Science-Up the Wobble

It is a fairly common belief that if the wobble measures 1″ at the muzzle, it will measure about that same size on the target. Sounds reasonable, right?

But try this experiment. Hold your arm out as if you were aiming at the
target and then swing it so it’s pointing down at a 45 degree angle. The tip
of your finger is now about two feet below the center of the target but, I’m
sure you can see, if your finger were a gun and you shot right now, the bullet
is going into the ground, and a whole lot closer than two feet below the
center of the target.

That’s because this belief that 1″ of wobble means 1″ of error in the
target just plain isn’t true. It’s a myth, a nice one, but still a myth.

In reality, your arm pivots around a point in the shoulder. That point is
fixed and, as your arm moves around, the gun is not always pointed at
the target. (Remember the 45 degree down experiment?)

Any displacement away from the perfect sight picture of sights and target in perfect alignment actually describes a triangle with a narrow angle at the shooter’s shoulder. The bigger the motion, the bigger the angle and the bigger the error. And that error is “angular” so that, as the target is moved farther and farther away, even though the angle may not change, the error (distance away from target center to which the bullet will fly) grows larger, and in direct proportion to the distance.

Fortunately, we don’t need trigonometry to figure out how much wobble results in how big a spread at the target. A simple ratio will do.

Indeed, I figured it out (below) for 50 yard Slow Fire, my primary nemesis. Here’s what I did.

I wanted to know how small does my wobble have to be to get a scoring shot. (We’ll worry about the X-ring later. The procedure is the same. Let’s just get something that scores, first.)

Ok, the largest ring on the B-6 NRA 50 yard Slow Fire target is the 5-ring. According to the NRA, it measures 19.68 inches in diameter.

To illustrate how the ratio is going to work, let’s first consider the case where the target is placed right at the muzzle, paper touching gun. Obviously, the wobble can be as large as 19.68 inches in diameter and we will still have a scoring hit if we pull the trigger (and the blast doesn’t shred or ignite the target).

Notice in this first case that the target is roughly 30″ away from the pivot of the shoulder. Arm length varies, of course. Mine is 31-32″ from shoulder to front sight, depending on which gun I’m holding. We’ll use 30″ here because it probably fits some shooters, and also because, frankly, the numbers will be easier to do.

Ok, let’s move the target out to double that distance, to 60″ from the shoulder, or 30″ from the muzzle if you’d rather measure it there.

Now how big a wobble can be tolerated and still have a shot that lands in the five ring or better?

Since the target is now 60″ away, the ratio of arm length to target distance (30/60) times the size of the 5 ring (19.68″) tells us the muzzle can move 9.84″, centered on the bull, and still result a scoring hole.

At four times the distance (120″), the wobble is 0.25 times (30/120) the 5 ring size, or slightly less than five inches.

What about at 50 yards? Well, 50 yards is 1800 inches and continuing with the 30″ arm measurement, the ratio of 30/1800 — let’s see, drop the 0 and we have 3/180, so divide the 180 by 3 and we have reduced the fraction to 1/60, so 1/60th of 19.68 inches is 0.328 inches (almost exactly 5/16″ [0.3125″] which is the size of the hole in the 3-hole notebook paper I have in my loose leaf notebook).

So far, so good.

Unfortunately, my gun has a “wobble” of its own. That is, from shot to shot, the bullets don’t always land in the same place because of inaccuracies in the gun itself.

My Springfield Armory Mil-Spec, off the shelf, was measured on a Ransom Rest to have about a 6″ spread at 50 yards.

How much is that at the muzzle? It’s 1/60th of 6″ or about 1/10″. (Boy, that sounds like a lot!)

What this really means is that in order for me to keep all my shots within the five ring, I need to be able to hold, centered on the bull, with a wobble of slightly less than 1/4″ (0.328″ – 0.100″ = 0.228″, or very close to the hole made by a 7/32″ drill [0.21875″ without wobble!]).

But let’s keep this easy. Let’s use the 1/4″ measurement because it’s “close enough” and easy to work with.

