Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Sectional density
open-in-new
<h2 id="formula">Formula</h2> <p>In a general physics context, sectional density is defined as: </p> S D = M A {\displaystyle SD={\frac {M}{A}}} <a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> <ul><li><i>SD</i> is the sectional density</li> <li><i>M</i> is the mass of the projectile</li> <li><i>A</i> is the cross-sectional area</li></ul> <p>The <a href="/facts/SI_derived_unit/RLu52lWy">SI derived unit</a> for sectional density is kilograms per square meter (kg/m2). The general formula with units then becomes: </p> S D kg / m 2 = m kg A m 2 {\displaystyle SD_{{\text{kg}}/{\text{m}}^{2}}={\frac {m_{\text{kg}}}{A_{{\text{m}}^{2}}}}} <p>where: </p> <ul><li><i>SD</i>kg/m2 is the sectional density in kilograms per <a href="/facts/Square_meter/u5nT9y0W">square meters</a></li> <li><i>m</i>kg is the weight of the object <i>in <a href="/facts/Kilogram/lU2zbPk8">kilograms</a></i></li> <li><i>A</i>m2 is the cross sectional area of the object <i>in meters</i></li></ul> <h2 id="units-conversion-table">Units conversion table</h2> Conversions between units for sectional density<table><tbody><tr><th></th><th>kg/m2</th><th>kg/cm2</th><th>g/mm2</th><th>lbm/in2</th></tr><tr><th>1 kg/m2 =</th><td>1</td><td>0.0001</td><td>0.001</td><td>0.001422334</td></tr><tr><th>1 kg/cm2 =</th><td>10000</td><td>1</td><td>10</td><td>14.223343307</td></tr><tr><th>1 g/mm2 =</th><td>1000</td><td>0.1</td><td>1</td><td>1.4223343307</td></tr><tr><th>1 lbm/in2 =</th><td>703.069579639</td><td>0.070306957</td><td>0.703069579</td><td>1</td></tr></tbody></table><p> (Values in bold face are exact.) </p><ul><li>1 g/mm2 equals exactly 1000 kg/m2.</li> <li>1 kg/cm2 equals exactly 10000 kg/m2.</li> <li>With the pound and inch legally defined as 0.45359237 kg and 0.0254 m respectively, it follows that the (mass) pounds per square inch is approximately: 1 lbm/in2 = 0.45359237 kg/(0.0254 m × 0.0254 m) ≈ 703.06958 kg/m2</li></ul> <h2 id="use-in-ballistics">Use in ballistics</h2> <p>The sectional density of a projectile can be employed in two areas of <a href="/facts/Ballistics/3WHTox0u">ballistics</a>. Within <a href="/facts/External_ballistics/cF2PHJ4W">external ballistics</a>, when the sectional density of a projectile is divided by its coefficient of form (form factor in commercial small arms jargon<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>); it yields the projectile's <a href="/facts/Ballistic_coefficient/cbA1Hw5b">ballistic coefficient</a>.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> Sectional density has the same (implied) units as the <a href="/facts/Ballistic_coefficient/cbA1Hw5b">ballistic coefficient</a>. </p><p>Within <a href="/facts/Terminal_ballistics/kYCJWHAT">terminal ballistics</a>, the sectional density of a projectile is one of the determining factors for projectile penetration. The interaction between projectile (fragments) and target media is however a complex subject. A study regarding hunting bullets shows that besides sectional density several other parameters determine bullet penetration.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a><a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> </p><p>If all other factors are equal, the projectile with the greatest amount of sectional density will penetrate the deepest. </p> <h3>Metric units</h3> <p>When working with ballistics using SI units, it is common to use either <i>grams per square millimeter</i> or <i>kilograms per square centimeter</i>. Their relationship to the base unit <i>kilograms per square meter</i> is shown in the conversion table above. </p> <h4>Grams per square millimeter</h4> <p>Using grams per square millimeter (g/mm2), the formula then becomes: </p> S D g / mm 2 = 4 m g π ⋅ d mm 2 {\displaystyle SD_{{\text{g}}/{\text{mm}}^{2}}={\frac {4m_{\text{g}}}{{\pi \cdot d_{\text{mm}}}^{2}}}} <p>Where: </p> <ul><li><i>SD</i>g/mm2 is the sectional density in grams per square millimeters</li> <li><i>m</i>g is the mass of the projectile <i>in grams</i></li> <li><i>d</i>mm is the diameter of the projectile <i>in millimeters</i></li></ul> <p>For example, a small arms bullet with a mass of 10.4 grams (160 gr) and having a diameter of 6.70 mm (0.264 in) has a sectional density of: </p> 4 · 10.4 / (π·6.72) = 0.295 g/mm2 <h4>Kilograms per square centimeter</h4> <p>Using kilograms per square centimeter (kg/cm2), the formula then becomes: </p> S D kg / cm 2 = 4 m kg π d cm 2 {\displaystyle SD_{{\text{kg}}/{\text{cm}}^{2}}={\frac {4m_{\text{kg}}}{{\pi d_{\text{cm}}}^{2}}}} <p>Where: </p> <ul><li><i>SD</i>kg/cm2 is the sectional density in kilograms per square centimeter</li> <li><i>m</i>g is the mass of the projectile <i>in grams</i></li> <li><i>d</i>cm is the diameter of the projectile <i>in centimeters</i></li></ul> <p>For example, an <a href="/facts/M107_projectile/wvRbx79I">M107 projectile</a> with a mass of 43.2 kg and having a body diameter of 154.71 millimetres (15.471 cm) has a sectional density of: </p> 4 · 43.2 / (π·154.712) = 0.230 kg/cm2 <h3>English units</h3> <p>In older ballistics literature from English speaking countries, and still to this day, the most commonly used unit for sectional density of circular cross-sections is (mass) pounds per square inch (lbm/in2) The formula then becomes: </p> S D lb / in 2 = 4 m lb π ⋅ d in 2 = 4 m gr π ⋅ 7000 d in 2 {\displaystyle SD_{{\text{lb}}/{\text{in}}^{2}}={\frac {4m_{\text{lb}}}{{\pi \cdot d_{\text{in}}}^{2}}}={\frac {4m_{\text{gr}}}{\pi \cdot 7000\,{d_{\text{in}}}^{2}}}} <a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a><a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a><a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> S D l b s / s q i n = 4 ⋅ m l b π ⋅ d i n 2 = 4 ⋅ m g r π ⋅ 7000 d i n 2 {\displaystyle SD_{\mathrm {lbs/sqin} }={\frac {4\cdot m_{\mathrm {lb} }}{{\pi \cdot d_{\mathrm {in} }}^{2}}}={\frac {4\cdot m_{\mathrm {gr} }}{\pi \cdot 7000\,{d_{\mathrm {in} }}^{2}}}} <p>where: </p> <ul><li><i>SD</i> is the sectional density in (mass) <a href="/facts/Pounds_per_square_inch/RMdeTlB0">pounds per square inch</a></li> <li>the mass of the projectile is: <ul><li><i>m</i>lb in pounds</li> <li><i>m</i>gr in <a href="/facts/Grain_(unit)/kkDKk6na">grains</a></li></ul></li> <li><i>d</i>in is the diameter of the projectile in inches</li></ul> <p>The sectional density defined this way is usually presented without units. In Europe the derivative unit g/cm2 is also used in literature regarding <a href="/facts/Small_arms/GuHx4aGE">small arms</a> projectiles to get a number in front of the decimal separator. </p><p>As an example, a bullet with a mass of 160 grains (10.4 g) and a diameter of 0.264 in (6.7 mm), has a sectional density (<i>SD</i>) of: </p> 4·(160 gr/7000) / (π·0.264 in2) = 0.418 lbm/in2 <p>As another example, the M107 projectile mentioned above with a mass of 95.2 pounds (43.2 kg) and having a body diameter of 6.0909 inches (154.71 mm) has a sectional density of: </p> 4 · (95.24) / (π·6.09092) = 3.268 lbm/in2 <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Ballistic_coefficient/cbA1Hw5b">Ballistic coefficient</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Les étranges obus du fort de Neufchâteau (in French) <a href="http://derelicta.pagesperso-orange.fr/aubin3.htm" target="_blank">http://derelicta.pagesperso-orange.fr/aubin3.htm</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Wound Ballistics: Basics and Applications <a href="https://books.google.com/books?id=q4jzcfLhBcYC&dq=sectional+density+cross+sectional+area&pg=PA203" target="_blank">https://books.google.com/books?id=q4jzcfLhBcYC&dq=sectional+density+cross+sectional+area&pg=PA203</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Hornady Handbook of Cartridge Reloading: Rifle, Pistol Vol. II (1973) Hornady Manufacturing Company, Fourth Printing July 1978, p505 <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Bryan Litz. Applied Ballistics for Long Range Shooting. <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>"Shooting Holes in Wounding Theories: The Mechanics of Terminal Ballistics". Archived from the original on 2021-06-24. Retrieved 2009-07-25. <a href="https://web.archive.org/web/20210624031342/https://rathcoombe.net/sci-tech/ballistics/wounding.html" target="_blank">https://web.archive.org/web/20210624031342/https://rathcoombe.net/sci-tech/ballistics/wounding.html</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>MacPherson D: Bullet Penetration—Modeling the Dynamics and the Incapacitation Resulting From Wound Trauma. Ballistics Publications, El Segundo, CA, 1994. <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Schultz, Gerard. "Sectional Density - A Practical Joke?". Archived from the original on 2023-01-15. <a href="https://web.archive.org/web/20230115024756/http://www.gsgroup.co.za/articlesd.html" target="_blank">https://web.archive.org/web/20230115024756/http://www.gsgroup.co.za/articlesd.html</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>The Sectional Density of Rifle Bullets By Chuck Hawks <a href="http://www.chuckhawks.com/sd.htm" target="_blank">http://www.chuckhawks.com/sd.htm</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Sectional Density and Ballistic Coefficients <a href="http://www.jbmballistics.com/ballistics/topics/secdens.shtml" target="_blank">http://www.jbmballistics.com/ballistics/topics/secdens.shtml</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Sectional Density for Beginners By Bob Beers <a href="http://www.chuckhawks.com/sd_beginners.htm" target="_blank">http://www.chuckhawks.com/sd_beginners.htm</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> </ol>