Most of this math is based on a Fulton Armory M1A NM Scout shooting Lithuanian surplus .308 at a torso-sized steel target about 16"Wx33"H

I am using the online ballistics calculator assuming typical conditions in my area:

http://www.eskimo.com/~jbm/calculations/traj/traj.html

Ideally, I'd do something like this:

http://mywebpages.comcast.net/jesse99/shooting600yards.html

but I am using some math shortcuts.

I also use the Root mean squared rule to combine MOAs from two different sources to estimate the combined MOA:

http://www.boomershoot.org/general/AccuracyWind.htm#General

I am assuming the following ammo/ballistics:

M80 Ball 150 gr, 0.195 G7 .308

The Lith surplus was chronographed at my last range trip at 2850fps with a standard deviation of 33fps, although this seems quite high for standard M80 ball ammo. Maybe it's my barrel.

**Conclusions.**So anyone interested doesn't have to read through the long math part, my conclusions are as follows:

- The math verifies the "rifleman" concept, which I understand as: take a 3-4 MOA rifle, put it in the hands of a marksman with a knowledge of wind and elevation ballistics for average conditions, give him basic (not match grade) ammo, and he'll be pretty accurate to 500 to 600 yards on a torso sized target. No fancy ballistics or laser rangefinders are needed (assuming he can range the target to 10% or so) and be moderately good at reading the wind. All he needs is his rifle, zeroed fairly close to his conditions. I'd even venture to say if he has more like a 2-3 MOA rifle (like a standard grade M1A), he can definately be one-shot/one hit to about six hundred yards.

- 800 yards is about the limit of basic ammo pecision for the M1A for a torso-sized target, and between 600-800 yards, you really need to be careful about ranging precision and probably start drawing sketches and ranging multiple objects unless you have a laser or other accurate rangefinder - unless of course you can dial in trial shots. You also need to be fairly good at reading wind. A skilled rifleman with an accurized M1A, match ammo, and some honed skills could probably still be accurate at this range, even on the first shot.

- For consistent hits at 800 to 1000 yards, you definately need a match grade/accurized M1A and match grade ammo. Also, a lot of little things start conspiring together to throw off your shot, like temperature. A one size fits all ballistics table isn't going to cut it if you can't take trial shots to dial your target in. Ranging the target is critical, and even if you get everything right, hitting a torso target at 1000 yards is very tough with a rifle like the M1A. One shot/one hit is even more difficult, because you need to range, read wind, know whether conditions (and the ballistics for those conditions) very accurately and adjust for things I haven't even thought of. This is where the difference between a .308 bolt gun with higher muzzle velocity and higher inherent accuracy really makes a difference in hitting the target or not, assuming you are up to the task of taking advantage of it. If you can make one shot/one hit shots at this range with an M1A or bolt gun under a variety of conditions, you are truly a very skilled marksman/sniper. At this range, it sure wouldn't hurt to have a rifle cant indicator, either.

- Assuming the shooter is much more accurate than the rifle, MOA at 100 yards is probably a pretty good indicator of rifle/ammo precision. Even out to 300 yards, assuming the wind is not a factor, the MOA is probably indicative of the rifle/ammo, unless the ammo is bad. Beyond that, all sorts of things like muzzle velocity variations, minor wind variations and things beyond the shooter's control start making MOA "grow." It would not be unusual to expect a 0.5 MOA shooter/rifle/ammo at 100 yards to have 1 MOA or less accuracy at 1000 yards - it's just the way the math works.

**Rifle Precision.**It's not an exaggeration to say many people are obsessed with how accurate a rifle is is in terms of MOA. I believe my rifle is currently shooting the Lithuanian surplus about 2 MOA in my hands and is probably capable of 1.5 MOA as-is, or if I'm lucky 1 MOA with match grade ammo. What does this mean for it's effective range? How much would I actually improve if I had a 0.5 or even a 0.25 MOA rifle? I've been under the misconception that a 2 MOA rifle is a 2 MOA rifle at any range, not just 100 yards. I've heard that MOA tends to grow with range, but just assumed it was due to varying winds, which have more impact at longer range. This is not the case.

