Sectional density (often abbreviated SD) is the
ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
of an object's
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
to its
cross section
Cross section may refer to:
* Cross section (geometry)
** Cross-sectional views in architecture & engineering 3D
*Cross section (geology)
* Cross section (electronics)
* Radar cross section, measure of detectability
* Cross section (physics)
**Abs ...
al
area
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape
A shape or figure is a graphics, graphical representation of an obje ...
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,
gram
The gram (originally gramme; SI unit symbol g) is a Physical unit, unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram.
Originally defined as of 1795 as "the absolute weight of a volume of pure wate ...
s,
pounds or
grain
A grain is a small, hard, dry fruit (caryopsis) – with or without an attached hull layer – harvested for human or animal consumption. A grain crop is a grain-producing plant. The two main types of commercial grain crops are cereals and legum ...
s) to its
transverse section
The transverse plane (also known as the horizontal plane, axial plane and transaxial plane) is an anatomical plane that divides the body into superior and inferior sections. It is perpendicular to the coronal and sagittal planes.
List of cli ...
(often in either
square centimeter
The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square w ...
s,
square millimeters or
square inch
A square inch (plural: square inches) is a unit of area, equal to the area of a square with sides of one inch. The following symbols are used to denote square inches:
*square in
*sq inches, sq inch, sq in
*inches/-2, inch/-2, in/-2
*inches^2, inc ...
es), 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
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
,
bunker-busting Röchling shell
Röchling shells were bunker-busting artillery shells, developed by German engineer August Cönders during World War II, based on the theory of increasing the sectional density to improve penetration.
Description
The fin-stabilised shells mad ...
s were developed by German engineer
August Cönders
August Cönders was a German engineer working for Röchling'sche Eisen und Stahlwerke GmbH during World War II after having worked in the UK and in Putaux, France, before the war.
He designed the Röchling shell that was tested in 1942 and 1943 a ...
, 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
The Fort of Aubin-Neufchâteau (french: Fort d'Aubin-Neufchâteau) is a Belgian fortification located near Neufchâteau. The fort was built in the 1930s as part of the fortified position of Liège, augmenting the twelve original forts built to de ...
and saw very limited use during World War II.
Formula
In a general physics context, sectional density is defined as:
:
* ''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:
:
where:
* ''SD''
kg/m2 is the sectional density in kilograms per
square meter
The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter ( American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square ...
s
* ''m''
kg is the weight of the object ''in
kilograms''
* ''A''
m2 is the cross sectional area of the object ''in meters''
Units conversion table
(Values in bold face are exact.)
* 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 (mass) pounds per square inch is approximately:
*: 1 lb/in2 = /(0.0254 m × 0.0254 m) ≈
Use in ballistics
The sectional density of a projectile can be employed in two areas of ballistics. Within external ballistics
External ballistics or exterior ballistics is the part of ballistics that deals with the behavior of a projectile in flight. The projectile may be powered or un-powered, guided or unguided, spin or fin stabilized, flying through an atmosphere o ...
, when the sectional density of a projectile is divided by its coefficient of form (form factor in commercial small arms jargon); it yields the projectile's ballistic coefficient
In ballistics, the ballistic coefficient (BC, ''C'') of a body is a measure of its ability to overcome air resistance in flight. It is inversely proportional to the negative acceleration: a high number indicates a low negative acceleration—the ...
. Sectional density has the same (implied) units as the ballistic coefficient
In ballistics, the ballistic coefficient (BC, ''C'') of a body is a measure of its ability to overcome air resistance in flight. It is inversely proportional to the negative acceleration: a high number indicates a low negative acceleration—the ...
.
Within terminal ballistics
Terminal ballistics (also known as wound ballistics) is a sub-field of ballistics concerned with the behavior and effects of a projectile when it hits and transfers its energy to a target.
Bullet design (as well as the velocity of impact) larg ...
, 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.
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 (g/mm2), the formula then becomes:
:
Where:
* ''SD''g/mm2 is the sectional density in grams per square millimeters
* ''m''g is the weight of the projectile ''in grams''
* ''d''mm is the diameter of the projectile ''in millimeters''
For example, a small arms bullet weighing and having a diameter of has a sectional density of:
: 10.4 g/(7.2 mm) = 0.200 g/mm2
Kilograms per square centimeter
Using kilograms per square centimeter (kg/cm2), the formula then becomes:
:
Where:
* ''SD''kg/cm2 is the sectional density in kilograms per square centimeter
* ''m''g is the weight of the projectile ''in grams''
* ''d''cm is the diameter of the projectile ''in centimeters''
For example, an M107 projectile
The M107 155 mm projectile was the standard 155 mm high explosive (HE) projectile for howitzers of the US Army and US Marine Corps. A bursting round with fragmentation and blast effects, the M107 is being superseded in the US military by th ...
weighing 43.2 kg and having a body diameter of has a sectional density of:
: 43.2 kg/(15.471 mm) = 0.180 kg/cm2
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 (mass) pounds per square inch (lbm/in2) The formula then becomes:
: Sectional Density for Beginners By Bob Beers
/ref>
where:
* ''SD'' is the sectional density in (mass) pounds per square inch
* the weight of the projectile is:
** ''W''lb in pounds
** ''W''gr in grains
A grain is a small, hard, dry fruit (caryopsis) – with or without an attached hull layer – harvested for human or animal consumption. A grain crop is a grain-producing plant. The two main types of commercial grain crops are cereals and legumes ...
* ''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/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 in weight and a diameter of , has a sectional density (''SD'') of:
: 160 g/ 000 × (0.284 in)= 0.283 lb/in2
As another example, the M107 projectile mentioned above weighing and having a body diameter of has a sectional density of:
: 95.2 lb/( in) = 2.567 lbm/in2
See also
* Ballistic coefficient
In ballistics, the ballistic coefficient (BC, ''C'') of a body is a measure of its ability to overcome air resistance in flight. It is inversely proportional to the negative acceleration: a high number indicates a low negative acceleration—the ...
References
{{Reflist
External links
Sectional Density - A Practical Joke? By Gerard Schultz
Projectiles
Aerodynamics
Ballistics