MOA and linearity

I suspect you will get two kind of answers--one is yes--accuracy is linear to some extent-ceterus paribus. On a heavy barrel match type barrel with perfect bedding etc. my guess is that you might find it so.

The other will be it depends on the firearm--Enfields, in particular, the Mark VII bullet, apparently reacted in such as way to the barrel's harmonic resonance where the bullet became accurate enough to win military shooting matches at long range but pedestrian accuracy close in.

I guess category two makes it fun for handloaders.

MOA is MOA no matter the distance, and the only way to know if a gun that shoots into an inch at 100 will do 2 at 200 is to shoot it at 200. There are no guarantees

There's no chart. It has a lot to do with how concentric the bullet itself is and the chamber, how concentric the bullet enters the chamber, etc. All these types of errors get amplified the farther the bullet travels. Folks interested in extreme accuracy measure this stuff to 10 thousands of an inch and spend big bucks for precision loading dies, bullets, gunsmiths who know this stuff etc.

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)

Well, wind and gravity have nothing to do with it, gravity is a constant and wind is a variable that in theory, if read perfectly for each shot, wouldn't matter.

I think that thinking in linear terms out to the bullet's transonic range is fine for estimating the rifle's best-case accuracy potential w/o the human factor. Though, in practice even with the rifle locked in a vice and perfectly calm wind, it probably won't be linear due to small variances having more pronounced effects at range. That said, 1/2 MOA heavy bench guns are doing their 1/2 MOA thing at 1000 yds in competitions when the shooter does their part.

Bryan Litz of Applied Ballistics covered that very topic in one of his articles

http://www.appliedballisticsllc.com/Articles/ABDOC101_1_MaxEffectiveRange.pdf

The aerodynamics of speeding bullets cause them to slightly corkscrew through the air. At some range, sometimes 200 yards, the bullet "goes to sleep", and flies true. After that point, accuracy is better.

Different bullets at different speeds will have this happen at different ranges.

The aerodynamics of speeding bullets cause them to slightly corkscrew through the air. At some range, sometimes 200 yards, the bullet "goes to sleep", and flies true. After that point, accuracy is better.

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If you can demonstrate this, Bryan Litz will pay your expenses to do so:
http://www.longrangehunting.com/forums/f19/applied-ballistics-shoot-thru-target-challenge-144359/

In my Unique Alpine TPG 1 in 6.5x55, 28" barrel, 1 in 8 twist, i witness that I get 10 mm groups at 50 metres and 6 to 7 mm groups at 100 metres.
shooting factory Lapua Match ammo with 123 gr HPBT Scenar bullet.

I'm not shure but some say this has something to do with bullet stabilisation.

The same fenomenon is often witnessed in gun magazine test of sniper type rifles (the real stuff) were 300 m accuracy is often better then 100 m (in MOA)

If you look at benchrest records and groups through 300 yards, you'll see they increase about 1/10th MOA for each hundred yards. The best shoot inside .3 MOA at 100, .4 MOA at 200 and .5 MOA at 300.

Use ballistic software to calculate bullet drop for a 20 fps spread for each hundred yards to a thousand. Same for wind drift with a 1 mph change in crosswind. And see how much a 2% change in bullet BC makes; they are not all perfectly balanced.

There's no way bullets at their edges of a mid range group know which direction and how much to move back to group center.

However, if bullets leave on the right place on the muzzle axis up swing, they'll group smaller at long range than mid range. Slows ones leave at higher angles to the LOS and their greater drop at longer range is compensated for. Tuners on barrels are moved back and forth to change the muzzle axis vibration frequency for the ammo's barrel time so bullets exit at the right place.

It's my opinion that a good rule of thumb is groups open up about 10% for each hundred yards through 1000 for good rifles and ammo. More for sloppier ammo and rifles

bikemutt said:

Let me clarify; of I'm not asking about how linear a particular rifle will shoot, I'm asking about how linear various calibers/bullets are.

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You can make your own chart easily enough. The primary sources of non-linear imprecision are wind in the horizontal direction, and muzzle velocity spread in the vertical direction. So chrono your load and get a good mean and standard deviation. Then run the +2 SD and -2 SD shots through a ballistic calculator. That's what your extra vertical dispersion will look like. Then run a 1 MPH windage (call it wind call error or whatever) and do the same thing obviously if your wind call error is 2 MPH instead, the spread will be twice as wide.

What you'll find is that horizontal grouping at range is highly caliber/bullet dependent - a 28 Nosler will always have less horizontal group size growth at distance than a .308. But vertical group size growth is ammo quality dependent - a .308 with carefully loaded low-SD ammo will have less vertical stringing than a .28 Nosler shooting junk.

In most cases a rifle and shooter capable of shooting 1 MOA at 100 yards will still shoot very close to 1 MOA at longer ranges. You usually see some increase in MOA as ranges increase, but not much. I think it is more human error than mechanical. I've never calculated the exact difference, but the numbers Bart posted seem about right based on my informal observations.

