Is it safe to shoot up? An analysis of the lethality of subsonic projectiles

Silva, Saulo Luis Lima da; Fumiã, Herman Fialho

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Revista Brasileira de Ensino de Física

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Artigos Gerais • Rev. Bras. Ensino Fís. 41 (3) • 2019 • https://doi.org/10.1590/1806-9126-RBEF-2018-0260 copy

Is it safe to shoot up? An analysis of the lethality of subsonic projectiles

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Celebratory gunfire is the shooting of a firearm into the air in celebration. This is common in countries as Afghanistan, Pakistan and regions of Latin American. In this article, we have solved the problem of a projectile with subsonic speed shooted upward, considering the air resistance. For didactic purposes, we draw a parallel between the case with and without air resistance. We conclude that even small-caliber projectile can be lethal when falling, a despite the decrease in speed and kinetics energy.

Keywords:
bullet; lethality; drag; air resistance

Calibre	m (g)	$v_{0}$ (m/s)
.22 short (5.6 mm short)	1,8	290
.22 long rifle	1,8	330
6.35 mm Browning	3,2	230
7.65 mm Browning	4,7	300
9x18 mm Police	6,1	300
7.62 mm Nagant	7,0	290
.32 Smith and Wesson	5,5	200
.38 Smith and Wesson	9,4	210
.38 Smith and Wesson special	10,2	260
.45 Automatic Colt Pistol	14,9	260

Calibre	$t_{s}$	$t_{d}$	$t_{total}$	$t_{d} / t_{s}$	$t_{0}$
	(s)	(s)	(s)	(s)
.22 short (5.6 mm short)	9,4	15,0	24,4	1,61	29,6
.22 long rifle	9,6	15,9	25,5	1,67	33,7
6.35 mm Browning	10,2	14,6	24,9	1,43	23,5
7.65 mm Browning	10,6	16,5	27,2	1,55	30,6
9x18 mm Police	10,3	13,9	24,1	1,36	20,4
7.62 mm Nagant	10,7	16,6	27,3	1,55	30,6
.32 Smith and Wesson	12,4	18,0	30,4	1,45	29,6
.38 Smith and Wesson	11,4	15,1	26,4	1,33	21,4
.38 Smith and Wesson special	12,5	17,4	29,8	1,39	26,5
.45 Automatic Colt Pistol	12,1	17,0	29,1	1,41	26,5

Calibre	$h_{m a x}$ (m)	$h_{O m a x}$ (m)	$h_{\underline{O m a x}} h_{m a x}$
.22 short (5.6 mm short)	705	4291	6,1
.22 long rifle	764	5556	7,3
6.35 mm Browning	743	2699	3,6
7.65 mm Browning	879	4592	5,2
9x18 mm Police	704	2041	2,9
7.62 mm Nagant	884	4592	5,2
.32 Smith and Wesson	1109	4291	3,9
.38 Smith and Wesson	845	2250	2,7
.38 Smith and Wesson special	1072	3449	3,2
.45 Automatic Colt Pistol	1019	3449	3,4

Calibre	$v_{0}$	$v_{q}$	$\frac{\| Δ E_{m} \|}{k_{0}}$	$v_{t}$	$\frac{v_{q}}{v_{t}}$
	(m/s)	(m/s)		(m/s)
.22 short (5.6 mm short)	290	66,7	0,95	68,6	0,97
.22 long rifle	330	67,1	0,96	68,6	0,98
6.35 mm Browning	230	76,8	0,89	81,4	0,94
7.65 mm Browning	300	76,9	0,93	79,5	0,97
9x18 mm Police	200	79,3	0,84	86,4	0,92
7.62 mm Nagant	300	77,2	0,93	79,9	0,97
.32 Smith and Wesson	290	92,4	0,90	97,5	0,95
.38 Smith and Wesson	210	88,9	0,82	98,2	0,91
.38 Smith and Wesson special	260	95,2	0,87	102,2	0,93
.45 Automatic Colt Pistol	260	91,5	0,88	97,8	0,94

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[1] ^*Endereço de correspondência: saulolimasilva@yahoo.com.br.