7.5 FK

The 7.5 FK or the 7.5 FK BRNO (designated as the 7.5 FK by the C.I.P.) is a bottlenecked rimless centerfire automatic pistol cartridge developed by the Czech firearms and ammunition manufacturer FK Brno Engineering s.r.o. It is reported that the cartridge has recently been adopted by some law enforcement agencies and militaries engaged in ongoing conflicts by their special operations units. The cartridge is known for its long-range accuracy and high incapacitation capability when compared to other automatic pistol cartridges.
History.
Developed between 2009 and 2014 for the specific purpose of providing high capacity automatic pistols the ability to engage combatant targets at a range of between 75-150 meters while retaining more kinetic energy at that range than what a 9mm NATO cartridge can generate at the muzzle/point blank range.
Due to the length of the cartridge, relatively high energy, and a pressure that the cartridge generates, no modern existing, high-capacity automatic pistol design existed that can accommodate the new caliber so FK BRNO developed a specialized platform to accommodate and use this caliber.
Initially it was chambered in the all-steel FK Field Pistol which has a unique patented recoil attenuating system but subsequently FK BRNO developed a polymer version of that that design designated as the FK PSD. This recoil attenuating system allows the powerful 7.5 FK cartridge to be fired with high level controllability and accuracy.
Cartridge dimensions.
The 7.5 FK has 1.50 cm3 (23.21 grain of H2O) cartridge case capacity.
Americans would define the shoulder angle at alpha/2 = 30 degrees. The common rifling twist for this cartridge is 270mm (1 in 10.62” inch), 6 grooves, Ø lands = 7.5 mm, Ø grooves = 7.77mm, land width = 3.75 mm, and the primer type is small pistol.
Contrary to some published information, this cartridge is not based on a necked down 10mm auto case, and hand loaders cannot and should not attempt to make a 7.5 case from a 10mm auto case, as the case is longer, thicker, and operates at significantly higher pressure. Therefore, necking down and stretching the 10mm auto would create much thinner walls at the critical shoulder/neck area and can potentially be very dangerous to the user.
According to C.I.P rulings, the 7.5 FK case can handle up to 350 MPa (50,763 psi) piezo pressure. In C.I.P regulated countries every pistol cartridge combo has to be proofed at 130% of this maximum C.I.P pressure to certify for sale to consumers.
Conversions.
No current pistol caliber and no current automatic pistol design other than the products of FK BRNO can be converted to the 7.5 FK cartridge due to the longer cartridge length and higher operating pressure renders conversion not possible. However, the opposite is possible, and done by the PSD variant. A conversion barrel allows for the use of 10mm auto and .40 smith and Wesson ammunition or a conversion of the barrel, recoil spring, and magazine can fire 9x19mm.
Characteristics.
The goal of the 7.5 FK project was to create a cartridge with a level of performance that could exceed that of the highly effective 125 grain (8.1 g) JHP 357 magnum load and at least as effective terminally as the 7.62 x 39 Russian or 5.56 NATO cartridges when fired from short barrel (20- 25.2 cm or 8-10 inches) in AK/AR type platforms, and to provide it in a package small enough to fit a standard-size military automatic pistol platform. Another goal was to have a flat trajectory and to be accurate enough to engage targets at 75-150 meters which is the most common engagement distance in modern combat situations and therefore to be considered as a second weapon as opposed to a secondary weapon which is what most military pistols using standard NATO and other automatic pistol calibers are considered.
Measurements of standard 7.5 cartridges loaded with 95 grain (6.16 g) showed a muzzle velocity of 2000fps (610m/s) out of a 5.3-inch barrel equal to 4-inch of free bore (13.46 cm equal to 10 cm free bore) and a muzzle energy of 845ft ft/lbs (1146 jouls) which is almost 50% higher than the venerable 357 magnum 125 grain JHP when using quality high pressure ammunition where the measured muzzle velocity is 1450 fps (442 m/s) and muzzle energy of 584 ft/lbs (799 jouls) when fired from a 4-inch barrel, so essentially from the same barrel length as the 7.5 FK.
More importantly the 7.5 FK cartridge achieves this performance without compromising the sectional density of the projectile which is critical for the penetrating depth and incapacitating capability. The 95 grain 7.5 FK cartridge has a sectional density of 0.150 while the 101 grain 7.5 FK cartridge has a sectional density of 0.160. In comparison the 357 magnum 125 cartridge has a sectional density of 0.140. The higher sectional density allows the 7.5 FK projectile to retain higher velocity and lower trajectory at longer ranges, while having significantly deeper penetration especially since it has 40% more velocity. It is interesting to note that the measured velocity and energy of the 95 grain load 7.5 FK cartridge at the minimum design engagement distance of 75 meters is 1650 fps (503 m/s) and 577 ft/lbs (783 joules) respectively. Which is essentially almost the same as what the 125 grain JHP 357 magnum generates at the muzzle / point black range from the same barrel length.
Performance.
The table below shows common performance parameters for several common automatic pistol calibers using kinetic energy as the main form of power comparison, using premium high-end ammunition using a 5-inch barrel.
The concept of using kinetic energy tables as a measuring method for incapacitating power has been used for almost a century but has been disputed for almost as long by various different authorities, scholars, and writers as it does not take into account the projectile construction and design which may affect terminal performance significantly. It also does not take into account penetration capability which is highly influence by projectile material, design, and sectional density. Several theories have been published that claim better prediction of incapacitating power than kinetic energy such as Tylor KO index, Hatchers theory, Lethality index, Bekker knock out formula, and Hornady HITS among others. FK BRNO has published their own alternative method which they claim is more efficient and more accurate predictor of incapacitating power which they call Dynamic Shock Index (DSI). They have also published a video showing the 7.5 cartridge being used to hunt large boars where they claim that the terminal ballistics efficiency shown in the video is due to the high DSI of these loads.
Dynamic Shock Index.
The DSI concept takes into account meplat diameter (meplat=frontal flat area of a projectile), the sectional density of the projectile and several velocity parameters. The mass of the projectile is not taken into account directly thought it is used in order to calculate the sectional density.
The following is the formula for the Dynamic Shock Index as published by FK BRNO:
"DSI = meplat diameter x impact velocity – (1500-impact velocity) x sectional density"
The following are examples of how some powerful versions with very high meplat diameter of popular ammunition calibers score using muzzle velocity for illustrative purposes (as opposed to impact velocity) in comparison with the 7.5 FK.
Available loads.
F9: All copper monolithic wide meplat flat nose. This bullet is designed to create a wide and very deep permanent wound channel in addition to a very high dynamic shock effect. Accurate and effective for defence and medium game hunting up to 300 lbs to 100 yards, and dangerous game up to 500 lbs to 50 yards. 
S95: Jacketed Hollow point made by Sierra bullets exclusively for FKB, it is designed to explode and shatter on impact. This bullet makes huge, but shallower wound channels than the other versions. Accurate and effective for defence and medium game hunting up to 100 lbs at 100 yards.
F5: All copper, monolithic nose discarding hollow point. The nose is designed to break off on impact, leaving a jagged 7mm meplat to create a large deep penetrating wound channel and a High Terminal Effect. Accurate and effective for defence and medium game hunting up to 200 lbs to 100 yards.