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 (by its shape) to overcome resistance along that axis. For illustration, a nail can penetrate a target medium with its pointy end first with less force than a coin of the same mass lying flat on the target medium.

Sectional density is used in gun ballistics. It is defined either as a projectile's mass divided by its cross sectional area, or as a projectile's mass in pounds divided by the square of its diameter in inches.

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.

Formula

General

In a physics context sectional density is defined as:

$SD = \frac{M}{A}$^[2]

• SD is the sectional density
• M is the mass of the projectile
• A is the cross-sectional area

Ballistics

In a ballistics context sectional density of circular cross-sections is most commonly defined as:

$SD = \frac{ M_\mathrm{lb} }{ {d_\mathrm{in}}^2} = \frac{ M_\mathrm{gr} }{ 7000 \, {d_\mathrm{in}}^2 }$^[3][4][5]

• SD is the sectional density
• M_lb is the mass of the projectile in pounds
• M_gr is the mass of the projectile in grains
• d_in is the projectile diameter in inches

The sectional density defined this way is usually presented without units.

Historical background

For historical reasons, within the field of ballistics it is often assumed that the unit of mass is the pound, and the unit of length is the inch. For example: ".357 magnum" (not ".357 inch magnum"). By fixing the units, quantities can be treated as dimensionless.

This is the legacy of Francis Bashforth of England who was the first to propose using standard projectiles (circa 1870). Bashforth's proposed standard projectiles all have a weight of one pound and a diameter of one inch, which gives them a sectional density of 1 (lb/in²). For any standard projectile, the sectional density, BC, and coefficient of form are 1.

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 (form factor in commercial small arms jargon^[6]); it yields the projectile's ballistic coefficient.^[7]

Sectional density has the same (implied) 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 (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.^[8][9][10]

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. Wound Ballistics: Basics and Applications
3. The Sectional Density of Rifle Bullets By Chuck Hawks
4. Sectional Density and Ballistic Coefficients
5. Sectional Density for Beginners By Bob Beers
6. Hornady Handbook of Cartridge Reloading:Rifle,Pistol Vol. II (1973) Hornady Manufacturing Company, Fourth Printing July 1978, p505
7. Bryan Litz. Applied Ballistics for Long Range Shooting.
8. Shooting Holes in Wounding Theories: The Mechanics of Terminal Ballistics
9. MacPherson D: Bullet Penetration—Modeling the Dynamics and the Incapacitation Resulting From Wound Trauma. Ballistics Publications, El Segundo, CA, 1994.
10. Sectional Density - A Practical Joke? By Gerard Schultz

External links

• Sectional Density - A Practical Joke? By Gerard Schultz