My friend and I are working on a realistic FPS sniper simulator and we wanted to be able to realistically model things like bullet drop, flight time, and impact energy. I've managed to find the drag coefficients for different rounds and I know the exit velocity, so now I want to use that to model the bullet's trajectory. Here is a sample using a .22 bullet:
[tex]C_d = 0.169\\
v_i = 330~m/s\\
m = 0.00259~kg\\
A = 2.45e\!- 5~m^2\\
\rho_{air} = 1.204~kg/m^3\\[/tex]
[tex]F = m\cdot a\\
F_d = \frac{1}{2} \rho v^2 C_d A\\
v_f = v_i + a\cdot t
[/tex]
I can set this up to be solved in discrete time-steps, but I can't figure out how to get a continuous solution since drag is dependent on the velocity and the velocity depends on the drag. I found a few solutions for determining terminal velocity for an object in free-fall, but I can't figure out how to apply that here; it's been a long time since Diff. Eq. Any thoughts?
[tex]C_d = 0.169\\
v_i = 330~m/s\\
m = 0.00259~kg\\
A = 2.45e\!- 5~m^2\\
\rho_{air} = 1.204~kg/m^3\\[/tex]
[tex]F = m\cdot a\\
F_d = \frac{1}{2} \rho v^2 C_d A\\
v_f = v_i + a\cdot t
[/tex]
I can set this up to be solved in discrete time-steps, but I can't figure out how to get a continuous solution since drag is dependent on the velocity and the velocity depends on the drag. I found a few solutions for determining terminal velocity for an object in free-fall, but I can't figure out how to apply that here; it's been a long time since Diff. Eq. Any thoughts?