1. Has any military ever used hollow points?
Yes, the British Army adopted a jacketed hollow point round, the .303 Mk III, as the official service round in 1897. It was followed by the very similar Mk IV and Mk V, before the ratification of the Hague Convention of 1899. Hollow point bullets for the .455 revolver entered official service at about the same time.
More recently a 1985 opinion issued on behalf of the Judge Advocates General of the US Army, Navy and Air Force concluded that that bullets made as hollow points for reasons of accuracy rather than expansion, like the Sierra MatchKing, do not contravene the Hague accords, and so may be used in combat.As I understand it the M118 Special Ball, with a 175 gn MatchKing, is the current standard for sniper issue, replacing the M852 with its 168 gn MatchKing. Further, a 1993 JAG opinion was the basis for authorising the use by SOCOM of a .45 JHP for the H&K Mk 23.
2. When did they first come around?
Metford, among others, was working with hollow-point designs from about the 1860s, particularly after explosive rifle bullets were banned by international treaty in 1868. These early hollow points weren't jacketed though, jacketed ammunition being a development of the early 1880s.
3. How much of a difference does a HP or FMJ have on ballistics?
In the case of bullets like the MatchKing the accuracy is enhanced largely because the bullet is jacketed from the base, unlike FMJ which is jacketed from the nose. This allows the base to be formed more precisely, which in turn leads to a more consistent, stable delivery from the rifle muzzle.
As well, a large hollow tends to push the centre of mass further back, and further from the axis of rotation, enhancing stability in flight. Metford found this with his early designs. He used a very deep hollow point, often filled with some light material, and found that long range accuracy was markedly improved compared to standard cylindro-conoidal bullets. Of course the same effect could be had by using a nose cavity or nose filler under FMJ, like the .303 Mk VII.
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