Cellular 477 g (1.052 lb)
Mechanical keys
Home and sleep buttons
Volume control
Omits variable function switch like the iPad Air 2 and iPad Mini 4
Connectors
Lightning Connector
Apple Smart Connector
3.5 mm audio jack connector
Speakers
Quad stereo
Greenhouse gas emissions
240 kg CO2e[44] 210 kg CO2e[45] 122 kg CO2e[46] 100 kg CO2e[47]
Timeline[edit]
May 2018:9.7” iPad Models: MPGT2LLA, MR7G2LL/A, MR7F2LL/A, MRJN2LL/A
July 2017: 12.9” iPad Pro (2nd Gen) Models: A1670 (Wi-Fi), A1671 (4G), MQDA2LL/A, MP6G2LL/A, MP6J2LL/A
June 2017: 10.5” iPad Pro (2nd Gen) Models: A1701 (Wi-Fi), A1709 (4G), MQDT2CL/A, MQDW2LLA, MQDY2LL/A
April 2016: 9.7” iPad Pro (1st Gen) Models: A1673 (Wi-Fi), A1674 or A1675 (4G), MLMQ2CL/A, MLMQ2LL/A
March 2016: 9.7” iPad (7th Gen) Models: A1822 (Wi-Fi), A1823 (4G), MPGT2LL/A, MPGW2LL/A, MPGC2LL/A,
November 2015: 12.9” iPad Pro (1st Gen) Models: A1584 (Wi-Fi), A1652 (4G), MD517LL/A, ML3K2LL/A, ML0T2LL/A, MD517LL/A
September 2015: iPad Mini 4 (4th Gen Mini) Models: A1538 (Wi-Fi), A1550 (4G), MK9J2LL/A, MK8C2LL/A, MK9Q2LL/A, MK6K2LL/A
April 2015: iPad (4th Gen) Models: A1458 (Wi-Fi), A1459 (4G), A1460 (4G MM), MD511LL/A
October 2014: iPad Air 2 Models: A1566 (Wi-Fi), A1667 (4G), MH0W2LL/A, MNV72LL/A, MH182LL/A, MH1J2LL/A
iPad Mini 3 (3rd Gen Mini) Models: A1599 (Wi-Fi), A1600 (4G), MGNV2LL/A, MH3F2LL/A, MH382LL/A, MGGT2LL/A, MGP42LL/A, MH3M2LL/A
November 2013: iPad Air (5th Gen) Models: A1474 (Wi-Fi), A1475 (4G), MD788LL/B, MD789LL/A, MD790LL/A, ME906LL/A
iPad Mini 2 (2nd Gen Mini) Models: A1489 (Wi-Fi), A1490 (4G), ME279LL/A
October 2012: iPad Mini (1st Gen Mini) Models: A1432 (Wi-Fi), A1454 (4G), A1455 (4G MM), MD531LL/A
March 2012: iPad (3rd Gen) Models: A1416 (Wi-Fi), A1430 (4G), A1403 (4G VZ), MD328LL/A
March 2011: iPad (2nd Gen) Models: A1395 (Wi-Fi), A1396 (3G GSM), A1397 (3G CDMA), MC769LL/A
January 2010: iPad (1st Gen) Models: A1219 (Wi-Fi), A1337 (3G), MB294LL/A
Source: Apple Newsroom Archive[48]
See also[edit]
Apple A9X Mobile Processor
Apple A10X Mobile Processor
Pen computing
Graphics tablet
References[edit]
^ Jump up to: a b c d e "The A9X SoC & More To Come - The iPad Pro Preview: Taking Notes With iPad Pro". AnandTech. November 11, 2015. Retrieved November 11, 2015.
^ Jump up to: a b c d e f g h i j k l m n o p q "iPad Pro - Technical Specifications - Apple". Apple Inc.
^ Jump up to: a b Smith, Ryan (November 30, 2015). "More on Apple's A9X SoC". AnandTech. Retrieved November 30, 2015.
^ Jump up to: a b "iPad Pro Teardown". iFixit. November 11, 2015. Retrieved November 11, 2015.
Jump up ^ "iPad Pro 9.7" Teardown". iFixit. April 4, 2016. Retrieved April 4, 2016.
Jump up ^ "iPad Pro 10.5 inch teardown".
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Jump up ^ Dillet, Roman (September 9, 2015). "Apple Unveils The iPad Pro". TechCrunch. Retrieved September 9, 2015.
Jump up ^ "Apple - Press Info - Epic 12.9-inch iPad Pro Available to Order Online Wednesday & Arrives in Stores Later This Week". Apple Inc.
^ Jump up to: a b Seifert, Dan (March 21, 2016). "New iPad Pro announced: $599, 9.7-inch display, weighs less than one pound". The Verge. Retrieved August 14, 2016.
^ Jump up to: a b "Apple announces new 10.5-inch iPad Pro". Retrieved June 5, 2017.
Jump up ^ Mayo, Benjamin (16 April 2016). "Jony Ive designs one-of-a-kind iPad Pro, Smart Cover and Apple Pencil case for special Design Museum auction". 9to5Mac. Retrieved 21 October 2017.
Jump up ^ "Phillips: UK050316, Apple Inc". Phillips. Retrieved 21 October 2017.
Jump up ^ "10.5-inch and 12.9-inch 2017 iPad Pro FAQ: Everything you need to know!". iMore. Retrieved 2017-06-15.
Jump up ^ "iPad Accessories". Apple. September 15, 2015. Retrieved September 28, 2015.
