Sectional density

Sectional density (often abbreviated SD) is the ratio of an object's mass to its cross sectional area with respect to a given axis. It conveys how well an object's mass is distributed (by its shape) to overcome resistance along that axis. Sectional density is used in gun ballistics. In this context, it is the ratio of a projectile's weight (often in either kilograms, grams, pounds or grains) to its transverse section (often in either square centimeters, square millimeters or square inches), with respect to the axis of motion. It conveys how well an object's mass is distributed (by its shape) to overcome resistance along that axis. For illustration, a nail can penetrate a target medium with its pointed end first with less force than a coin of the same mass lying flat on the target medium. During World War II, bunker-busting Röchling shells were developed by German engineer August Coenders, 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 and saw very limited use during World War II.

Sectional density (often abbreviated SD) is the ratio of an object's mass to its cross sectional area with respect to a given axis. It conveys how well an object's mass is distributed (by its shape) to overcome resistance along that axis. Sectional density is used in gun ballistics. In this context, it is the ratio of a projectile's weight (often in either kilograms, grams, pounds or grains) to its transverse section (often in either square centimeters, square millimeters or square inches), with respect to the axis of motion. It conveys how well an object's mass is distributed (by its shape) to overcome resistance along that axis. For illustration, a nail can penetrate a target medium with its pointed end first with less force than a coin of the same mass lying flat on the target medium. During World War II, bunker-busting Röchling shells were developed by German engineer August Coenders, 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 and saw very limited use during World War II. SD = \frac{M}{A} SD is the sectional density M is the mass of the projectile A is the cross-sectional area The SI derived unit for sectional density is kilograms per square meter (kg/m 2 ). The general formula with units then becomes: SD_{\text{kg}/\text{m}^2} = \frac{ m_\text{kg} }{ {A_{\text{m}^2}} } where: SD kg/m 2 is the sectional density in kilograms per square meters m kg is the weight of the object in kilograms A m 2 is the cross sectional area of the object in meters 1 lb /in 2 = /(0.0254 m × 0.0254 m) ≈ SD_{\text{g}/\text{mm}^2} = \frac{ 4 m_\text{g} }{ { \pi \cdot d _\text{mm}}^2 } Where: SD g/mm 2 is the sectional density in grams per square millimeters m g is the mass of the projectile in grams d mm is the diameter of the projectile in millimeters For example, a small arms bullet with a mass of and having a diameter of has a sectional density of: 4 · 10.4 / (π·6.7 2 ) = 0.295 g/mm 2 SD_{\text{kg}/\text{cm}^2} = \frac{ 4 m_\text{kg} }{ {\pi d_{\text{cm}}}^2 } Where: SD kg/cm 2 is the sectional density in kilograms per square centimeter m g is the mass of the projectile in grams d cm is the diameter of the projectile in centimeters For example, an M107 projectile with a mass of 43.2 kg and having a body diameter of has a sectional density of: 4 · 43.2 / (π·154.71 2 ) = 0.230 kg/cm 2 SD_{\text{lb}/\text{in}^2} = \frac{ 4 m_\text{lb} }{ {\pi \cdot d_\text{in}}^2} = \frac{ 4 m_\text{gr} }{\pi \cdot 7000 \, {d_\text{in}}^2 } SD_\mathrm{lbs/sq in} = \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 } where: SD is the sectional density in (mass) pounds per square inch the mass of the projectile is: m lb in pounds m gr in grains d in is the diameter of the projectile in inches The sectional density defined this way is usually presented without units. In Europe the derivative unit g/cm 2 is also used in literature regarding small arms projectiles to get a number in front of the decimal separator. As an example, a bullet with a mass of and a diameter of , has a sectional density (SD) of: 4·(160 gr/7000) / (π·0.264 in 2 ) = 0.418 lb m /in 2 As another example, the M107 projectile mentioned above with a mass of and having a body diameter of has a sectional density of: 4 · (95.24) / (π·6.0909 2 ) = 3.268 lb m /in 2 ==References==

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