I have noted in rare cases, specific rifles shooting slightly better MOA at ranges farther than 100 yards. There are lots of theories as to why and I don't know the answer. I just know that I've had 2-3 rifles hunting rifles over the years that wouldn't do better than 1" at 100 yards (1 MOA). But at 200 yards were pretty consistent 1.5" guns (.75 MOA). But this isn't common in my experience. Most of the rifles I've owned were predictable at longer ranges after being zeroed at 100 yards.

For optics, the biggest issue is focus. If your optic is focused at distance A, and shooting at distance B, you will get extra variation as B gets farther from A (either direction) because your position in the eyebox will cause the crosshairs to move on the target. It doesn't alter group size much (assuming you maintain your cheek weld through the group) but does impact your total error from intended POI. This is why long range scopes have adjustable focus (sometimes called parallax).

Generally speaking you don't need any more maginification to shoot the same size groups at twice the distance. The target appears 1/2 the size, but then the total size of your group is allowed to doubled too. Often times when shooting at long distance, the max magnification a shooter will choose to use is based on mirage and stability of the shooting position, not distance. If the air is clear and you're stable, you use more magnification. If there's lots of mirage or the position sucks, use less.

For optics, the biggest issue is focus. If your optic is focused at distance A, and shooting at distance B, you will get extra variation as B gets farther from A (either direction) because your position in the eyebox will cause the crosshairs to move on the target. It doesn't alter group size much (assuming you maintain your cheek weld through the group) but does impact your total error from intended POI. This is why long range scopes have adjustable focus (sometimes called parallax).

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Its called parallax for a reason, generally you are better off adjusting the objective "focus" to minimize (ideally zero) the movement of the target aim point relative to the cross hairs as your eye position moves in the eye box even if it makes the target less sharply in focus. If the reticle is not in sharp focus, you have the eyepiece mis-adjusted.

The aerodynamics of speeding bullets cause them to slightly corkscrew through the air. At some range, sometimes 200 yards, the bullet "goes to sleep", and flies true. After that point, accuracy is better.

Click to expand...

If you can demonstrate this, Bryan Litz will pay your expenses to do so:
http://www.longrangehunting.com/foru...llenge-144359/

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I've read Bryan's article, and all he says is that he has not been able to find any mechanism that would account for this behavior. However, the mechanism is known.

Harold Vaughn was a distinguished aerodynamicist, and a key scientist at NASA and Sandia. In his book, Rifle Accuracy Facts, he explains the mechanism. That starts on page 182. Here is a snippet:

Of course the bullet is flying along in a cork screw trajectory around the average flight path. ... Notice that the bullet starts out with a high frequency (fast precession) coning motion that damps out fairly quickly and the motion settles down to a lower frequency coning motion (slow precession).

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Sierra bullets said bullets do corkscrew a little but typically go straight before reaching 100 yards. Match bullets do sooner than less precise ones. Corkscrew's typically less than caliber diameter so it's hard to distinguish with shoulder fired rifles.

Dr Mann made bullets corkscrew a lot over 100 years ago. Pictures proving it are in his book.

My dim recollection of undergrad physics does not contain any means by which a bullet could "corkscrew" around an axis - presumably the line of flight - OUTSIDE THE BULLET.
The ballisticians name a lot of different types of movement for a spinning projectile in air, but all I have seen described are still aligned somewhere near the center of gravity or the center of pressure which are within the outline of the bullet.

I have an out of context recollection of an old NRA article which says the "air spiral" is about a tenth of an inch.

When a distinguished aerodynamicist says "Of course the bullet is flying in a corkscrew trajectory around the average flight path..."

It is not a matter of course to me and I suspect not to most of his readers. I need an explanation of the force acting to keep the bullet from moving off at a tangent the moment its movement leaves a line drawn through the bullet. And, as Bart says, I need an explanation of the restoring force bringing the corkscrewing bullet back to the SAME line of flight EVERY TIME to give convergence on the target.

Better yet, I need one of these marksmen to demonstrate it with Bryan Litz watching.

There was a guy who set up an Oehler Accoustic Target at 100 yards and a paper target at 335 yards. He saw no single group smaller in MOA at 335 than at 100. He was of course criticized for not using the right bullets to demonstrate convergence.

I'm with Litz on this - if this bullet takes this "corkscrew" path, there must be some forces that move it around to do that, and those forces must "know" where the average flight path is so they know which way to push. What are those forces?

The fact that there's no explanation AND no one can produce evidence of the effect itself is suggestive that perhaps the effect doesn't exist...

As I understand it, spinning bullets precess because of the force of gravity acting at right angles to the spin axis. The point of the bullet traces out a circle.

When the bullet points slightly right, the drag vector points mostly back, but slightly left. Since the drag vector has a leftward component, the bullet is drawn to the left.

As the bullet nose precesses another 180 degrees, the bullet is drawn right. When the nose is up, the bullet is drawn down. When the nose is down, the bullet is drawn up.

Connect all the dots and you have a corkscrew.

Yes, but the corkscrew is of the NOSE of the bullet.
I really doubt that the whole bullet is somehow in orbit around the line of flight.

denton said:

When the bullet points slightly right, the drag vector points mostly back, but slightly left.

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Why? The simplistic assumption that drag forces are tangential to the surface upon which the air impacts suggests the opposite.