Jump up ^ Ziegler, Chris (September 9, 2015). "The iPad Pro has an optional Smart Keyboard cover for $169". The Verge. Retrieved September 28, 2015.
Jump up ^ "Hands-on with the iPad Pro's Smart Keyboard". Macworld. Retrieved 2017-06-19.
Jump up ^ "Apple Introduces iPad Pro Featuring Epic 12.9-inch Retina Display". Apple.com. Apple Press Info. Archived from the original on September 11, 2015. Retrieved September 11, 2015.
Jump up ^ Ulanoff, Lance (September 12, 2015). "Apple is not following Jobs' script and that's OK". Mashable. Archived from the original on September 15, 2015. Retrieved September 15, 2015.
Jump up ^ Statt, Nick (September 9, 2015). "Here's why Apple made the stylus that Steve Jobs hated: Styluses and screens have come a long way". The Verge. The Verge. Archived from the original on September 10, 2015. Retrieved September 10, 2015.
Jump up ^ Harley; et al. "United States Patent: 8638320". Patent Full Text. Retrieved September 10, 2015.
Jump up ^ King, Hope. "Apple criticized for Photoshopping smile on woman's face". CNN.com. CNN Money. Archived from the original on September 10, 2015. Retrieved September 10, 2015.
Jump up ^ Price, Rob (September 9, 2015). "Apple just announced a product that Steve Jobs famously hated". Business Insider. Archived from the original on September 15, 2015. Retrieved September 15, 2015.
Jump up ^ Davies, Chris (September 9, 2015). "Apple Pencil for iPad Pro revealed: The stylus' time has come". Slashgear. Archived from the original on September 10, 2015. Retrieved September 15, 2015.
Jump up ^ iPad Pro 9.7 analysis shows record display performance, iPhone 7 screen upgrade possibilities 9to5 Mac
Jump up ^ "iPad Pro - What's a Computer?". Apple Inc. on YouTube. August 1, 2016. Retrieved August 13, 2016.
Jump up ^ iPad Pro 9.7 review: Apple's best tablet, but it won't replace a laptop
Jump up ^ No, The 9.7 iPad Pro Won't Replace A Windows Laptop - Forbes
Jump up ^ Microsoft Surface Pro (2017) vs. Apple iPad Pro (2017): Best Productivity Tablet PC Perspective, Retrieved July 31, 2017.
Jump up ^ Stein, Scott (March 30, 2016). "iPad Pro 9.7-inch review".
Jump up ^ Swider, Matt (January 27, 2018). "iPad Pro 9.7 review". TechRadar.
Jump up ^ Beavis, Gareth. "iPad Pro 12.9 (2015) review". TechRadar. Retrieved April 3, 2018.
Jump up ^ Parker, Max (March 9, 2018). "iPad Pro 10.5 review". trustedreviews.
Jump up ^ Beavis, Gareth. "iPad Pro 10.5 review". TechRadar. Retrieved April 3, 2018.
Jump up ^ Lauren Goode (June 20, 2017). "iPad Pro 12.9-inch review". The Verge. Retrieved April 4, 2018.
Jump up ^ "Review: The 10.5-inch iPad Pro is much more "pro" than what it replaces". Ars Technica. Retrieved 2017-06-17.
Jump up ^ "Identifying iPad Models".
Jump up ^ "Apple - iPad - View countries with supported LTE networks".
Jump up ^ "New 2017 iPad Pro Models Now Available in Apple Stores". Retrieved 2017-06-17.
Jump up ^ Smith, Ryan (June 29, 2017). "TechInsights Confirms Apple's A10X SoC Is TSMC 10nm FF; 96.4mm2 Die Size". AnandTech. Retrieved December 30, 2017.
^ Jump up to: a b "iPad Pro 10.5" Teardown". iFixit. 2017-06-13. Retrieved 2017-06-17.
Jump up ^ "iPad Pro 9.7" Teardown". iFixit. Retrieved April 4, 2016.
Jump up ^ "iPad Pro 12.9in (2017) vs iPad Pro 12.9in (2015)". June 15, 2017. Retrieved August 14, 2017.
Jump up ^ "iPad Pro Environmental Report" (PDF). Apple Inc. November 2015. Archived from the original (PDF) on December 8, 2015. Retrieved November 11, 2015.
Jump up ^ "9.7-inch iPad Pro Environmental Report" (PDF). Measuring performance. One product at a time. Apple Inc. March 2016. Retrieved March 27, 2016.
Jump up ^ "iPad Pro (12.9-inch) Environmental Report" (PDF). June 5, 2017. Retrieved June 21, 2017.
Jump up ^ "iPad Pro (10.5-inch) Environmental Report" (PDF). June 5, 2017. Retrieved June 21, 2017.
Jump up ^ Apple Inc. (2010–2011). iPad News - Newsroom Archive. Retrieved June 7, 2018.
External links[edit]
Official website
Preceded by
– 12.9-inch iPad Pro
1st generation Succeeded by
12.9-inch iPad Pro 2nd generation
Preceded by
– 9.7-inch iPad Pro
1st generation Succeeded by
10.5-inch iPad Pro
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Retrieved from "https://en.wikipedia.org/w/index.php?title=IPad_Pro&oldid=844821078"
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IPad Pro – French
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IPad Pro – Italian
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IPad Pro – Georgian
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IPad Pro – Lombard
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IPad Pro – Malay
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IPad Pro – Dutch
nl
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IPad Pro – Japanese
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IPad Pro – Polish
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IPad Pro – Portuguese
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IPad Pro – Russian
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IPad Pro – Ukrainian
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IPad Pro – Vietnamese
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