Do Test Groups' MOA Size Change With Range?

Here is some under thinking.

One non-linear variable is the vertical spread at different ranges caused by muzzle velocity spread. A 308 Win bullet drops about 0.2 inch (0.2 MOA) more at 100 yards for each 50 fps less muzzle velocity. At 1000 yards, it's about 20 inches (2.0 MOA) more. Drop in each 100 yards of range is directly portional to time of flight across each.

Whatever that is for the ammo can be changed by the LOF angle above the LOS for each shot as the bullet leaves. The muzzle axis angle vibrates mostly vertical. All bullets don't leave at the same angle to the line of sight.
 
And, just to complicate things further, there are factors not related to physics. The psychological factors.

I have an M14 with which I routinely shoot smaller MOAs at 300 or 500 yards than I do at 100 yards. Though I can't prove this, I am pretty sure what happens is that 100 yards seem so close that I rush or at least don't take as much care in sending my shots. On the other hand, longer ranges intimidate me into bearing down and being a better shooter.
 
One of the military teams observing the ideosynchrocies of M14NM rifles learned M118 match ammo MOA accuracy at 300 yards was not quite as good as 600 yard results. Their conclusion reached for cause was the muzzle axis angle at bullet exit compensated for velocity spread better for drop at 600 than at 300.

Such phenomena has been observed for over a century. Adjustable weights near the muzzle nowadays tune the bore axis vibration frequency to best compensate for velocity spread. Slower bullets leave at slightly higher angles than faster ones. Both center and rimfire rifles use these tuners.
 
I'll add, per Bart and John's descriptions on drift induced by wind deflection that what John said about that kind of drift applies to other kinds of drift equally. For example, suppose you shoot a bullet whose center of mass (CM) is off of the bore line a quarter thousandth of an inch due either to manufacturing imperfection or to the bullet being cocked a few moa inside the bore. Because this off-center CM orbits the bore axis as it goes down the tube, it picks up off-axis momentum that causes such bullets to open groups by flying away (drifting) from the bore line at a fairly constant velocity that isn't reduced appreciably by drag during the time of flight (TOF). This travel is at the angular its CM had going around the bore, and its direction is random if you can't control what side of the bore the CM favors when you chamber the cartridge. It's the same effect as spinning a weight on a string around your head and letting go of the string. The weight's momentum carries it in a direction tangent to wherever it was along the swing circle at the moment you let go of it. For the bullet, getting clear of the muzzle is being let go of. The angular velocity (the drift velocity) is the bullet rpm/60 (to get revolutions per second) times 2 times pi times the distance of the center of gravity was from the bore axis in inches. The result is in inches per second.

Here's an example I worked out in Excel. I took the time of flight for a bullet to travel each multiple of 100 yards distance from a ballistics program. The bullet was 175 grains and started out at 2700 fps. The only thing to note is that because the drift is constant and the time needed for the slowing bullet to go each successive 100 yards is longer and longer, the number of moa of drift increases for each successive 100 yards.

Note that drop per hundred yards changes partly for the same reason and partly because gravity is accelerating the rate of fall as time goes by. Also, note that moa in this chart is mathematical moa rather than the usual shooter's 1 moa/inch/hundred-yards approximation, but it just comes out about 4½% smaller, so no biggie. Multiply each entry by 1.0472 to get the approximation version.

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There is alot to consider when working off charts . There are so many variables , I don't use a chronograph . When I find a load that shoots consistently tight groups at 100 yards in perfect condition I use that load from 1 to 2 hunderd yards , wind and temperature we can't control and human error is the only thing left . The rifle and round can only do so much , reading the wind is a talent . I keep it simple try not to over think , easy to blame the wind.
 
I'm the fly in the ointment. When someone at the range tells me their gun shoots 1 MOA at such and such distance I tell them to prove it and bet a couple of bucks. I've never lost my bet. A lot goes into getting 1 moa. Not only the rifle but the skill of the shooter.

I've shot 1/2 inch groups at 1oo yards with my 45/70 but I would never say it was possible because my next group could be 3 inches just from trying too hard.
 
So related to do this I'd like to ask you Bart--do you believe there is some kind of "auto-rotational stabilization" that happens with certain bullets that causes them to print tighter at 300 yds or so than at 100? I've heard top shooters weigh in on both sides of the argument and it's something I've always tried to understand. My personal opinion is that lacking control surfaces I don't see how that's possible.
 
