Box–Cox distribution: Difference between revisions

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'''Sectional density''' is the ratio of an object's mass to its cross-sectional area. It conveys how well an object's mass is distributed (by its shape) to overcome resistance. For illustration, a needle can penetrate a target medium with less force than a coin of the same mass.
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During [[World War II]] [[bunker buster|bunker-busting]] [[Röchling shell]]s were developed by German engineer [[August Cönders]], based on the theory of increasing sectional density to improve penetration. Röchling shells were tested in 1942 and 1943 against the Belgian [[Fort d'Aubin-Neufchâteau]]<ref>[http://derelicta.pagesperso-orange.fr/aubin3.htm Les étranges obus du fort de Neufchâteau {{fr icon}}]</ref> and saw very limited use during World War II.
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Sectional density is often used in [[Ballistics#Gun_ballistics|gun ballistics]] where sectional density is the ratio of a [[projectile]] [[weight]], to its [[diameter]].
 
==Formula==
===General===
Sectional density is stated as:
 
:<math>SD_{Physics} = \frac{M}{A}</math><ref>[http://www.jbmballistics.com/ballistics/topics/secdens.shtml Sectional Density and Ballistic Coefficients]</ref>
* SD = Sectional Density
* '''[[Mass|M]]''' = weight of the object, [[kg]], [[Gram|g]] or [[Pound (mass)|lb]], [[Grain (unit)|gr]]
* A = cross-sectional [[Area of a disk|area]], [[Metre|m<sup>2</sup>]] or [[Inch|in<sup>2</sup>]]
 
===Ballistics===
or for projectiles with a [[Circle|circular]] cross-sectional area like [[bullet]]s or [[Shell (projectile)|shell]]s:
 
:<math>SD_{Ballistics} = \frac{M}{d^2} \approx {p}</math><ref>[http://www.jbmballistics.com/ballistics/topics/secdens.shtml Sectional Density and Ballistic Coefficients]</ref>
* sd is the bullets or shells sectional density
* '''[[Mass|M]]''' is weight of the bullet, [[kg]], [[Gram|g]] or [[Pound (mass)|lb]], [[Grain (unit)|gr]]
* d<sup>2</sup> is the bullet or shell diameter squared, [[Metre|m<sup>2</sup>]] or [[Inch|in<sup>2</sup>]]
* p is [[pressure]]
Units of [[pressure]] are, kg/m<sup>2</sup> or lb/in<sup>2</sup>.<br>
In Europe the derivative unit g/cm<sup>2</sup> is also used in literature regarding [[small arms]] projectiles to get a number in front of the decimal separator.
 
==Use in ballistics==
The sectional density of a projectile can be employed in two area of [[ballistics]]. Within [[external ballistics]], when the sectional density of a projectile is divided by its [[form factor]]{{dn|date=November 2012}} it yields the projectile's [[ballistic coefficient]].<ref>Bryan Litz. Applied Ballistics for Long Range Shooting.</ref>
 
Within [[terminal ballistics]], 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.<ref>[http://www.rathcoombe.net/sci-tech/ballistics/wounding.html Shooting Holes in Wounding Theories: The Mechanics of Terminal Ballistics]</ref><ref>MacPherson D: Bullet Penetration—Modeling the Dynamics and the Incapacitation Resulting From Wound Trauma. Ballistics Publications, El Segundo, CA, 1994.</ref><ref>[http://www.gsgroup.co.za/articlesd.html Sectional Density - A Practical Joke? By Gerard Schultz]</ref>
 
Only if all other factors are equal, the projectile with the greatest amount of sectional density will penetrate the deepest.
 
==References==
{{Reflist}}
 
==External links==
* [http://www.chuckhawks.com/sd.htm The Sectional Density of Rifle Bullets By Chuck Hawks]
* [http://www.chuckhawks.com/sd_beginners.htm Sectional Density for Beginners By  Bob Beers]
* [http://www.gsgroup.co.za/articlesd.html Sectional Density - A Practical Joke? By Gerard Schultz]
 
[[Category:Projectiles]]
[[Category:Aerodynamics]]
[[Category:Ballistics]]

Latest revision as of 00:31, 9 September 2014

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