Bullet Drop Made Simple
BC
Ballistic Coefficient is a measure of how streamlined the bullet is. 0.1 would have a lot of drag, 0.5 is pretty streamlined.
There are different kinds of BC, using different drag models. Bullet manufacturers use the G1 or Ingalls system. It is an old system, but it is the one the bullet manufacturers use.
Many modern bullets don't fit into this system exactly, so bullet manufacturers may give different BC values for different velocities..
Confusing, but at least they all use the same system. For hunting, the single BC value on the ammo box for .308 Win out to 300 yards is fine. Long range competition shooters would use different BC values for the same bullet for different velocity ranges.
USA manufacturers seem to use "Army Standard Metro" for their BC values, 59o F (15o C), a barometric pressure of about 29.5275 inches of mercury (999,92 hPa), and a relative humidity of 78%.
Some bullets work fine with a single BC value. You either take the manufacturer's word for it or experiment on the range.
The BC is usually written on the box the bullets or loaded ammo came in. The manufacturer may have a data book or a website with different BC values for different velocities.
How Accurate is the Bullet Drop?
BC:
This program can't be more accurate than the BC values, which are approximations. Manufacturers may exaggerate BC values. So field results may be slightly different. If you know the bullet drops more than the BC predicts, you can reduce the BC value a little until the program agrees with the real world.
Wobble:
Wobbling bullets have more drag, but it is hard to predict wobble. For example, if the crown of the
muzzle is damaged, the bullet
will wobble more, but your PC doesn't know about the state of your muzzle. Bullets wobble as they leave
the muzzle, then settle
down a lot. When the bullet drops below the speed of sound (1116 ft/sec) more funny wobbbly stuff happens.
The rifling twist on
the barrel affects wobble, but this program doesn't model that.
Programs that deal with wobble and spin are called 6DOF (6 degrees of freedom), as opposed to 3DOF (up/down,
left/right.
forwards) programs like this one.
Other Variables:
Remember that your sight zero can shift if the rifle gets bumped. If you wear a different jacket, that
can affect your grip and
change scope parallax and point of aim. Firing from a field position may give you plus or minus 2"
wobble at practical ranges, the
rifle/ammunition may only be capable of a 2" group at 100 yards. These and other uncertainties
add up to be more significant than
ballistics for short range practical shooting.
Ammo temperature affects muzzle velocity, but this depends on which powder you use.
Summary:
Is the $60 commercial software more accurate than this?. I honestly don't think so, they all give different
results for the same
input anyway.
The good thing about multiple BC values is that you can fiddle the BC values to fit the bullet's observed
trajectory in the real world,
this is presumably what the bullet manufacturers do.
Precision shooting experts can tweak their BC values to fit the observed results.
- External Ballistics
External Ballistics deals with what happens to the bullet in between the muzzle and the target.
There are 3 approaches:- Use a different computer model written specially for each bullet. The US Army scientists can do that, not practical for the rest of us.
- Use a different computer model for each type of bullet. Then use a different drag constant (Ballistic Coefficient) to adjust for each bullet of that type a manufacturer sells. This is practical. The different types of computer bullet models are called G1, G2, G3, and so on. The drawback is that manufacturers use G1 for all their ballistic coefficients, so it's hard to know what the G7 ballistic coefficient is for a commercial Very Low Drag bullet. Plus a naughty bullet may not conform to the computer model that it's supposed to.
- Use the one computer model for all types of bullet. This wouldn't work well, but the fix is to give different ballistic coefficient values for different velocity ranges. It is a cheat, since the ballistic coefficient has nothing to do with velocity. So the numbers don't represent the bullet drag exactly, you just fiddle the "ballistic coefficient" numbers until you get the computer program to give you the right numbers to match the real world. This works well enough.
This program has a variety of drag models for approach 2) above, and multiple velocity "ballistic coefficients" for method 3). I like method 3), because it is based on real world results rather than pure theory. You have to take the manufacturer's word for the ballistic coefficients, or change them to get the results you observe on the range.
Shooting at an Angle
If you are shooting a target uphill at 45 degrees 100 yards away, how do you set your sights?
The easy way is The Rifleman's Method. If the range is 100 yards, 45 degrees uphill, flatten the hill in your imagination. The target will now be closer to you, 70 yards. That's the range you set your sights to. Uphill or downhill is the same (near enough).
The math is: Cosine of 45 degrees = -0.7. Multiply the 100 yard slope distance by 0.7, you get 70 yards
. You don't actually do
the math, just estimate what the horizontal distance would be.
US Army Field Manual FM 3-05.222 "Special Forces Sniper Training and Employment"
Table 3-9. "Compensation Factors Used When Firing From a Given Angle"
"Percent of Slope Angle Up or Down (Degrees)" = 45
"Multiply Range by" = 0.7
So it's good enough for US Special Forces snipers. It isn't 100% accurate, but it's better than ignoring
the slope.
I call this the "Cosine Height" method. The "Cosine Drop" method is more accurate,
and multiplies the bullet drop by the cosine
of the angle, but you can't do that in your head, unless you are really strange.
More accurate methods would involve an instrument to measure angles, and ballistic tables. You can buy
a device like a spirit
level which attaches to the rifle, and gives you the cosine of the angle.
Free Ballistic Simulator Software updated Sunday August 01 2010 at 11:43am. Email Frank Clarke About Frank Clarke