## Monday, September 1, 2014

### Playing with a Ballistics Calculator (hat-tip to Old NFO)

I have a deep interest in Robust Processes.  To refresh your memory, a Robust Process is a process that can absorb anticipatable variation in the inputs and still deliver an acceptable outcome.

I recently read a book about a law enforcement officer who was called upon to "snipe" a bad guy.  The question popped up in my head....just how tough is that?  What are the sensitivities?

According to the Hornady Ballistics Calculator, at 600 yards (the envelop typically assigned to the "spotter" on a military sniper team), a 30-06 with a 155* grain A-Max (3000 fps muzzle velocity) has the following sensitivities...

#### You will fail if:

You misjudged the cross wind by 2 MPH.  This is by far the greatest sensitivity.  It is also the greatest unknown because you typically do not walk the span between the aggressor and the shooting position.  Unlike the shooting range, there will be no wind flags or anemometers to give you downrange info.  The major underlying assumption is that width of a human's vitals are 11 inches across.  Yeah, I took a tape measure and estimated from one side of my rib cage to the other.  My dimensions are very close to 50%, Caucasian male.

You misjudged the range by more than +/-30 yards.  Not as big of a deal now days since laser range finders are common.  However, even experienced woodsmen, people who have walked (and subconsciously have pacing information available to them) the property will estimate 300 yards as 600 yards and 600 yards as over 1000 yards.  Underlying assumption that height of vitals are 24 inches tall.  I measured from collar bone to pubic crest.

Your muzzle velocity varies by more than 200 fps.  OK, I will let you call BS on this one because the dynamics of the rifle are likely to come into play.  But if you had a perfect rifle (perhaps an action and barrel embedded within a 6", concrete filled, Schedule 60 steel pipe) you would have to drop down to 2800 fps to cause a 12" drop in point of impact. Underlying assumption that height of vitals are 24 inches tall.

#### Final observations

Do not use these sensitivities for big game hunting!!!

The vital zones of game animals are shorter than a human's vital zone.  Also, the goals of shooting a game animal and a human combatant are different.  We shoot a game animal to "bring it to bag".  We shoot enemy combatants to eliminate them as a threat.  It is morally acceptable to hit an enemy combatant in the guts as long as he is sufficiently distracted by the event that he can no longer fight.  It is not morally acceptable to shoot a game animal in the guts because it may take 48 hours for the animal to die and that significantly reduces the chances of reducing it to possession.

The Effect of a More Accurate Rifle

A common standard for an "accurate" rifle is 1.0 MOA which is very close to one inch at one hundred yards.  This does scale out to six hundred yards.

The way to add independent sources of variation is to square each source, add them together, and then take the square root.  An example:  Two snipers are positioned along a power line which allows them to estimate the target's range within +/-30 yards at 600 yards.  That maps into a variation of +/-12" difference in vertical.  One of them is firing a "perfect" gun...that concrete filled pipe mentioned earlier.  The other is shooting an off-the-shelf, heavy barreled Savage 116 with a nominal accuracy of 1.0 MOA.

The first sniper will have a variation of +/-12 inches at 600 yards.  The second sniper will have a vertical variation of (12^2 + 3^2)^0.5 or +/-12.4 inches at 600 yards.  That +/- three inches @ 600 yards due to the intrinsic (in)accuracy of the rifle almost disappeared due to the dominating effect of range (mis)estimation.

Stated the other way around:  A rifle that shoots a 13.4 inch group at 600 yards in the field will not lose 6.0 inches in group size if you buy a perfect rifle.

You can prove me wrong if you are shooting at rocks that do not move or have a stable range reference point (like a window that the bad guy is framed within) that you can zero to.  That is why you need to know the details.  That is the only way to "cheat" the math.

#### Notes:

* Same simulation run with 208 grain A-Max launched at 2500 fps with very little difference in sensitivities at 600 yards.

#### 1 comment:

1. And you haven't even started into the REST of the calculations- zero 100-200 at ???, temp, density altitude, humidity, changes etc... It's NOT as easy as 1,2,3... Thanks for the h/t too! :-)

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