What accounts for the growing MOA at distance is not only varying winds, but varying muzzle speeds, and probably other factors as well. Given the chronograph data on the Lithuanian surplus, I can tweak the ballistic calculator to account for varying muzzle velocities and see the effects. Assuming mean plus 1.5 standard deviations as a cutoff, about 1 out of 7 shots will be a "flier" due to the varying muzzle velocities alone. I'll assume this is a proxy for MOA precision. For the Lith surplus, this means about 1 in 7 shots will have a muzzle velocity that differs from 2850 fps by 50 fps or more. Running the ballistics calculator gives no detectable difference at ranges up to 300 yards, about 0.5 MOA at 600 yards and about 1.4 MOA at 1000 yards. I assumed a 15 mph wind, so for calm conditions, the numbers would be slightly less. It's clear to me a sub-MOA rifle doesn't do much good at long range if you aren't shooting consistent loads (match grade ammo).

It appears that handloads, or at least match grade ammo can achieve as low as 15 fps deviation based on looking around the web, so using the same method as above, match grade ammo (same bullet weight and mean velocity) would result in differences of: 0.2 MOA at 600 yards and 0.6 MOA at 1000 yards. This is no surprise - you need good, consistent ammo to take advantage of an accurate rifle at long range, especially beyond 600 yards.

The ballistic calculator confirms that an error in the shooter's hold, or the way the rifle barrel whips results in a constant MOA error at any range, so MOA does not "grow" with distance.

What is surprising to me is that the accuracy difference between regular surplus (at least Lithuanian surplus) and match grade ammo should be unmeasurable at ranges under 300 yards if the only difference is muzzle velocity. If it is detectable, then something else is going on, like the varying loads are causing the barrel to whip different directions or amounts or it is impacting the shooter or rifle in some way. Maybe this is one place where the difference between a bull barrel and a thinner barrel starts to matter. I'm assuming the difference between match grade ammo and regular ammo is simply the powder charge, but in reality, variations in bullet diameter and weight all would have an impact. Also, match ammo would almost certainly have a different loading/bullet weight/powder than the Lithuanian surplus, but sisnce I don't have any statistics for match grade ammo in my rifle, I'm assuming it's solely due to charge variation.

Given a 0.5 MOA rifle, shooting sub-MOA at 1000 yards means everything else (shooter + ammo) is probably about as good as it can possibly get. Again, no surprises.

What about a rifle like the M1A? If I am shooting the rifle at 2 MOA using Lith surplus, I figure I should be able to shoot about 2.1 MOA at 600 yards and 2.4 MOA at 1000 assuming I get everything else right. Assuming I can improve that to shooting 1.5 MOA at 100 yards, I should be able to shoot 1.6 MOA at 600 yards and 2.1 MOA at 1000. Given the 16"Wx33"H steel target, it's clear I should be able to hit it all day long at 600 yards, but will miss a quite a few at 1000 yards, assuming of course I get range and wind right and there are no problems with the "subsonic threshold:"

http://www.fulton-armory.com/M1A_long_range.htm

http://yarchive.net/gun/rifle/supersonic.html

Splitting the difference, 800 yards is probably the effective range of the rifle, which jibes with what the military tends to report for the M-14, which I believe is with M80 ammo, although using M118LR round would probably help between 600-800 yards. The math seems to work. Assuming 1.5 MOA rifle+shooter and match grade ammo, I should be able to shoot about 1.6 MOA at 1000, and assuming I get everything else right, hit the target consistently, with a miss here and there. That's a big "if" for me personally, especially with any wind, but it's not out of line with what I've heard M1A NM rifles are capable of at 1000 yards, so again, the math seems to work.

**Rifle Cant.**A shooting buddy has told me that rifle cant matters. Assuming a 5-degree cant angle on my rifle, the ballistics calculator computes about a 0.8 MOA error at 1000 yards. In fact, this error is pretty consistently high starting at 0.6 MOA at 200 yards. At a 10 degree cant angle, it's about 1.1 MOA at 100 yards and 1.3 MOA at 1000 yards. It's safe to say if you zero your rifle while canted, you may have problems later, or if you shoot with an inconsistent cant angle, your MOA will suffer. I'd guess that if you aren't paying attention to cant at all, you may not even notice a 10 degree cant. I'd guess a 5-degree cant is relatively undetectable without aid if you are paying attention. In my case, it could make the difference in hitting the steel target or not, especially beyond 600 yards or so. If you are at least consistent in the way you hold the rifle when firing and zeroing, can't won't matter a whole lot.

