External Ballistics of Rifle Bullets
External Ballistics of Rifle Bullets
This Demonstration shows the trajectory of a rifle bullet determined as a function of bullet characteristics and settings of the telescopic sight of the rifle.
The equations describing the bullet trajectory are:
dx/dt=
V
x
dy/dt=
V
y
d/dt=-+
V
x
C
d
V
x
2
V
x
2
V
y
ddt=-+-g
V
y
C
d
V
y
2
V
x
2
V
y
with initial conditions
dx(0)/dt=(0)=cosθ
V
x
V
0
dy(0)/dt=(0)=sinθ
V
y
V
0
x(0)=0
y(0)=-h
Here
t
x
y
V
x
V
y
θ
C
d
g
h
These equations are solved using the built-in Mathematica function NDSolveValue. The result shows the bullet trajectory and bullet impact in a target at 100 yards for different settings of the telescopic sight. Published bullet velocities at the muzzle and at 100 yards are used to determine the overall drag coefficient . The solutions of this simple model agree closely with published ballistic tables obtained with advanced professional ballistic models [1].
C
d