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Bolt thrust
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<h2 id="calculating-bolt-thrust">Calculating bolt thrust</h2> <p>With a basic calculation the bolt thrust produced by a particular firearms cartridge can be calculated fairly accurately. </p> <h3>Formula</h3> F → b o l t = P m a x ⋅ A i n t e r n a l . {\displaystyle {\vec {F}}_{bolt}=P_{max}\cdot A_{internal}.} <a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> <p>where: </p> <ul><li><i>Fbolt</i> = the amount of bolt thrust</li> <li><i>Pmax</i> = the maximum (peak) chamber <a href="/facts/Pressure/eyc37GRG">pressure</a> of the firearms cartridge</li> <li><i>Ainternal</i> = the inside area (of the cartridge case head) that the <a href="/facts/Propellant/K88ymXRy">propellant</a> <a href="/facts/Deflagration/wIR4pGtC">deflagration</a> gas pressure acts against</li></ul> <p>Cartridge case heads and chambers are generally <a href="/facts/Circle/9fy5ggKn">circular</a>. The <a href="/facts/Area_of_a_disk/sRUeg8Cl">area enclosed by a circle</a> is: </p> A r e a = π r 2 ≈ 3 . 1416 ⋅ r 2 . {\displaystyle Area=\pi r^{2}\approx 3{.}1416\cdot r^{2}.} <p>where: </p> <ul><li><i>π</i> ≈ 3.1416</li> <li><i>r</i> = the radius of the circle</li></ul> <p>Equivalently, denoting the diameter of the circle by <i>d</i>. </p> A r e a = π d 2 4 ≈ 0 . 7854 ⋅ d 2 . {\displaystyle Area={\frac {\pi d^{2}}{4}}\approx 0{.}7854\cdot d^{2}.} <p>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. </p> <h3>Friction effects</h3> <p>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.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> </p><p>By oiling proof rounds during <a href="/facts/NATO_EPVAT_testing/R1R2MTEo">NATO EPVAT testing</a> procedures, NATO test centers intentionally lower case friction to promote high bolt thrust levels. </p> <h2 id="practical-method-to-estimate-bolt-thrust">Practical method to estimate bolt thrust</h2> <p>Instead of using the internal case head diameter, the external case head base diameter can also be measured with a <a href="/facts/Caliper/4c1LKQwu">caliper</a> or <a href="/facts/Micrometer_(device)/zNL4xpAQ">micrometer</a> or taken from the appropriate <a href="/facts/C.I.P./MulVWLJS">C.I.P.</a> or <a href="/facts/SAAMI/Bhuaf6Jz">SAAMI</a> cartridge or chamber data tables and used for bolt thrust estimation calculations. </p><p>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. </p> F b o l t → = P m a x ⋅ A e x t e r n a l . {\displaystyle {\vec {F_{bolt}}}=P_{max}\cdot A_{external}.} <p>where: </p> <ul><li><i>Fbolt</i> = the amount of bolt thrust</li> <li><i>Pmax</i> = the maximum (peak) chamber pressure of the firearms cartridge</li> <li><i>Aexternal</i> = the outside area of the cartridge case head</li></ul> <p>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 <a href="/facts/Chamber_(firearms)/X1Ekw5aK">chamber</a> that can result in <a href="/facts/Cooking_off/V1q7uSK3">cooking off</a> (i.e. a thermally induced unintended firing). </p> <h3>Bolt