Sectional density

Sectional density 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 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 to its transverse section, with respect to the axis of motion. It conveys how well an object's mass is distributed 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.

Formula

In a general physics context, sectional density is defined as:SD is the sectional densityM is the mass of the projectileA is the cross-sectional area
The SI derived unit for sectional density is kilograms per square meter. The general formula with units then becomes:
where:SD_kg/m² is the sectional density in kilograms per square metersm_kg is the weight of the object in kilogramsA_m² is the cross sectional area of the object ''in meters''

Units conversion table

1 g/mm² equals exactly kg/m².
1 kg/cm² equals exactly kg/m².
With the pound and inch legally defined as and 0.0254 m respectively, it follows that the pounds per square inch is approximately:
: 1 lb/in² = / ≈

Use in ballistics

The sectional density of a projectile can be employed in two areas of ballistics. Within external ballistics, when the sectional density of a projectile is divided by its coefficient of form ; it yields the projectile's ballistic coefficient. Sectional density has the same units as the ballistic coefficient.
Within terminal ballistics, the sectional density of a projectile is one of the determining factors for projectile penetration. The interaction between projectile and target media is however a complex subject. A study regarding hunting bullets shows that besides sectional density several other parameters determine bullet penetration.
If all other factors are equal, the projectile with the greatest amount of sectional density will penetrate the deepest.

Metric units

When working with ballistics using SI units, it is common to use either grams per square millimeter or kilograms per square centimeter. Their relationship to the base unit kilograms per square meter is shown in the conversion table above.

Grams per square millimeter

Using grams per square millimeter, the formula then becomes:
Where:SD_g/mm² is the sectional density in grams per square millimetersm_g is the mass of the projectile in gramsd_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:

Kilograms per square centimeter

Using kilograms per square centimeter, the formula then becomes:
Where:SD_kg/cm² is the sectional density in kilograms per square centimeterm_g is the mass of the projectile in gramsd_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:

English units

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 pounds per square inch The formula then becomes:
where:SD is the sectional density in pounds per square inch

the mass of the projectile is:
* m_lb in pounds
* m_gr in grainsd_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/cm² 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 of:
As another example, the M107 projectile mentioned above with a mass of and having a body diameter of has a sectional density of: