Shooter Tolerances, Part 3: Wrapping Up

I promised to wrap up this topic. Here goes. Along the same lines as last time, the target is still 4”. The following examples assume a perfect zero, a 168 grain .308 Hornady A-Max with a muzzle velocity of 2650, and a sight height of 1.6” (basically a typical .308 bolt action rifle).

I think I pretty much covered why thinking of the rifle’s point of impact as a point was not a good idea. A zone would be more appropriate. Allow me to beat a dead horse.

Perfectly zeroed shot:

Perfect Zero, no wind

It would take a 28 MPH full value wind (3 O’clock) to push the round to the edge of the target.

Perfect Zero 28 mph wind

28 MPH sounds like a ton of leeway. A real-deal, no-foolin’ 10 round, 1 MOA group at 100 will be right at the edge with a 20 mile per hour wind. But my rifle will rarely shoot a 10 shot MOA group. There are also times when prone with the bipod and rear bag aren’t feasible for whatever reason.

You may remember that in installment 1 of this series I stated the following:

-Exertion decreases precision and accuracy.
-Time stress decreases precision and accuracy.
-Precision and accuracy tend to degrade proportionally with the height of the shooting position from
the ground.

Along those lines, I found that in the last few months, the only example that I found of a seated group that I shot under time stress and exertion consisted of only 5 shots and was approximately 3.3 MOA. The following group is not identical, but should do for the sake of discussion:

Perfect zero, 3point3 MOA exerted sitting, no wind

The shooter tolerances being increased in this example means that a 3 O’clock wind of only 4 MPH will now conceivably put me at the edge of the target.

Perfect zero, 3point3 MOA exerted sitting, 4 mph wind

I could go on and on with more examples, but I think there’s enough already to make the point I want to make. I should also say that by using groups as my illustration, the extreme spread tends to stand out, and the extreme spread is not the most statistically significant measure of performance since the outliers tend to be most prominent. The last group with five rounds is also not a large enough sample size, but since I actually shot a group that large I thought it somewhat relevant.

Here’s the point of all this. I told you I was going to explain why I spent so much time working on getting my zero just right. All of the examples from the previous articles assumed a perfect zero. I don’t know if I’ve ever had a perfect zero. The one I posted might be the best I’ve had.

Cumulative Group
If I tried to get a better zero I’d overshoot and be worse off.

If the other articles demonstrated how easily our ballistics charts can essentially lie to us because of the phenomenon of grouping, if the safety and surety of the point blank zero can be undone with a bit more wobble, if a little wind can become a big problem with realistic dispersion, what happens to all that when the rifle isn’t actually zeroed?

If I do what I normally have done, and after zeroing with 3 or 5 rounds, put it in my mind that “I’m zeroed” and move on to the next thing, it might be frustrating when I start seeing rounds several inches off target, and there’s “barely” any wind, I “know” I’m zeroed, I’ve shot a few sub-minute 5 shot groups with the rifle, etc… It takes some time, patience, and more than a few rounds downrange to get a realistic idea of the system’s capabilities alone. I would recommend stacking several 10 round groups on top of each other with the same sight setting before considering the system zeroed. Anything that compromises the shooter’s ability to maintain a steady hold gets added on top of that, and that takes a long time to learn as well. Precise measuring, good documentation, and use of analyses that are more statistically significant than the old standby, extreme spread, will all help.  I should also note that it’s possible with a lot of the ballistics programs to input the variance of the loads zero from the point of aim at the zero range, which will allow for a better use of that technology.

Good luck.

Shooter Tolerances and the Point Blank Range Concept

 In this article I want to consider realistic grouping in relation to a point blank zero. The basic way I understand that point blank zero (PBZ) works is that the zero is set so that when the rifle is fired with the point of aim centered on the target, the maximum ordinate (the top of the arc) of the trajectory would be at the top of whatever size target you have in mind. The distance at which the bullet drops to the bottom of the target dimension is the maximum point blank range. The actual zero range, somewhere in between, is just an afterthought.

The basic idea for the point blank zero is to remove as many things that the shooter needs to pay attention to as possible through taking into account the amount of leeway the size of the target allows. Another way of saying it, relating to the analogy of tolerances, is that as the target gets larger, and the sighting system adjusted accordingly, some of the rest of the tolerances of the shooting system can be loosened. Looser tolerances means that the process is easier and faster. The guiding requirement is that the shooter hits the target. Where the bullet strikes the target is not so critical. Simply aim at the target center and still hit some part of it. The primary variables that are typically taken into account when optimizing a point blank zero are the size of the target and the trajectory of the round as it relates to the point of aim.

