AR Sponsor
| 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 deal-real 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) |
|
This site should tell you everything you need. Ballistics Website |
I'm in love  |
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) |
AR Sponsor