Game Development Reference
In-Depth Information
the impact angle of the projectile, the thickness of the target, and the material properties of the
target.
Creating a detailed model of projectile penetration into a target would be very complicated
and not appropriate for game programming applications. For some situations, such as a shell
hitting a steel plate, there are fairly simply mathematical formulas that can estimate whether a
projectile will penetrate a target. In other situations, there may be experimental data that you
can apply.
Let's take a look at a few specific ballistic impact situations in more detail, starting with a
projectile impacting steel armor.
Steel Armor
Whether it's ships, tanks, or knights in shining armor, iron or steel has been a favorite armor
material for thousands of years. For just as many years, people have developed weapons to
penetrate iron or steel armor. When developing a game simulation in which the combatants
are wearing armor, the simulation must determine whether a projectile that strikes the armor
will penetrate the armor.
In the 1930s at the U.S. Naval Proving Ground, Dr. L. Thompson developed a relation
known as the Thompson “F-Formula” all-purpose armor penetration formula
1
that predicted
the armor thickness required to prevent a projectile from penetrating a steel plate. The equa-
tion was presented as a ratio between the plate thickness and the diameter of the projectile.
2
t
mv
2
=
0.0623
cos
θ
(12.3)
32
d
d F
The armor thickness,
t
, and the projectile diameter,
d
, are in units of
m
. The mass of the
projectile,
m
, is in
kg
, and the angle of impact,
q
, is in degrees. The angle of impact is zero for a
head-on impact in which the projectile strike is perpendicular to the steel plate.
The coefficient
F
is a measure of the penetration resistance of the armor. Harder, more
difficult to penetrate armor will have a higher
F
value. Based on tests conducted at the U.S.
Naval Proving Ground, an equation was developed to compute the “standard” value of
F
based
on impacts between chromium-nickel-steel armor and standard navy armor piercing shells.
⎛
⎟
t
(
)
⎜
2
F
=
1.8288
−
0.45
θ
+
2000
+
12192
⎟
(12.4)
⎜
⎟
⎝
d
⎠
The value for the
F
coefficient given by Equation (12.4) is based on a “standard” projectile
striking “standard” steel armor. One way to model a different type of steel armor that was more
or less resistant to penetration than “standard” steel would be to multiply the results from
standard
F
equation by a scale factor.
The original equation was expressed in terms of the ratio of the armor thickness to the
projectile diameter, but it is also possible to rearrange the Thompson formula so that it is in
terms of the minimum projectile kinetic energy,
E
k
, necessary to penetrate the armor.
22
1
td F
2
E
==
v
8.025
(12.5)
k
2
cos
2
θ