thrust estimations for various pistol/revolver cartridges</h3> <table><tbody><tr><th>Chambering</th><th>P1 diameter (mm)</th><th>Aexternal (cm2)</th><th>Pmax (<a href="/facts/Bar_(unit)/wwFWTTkT">bar</a>)</th><th>Fbolt (<a href="/facts/Kilogram-force/RtMF3WhP">kgf</a>)</th><th>Fbolt</th></tr><tr><td><a href="/facts/.22_Long_Rifle/lYgYNrNV">.22 Long Rifle</a></td><td>5.74</td><td>0.2587</td><td>1,650</td><td>427</td><td>4,268 N (959 lbf)</td></tr><tr><td><a href="/facts/FN_5.7%25C3%259728_mm/oK3UqfCw">FN 5.7×28 mm</a></td><td>7.95</td><td>0.4964</td><td>3,450</td><td>1,713</td><td>16,794 <a href="/facts/Newton_(unit)/Ral9XgNl">N</a> (3,775 <a href="/facts/Pound_(force)/w62gn6Y0">lbf</a>)</td></tr><tr><td><a href="/facts/9%25C3%259719_mm_Parabellum/m8sP9Hz9">9×19 mm Parabellum</a></td><td>9.93</td><td>0.7744</td><td>2,350</td><td>1,820</td><td>17,847 <a href="/facts/Newton_(unit)/Ral9XgNl">N</a> (4,012 <a href="/facts/Pound_(force)/w62gn6Y0">lbf</a>)</td></tr><tr><td><a href="/facts/HK_4.6%25C3%259730_mm/f0Y0fTPW">HK 4.6×30 mm</a></td><td>8.02</td><td>0.5051</td><td>4,000</td><td>2,021</td><td>19,816 <a href="/facts/Newton_(unit)/Ral9XgNl">N</a> (4,455 <a href="/facts/Pound_(force)/w62gn6Y0">lbf</a>)</td></tr><tr><td><a href="/facts/.357_Magnum/zSt5k3wJ">.357 Magnum</a></td><td>9.63</td><td>0.7284</td><td>3,000</td><td>2,185</td><td>21,428 N (4,817 lbf)</td></tr><tr><td><a href="/facts/.357_SIG/8lj7zXVT">.357 SIG</a></td><td>10.77</td><td>0.9110</td><td>3,050</td><td>2,779</td><td>27,248 N (6,126 lbf)</td></tr><tr><td><a href="/facts/.380_ACP/9Xd14XyY">.380 ACP</a></td><td>9.70</td><td>0.7390</td><td>1,500</td><td>1,130</td><td>11,085 N (2,492 lbf)</td></tr><tr><td><a href="/facts/.40_S%2526W/8vNVH7uB">.40 S&W</a></td><td>10.77</td><td>0.9110</td><td>2,250</td><td>2,050</td><td>20,101 N (4,519 lbf)</td></tr><tr><td><a href="/facts/10_mm_Auto/rBHW5WRJ">10 mm Auto</a></td><td>10.81</td><td>0.9178</td><td>2,300</td><td>2,111</td><td>20,701 N (4,654 lbf)</td></tr><tr><td><a href="/facts/.41_Remington_Magnum/XQvRvGqs">.41 Remington Magnum</a></td><td>11.05</td><td>0.9590</td><td>3,000</td><td>2,877</td><td>28,213 N (6,343 lbf)</td></tr><tr><td><a href="/facts/.44_Remington_Magnum/lnBmPcIl">.44 Remington Magnum</a></td><td>11.61</td><td>1.0587</td><td>2,800</td><td>2,964</td><td>29,069 N (6,535 lbf)</td></tr><tr><td><a href="/facts/.45_ACP/hEdjsBlQ">.45 ACP</a></td><td>12.09</td><td>1.1671</td><td>1,300</td><td>1,517</td><td>14,879 N (3,345 lbf)</td></tr><tr><td><a href="/facts/.454_Casull/KW3NADeF">.454 Casull</a></td><td>12.13</td><td>1.1556</td><td>3,900</td><td>4,507</td><td>44,197 N (9,936 lbf)</td></tr><tr><td><a href="/facts/.500_S%2526W_Magnum/hnMmAcH5">.500 S&W Magnum</a></td><td>13.46</td><td>1.4229</td><td>4,270</td><td>6,076</td><td>59,584 N (13,395 lbf)</td></tr></tbody></table> <p>The P1 (cartridge case base) diameters and Pmax used in the calculations were taken from the appropriate <a href="/facts/C.I.P./MulVWLJS">C.I.P.