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Are you sure you wish to do this? Member Login  [ARCHIVED THREAD] - External Ballistic Equations  Joined Mar 2004 Posts 19 EE Offline CO, USA Posted: 10/27/2004 4:18:22 PM EST I am looking for equations to determine the External ballistics of a round. (aka. bullet Drop), given the weight in grains of the bullet and velocity of the round. Hope someone out there is smarter than me!  Joined Aug 2004 Posts 6 EE Offline NM, USA  Posted: 10/27/2004 4:54:49 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 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.
 Ammunition Moderator   Joined Oct 2001 Posts 2145 EE Offline VEN  Posted: 10/27/2004 5:03:29 PM EST Initial variables: A : Angle of elevation, in radiansV : Velocity at release, in m/sM : Mass of projectile, in kgC : Coefficient of drag, pure numberD : Diameter of head of projectile, in mF : Drag factor, in m^(-1)T : Time increment, in sH : Height at release, in mG : Acceleration due to gravity, in m/s^2F = -0.473595 * C * D^2 / MT = 0.004 : for most computationsT = 0.001 : to be painfully accurateG = -9.80665Loop variables: v : Velocity, in m/sx : Horizontal velocity, in m/sy : Vertical velocity, in m/ss : Range, in mh : Height, in mt : Flight time, in sPrior to the first iteration: v = Vx = V * cos ( A )y = V * sin ( A )s = 0h = Ht = 0Iterate generating new values for the loop variables: sA : Sine of angle of travelcA : Cosine of angle of traveld : Acceleration due to dragdx : Horizontal accelerationdy : Vertical accelerationsA = y / v : avoid doing trig functionscA = x / v : avoid doing trig functionsd = F * v^2 : drag depends on square of velocity at these speedsdx = d * cA : drag slows horizontallydy = G + d * sA : drag slows vertically, plus gravity slows on ascent and accelerates on descents = s + ( x * T ) + ( 0.5 * dx * T^2 ) : s = ut + 1/2 at^2h = h + ( y * T ) + ( 0.5 * dy * T^2 ) : s = ut + 1/2 at^2x = x + ( dx * T ) : v = u + aty = y + ( dy * T ) : v = u + atv = sqrt ( x^2 + y^2 ) : avoid doing trig functionst = t + T : tickAfter the final iteration, correct s, h, and t so that they match the exact moment of impact with ground: dh : Correction to hds : Correction to sdt : Correction to tdh = hh = h - dhdt = dh / yt = t - dtds = x * dts = s - dsAnd that's it.(From: James Prescot) "...no secret so close as that between rider and horse."http://www.ammo-oracle.com- tatjana@ar15.com  Joined Aug 2004 Posts 7 EE Offline NM, USA  Posted: 10/27/2004 5:11:49 PM EST That looks good! Thanks on behalf of grooVe and me.  Joined May 2001 Posts 4145 EE Offline VA, USA  Posted: 10/27/2004 6:42:21 PM EST I just cheat and use published ballistic tables.   Joined Mar 2004 Posts 20 EE Offline CO, USA  Posted: 10/27/2004 7:39:31 PM EST Hey, thanks alot guys! This will help out a ton!  Joined Aug 2002 Posts 8 EE Offline MI, USA  Posted: 10/28/2004 1:34:17 PM EST This site should tell you everything you need.Ballistics Website
 Originally Posted By tatjana:Initial variables: A : Angle of elevation, in radiansV : Velocity at release, in m/sM : Mass of projectile, in kgC : Coefficient of drag, pure numberD : Diameter of head of projectile, in mF : Drag factor, in m^(-1)T : Time increment, in sH : Height at release, in mG : Acceleration due to gravity, in m/s^2F = -0.473595 * C * D^2 / MT = 0.004 : for most computationsT = 0.001 : to be painfully accurateG = -9.80665Loop variables: v : Velocity, in m/sx : Horizontal velocity, in m/sy : Vertical velocity, in m/ss : Range, in mh : Height, in mt : Flight time, in sPrior to the first iteration: v = Vx = V * cos ( A )y = V * sin ( A )s = 0h = Ht = 0Iterate generating new values for the loop variables: sA : Sine of angle of travelcA : Cosine of angle of traveld : Acceleration due to dragdx : Horizontal accelerationdy : Vertical accelerationsA = y / v : avoid doing trig functionscA = x / v : avoid doing trig functionsd = F * v^2 : drag depends on square of velocity at these speedsdx = d * cA : drag slows horizontallydy = G + d * sA : drag slows vertically, plus gravity slows on ascent and accelerates on descents = s + ( x * T ) + ( 0.5 * dx * T^2 ) : s = ut + 1/2 at^2h = h + ( y * T ) + ( 0.5 * dy * T^2 ) : s = ut + 1/2 at^2x = x + ( dx * T ) : v = u + aty = y + ( dy * T ) : v = u + atv = sqrt ( x^2 + y^2 ) : avoid doing trig functionst = t + T : tickAfter the final iteration, correct s, h, and t so that they match the exact moment of impact with ground: dh : Correction to hds : Correction to sdt : Correction to tdh = hh = h - dhdt = dh / yt = t - dtds = x * dts = s - dsAnd that's it.(From: James Prescot)

I'm in love Originally Posted By tatjana:Initial variables: ...And that's it.(From: James Prescot)

Nicely done. I've added the information to my reference library.

Thanks Tatjana.

~Craig
 Originally Posted By grooVe:I am looking for equations to determine the External ballistics of a round. (aka. bullet Drop), given the weight in grains of the bullet and velocity of the round. Hope someone out there is smarter than me! go to realguns.com and register for their online ballistics calculator, it's free and easy.
 Originally Posted By tatjana:Initial variables: ...And that's it.(From: James Prescot)

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.

Originally Posted By Amric:
 Originally Posted By tatjana:Initial variables: ...And that's it.(From: James Prescot)

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) [ARCHIVED THREAD] - External Ballistic Equations Top Top