Take for example the AR I’ve been using lately and the 4” target I’m working with. I hit a snag right off the bat because I have to divide the 4” into a top half and bottom half, each 2” tall. The sight height on the AR at this moment is 2.6”, which is greater than 2”. So in this case when the rifle is aimed at the target center and fired, the bullet doesn’t rise to the bottom of the target until about 10 yards.

Close Range AR mechanical offset issues
Red crosshairs indicate point of aim. Black dot indicates point of impact at close range (inside 10 yards or so). Neither this, nor any or the other illustrations that follow are precise. They are relatively close approximations intended to convey the idea.

Therefore, technically a point blank zero is not possible with a 4” target and that AR. I would have to be doing something wrong to accidentally get a hit if the target were closer than 10 yards and I actually aimed at it. Getting a hit because two or more things I did were mistakes does not sit well with me. A 5.2” target would theoretically be just fine for a point blank zero.

If I just figure that I’ll adjust my point of aim to adjust for mechanical offset for close range shots and still roll with my attempt at the PBZ with the AR and 4” target, and I set the initial intersection for 50 yards (which is a common zero, known as the “Improved Battlesight Zero”), using Federal XM193 from the Noveske 16” barrel, and an average muzzle velocity of 3041, the maximum ordinate listed in my ballistics program (Shooter) is 1.9” from 125 yards to 150 yards. The actual zero turns out to be 220. The bullet drops to 1.8” below the point of aim at 250 yards. 255 turns out to be too far, with 2.2” below the point of aim. To sum up, the 220 yard zero theoretically keeps my bullet within the target out to 250 yards, which would be the maximum point blank range, again assuming we ignore that first 10 yards.

PBR 220 Yards
The big problem with this illustration, which I reused from a 2011 article, is that the muzzle is quite incorrectly depicted as being above the initial intersection, which with the theoretical AR discussed in the article, would would actually occur at approximately 50 yards (the initial intersection).

Points of Impact 220 Yard PBZ


The ballistics program does not take the phenomenon of grouping into account. It assumes a single point of impact for a given zero at a given distance. Because we often let computers do our thinking for us, it can also lull the shooter into thinking the same thing.

If I did a good job at setting my zero, the center of my group would be at my exact point of aim at the zero distance. That means at the maximum ordinate and at the maximum point blank range (at the extreme ends of the tolerances), about half of my rounds will miss the target.

250 PBZ with Groups
Black impacts are simulated at the maximum ordinate. Green rounds are at actual zero. Red rounds are at maximum point blank range.   

What if I adjust the point blank zero according to how the rifle shoots this ammo? I have a 10 round 1.5 MOA group with this ammo. It would probably be safe to extrapolate that over the course of many more rounds it might keep them inside 2 minutes. I could take that data into account when setting my PBZ. Since my theoretical group in this instance is 2 MOA, and half of it is going over the target at the maximum ordinate, I need to build in a 1 MOA buffer. This turns the whole affair into a trial and error game with the ballistics program. I found that if I set my initial intersection to 67 yards, the maximum ordinate is 0.7” from 115 to 125 yards. One MOA at 125 (1.047*1.25) is about 1.3”, which makes it look like this could work. The zero range turns out to be 170 yards. Unfortunately, in order to keep a 1 MOA buffer at the bottom of the target, it means that 175 is my maximum point blank range. That’s still a pretty good deal for such a small target (approximately 2.2 MOA at that range).

170 Yard PBZ

Come to think of it now, I shot that 1.5 MOA group from a rest. What if I had to use a field position? The only thing close to that is a 10 shot group fired from the open leg sitting position, which was approximately 2.8 MOA. I have no long term data to extrapolate that out, so let’s just take it at face value. Setting the initial intersection at 82 yards would keep me in the target on the high end, which occurs at 125 yards. The actual zero distance would be 140 yards. At 140 yards I have pretty much no extra leeway in my seated group to take it any farther and still keep them inside the target (a target that is perfectly shaped, easily visible, at a known distance, and completely stationary).

So what on paper initially looked like an ability to shoot out to 250 yards without worrying at all about elevation, turned out to be a dicey proposition at 140 yards from what is actually quite a steady position. If I had to use something less stable, such as kneeling or offhand, my own limitations as a shooter are going to keep me way inside that distance anyway. That would also mess up all the numbers I ran to get that point blank zero to work, and I would probably be sending some of the rounds over the target even within a range that I would be good with if I had stuck with the 100 yard zero.

Aside from the two variables that are typically considered, target size and trajectory, it’s crucial to consider the capabilities of the shooting system (including the shooter) to maintain a small enough grouping to stay inside the target. Limiting the discussion to a 4” target does make for an extreme example, but is also a good way to illustrate that there are some practical limitations to the point blank zero concept. If I were shooting at a larger target such as a big game vital zone I would have more leeway to make the point blank zero concept actually do something for me. The larger target would allow for looser tolerances in the shooting process.  I don’t know if it would reasonably allow for my typical standing group size though.