</a> data sheets. </p> <h3>Bolt thrust estimations for various rifle cartridges</h3> <table><tbody><tr><th>Chambering</th><th>P1 diameter (mm)</th><th>Aexternal (cm2)</th><th>Pmax (<a href="/facts/Bar_(unit)/wwFWTTkT">bar</a>)</th><th>Fbolt (<a href="/facts/Kilogram-force/RtMF3WhP">kgf</a>)</th><th>Fbolt</th></tr><tr><td><a href="/facts/5.45%25C3%259739mm/bapdLmuB">5.45×39mm</a></td><td>10.00</td><td>0.7854</td><td>3,800</td><td>2,985</td><td>29,268 <a href="/facts/Newton_(unit)/Ral9XgNl">N</a> (6,580 <a href="/facts/Pound_(force)/w62gn6Y0">lbf</a>)</td></tr><tr><td><a href="/facts/.223_Remington/bsTRP3sN">.223 Remington</a></td><td>9.58</td><td>0.7208</td><td>4,300</td><td>3,099</td><td>30,396 N (6,833 lbf)</td></tr><tr><td><a href="/facts/7.62%25C3%259739mm/UYD49hm5">7.62×39mm</a></td><td>11.35</td><td>1.0118</td><td>3,550</td><td>3,592</td><td>35,223 N (7,918 lbf)</td></tr><tr><td><a href="/facts/6mm_ARC/qVL2MTl8">6mm ARC</a></td><td>11.20</td><td>0.9852</td><td>3,800</td><td>3,744</td><td>36,714 N (8,254 lbf)</td></tr><tr><td><a href="/facts/.303_British/14TNrCEH">.303 British</a></td><td>11.68</td><td>1.0715</td><td>3,650</td><td>3,911</td><td>38,352 N (8,622 lbf)</td></tr><tr><td><a href="/facts/7.92%25C3%259757mm_Mauser/Bps6XPmC">7.92×57mm Mauser</a></td><td>11.97</td><td>1.1197</td><td>3,900</td><td>4,367</td><td>42,824 N (9,627 lbf)</td></tr><tr><td><a href="/facts/7.65%25C3%259753mm_Mauser/aug0uQe3">7.65×53mm Mauser</a> / <a href="/facts/7%25C3%259757mm/bQp4T9SD">7×57mm</a></td><td>12.01</td><td>1.1329</td><td>3,900</td><td>4,418</td><td>43,327 N (9,740 lbf)</td></tr><tr><td><a href="/facts/6.5%25C3%259755mm/jc5UBJvk">6.5×55mm</a></td><td>12.20</td><td>1.1690</td><td>3,800</td><td>4,442</td><td>43,563 N (9,793 lbf)</td></tr><tr><td><a href="/facts/.30-06_Springfield/66Vbr9rW">.30-06 Springfield</a> / <a href="/facts/.308_Winchester/kgruBvBd">.308 Winchester</a></td><td>11.96</td><td>1.1234</td><td>4,150</td><td>4,662</td><td>45,722 N (10,279 lbf)</td></tr><tr><td><a href="/facts/7.62%25C3%259754mmR/S26NjXPE">7.62×54mmR</a></td><td>12.37</td><td>1.2018</td><td>3,900</td><td>4,687</td><td>45,964 N (10,333 lbf)</td></tr><tr><td><a href="/facts/8mm_Lebel/AB3EKMTF">8mm Lebel</a></td><td>13.77</td><td>1.4892</td><td>3,200</td><td>4,765</td><td>46,734 N (10,506 lbf)</td></tr><tr><td><a href="/facts/7.5%25C3%259755mm_Swiss/cloVofGa">7.5×55mm Swiss GP 11</a></td><td>12.64</td><td>1.2548</td><td>3,800</td><td>4,768</td><td>46,761 N (10,512 lbf)</td></tr><tr><td><a href="/facts/.375_Holland_%2526_Holland_Magnum/av4Aq2wq">.375 Holland & Holland Magnum</a> / <a href="/facts/.300_Winchester_Magnum/zz9nHl2t">.300 Winchester Magnum</a></td><td>13.03</td><td>1.3335</td><td>4,300</td><td>5,734</td><td>56,230 N (12,640 lbf)</td></tr><tr><td><a href="/facts/6.5%25C3%259768mm/RC45HdXq">6.5×68mm</a> / <a href="/facts/8%25C3%259768mm_S/9EV9HS38">8×68mm S</a></td><td>13.30</td><td>1.3893</td><td>4,400</td><td>6,113</td><td>59,947 N (13,477 lbf)</td></tr><tr><td><a href="/facts/.375_Ruger/tpBcgFC6">.375 Ruger</a> / <a