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The .32 North American Arms cartridge is a new introduction to the world of pocket pistols and is essentially a .380ACP case 'necked-down' to accept .32 caliber bullets.
From a standpoint of bullet effectiveness, the .32NAA could pan out to be the best choice in 'mousegun' ammunition - most .380ACP ammunition cannot reach a velocity high enough for expansion and proper penetration when fired from a small pistol with a short barrel, while .32ACP ammunition from a similar sized pistol can either expand or retain a FMJ-type profile and penetrate to reasonable depths.
The .32NAA, from the tests posted on this website, appears to offer the best of both worlds in this regard - from a mousegun, it should be possible to get a JHP to expand to .45 caliber and penetrate to the FBI-standard minimum depth of 12" in ballistic gelatin.
Below is a picture of the track made by a Hornady 85 grain XTP hollowpoint, loaded to maximum .32NAA pressure and fired out of a 2.75" barrel length. This particular bullet expanded to 39 caliber (0.390" diameter) and penetrated to 16" and then some. The performance of this cartridge out of a 'mousegun' can be optimized by the utilization of a bullet of similar weight and velocity, but with greater expansion.
To compare the performance of the 85 grain XTP to the only .380ACP that I have found to penetrate to the FBI minimum depth of 12" and that expanded (when fired from a 2.75" barrel) - the 90 grain Federal Hydra-Shok, a brief analysis will be made regarding the theoretical volume of the hole that each bullet pushed into the gelatin block:
The area of a disc is pi*radius*radius. When looking straight at the business end of a bullet, the frontal area is assumed to be shaped like a disc. The penetration depth that the bullet reached is then multiplied by the frontal area to determine the volume of the potential wound.
For the Hydra-Shok: 3.14159(pi) * 0.235inch * 0.235inch * 12.23inch = 2.121 in^3 (cubic inches).
For the .32NAA 85 grain XTP: pi * 0.195inch * 0.195inch * 16 inch = 1.911 in^3.
More typical of .380ACP from short barrels is this (maximum pressure 90 grain Speer Gold Dot): pi * .219in * .219in * 11 = 1.657 in^3.
The performance of the .32NAA can still be greatly improved by a bullet that has greater expansion and subsequently penetrates to around 12" (as opposed to the 16+ inches recorded in this initial test session) in calibrated ballistic gelatin. As it stands, the tested .32NAA bullet produces 15% greater potential wound volume than a typical .380ACP and 10% less potential wound volume than an optimum .380ACP, when fired from short barreled pistols.
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