I’m writing this, even though this topic isn’t related to Recoil Science, because it is something that we ran into while doing hi-speed video R&D on brakes, and then did some follow-up testing to proof out what we were seeing.
Non-Linear Divergence is the phenomena of a rifle grouping at longer distances than closer. To be clear, bullets DO NOT become more accurate as they fly. It IS a myth. If you don’t believe me, ask the ballisticians at Berger, or Lapua, or Hornady.
Now, we’ve all seen and or heard stories of a rifle shooting smaller groups at 200 or 300yds than they do at 100yds. I’ll tell you a secret, It DOES happen.
I know, now you’re scratching your head thinking, “I thought you said it’s a myth”. I did and it is. And NOW you’re thinking, “He must be drinking?” I’m not, Yet.
Before you decide it’s time for the guys with the white coats to pick me up, here at the Kahnpound, and take me to a nice padded room, Let me explain.
Rifle barrels flex, A LOT, relatively speaking. Barrels do not move along a single plane as they flex, It’s actually more of a circular whipping motion. Think of starting a jump-rope that is only being swung from one end. All of this occurs as the bullet starts, engages the rifling, and then travels down the barrel to the muzzle.
Because of the mechanics, as the motion is started, the barrel flexes and the muzzle end, due to inertia, tries to maintain it’s orientation as the middle portion of the barrel moves in a circle around the original line of the bore. The muzzle does end up moving in a circular motion, around the original bore-line, but the last few inches stay straight due to the lack of leverage to overcame the rigidity of the steel, and maintains its orientation towards the target. These actions are amplified/mitigated by changing barrel length and contour.
So Now, you know what’s going on with the barrel when you shoot. What does that have to do with Non-Linear Divergance?
Literal NLD is based on the assumption that just because your crosshairs are on the same point with each shot, the muzzle is in the same place with each shot, and if that were true, you’d never see or hear of NLD.
What ACTUALLY happens is, You Aim, You pull the trigger, The bullet goes down the barrel, the barrel whips in a circle, the muzzle moves in a circle around where the muzzle/bore was at the time you broke the trigger, and the bullet exits drawing a straight line from the muzzle(at time of exit) to the Point of Aim. The important thing to remember here is, the location of the muzzle at time of exit is not the same location as when you broke the trigger.
What does all of this mean? It means that even though the bullet ALWAYS travels in a straight line(barring outside influence), you can still see groups get smaller until you reach the point of convergence, which is where the different straight lines(bullet paths) are intersecting.
Depending on the quality of barrel, length of barrel, contour of barrel, and Fineness of Optic, you may or may not ever see occurrences of apparent NLD. But, it’s entirely possible, with a skinny barrel, or even a long heavy barrel, to see a rifle that “won’t group at 100, but shoots great at 200”, but it’s not because of curving bullets, It’s because the group starts out large at the muzzle and gets smaller until you hit the convergence point and then opens back up at the same rate as the original convergence. However, I will note that depending on barrel contour and barrel/action interface rigidity, that some barrels won’t group any smaller than the muzzle group size, regardless of distance, because something in the system is not allowing the barrel tip to maintain it’s orientation.
Here are some recorded examples of muzzle group sizes(actually 12″ from muzzle) to show how much muzzle movement some barrels exhibited: 26″sporter 300wm, Muzzle 1.615″. 20″ HvyPlma 308, Muzzle .420″. 24″ sendero 300wm, .825″
I hope this clears up, Why you can witness, Something that doesn’t actually happen.
This is only one of many reasons that can cause “apparent” NLD, but Litz and others have covered most of them, such as; Parallax, Shooter focus, optic Quality, etc. , and to be honest, most of us with quality rifles, will never see a noticeable occurrence due to rigid systems, but it can and will effect some rifles.