href="/facts/.416_Ruger/Cf28eKXE">.416 Ruger</a></td><td>13.52</td><td>1.4356</td><td>4,300</td><td>6,173</td><td>60,539 N (13,610 lbf)</td></tr><tr><td><a href="/facts/.277_FURY/kgEmzPfm">.277 FURY</a> (<a href="/facts/SAAMI/Bhuaf6Jz">SAAMI</a> specifications)</td><td>11.95</td><td>1.1216</td><td>5,516</td><td>6,187</td><td>60,670 N (13,640 lbf)</td></tr><tr><td><a href="/facts/.300_Remington_Ultra_Magnum/lr1of3Na">.300 Remington Ultra Magnum</a></td><td>13.97</td><td>1.5328</td><td>4,400</td><td>6,744</td><td>66,139 N (14,869 lbf)</td></tr><tr><td><a href="/facts/.300_Winchester_Short_Magnum/WIRfPUt2">.300 Winchester Short Magnum</a></td><td>14.12</td><td>1.5659</td><td>4,400</td><td>6,890</td><td>67,567 N (15,190 lbf)</td></tr><tr><td><a href="/facts/.338_Lapua_Magnum/b5BHH3s4">.338 Lapua Magnum</a></td><td>14.91</td><td>1.7460</td><td>4,200</td><td>7,333</td><td>71,914 N (16,167 lbf)</td></tr><tr><td><a href="/facts/.300_Norma_Magnum/mbFaDysM">.300 Norma Magnum</a> / <a href="/facts/.338_Norma_Magnum/KcbUAH7s">.338 Norma Magnum</a></td><td>14.87</td><td>1.7366</td><td>4,400</td><td>7,641</td><td>74,935 N (16,846 lbf)</td></tr><tr><td><a href="/facts/.300_Lapua_Magnum/CDDBxFMa">.300 Lapua Magnum</a> / <a href="/facts/7.62_UKM/XBy5N1yD">7.62 UKM</a></td><td>14.91</td><td>1.7460</td><td>4,400</td><td>7,807</td><td>76,556 N (17,210 lbf)</td></tr><tr><td><a href="/facts/.408_CheyTac/1LJNnRxW">.375 CheyTac / .408 CheyTac</a></td><td>16.18</td><td>2.0561</td><td>4,400</td><td>8,224</td><td>80,654 N (18,132 lbf)</td></tr><tr><td><a href="/facts/.50_BMG/oADnDkyC">.50 BMG</a></td><td>20.42</td><td>3.2749</td><td>3,700</td><td>12,117</td><td>118,829 N (26,714 lbf)</td></tr><tr><td><a href="/facts/14.5%25C3%2597114mm/8QE3J5Q2">14.5×114mm</a></td><td>26.95</td><td>5.7044</td><td>3,600</td><td>20,536</td><td>201,387 N (45,274 lbf)</td></tr></tbody></table> <p>The P1 (cartridge case base) diameters and Pmax used in the calculations were taken from the appropriate <a href="/facts/C.I.P./MulVWLJS">C.I.P.</a> data sheets. </p> <h2 id="external-links">External links</h2> <ul><li><a href="https://web.archive.org/web/20130505030534/http://lutz-moeller-jagd.de/Waffen/Blaser/R93/Blaser-R93.html">Blaser R93 Unfälle - zur Verschlußbelastung (in German)</a></li> <li><a href="https://web.archive.org/web/20130603114006/http://lutz-moeller-jagd.de/Waffen/Technik/Zylinderverschluss/Zylinderverschluesse.htm">Zylinderverschluß - Verschlußkräfte (in German)</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>A Look at Bolt Lug Strength By Dan Lilja Archived March 3, 2010, at the Wayback Machine <a href="http://www.riflebarrels.com/articles/custom_actions/bolt_lug_strength.htm" target="_blank">http://www.riflebarrels.com/articles/custom_actions/bolt_lug_strength.htm</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Stolle Panda Bolt Stress and Deflection Analysis <a href="http://www.varmintal.net/abolt.htm" target="_blank">http://www.varmintal.net/abolt.htm</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> </ol>