Game Development Reference
In-Depth Information
•
The density of the air in which the bullet is fired
•
The direction and velocity of the wind
There are many types of bullets in the world today, and they vary in terms of mass, diameter,
and muzzle velocity. Table 5-6 lists specifications for some representative types of bullets. The
abbreviation FMJ stands for Full Metal Jacket and indicates a bullet with a lead core covered
with a copper-zinc alloy jacket. The last three bullets in the table are military bullets used by
NATO countries.
Table 5-6.
Characteristics of Some Representative Bullets
Bullet
Muzzle Velocity (
m/s
)
Mass (
gm
)
Diameter (
mm
)
.22 Long rifle round nose
330
2.6
5.6
.32 ACP FMJ round nose
262
4.7
7.84
.357 Magnum
506
7.3
9
.38 ACP FMJ round nose
322
6.2
9.7
9
mm
FMJ
341-373
8.0
9
9
mm
FMJ high velocity
436
8.2
9
.44 Magnum
436
15.6
11.2
M74 (5.45
mm
)
917
3.44
5.64
M80 (7.62
mm
FMJ)
877
9.5
7.82
M2 .30 armor piercing
869
10.8
7.7
The drag coefficient for bullets varies with Reynolds number and therefore depends on the
velocity and length of the bullet. For the M80 bullet, the drag coefficient at the muzzle velocity
of 877
m/s
is about 0.3. As the velocity decreases, the drag coefficient increases until the speed
of the velocity of the bullet reaches the speed of sound (about 340
m/s
) at which point the drag
coefficient is about 0.45. At subsonic velocities, the coefficient of drag for the M80 bullet drops
below 0.2. If you want to use a constant coefficient of drag for the bullets used in your game
programming, a value of 0.3 is a fairly representative value.
Cannonballs
Modeling a cannonball in flight is fairly straightforward since you can assume that a cannon-
ball is a solid sphere. Depending on the Reynolds number, the drag coefficient can be assumed
to be 0.4 (for laminar flow) or 0.2 (for turbulent flow). A cannonball in flight will be subject to
the forces of gravity, wind, and aerodynamic drag. Depending on the spin given to the cannon-
ball, Magnus force effects may also have to be considered.
