View Full Version : all yardage group size

June 1, 2013, 03:09 PM
When I worked out my load for my rifle, shooting from a bench I got 3 bullets touching @100 yrds. With all conditions being perfect should I get the same size grouping for 200, 300, 400 etc etc
Thanks Steve

June 1, 2013, 05:55 PM
If you do, please tell the rest of us how.
The angle will stay the same, but the distance between the holes in the target will increase with distance.
You know, if an angle of measurement is equal to x inch at 100 yds, then it's equal to 2x at 200 yds, 3x at 300 yds and so on.
Hope that made some sense.

June 1, 2013, 06:15 PM
In addition to the linear dispersion described above, you also get additional dispersion as the distance increases due to imperfections in the load and bullet. Variations in velocity will cause each shot to fly a slightly different path. This is why the most serious competitive shooters handload. Then they can trim all the brass, weigh all the bullets, measure every powder charge, etc, to make sure the variation between rounds is kept to a minimum. Since you are already working up loads yourself, you can control some of this.

Then there is wind, humidity, ...it goes on and on.

June 3, 2013, 06:01 PM
And a ten-shot group will be 50% larger than a 3-shot group.

Dave P
June 3, 2013, 06:12 PM
"With all conditions being perfect ... "

Please invite me to your range. I love perfect conditions!

June 3, 2013, 09:18 PM
Bullets are driven off course by different factors, but the ones that affect how group MOA can deteriorate with range are mostly due either to variation in muzzle velocity or are those that are introduced by drift. As the bullet flies down range, it is slowing down so that each successive 100 yards takes longer to traverse than the previous 100 yards did. That gives both gravity and drift more time to move the bullet, so the effect of gravity on difference in time-to-target and of drift on the group size is greater with each successive 100 yards. And of course these errors accumulate.

To estimate the effect, take a ballistics program that shows how long it takes for your bullet to reach each range in your atmospheric conditions. Then calculate the time the bullet would take to get there if it stayed at muzzle velocity (like in a vacuum). Subtract that calculated time from the actual time. Drift components will affect the bullet in proportion to the size of that time difference.

June 5, 2013, 09:51 PM
Thanks for all responses
Looking for an answer for group size other than gravity and wind and humidity and so on, thats what I mean with perfect conditions I KNOW CONDITIONDS ARE'NT PERFECT all I'm asking is
Will my group size be the same at 100 200 300 and so on.
Or will my grouping in large with longer yardages
If I shoot a 1"group @ 100 yrds will my group size be 10" @ 1000 yrds
or will the group size remain the same at 1000 yrds
I do my own reloading about 5yrs pistol 3 yrs for rifle , I reload for all my hunting rifles and doing very well with and love it

June 6, 2013, 12:39 AM
If everything is perfect and nothing but distance changes, it would be reasonable to see a linear increase in group size as the distance stretches.

So a 1" group at 100 yards would be a 2" group at 200 yards, 3" at 300, 6" at 600, and so on. It's not quite that simple, but that will get you in the ballpark.

In practice, the group size will increase MORE than that because wind will have more effect as the distance stretches, aiming will be more difficult as atmospheric conditions make it harder to see the target perfectly, etc.

June 6, 2013, 07:13 AM
When I worked out my load for my rifle, shooting from a bench I got 3 bullets touching @100 yrdsUnless you can repeat that small group with another three-shot group to confirm it, you may be in for a surprise. There is too much of a possibility that the three bullets were touching just by random chance. Re-shoot that load before you get your hopes too high.

Brian Pfleuger
June 6, 2013, 10:27 AM
If I shoot a 1"group @ 100 yrds will my group size be 10" @ 1000 yrds
or will the group size remain the same at 1000 yrds

In the real world, you can expect an absolute minimum 10% MOA increase in group size per 100 yards.