The point of this installment of the shooter tolerance stack is that there are times when you can leave a lot of the details out of your mind and still get a hit. An extremely steady shooting position will provide a cushion for compromise or mistakes in other areas, as will a large target. Carrying that concept over to small targets and unstable positions, such as standing, will not yield consistent results. If conditions force you to fire from your feet, the burden on you to account for other variables is greatly increased.

I’ll round out my thoughts on this subject in the next installment.

The Shooter Tolerance Stack

Alternate titles:

-Why Having a Precise Zero is Important
-How on Earth Did I Just Miss That Shot?
-Why You Shouldn’t Disregard Everything!

-Why Wearing Underwear as a Hat is a Good Idea (just kidding)

In January I spent a lot of time, ammo, and careful measuring in establishing where my rifle was shooting. In February I shared my results in the form of a cumulative 60 round group comprised of 6 10-shot groups shot with the same zero setting over the course of a month, as measured by On Target TDS. In that last article I promised to explain why I would go to all that trouble. Here’s where I do my best to make good on that promise.

Before even entering into this discussion, I should frame it by asking you to keep a few generalities in mind:

-Exertion decreases precision and accuracy.
-Time stress decreases precision and accuracy.
-Precision and accuracy tend to degrade proportionally with the height of the shooting position from the ground.
-The ability to precisely target internal anatomy is a skill in and of itself.

The basic premise of this series of articles will center on a concept that I think of as the “shooter tolerance, stack”. In machines such as guns, variations in dimension in parts are a reality. Some dimensional variance is expected. The manufacturer will specify a certain acceptable range of variance, called a tolerance, for each part. The idea is that even with the specified tolerance, the parts will be able to be assembled into a machine that will function properly and reliably. As I understand it, a problem can arise when several parts are at the extreme end of the specified tolerance. This is called a tolerance stack.

Shooter tolerance stacking as I define it occurs when more than one process or condition involved in placing a round on a target is on the edge of what any one process or condition, by itself, would still be acceptable to facilitate a hit on the desired target.  Because more than one variable is involved in the tolerance stack, what by itself would be insignificant could, in concert with other variables, result in a miss.  I think that this is most likely to be a problem in practical shooting situations that don’t allow a high degree of control on the part of the shooter. This would likely be an uncommon occurrence, but as they say, “stuff happens”.

The smart shooter, especially when working with a target or vital zone of a known and relatively fixed dimension, will adjust his sight to allow for a maximum point blank zero that maximizes the potential of his round’s trajectory. This is a great strategy, and to some degree will usually allow the shooter to fire a shot without having to compensate for distance or atmospheric conditions. I believe that although this is a sound strategy, if only understood at a surface level it can lull the shooter to completely disregard trajectory and wind.

Problem #1

Most shooters think of zeroing as a matter of aligning point of aim and point of impact. The point of aim, especially in a rifle scope, appears as a finite point that is easy to see. It’s so easy to forget that the next shot that comes out of the barrel is part of a potential group (the group that would appear if you just kept firing round after round of a particular ammo using a particular sight setting). Unlike your point of aim, the rifle’s point of impact is not exactly a finite point, and could be more accurately called a “zone of impact”.

Something that exacerbates the shooter’s tendency to disregard the potential shot group is that group sizes in gun magazines tend to be evaluated in terms of 3 or 5 shot groups. Groups have this strange tendency to get larger as more rounds are fired, and 3 or 5 shots will not be indicative of what your rifle will actually do.  In practical terms, this means that the 0.75 MOA capability, as defined by a typical gun magazine, might actually mean that the 3 groups that formed that group are actually part of a larger potential group that is probably closer to 1.5 or 2 MOA, and you don’t know where the three round sample fits into the bigger picture of the rifle’s potential group. If you’ve found yourself adjusting your zero on successive range trips you may be using too small a sample size to set your zero (assuming quality components, which is a huge assumption). Groups on the internet are often made up of a larger number of rounds, but are almost always cherry picked examples shot under perfect alignment of celestial bodies (mine excepted of course). In short, many of us have unrealistic expectations from our rifles.

Cumulative Group
An accurate representation of a 60 round group made up of 6 10-round groups shot over a month with the same sight setting, as measured by On Target TDS. Notice the frequency of shots in various locations in the group. Pick any three shots that seem statistically reasonable to you. Now ask yourself a.) whether the size of that 3-round group is indicative of the size of the rifle’s “bigger picture” group, and b.), whether the center of those three shots coincides with that of the 60 round group. Also consider whether five rounds is going to show you much more.

I’ll continue this next time. Hopefully it won’t be a month before then.