Shorty, after previous efforts to get you to explain met with your refusal to respond, I glad you have given your best answer. Unfortunately it remains unsatisfactory, graph notwithstanding.
The following are your own words from a previous post on this forum.
Many shooters make the erroneous assumption that dispersion increases with distance, that group size only becomes larger as distance grows. This is incorrect.
Beginning from the muzzle, dispersion increases until about halfway to the ideal distance at which convergence occurs. From about the halfway point up to the ideal distance group dispersion begins decreasing again in terms of MOA.
Your idea is that a good rifle will shoot to a larger MOA at about 25 or so yards than at 50 (or at 50 than at 100). That's nonsense. It's doubtful anyone, including you, will find evidence from elsewhere that supports your view.
Gravity and MV variation alone ensures that dispersion is less at 25 than at 50 or less at 50 than at 100. It might help your position if positive compensation was perfect and completely achieved. Of course, it's not.
Nothing further need be said unless someone wishes to support Shorty with reliable information.
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Glenn, it is basic ballistic theory. Go here:
https://www.jbmballistics.com/cgi-bin/jbmtraj-5.1.cgi
Select Eley Club for the bullet. That will make it use the appropriate values for the first three entry boxes, so what they say will then be irrelevant. Here are the rest of the values used, most of which should just be default already, and some that are irrelevant but listed anyway:
Muzzle Velocity: 1060
Distance to Chronograph: 0
Sight Height: 1.5
Sight Offset: 0
Zero Height: 0
Zero Offset: 0
Windage: 0
Elevation: 0
Line Of Sight Angle: 0
Cant Angle: 0
Wind Speed: 0
Wing Angle: 90
Target Speed: 0
Target Angle: 90
Target Height: 10
Minimum Range: 0
Maximum Range: 100
Range Increment: 1
Zero Range: 50
Temperature: 59
Pressure: 29.92
Humidity: 0
Altitude: 0
Vital Zone Radius: 5
Energy Column Formula: Energy (ft-lbs)
Column 1 Units: 0.1 in (to move the decimal place one spot to get another decimal of accuracy to be output)
Column 2 Units: 0.1 MOA (same accuracy deal)
Elevation Correction for Zero Range: checkmark
Windage Correction for Zero Range: no checkmark
Range in Meters: no checkmark
Target Relative Drops: checkmark
Zero at Max. Point Blank Range: no checkmark
Mark Sound Barrier Crossing: no checkmark
Include Extra Rows: no checkmark
Round Output to Whole Numbers: no checkmark
Include Danger Space: no checkmark
After hitting Calculate with all of that set and recording the results I then hit Back in the browser to get back to the input page, and I change the muzzle velocity from 1060 to 1085 and hit Calculate again and record that data. That gives this after dividing the drop by 10 to bring us back to the proper decimal places and gives this, which you can double check for yourself by entering the same stuff into the same calculator:
And results in this graph of drop versus yardage for both shots:
That gives you two shots, one at 1060 fps and one at 1085 fps, from a rifle that has been tuned for 50 yards. As you can see in the data, the elevation delta starts at 0 at the muzzle and grows until about the halfway point to the target, and the dispersion maxes out at 0.05" at the 28-yard mark. After that point it continues falling until it reaches the 50-yard target and tuning point, at which point the delta is 0, or going through the same hole. After that point the dispersion continues growing until the end of our data at 100 yards. It would continue growing past that point if you care to enlarge the data pool. If you change the tuning point / target distance / zero distance to 100 yards instead and calculate the data out to 200 yards you will see a similar thing happen, only with the dispersion steadily growing until somewhere around the 40-60 yard region, the exact answer being limited by the decimal places that this particular calculator is capable of, and then shrinking until we get to the 100-yard tuned/target distance. And, again, after that point it will begin growing again and will continue growing. That's just basic ballistics. If you can tune for a particular distance that's what will happen. If you don't tune at all and just live with what the barrel naturally does then you could figure out what the barrel's natural tuning distance is with a given ammo by shooting lots of shots at a lot of distances. And once you figure out what that natural tuning distance is you will see the same pattern, where the dispersion steadily grows from the muzzle until about halfway to that natural tuning distance and then it will decrease until it reaches that distance. And beyond that distance it will continue growing as you go further and further out.
Every single barrel that has ever shot a projectile behaves in this fashion. The only barrel that would not exhibit this behaviour is one that is incapable of flexing. If you had a "barrel" made out of a solid 1-cubic-metre block of steel that had a 22 LR bore drilled, reamed, rifled, lapped, chambered, and crowned through the centre of it and attached an action to it then it probably would not flex enough to notice any flex at all. And you'd get dispersion exactly equal to the amount of muzzle velocity variation seen present in the ammo. It would start at 0 at the muzzle and continually grow from that point forward, exactly as you describe and imagine it does with the actual barrels you own. But the problem is none of the barrels you actually own are devoid of flex. They all flex. Every single one of them. They all flex during firing and the vibration pattern that is present because they can flex makes them behave exactly as I describe, not as you imagine. Your supposition is only correct in the example of a barrel that is incapable of flexing and thus vibrating. Since all of our barrels flex and vibrate your supposition is incorrect. They all have their own unique vibration pattern, as the one I showed earlier would be unique to the barrel it is patterned on. This is what determines how they behave with any given ammo at any given distance. This is what gives them their own unique natural tuned distance. And it is what allows one to use an add-on tuner to alter that tuned distance, hopefully in a favourable manner for your target distance of choice.
It isn't *my* idea. It is basic ballistic theory that anyone can confirm with their own ballistic calculator of choice. It's basic physics. It's just math. It's the physical world doing what it does due to the rules it follows. It's got nothing to do with me or what I think. Like I told you before, Glenn, take one of your shooting days and set it aside to do a test where you'll fire 100 shots at 10 yards, 100 shots at 20 yards, 100 shots at 30 yards, 100 shots at 40 yards... on up to 100 shots at 100 yards without touching any of the controls on your rifle other than the parallax to ensure you're focused to see the target and check out the results for yourself. You might find the current tuned distance within that first 100 yards, or you might have to continue the experiment beyond that to find it, but that tuned distance is there to find. The smallest amount of dispersion in terms of MOA will not be as close as you can get to the gun, bar not being able to actually measure small enough at that distance. Using OnTarget's practice ARA target #7 and shooting one shot per bull will help get around that issue by allowing you to scan them and place the shots pretty accurately in the program, allowing it to give you pretty accurate measurements. You'll find something similar to this ballistic calculator exercise. The distances that the various things happen at will be up to your barrel's behaviour, but you will find the same things. Dispersion growing until around the halfway point of the tuned distance, shrinking until it reaches that tuned distance, and then continually growing once beyond that. That's just ballistics.