Drawing a 1/4″ diameter circle on a post-it note and sticking that to the wall, I can point my outstretched arm and finger at it, point-blank range, and see that *most* of the time, my wobble really is inside that circle. If I were holding my Springfield Armory 1911 and able to release the shot without disturbing anything (hah!), I’d almost certainly have a scoring hit, 5-ring or better (wind, ammunition, lock-up and all sorts of other factors permitting, of course).

But to be completely honest, when my finger is pointed at the circle on the Post-It note, I occasionally lurch outside the circle or my attention drifts and so does my point of aim. And to make matters worse, I still jerk the gun when releasing shots far more often than I’d like to admit. So, for me, that 1/4″ of motion at the tip of the gun is a goal toward which I’m working, but not a reality I can repeat on every shot.

For those who aspire to High Master status, here are the numbers of interest. The “X” ring is 1.695″ in diameter. Assuming a gun that shoots sub 1″ groups at 50 yards (which is quite a feat in itself), the shooter’s wobble must be within a 0.02825″ circle, just a little bit smaller than 1/32″ (0.03125).

Have you ever watched the tip of the muzzle when a High Master is shooting? I have, and the stillness they can achieve is truly astonishing. You’re looking at a wobble of less than 1/32″ all the way out at the end of the High Master’s arm, at the tip of the muzzle. Amazing!

Does that mean that when I score an “X” that I’ve held the gun to 1/32″ and released the shot?

Hah, don’t I wish!

Far more likely is that the error from the wobble at the instant of release was added to the gun’s error on that shot, and that when those two errors were combined with my jerk and lurch, well, I just got lucky.

But it is also true that as my trigger control improves and my wobble shrinks and the lurches become less and less frequent, the probability of punching out the “X” does improve.

Finally, it’s worth asking when should I have a competition grade barrel fitted to my factory Springfield Armory Mil-Spec?

Well, if the gun has a 6″ group at 50 yards, my gut-feel is that when my ability is penalized more than 25% because of the gun, then it’s time to get it fixed. Roughly speaking, that means that when my shots are consistently within the 6 ring or better, it’s time to fix the gun.

Do I believe these numbers? Do they sound credible? Do they match my experience?

Yes.

When my arm is rock steady and I release a shot well, it scores. But when my arm lurches and the shot goes, it’s not even in the paper. And similarly, when I jerk or heel or milk the gun while releasing the shot, it’s “Hello paster!”

At the next competition, try this. When you finish your slow fire, put your gun down, take a couple of steps back and pick out the best shooter there and watch the tip of his/her gun against some distant object while they release the shot. For some of the shooters I’ve watched like this, the wobble is imperceptable — I couldn’t see any movement at all from where I was standing. That doesn’t mean they have no wobble, but just that it is very, very hard to see.

After all, how far away can you see 1/32″ of motion?

1 thought on “Science-Up the Wobble

  1. I have a bachelor’s degree in math and i understand what your reasoning is but i happen to shoot bullseye matches and your reasoning is wrong. in reality-if you shoot properly you do not let your arm pivot on the shoulder. what happens is as you have your natural wobble area and decide to start applying pressure on the trigger the front and rear sights are supposed to be aligned with each other perfectly (with respect to each other) and that perfect sight picture moves around on the target. in other words. you keep the front and rear sight matched exactly even though it moves around on the target down range. if your arm, wrist, and hand were solid and you pivot at the shoulder a tiny bit (as you are reasoning) then your front and rear sight would be off from each other. so when done properly- to prevent misaligning, if the arm and gun wobbles up, then the turns down a tiny bit to make the front sight and rear sight still be aligned even though they are together pointing a little higher on the target down range. by aiming this way you can have a little more acuracy down range with the same given wobble.

    truth is, however. that what moves your shot around down range are moreso your smooth (surprize) trigger, how straight back the trigger is pulled. and all the other details of breathing and stance and finger pressurs on the gun than the wobble. everyone has somewhat wobble but the other facters determine the score more.

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