Uncertainty coefficient

Bolt thrust or breech pressure is a term used in internal ballistics and firearms (whether small arms or artillery) that describes the amount of rearward force exerted by the propellant gases on the bolt or breech of a firearm action or breech when a projectile is fired. The applied force has both magnitude and direction, making it a vector quantity.

Bolt thrust is an important factor in weapons design. The greater the bolt thrust, the stronger the locking mechanism has to be to withstand it. Assuming equal engineering solutions and materiel adding strength to a locking mechanism causes an increase in weight and size of locking mechanism components.
Bolt thrust is not a measure to determine the amount of recoil/free recoil.

Calculating bolt thrust

With a basic calculation the bolt thrust produced by a particular firearms cartridge can be calculated fairly accurately.

Formula

${\vec {F}}_{bolt}=P_{max}\cdot A_{internal}.$

where:

• F_bolt = the amount of bolt thrust
• P_max = the maximum (peak) chamber pressure of the firearms cartridge
• A_internal = the inside area (of the cartridge case head) that the propellant deflagration gas pressure acts against

Cartridge case heads and chambers are generally circular. The area enclosed by a circle is:

$Area=\pi r^{2}\approx 3{.}1416\cdot r^{2}.$

where:

• π ≈ 3.1416
• r = the radius of the circle

Equivalently, denoting the diameter of the circle by d.

$Area={\frac {\pi d^{2}}{4}}\approx 0{.}7854\cdot d^{2}.$

The green line denotes the internal case head diameter and the red line the external case head base diameter of a rifle cartridge case.

A practical problem regarding this method is that the internal case head diameter of a particular production lot of cartridge cases (different brands and lots normally differ dimensionally) can not be easily measured without damaging them.

Friction effects

A complicating matter regarding bolt thrust is that a cartridge case expands and deforms under high pressure and starts to "stick" to the chamber. This "friction-effect" can be accounted for with finite elements calculations on a computer, but it is a lot of specialized work and generally not worth the trouble.

By oiling proof rounds during NATO EPVAT testing procedures, NATO test centers intentionally lower case friction to promote high bolt thrust levels.

Practical method to estimate bolt thrust

Instead of using the internal case head diameter, the external case head base diameter can also be measured with a caliper or micrometer or taken from the appropriate C.I.P. or SAAMI cartridge or chamber data tables and used for bolt thrust estimation calculations.

The basic calculation method is almost the same, but now the larger outside area of the cartridge case head is used instead of the smaller inside area.

${\vec {F_{bolt}}}=P_{max}\cdot A_{external}.$

where:

• F_bolt = the amount of bolt thrust
• P_max = the maximum (peak) chamber pressure of the firearms cartridge
• A_external = the outside area of the cartridge case head

This method is fine for getting a good estimate regarding bolt thrust and assumes an overly large area that the gas pressure acts against yielding pessimistic estimations, generating a safety margin in the process for worse case scenarios which can result in increased maximum (peak) chamber pressure of the firearms cartridge, like a round that is chambered in an already very warm chamber that can result in cooking off (i.e. a thermally induced unintended firing).

Bolt thrust estimations for various pistol/revolver cartridges

Chambering	P1 diameter (mm)	Aexternal (cm2)	Pmax (bar)	Fbolt (kgf)	Fbolt
.22 Long Rifle	5.74	0.2587	1,650	435	Template:Convert
9x19 mm Parabellum	9.93	0.7744	2,350	1,820	Template:Convert
.357 SIG	10.77	0.9110	3,050	2,779	Template:Convert
.380 ACP	9.70	0.7390	1,500	1,130	Template:Convert
.40 S&W	10.77	0.9110	2,250	2,050	Template:Convert
10 mm Auto	10.81	0.9178	2,300	2,111	Template:Convert
.45 ACP	12.09	1.1671	1,300	1,517	Template:Convert
.454 Casull	12.13	1.1556	3,900	4,507	Template:Convert
.500 S&W Magnum	13.46	1.4229	4,270	6,076	Template:Convert

The P1 (cartridge case base) diameters and P_max used in the calculations were taken from the appropriate C.I.P. data sheets.

Bolt thrust estimations for various rifle cartridges

Chambering	P1 diameter (mm)	Aexternal (cm2)	Pmax (bar)	Fbolt (kgf)	Fbolt
5.45x39mm	10.00	0.7854	3,800	2,985	Template:Convert
.223 Remington	9.58	0.7208	4,300	3,099	Template:Convert
7.62x39mm	11.35	1.0118	3,550	3,592	Template:Convert
.308 Winchester	11.96	1.1234	4,150	4,662	Template:Convert
.300 Winchester Magnum	13.03	1.3335	4,300	5,734	Template:Convert
.300 WSM	14.12	1.5659	4,450	6,968	Template:Convert
.300 Remington Ultra Magnum	13.97	1.5328	4,480	6,876	Template:Convert
.338 Lapua Magnum	14.91	1.7460	4,200	7,333	Template:Convert
.300 Lapua Magnum	14.91	1.7460	4,700	8,339	Template:Convert
.50 BMG	20.42	3.2749	3,700	12,117	Template:Convert
14.5x114mm	26.95	5.7044	3,600	20,536	Template:Convert

The P1 (cartridge case base) diameters and P_max used in the calculations were taken from the appropriate C.I.P. data sheets.

References

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External links

• Blaser R93 Unfälle - zur Verschlußbelastung Template:De icon
• Zylinderverschluß - Verschlußkräfte Template:De icon