# need external ballistics formula

roscoe

May 2, 2005, 11:25 AM

Does anyone know where to find the formula to calculate bullet drop where the variables entered are: muzzle velocity, ballistic coefficient, and distance to zero? I am trying to set up a ballistics spreadsheet for Excel.

Thanks!

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Jim K

May 2, 2005, 11:30 AM

Don't reinvent the wheel. Enter "ballistics software" into Google and take your pick of a dozen ballistics packages that will do what you want to do, and at pretty reasonable prices.

Jim

Zak Smith

May 2, 2005, 12:48 PM

There is no single formula to calculate the trajectory of a symmetric projectile in atmosphere. The flight is governed by a set of differential equations with no analytical solution. Small arms use a flat-fire approximation (less than 15 degrees inclination) and the two most popular numeric methods are the Siacci and Point-Mass. Here is a good introduction: http://www.aeroballisticsonline.com/ballistics/trajectory_part_2.html

The best reference in Robert McCoy's "Modern External Ballistics"

The basic answer is that you find or buy a progam which does the modelling for you, such as ExBal, Sierra Ballistic Explorer, JBM, etc.

The parameters which determine trajectory are: bullet BC, muzzle velocity, sight over bore distance, zero distance, wind direction and speed, and atmospheric density (density altitude, density ratio, pressure, altitude, etc).

brickeyee

May 2, 2005, 01:53 PM

There are any number of ballistics programs available. Just be aware that BC is a function of velocity so a single number isnot always suitable.

The BC measured over a 100 yard range will not be the same as for 200 yard range given the same muzzle velocity. Some manufacturers have data available as a function of velocity, and when this is used in conjunction with good software a good answer can be calculated.

Zak Smith

May 2, 2005, 02:11 PM

Just be aware that BC is a function of velocity so a single number isnot always suitable.

Note that the "G" drag functions (the most common being the G1) are already parameterized based on mach number (important: not velocity as such).

http://www.snipercountry.com/ballistics/tables/G1_Drag_Function.txt

If a bullet differs from the reference bullet for the drag function used, then multiple BC's may be provided which then work "on top of" the Gx parameterization. The difference is small, however. If you run a 175SMK using the average BC for its velocity range vs. the multiple BC's published by Sierra, the difference is extremely small even at 1000 yards. The first uses the multiple BC's, and the second two lines use one of the first two BC regions. The second (0.496) is clearly more appropriate over the velocity range for this load.

_Bullet_ _BC_ _MV_ 0 200 400 600 800 1000 | YARDS

175SMK 0.51* 2700 > -0.00 1.68 7.27 14.57 23.81 35.57 | drop (moa)

175SMK/first 0.505 2700 > -0.00 1.67 7.23 14.46 23.56 35.03 | drop (moa)

175SMK/second 0.496 2700 > -0.00 1.68 7.27 14.57 23.80 35.49 | drop (moa)

175SMK 0.51* 2700 > 0.00 1.34 2.88 4.66 6.74 9.11 | wind (moa)

175SMK/first 0.505 2700 > 0.00 1.31 2.82 4.56 6.56 8.83 | wind (moa)

175SMK/second 0.496 2700 > 0.00 1.34 2.88 4.66 6.71 9.05 | wind (moa)

175SMK 0.51* 2700 > 2700 2351 2028 1733 1468 1251 | velocity (fps)

175SMK/first 0.505 2700 > 2700 2357 2039 1749 1492 1277 | velocity (fps)

175SMK/second 0.496 2700 > 2700 2351 2028 1734 1475 1260 | velocity (fps)

roscoe

May 2, 2005, 05:09 PM

The flight is governed by a set of differential equations with no analytical solution.

Holy cow- OK, that will make it harder than I thought.

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