MOA is "Minute of Angle". One MOA at 100 yards is 1.047 inches, generally considered to be 1 inch. It's an angle, so it's growing larger with distance, double the distance, double the size. Triple the distance, triple the size. Your bullets, unless they all go through the exact same, single bullet sized hole, are dispersing at an angle. They all left from one hole, aimed at the same spot. If they weren't moving away from each other, they'd all hit the same spot.

As mentioned above, there are compounding errors causing that dispersion. Those errors don't stop and remain constant, they grow. So, for an absolute minimum, a 1 MOA (1 inch) group at 100 yards will be 1.1MOA (2.2 inch) group at 200, a 1.21 MOA (3.63 inch) group at 300, 1.33MOA (5.32 inch) at 400... etc, etc.... out to 2.356 MOA at 1,000 yards. 1,000 is (obviously) 10 times as far as 100, so 1 MOA is 10 times as large... in other words, 1 MOA at 1000 is 10.47 inches. So, that 1 MOA (1 inch) group at 100 will be AT LEAST 2.356 MOA (24.66 inches) at 1000.

Bart B.
June 6, 2013, 12:09 PM
Things that make groups open up to more MOA's as range increases.......

Muzzle velocity spread.

Bullet's BC spread (caused by how much out of balance they are; they ain't all perfect).

Subtle air currents in all directions we cannot see; even with properly set spotting scopes.

Air density variables caused by different temperature bands the bullets go through.

And the group size at the muzzle is always zero MOA, isn't it?

June 6, 2013, 05:09 PM
Just to clarify, the angle mentioned has the rifle as its vertex and the width of the group is a chord that subtends some angle. At 100 yards, one inch subtends an angle of 0.955 minutes (0.955 60ths of a degree).

This is not intuitive to everyone, so think of it this way: Suppose you put two holes on a 100 yard target an inch apart. Further suppose there was a second target behind it at 200 yards. If you could look through the center of your sight at the first hole, you could draw a straight line through it to the 200 yard target. Now suppose you looked at the 200 yard target through the second hole and drew a second straight line through it. You'd have to move the rifle slightly to put that second hole in the center of the sight. That slight movement represents a small change in the angle at which you are viewing the target, assuming the rifle pivots around a fixed point on the bags. So the two lines you drew would meet at that pivot point (the vertex of the angle). But because the sides of any angle diverge in proportion to their length, you would find the two lines met the paper on the 200 yard target twice as far apart as they were on the first line.


You can actually try that experiment, by the way. Put up a 200 yard target and put a 100 yard target right in front of it that is half the size so you can tell when the two are lined. With a typical high power rifle cartridge, you will strike find the bullet drops a couple of inches between the 100 and 200 yard targets, but will hit both and let you see the dispersion. It is best if the 100 target has a big hole cut out of its backer where you are going to shoot it, so only the thickness of the paper affects the bullet. Going through something heavier can introduce some deflection drift. Plain paper won't have a significant effect at the ranges we're talking about. Bryan Litz did this with bullets flying to 1000 yards without incurring trouble with the process.

If you try the experiment, as already explained, a 1" group will normally actually be slightly over 2" at 200 yards owing to drift components having increasing amounts of time to act over each successive 100 yards. There are some funny circumstances in which that may not occur and randomly some drift factors can work to tighten the group, but that's not as common as the reverse.

Bart B.
June 7, 2013, 05:24 PM
Another couple of interesting things about groups; all sizes large and small plus all those in between.

The smallest groups happen when one of two things occur; everything is perfect and 100% repeatable for each shot. Muzzle velocity, shooters' hold and aiming point remains the same while the bullet goes down the barrel, all bullets are perfect and everthing else that has variables. There are no variables whatsoever. The other is all the variables' size and direction somehow cancel each other out so all shots go into one hole.

The largest groups happen when all the variables in one direction mentioned above add up to put the bullet holes furthest from center where they are.

June 7, 2013, 05:55 PM
Thanks for all replies
I understand what everyone is saying
so the same goes for left and right as well ?


