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Posted: 10/27/2004 4:18:22 PM EST



If you will be satisfied with calculating the bullet's trajectory in a vacuum, get any college freshman level physics textbook. If you want the real dealreal bullets travelling through real air and are at home with ODE's and PDE's, let me know and I will see what I can dig up.



Initial variables:
A : Angle of elevation, in radians V : Velocity at release, in m/s M : Mass of projectile, in kg C : Coefficient of drag, pure number D : Diameter of head of projectile, in m F : Drag factor, in m^(1) T : Time increment, in s H : Height at release, in m G : Acceleration due to gravity, in m/s^2 F = 0.473595 * C * D^2 / M T = 0.004 : for most computations T = 0.001 : to be painfully accurate G = 9.80665 Loop variables: v : Velocity, in m/s x : Horizontal velocity, in m/s y : Vertical velocity, in m/s s : Range, in m h : Height, in m t : Flight time, in s Prior to the first iteration: v = V x = V * cos ( A ) y = V * sin ( A ) s = 0 h = H t = 0 Iterate generating new values for the loop variables: sA : Sine of angle of travel cA : Cosine of angle of travel d : Acceleration due to drag dx : Horizontal acceleration dy : Vertical acceleration sA = y / v : avoid doing trig functions cA = x / v : avoid doing trig functions d = F * v^2 : drag depends on square of velocity at these speeds dx = d * cA : drag slows horizontally dy = G + d * sA : drag slows vertically, plus gravity slows on ascent and accelerates on descent s = s + ( x * T ) + ( 0.5 * dx * T^2 ) : s = ut + 1/2 at^2 h = h + ( y * T ) + ( 0.5 * dy * T^2 ) : s = ut + 1/2 at^2 x = x + ( dx * T ) : v = u + at y = y + ( dy * T ) : v = u + at v = sqrt ( x^2 + y^2 ) : avoid doing trig functions t = t + T : tick After the final iteration, correct s, h, and t so that they match the exact moment of impact with ground: dh : Correction to h ds : Correction to s dt : Correction to t dh = h h = h  dh dt = dh / y t = t  dt ds = x * dt s = s  ds And that's it. (From: James Prescot) 

"...no secret so close as that between rider and horse."
http://www.ammooracle.com  tatjana@ar15.com 
That looks good! Thanks on behalf of grooVe and me.



I just cheat and use published ballistic tables.



Hey, thanks alot guys! This will help out a ton!






I'm in love 


Nicely done. I've added the information to my reference library. Thanks Tatjana. ~Craig 


go to realguns.com and register for their online ballistics calculator, it's free and easy. 


This will only get you in the ballpark, as it does not take into account the shape of the bullet (BC). For example if you were shooting a boattail , how would you account for this. Also, the BC changes with velocity, and usually tables are required such as the military Ingals tables to account for these changes. 


Sure it does  see variables C & D (Cd and Diam) 

Shoot Straight
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