Because bullets are designed with very specific performance parameters in mind. In the case of the 5.56 NATO they were:
* .22 Caliber
* Bullet exceeding supersonic speed at 500 yards
* Rifle weight of 6 lb
* Magazine capacity of 20 rounds
* Select fire for both semi-automatic and fully automatic use
* Penetration of US steel helmet through one side at 500 yards
* Penetration of .135-inch steel plate at 500 yards
* Accuracy and ballistics equal to M2 ball ammunition (.30-06 Springfield) out to 500 yards
* Wounding ability equal to M1 Carbine
On top of all that, they wanted a round with less recoil than the M2.
After development and testing of many different new ammunitions, the brand new .223 remington was the round that had the best results for the specified parameters. It was later officially adopted by the US military and renamed “Cartridge, 5.56mm Ball, M193.” This round was further developed and became the 5.56×45mm NATO with the subsequent military designation of SS109 in NATO and M855 in the U.S.
While 5.56 may sound arbitrary, it was the result of a 13 year project that spanned multiple countries and involved every major gun and ammunition company of the time, to create a small caliber, high velocity firearm for military use.
Latest Answers