June 7, 2013, 06:15 PM
More or less. As the range stretches, muzzle velocity variations, if significant, could cause more vertical stringing and open the groups more than one might expect by predicting group size as a linear expansion. So if you're shooting on a clear day with no wind, you might see your horizontal group size expand linearly with distance while your vertical group size might stretch more than that.

On the other hand, if you were shooting a loading with very consistent muzzle velocity but on a day with light wind, you might find that your group sizes expanded linearly in a vertical direction but tended to stretch in the horizontal to a greater degree.

June 8, 2013, 02:50 PM
It's tricky to add all the parts up. Harold Vaughn has a graph in his book showing how a side wind also changes vertical impact, with the amount of vertical change depending on the gyroscopic stability factor of the bullet. The result was diagonal stringing with gusting side winds, with the higher spin rates causing the angle of the diagonal string on paper off of horizontal to increase. The angle is not steep. Usually less than 20° for common stability factors. He had an article in the November, 1994 issue of Precision Shooting on this particular effect. In any event, a side wind thus also has a smaller effect on vertical group size.

June 8, 2013, 07:23 PM
...a side wind also changes vertical impact, with the amount of vertical change depending on the gyroscopic stability factor of the bullet.That's correct. A wind from the side will either raise or lower the point of impact based on the bullet's direction of spin. The lift or drop is caused by the Magnus Effect.

A clockwise spinning bullet (with respect to the shooter) will tend to impact lower on the target in a right to left wind and higher in a left to right wind. It reverses if the bullet is spinning the other way.

The simplest way to think about it is that the spinning bullet drags a very thin layer of air around it as it spins. If the bullet is spinning clockwise (with respect to the shooter) and the wind is from the right, that spinning air will tend to "bunch up" at the top of the bullet because of the wind and will tend to move faster at the bottom of the bullet because it's going the same direction as the wind. That raises the pressure above the bullet and lowers it below the bullet and that makes the bullet tend to fall a little faster than it would otherwise.

It's not a huge effect, but it can make a difference as the range stretches.

June 8, 2013, 08:06 PM
Thanks again for your time and information.
All information was very helpful.
Thanks again

Bart B.
June 9, 2013, 08:18 AM
That Magnus effect's most noticed by smallbore shooters with their 40-gr. lead roundnose bullets at 50 and 100 yards. They have a distict 2:1 ratio for cross winds. For every 2 MOA sight movement in windage, you have to make a 1 MOA change in elevation. UP for going right, DOWN for going left. Uncorrected, they'll string from 10 o'clock to 4 o'clock on the target for right hand twist rifling. Some competitors mount their rear sight with the windage arm angled 30 degrees to the horizontal from 8 o'clock to 2 o'clock to automatically compensate for it. Those bullets hav a BC of about .180 and drift .32" per mph at 100 yards and .08" per mph at 50 yards.

Centerfire bullets have much less effect per mph of wind. The ratio's about 15:1 in my experience. With 30 caliber bullets at 1000 yards drifting from 7 to 12 inches per mph at 1000 yards, it takes a big windage correction before any elevation change is needed; 1 MOA in elevation for every 15 MOA of cross wind. Shooting long range in fishtailing 5 to 8 mph head or tail winds, I never corrected for it.

June 9, 2013, 02:04 PM
John and Bart,

FYI, Vaughn, who was Head Aeroballistician for Sandia National labs and who co-authored an American Institute of Aerodynamics and Astronautics paper in 1973 called "A Magnus Theory", said that bullet vertical drift is not due to Magnus effect. In Rifle Accuracy Facts (Precision Shooting Pub, 2nd ed, 2000, pp 195-196) he summarizes:

"A lively discussion recently took place in "Precision Shooting" on how the vertical component of wind drift must be due to Magnus force. Since I am very familiar with Magnus effects {references his paper here} I wrote an article that appeared in the November 1994 issue of "Precision Shooting" explaining that Magnus force acts in the wrong direction and is much too small to cause the observed effect."

Vaughn doesn't go into detail in the book, but the reason Magnus force is not responsible is that wind doesn't blow over a bullet sideways, which is necessary to create the effect. Instead, precession constantly corrects the point of the bullet into the wind coming at it, so a side wind results in the bullet pointing into the net vector of that wind combined with the head wind caused by the bullet's velocity. A bullet at 2500 fps in a 3:00 20 mph side wind, will correct its point 0.67° to the right so the net wind it experiences is at the same angle to it that it would experience in still air. Drag being straight to the rear of the bullet and opposite the direction it points to, the drag now has that same vector angle off the still air trajectory, which is what pulls the bullet to the left (wind drift) in the 3:00 wind. It is not being blown that way by wind against its side.

The only error in all that is that precession reaches equilibrium with directing the point of the bullet into the oncoming air stream slightly off straight at the yaw of repose. This is a very small angle on the order of one moa in most instances, and it is this small pointing error that is responsible for spin drift by introducing a slight side drag. This drag is to the right for bullets from a right hand twist barrel, and to the a left for those from a left hand twist barrel. This yaw actually turns the side of the bullet slightly into the wind on the side that the bottom surface of the bullet is rotating toward. So the bottom of the bullet always has the faster speed into that tiny off-axis wind vector with the result that the small amount of Magnus force it introduces is always pushing the bullet up. That will be true whether the wind is from the left or from the right, and true whether the bullet is spinning clockwise or counterclockwise.

Vaughn goes on to say:

"Instead of Magnus effects causing the vertical wind drift component it is caused by gyroscopic moments similar to {those that cause} the yaw of repose…."

June 9, 2013, 05:40 PM
So the bottom of the bullet always has the faster speed into that tiny off-axis wind vector with the result that the small amount of Magnus force it introduces is always pushing the bullet up. Except that we have evidence that it doesn't always push the bullet up.For every 2 MOA sight movement in windage, you have to make a 1 MOA change in elevation. UP for going right, DOWN for going left.I think that Mr. Vaughn should spend some time on the range to test his theory.

Bart B.
June 9, 2013, 11:36 PM
If it is not Magnus, I'll call it something else. It happens.

June 10, 2013, 11:05 AM
Except that we have evidence that it doesn't always push the bullet up.

Let me clarify what I was saying: The actual Magnus force acting on the bullet in the vertical plane is miniscule, and rechecking in Robert L. McCoy's Modern Exterior Ballistics, Magnus force mainly acts in the horizontal plane, anyway. Any vertical component is so small that even though it would push up, regardless of the direction of the wind (or lack thereof) it's of an order of magnitude that would produce a small fraction of an inch of elevation difference at 1000 yards. Really, really small. McCoy says that at the BRL precision free-flight spark range tests, they were never able to detect, much less measure, Magnus force effects on projectiles at all.

I think that Mr. Vaughn should spend some time on the range to test his theory.

If you read Vaughn's book you get instrumentation envy. Everything is rigorously tested.

I think you've mistakenly got the impression that because Vaughn shows Magnus force is not responsible for vertical wind drift that he is somehow suggesting that there is no vertical wind drift. That's not the case at all. He just shows it has a different cause than Magnus force.

Vaughn goes on to predict the angle off horizontal that wind-induced stringing will have at different gyroscopic stability factors. He includes a high contrast image of a 200 yard group fired in varying 3:00 wind from a 6 mm BR integral machine rest test bed gun that fires bugholes in no wind. It shows the predicted 17° angle off horizontal for that bullet's stability factor (about 1.6). He shows that a bullet with an average stability factor of 3 will result in about 1 click elevation change for two clicks windage change, as Bart suggested, and with the same up and down direction relationship he suggested (for a right hand twist barrel; it reverses with a left hand twist barrel). A bullet with an average stability factor of 1.4 will be about 1 click up for 4 clicks left.