08-04-2011, 02:47 AM
One of the fun we have with our siege weapons is doing the math of the physics behind them.
So after a lot of internal debate if we should consider drag or not in our range equations, I settled by considering using a discrete system and a simple excel sheet for computation (as opposed to solving the diferential equations).
So we came up with a nice simulator that with a given angle will bring up range and impact energy.
For our computations we assumed our exit speed of 120m/s (our theoretical exit speed was of 132m/s but measured with a high speed camera we came up with 120m/s) a Drag Coeficient of 0.35, our section Area is 0.177x 10^-3 m^2, projectile mass is 0.175 kg and we assumed air density at 1 atm 25ºC (1.18kg/m^3).
So at 120m we hit with 1150 J.
For comparison a .357 magnum hits at 60m with 782 J (.008kg at an exit speed of 442 m/s - no drag).
Our bolts will decrease their impact energy to 755J at 293 m. We tap hard...
Now you might be asking why do we bother, our why should you care. First we find it fun, much like shooting them, predicting and analysing the forces involved in a siege weapon is fun.
Second you might find it interesting as well. I'll update ou page this weekend with all the computations and variables as well as an expanded page with the final physics (ballistics), and I'm considering puting a range simulator for fun as well.
So after a lot of internal debate if we should consider drag or not in our range equations, I settled by considering using a discrete system and a simple excel sheet for computation (as opposed to solving the diferential equations).
So we came up with a nice simulator that with a given angle will bring up range and impact energy.
For our computations we assumed our exit speed of 120m/s (our theoretical exit speed was of 132m/s but measured with a high speed camera we came up with 120m/s) a Drag Coeficient of 0.35, our section Area is 0.177x 10^-3 m^2, projectile mass is 0.175 kg and we assumed air density at 1 atm 25ºC (1.18kg/m^3).
So at 120m we hit with 1150 J.
For comparison a .357 magnum hits at 60m with 782 J (.008kg at an exit speed of 442 m/s - no drag).
Our bolts will decrease their impact energy to 755J at 293 m. We tap hard...
Now you might be asking why do we bother, our why should you care. First we find it fun, much like shooting them, predicting and analysing the forces involved in a siege weapon is fun.
Second you might find it interesting as well. I'll update ou page this weekend with all the computations and variables as well as an expanded page with the final physics (ballistics), and I'm considering puting a range simulator for fun as well.