**Wind.**Any long range shooter knows about wind, but I've never really seen anything on how accurately the wind needs to be estimated. I'm guessing that I can't personally read the wind any closer than 3 mph without aid such as a windmeter and range flags. How much diffrence would that make? That's 0.8 MOA at 600 yards, 1.5 MOA at 800 yards, and 2.3 MOA at 1000 yards for a crosswind. About 800 yards is where I'm really going to feel the ability to read wind more accurately make a difference, at least when trying to hit a steel target. I can of course correct for wind error by dialing in, but wind conditions around here can change fairly rapidly.

**Ranging Error.**Assuming I have an object of known size, I can use my scope to range it. How accurately can I do this? I'm guessing 10%, especially if I don't know the exact size of the object, and maybe 5% if I do. If I'm really paying attention, and have the time, I could probably do better by drawing a sketch and ranging multiple objects and splitting the difference. At 300 yards, 10% error is about 0.8 MOA. At 600 yards, it's about 1.5 MOA. At 800 yards it's about 3 MOA and at 1000 yards, it's 6 MOA. A 5% ranging error would be about half these values. If given the opportunity to dial in your range, none of this matters, but if I need to hit that steel target at unknown range on the first shot, a laser rangefinder is probably a must beyond 700-800 yards or so. If I want to bump up my first-shot accuracy fairly easily between 300-700 yards, it certainly wouldn't hurt to have one.

**Weather/Altitude.**It's a given that you should zero your rifle whenever given the opportunity for changing conditions, but I must admit, I rarely do. How badly does this affect accuracy? If you shoot in St. Paul Alaska (a place in the US where the barometric pressure changes the most), the calculator says you'll see about 1.0 MOA variation at most at 1000 yards, if you zero for the average pressure. If you are in San Diego, where pressure changes little, you'd see 0.3 MOA variation at 1000 yards. For my purposes, barometric pressure matters little, but if you're trying to shoot a 0.25 MOA rifle at 800 to 1000 yards without the benefit of dialing it in, you probably ought to take it into account. In my area (Colorado), altitude varies quite a bit. A 500 foot variation results in about 0.6 MOA at 1000 yards. If I were climbing several thousand feet after zeroing the rifle at the start, I'd probably want to adjust for altitude and pressure if taking a 1000 yard shot. Unfortunately, both of the above (altitude and pressure) tend to move together in terms of throwing your shot off. Fortunately, temperature tends to move the opposite way - temperatures usually drop with increasing altitude, which decreases muzzle velocity and somewhat counteracts the effects of increased altitude and decreased pressure.

In the case of temperature, the ballistic calculator adjusts air density to account for temperature, but the powder temperature in the cartridge also impacts muzzle velocity. You get higher muzzle velocities with temperature, and as far as I can tell, it's anywhere from 1 fps/degree F to 2 fps/deg F:

http://www.exteriorballistics.com/ebexplained/4th/56.cfm

http://www.riflebarrels.com/articles/bullets_ballastics/long_barrel_velocity.htm

Abnormal temperatures also can have an impact on bullet stability, but I'm ignoring that:

http://www.frfrogspad.com/miscellb.htm#stabilize

Thus, temperature conspires in two different ways to impact accuracy, both before the bullet leaves the muzzle and after. So, for the situation of the M1A, assuming 2 fps /degree F, a 20 degree change in temperature can have 0.1 MOA impact at 100 yards, 0.8 MOA impact at 600 yards and 2.4 MOA impact at 1000 yards. Here in Colorado, it's not unusual to fluctuate that much or more during the course of a shooting day. If you're wanting one shot - one hit accuracy at 1000 yards, I conclude temperature needs to be taken into account beyond 800 yards or so. If you wait long enough, it's possible you may not hit the same target you were hitting previously at 800 yards or beyond if you don't account for temperature.

For humidity, a change from 0% to 50% has barely 0.1 MOA impact at 1000 yards, so it can be neglected.

**Other Factors.**I'm ignoring all the other factors such as scope accuracy:

http://www.precisionworkbench.com/3.htm

Coriolis force:

http://www.frfrogspad.com/miscellj.htm#Coriolis

or any other factors people have discovered that turn shots into misses.