# Sectional density

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.

During World War II bunker-busting Röchling shells 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[1] and saw very limited use during World War II.

Sectional density is often used in gun ballistics where sectional density is the ratio of a projectile weight, to its diameter.

## Formula

### General

Sectional density is stated as:

$SD_{Physics} = \frac{M}{A}$[2]
• SD = Sectional Density
• M = weight of the object, kg, g or lb, gr
• A = cross-sectional area, m2 or in2

### Ballistics

or for projectiles with a circular cross-sectional area like bullets or shells:

$SD_{Ballistics} = \frac{M}{d^2} \approx {p}$[3]
• sd is the bullets or shells sectional density
• M is weight of the bullet, kg, g or lb, gr
• d2 is the bullet or shell diameter squared, m2 or in2
• p is pressure

Units of pressure are, kg/m2 or lb/in2.
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.

## 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[disambiguation needed] it yields the projectile's ballistic coefficient.[4]

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.[5][6][7]

Only if all other factors are equal, the projectile with the greatest amount of sectional density will penetrate the deepest.

## References

1. ^ Les étranges obus du fort de Neufchâteau (French)
2. ^ Sectional Density and Ballistic Coefficients
3. ^ Sectional Density and Ballistic Coefficients
4. ^ Bryan Litz. Applied Ballistics for Long Range Shooting.
5. ^ Shooting Holes in Wounding Theories: The Mechanics of Terminal Ballistics
6. ^ MacPherson D: Bullet Penetration—Modeling the Dynamics and the Incapacitation Resulting From Wound Trauma. Ballistics Publications, El Segundo, CA, 1994.
7. ^ Sectional Density - A Practical Joke? By Gerard Schultz