# 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