Have a collet made to hold your bullet, then put it in a Dremel Moto Tool that runs at least 30,000 rpm

Connect an ampmeter between the Moto tool and power outlet.

Put a bullet in the upward pointed collet, turn the tool on.

Bullets out of balance will draw more current. Those way out of balance may fly out of the collet. Best balanced bullets draw least current, they are most accurate.
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This is certainly something I've missed BartB, that sounds simple. Do you (or match shooters) often do this when loading for accuracy?
 
stagpanther said:
So related to do this I'd like to ask you Bart--do you believe there is some kind of "auto-rotational stabilization" that happens with certain bullets that causes them to print tighter at 300 yds or so than at 100? I've heard top shooters weigh in on both sides of the argument and it's something I've always tried to understand. My personal opinion is that lacking control surfaces I don't see how that's possible.
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Yes, that can happen. But not because of bullet spinning. Was first documented over a century ago by the British on their SMLE 303's accuracy at long range.

When all bullets leave on the bore axis upswing, slower ones depart on higher angles than faster ones because their barrel time is longer than faster ones. Their trajectories cross at some point down range. Slower bullets will be higher above the LOS than faster ones at about 5/8ths of the range where they cross. Then lower past the crossing point at target range

This is called positive compensation. Adjustable weights are sometimes put on barrels at their muzzle to adjust the bore axis vibration frequency tuning it for what is best for a given load at target range.
 
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berettaprofessor said:
This is certainly something I've missed BartB, that sounds simple. Do you (or match shooters) often do this when loading for accuracy?
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I have not done that.

A few used the Juenke jacket thickness sensor that helped but it is no longer made.

The best commercial match bullets today shoot under 1/3 MOA at 100 yards, 2/3 at 1000. Group records are the smallest shot in matches
 
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When all bullets leave on the bore axis upswing, slower ones depart on higher angles than faster ones because their barrel time is longer than faster ones. Their trajectories cross at some point down range. Slower bullets will be higher above the LOS than faster ones at about 5/8ths of the range where they cross. Then lower past the crossing point at target range

This is called positive compensation. Adjustable weights are sometimes put on barrels at their muzzle to adjust the bore axis vibration frequency tuning it for what is best for a given load at target range.
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Thanks for enlightening me--so is this due in part to the velocity of the bullet, the gas impulse in the barrel, and the time the projectile exists in relation to that impulse??
 
I have a pressure trace and have seen some interesting behavior in pressure plots as the bullet goes down the bore. There's even a theoretical pulse that goes down the barrel and "rebounds" back to the projectile before it even exists the muzzle that I've heard about.
 
stagpanther said:
I have a pressure trace and have seen some interesting behavior in pressure plots as the bullet goes down the bore. There's even a theoretical pulse that goes down the barrel and "rebounds" back to the projectile before it even exists the muzzle that I've heard about.
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Yes, that shock wave goes back and forth in the barrel. When it is at the barrel muzzle, the claim is it enlarges the bore a few millionths inch and that degrades accuracy. Modes 4 and 8 in that link shows the muzzle diameter changing but no back and forth shock wave claimed in this web site:

http://www.the-long-family.com/OBT_paper.htm

I and others have had Garand match barrels whose bore at the muzzle enlarged well over a thousandth inch from steel cleaning rod wear that had no accuracy loss. They still tested sub MOA at 600 yards.
 
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My tests have been on AR's--which are difficult because most of the chamber is usually covered by the barrel nut--and many of the barrels are made of SS416 which supposedly has an "erratic" molecular expansion and contraction behavior compared to say conventional 4150 CM.
 
I've done hoop stress analysis suggesting upwards of a quarter of a thousandth deformation can occur. The impulse seems to be initiated when the bullet hits the throat on its way out of the case. At that one moment, it pushes forward on the barrel and the reaction force applied to the breech end causes the chamber to stretch a little. As the bullet eases into the throat and gets to build up speed again, the chamber snaps back into position and those seem to be the pressure wave initiating forces.

Interestingly, those waves were first described (AFAIK) by Dr. Lloyd Brownell in his 1965 study of absolute pressure at the U of Michigan with funding from DuPont. You can seem them as small wiggles superimposed on the pressure curve where they occur. They don't seem to have equal magnitude in different loads and I have not done Pressure Trace readings to see if starting with the bullet in contact with the lands, which eliminates the bullet bumping into the throat, also mitigates the waves.

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