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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!
Link 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.
Link Posted: 10/27/2004 5:03:29 PM EST
Link Posted: 10/27/2004 5:11:49 PM EST
That looks good! Thanks on behalf of grooVe and me.
Link Posted: 10/27/2004 6:42:21 PM EST
I just cheat and use published ballistic tables.
Link Posted: 10/27/2004 7:39:31 PM EST
Hey, thanks alot guys! This will help out a ton!
Link Posted: 10/28/2004 1:34:17 PM EST
This site should tell you everything you need.

Ballistics Website
Link Posted: 10/28/2004 6:48:26 PM EST

Originally Posted By tatjana:
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)



I'm in love
Link Posted: 10/30/2004 10:05:00 AM EST

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
Link Posted: 10/30/2004 12:17:51 PM EST

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.
Link Posted: 10/31/2004 8:31:27 AM EST

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.
Link Posted: 10/31/2004 12:32:14 PM EST

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)
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