MOA and linearity

[Sunray]

"...how linear various calibers/bullets are..." They aren't. While you might get a 1/4" group at 50, but there's no 100% guarantee or chart that says you will.
"...but typically go straight before reaching 100 yards..." Depends on the cartridge and its bullet velocity, mostly. A .30 M2's 152 grain bullet, for example, doesn't stabilize until it's travelled 300 yards. Doesn't corkscrew or the aerodynamics though. It's pitching and yawing caused by the inherent instability created by the rifling. Base of the bullet rotates in a sort of oval until it stabilizes, also caused by the rifling. That's best and easiest seen with a wooden arrow(slow enough to see from the side.). Fletching end pitches and yaws for about 5 yards, then, like a switch was turned on, the fletching starts working and the arrow stops pitching and yawing and flies straight, like, um, an arrow.

 

[Offfhand]

For anyone really interest in vector effects on bullet stability and downrange performance the best book on the subject is "New Methods in Exterior Ballistics." by Moulton. It was the standard textbook on the subject when I was in school many moons ago and still proved to be useful later when I was a young engineer at Aberdeen. The book has numerous diagrams and easy to understand explanations of the ballistic anomalies we often encounter. Probably out of print now but can probably be found on Amazon, etc. and worth the money at any price for anyone interested in the way bullets fly.

 

[denton]

To understand the corkscrew effect, it helps to understand windage.

A speeding bullet will always orient itself for minimum drag. This means that the stream lines and hence the drag vector will be aligned with the axis of the bullet. This has some very important consequences. It means that if there is a cross wind, the bullet will slightly nose into the wind, and the drag vector will no longer point directly back at the muzzle. It will point slightly to the side, in the direction that the wind is blowing.

It's convenient to break the drag vector down into two components. One points opposite to the direction of travel. The other points to the side. It is this sideways force vector component that pulls the bullet left or right in a crosswind (much more than the effect of the wind blowing against the side of the bullet).

The same principle applies when the bullet precesses. Precession causes the nose of the bullet to trace out a circle. This causes the bullet to in turn be pulled up, left, down, and right, like a corkscrew. Over the course of a typical trajectory, the pulling up, down and sideways averages to about zero.

This is not exactly an unknown effect. When I consulted with LCAAP on some of their bullet problems, some of the R&D engineers there were well acquainted with the phenomenon, and were pleased and a little surprised when an outsider showed some knowledge of it.

 

[BWB]

Typically, when the round approaches sonic speed all bets are essentially off. All other factors accumulate and can therefore be comoensated for, but crossing the sonic treshold is simply too violent to predict well (slowing to an unstable spin condition is a similar wildcard, though it can coincide with the sonic threshold)

Not so. Tactically oriented shooters such as Todd Hodnett at Accuracy First, and competitive shooters/ballisticians like Brian Litz are unconcerned about trans-sonic and subsonic changes. Predictable first round hits are normal with the .308 beyond well 1000 meters.
http://www.accurateshooter.com/featured/transonic-effects-on-bullet-stability-bc/

 

[HankB]

In Hatcher's Notebook, the section on penetration shows a striking difference between the amount of oak a 150 grain FMJ would penetrate at 200 yards (32.5") and at 50 yards (11.25"). The reason given is that at 50 yards the bullet "had not settled down to stable flight, and when it encountered the resistance of the oak it had yawed badly . . . "

I remember seeing a high speed video some years back of a conventional artillery round being fired - it showed the projectile was yawing quite visibly right after leaving the muzzle.

I also came across a series of articles which seek to explain gyroscopic precession, spin drift, etc., a few of which are linked below:

https://thearmsguide.com/5315/exter...-of-a-bullet-vertical-plane-3-theory-section/

https://thearmsguide.com/6211/long-range-shooting-external-ballistics-static-stability/

https://thearmsguide.com/5322/exter...f-a-bullet-horizontal-plane-4-theory-section/

https://thearmsguide.com/5346/long-range-shooting-external-ballistics-spin-drift-13-theory-section/

 

[DocUSMCRetired]

Non-Linear Divergence has been a hot topic for some time. It is actually covered in the new book. While people have claimed it, it has yet to be proven in the lab. With countless hours spent studying it, their are some theories as to why this happens. Most of them are related to the shooter, not the rifle. Even going as far as to damaging bullets before they are fired to try to force this to happen, and it didn't.

As far as we know right now, it just does not happen. Bullets "go to sleep" very quickly. 2 - 3 precession cycles. Basically very soon after leaving the barrel. However, if you believe you can prove this theory then you can go up to the lab. If you successfully prove it, then Bryan will pay for your way back home. No one so far has successfully proved it.

 

[Bart B.]

Sierra Bullets' Martin Hull knew decent bullets stabilize a couple dozen yards down range decades before Litz did. How else did such bullets shoot in the 1's and sub 1's at 100 yards?

Dr. Mann damaged bullets over a century ago. They spiraled about their trajectory mean axis, didn't they? Read all about it in:

https://books.google.com/books/about/The_Bullet_s_Flight_from_Powder_to_Targe.html?id=QdQqAAAAYAAJ