Cartridge mass

The mass of one loaded round from its bullet and its case, fitted to cartridges whose mass a source states.

The model

The loaded-weight check does not guess what a magazine of rounds weighs: it works it out from the cartridge, with a model fitted to cartridge masses that sources state.

V = \frac{π}{4} {d_{b}}^{2} L_{c}

m_{r} = m_{b} + k V, k = 2.5 g {cm}^{- 3}

where

$V$: the case envelope, the cylinder the case occupies, in cm³
$d_{b}, L_{c}$: the case's base diameter and length, in cm
$m_{r}, m_{b}$: the mass of one loaded round and of its bullet, in g
$k$: case and powder per cm³ of envelope, fitted to published cartridge masses; its bounds allow for rimfire and the largest rounds

Cartridge brass (C26000) is 8.53 g per cm³ and smokeless powder 0.8 to 1.0 g per cm³ in bulk; the fitted 2.5 g per cm³ sits between them because the case wall and head fill only part of the envelope.

Fitted to published cartridges

Each row is a cartridge whose loaded mass a source states. The prediction uses only the bullet and the catalogue's own case dimensions; every one lands within 10%.

Load	Published	Predicted	Off by	Source
.45 ACPM1911 ball	21.19 g	21.45 g	+1.2%	man.fas.org
5.56×45mm NATOM855	12.31 g	12.08 g	−1.9%	en.wikipedia.org
7.62×39mm57-N-231	16.30 g	17.69 g	+8.5%	en.wikipedia.org
7.62×51mm NATOM80 ball	25.40 g	23.66 g	−6.9%	en.wikipedia.org

.45 ACP (M1911 ball): the model should land within 10% of the published mass

19.07 g23.31 gpredicted: 21.45 g

Answer: 21.45 g is within 10% of the published 21.19 g, so the model holds for this round.

The model

Fitted to published cartridges

Checks that use this method