Another Way of Looking at ES

Most of you will know that for the vast majority of shooting I suggest a 4% or smaller Extreme Spread (ES), ie the difference in velocity between the fastest and slowest shot, compared to the average velocity.... I've written numerous posts about why I use that number, but perhaps it's time I looked at it from a different perspective.... Most of my guns are tuned to shoot in the low 900s, and I seldom use anything but a round-nosed pellet, so that is what I have used to develop my 4% ES idea.... Let's look at what happens if we use a pellet with a much different BC.... or use a vastly different velocity....

I used three different velocities, 1000, 750, and 500 fps.... Then I used three different ES, representing 2%, 4%, and 10%.... I used three ranges, 20, 50, and 100 yards.... Lastly, I used three different BC's, of 0.010, 0.030, and 0.050....This should cover nearly all the shooting conditions except 10M competitions, and I'll even comment about that later.... I used ChairGun's Vertical Stringing Widget to calculate the total height of the string due to velocity change for each combination.... The table below gives the results for each velocity, and the values in red exceed 1 MOA vertical dispersion at that range.... I used that as an arbitrary value, but in fact any shooter who expects MOA accuracy from his gun will want the vertical stringing from velocity to be maybe half that value, meaning an even tighter ES to attain that at the range he is shooting....

1000 fps

http://i378.photobucket.com/albums/o...psihmbnnzs.jpg

Note that at these velocities, the BC doesn't make a lot of difference until you push out past 50 yards.... The fact that the vertical stringing is worse with a wadcutter at 100 yards doesn't matter to us, as we would never use them at that range anyway.... With decent pellets, a 2% ES results in about a 2/3 MOA vertical stringing at 100 yards, about the maximum most shooters would accept.... The same thing applies to a 4% ES at 50 yards, which is why I have always used that.... At 20 yards, a 10% ES works out the same, about a 2/3 MOA dispersion....

750 fps

http://i378.photobucket.com/albums/o...pszbgzlpux.jpg

When we drop down to 750 fps, we need to tighten up the ES to stay within the 1 MOA vertical stringing.... In fact, at 50 yards, a 2% ES is about the same as a 4% ES at 100 yards when you are shooting at 1000 fps.... A 10% ES will no longer hold a 1 MOA vertical dispersion at 20 yards.... You can also see the effect of a poor BC on the results at closer ranges....

500 fps

http://i378.photobucket.com/albums/o...psngoeertc.jpg

When we drop down to 500 fps (as is the case with non-PAL airguns), the required ES tightens up even more.... In fact, the only combination that is under 1 MOA in the chart is a 2% ES at 20 yards.... A 2% ES is about 1.5 MOA stringing at 50 yards, and a 4% ES is over 1 MOA at 20 yards.... It is pretty obvious that for non-PAL airguns, you want to keep the ES as small as possible, even at the relatively close ranges they are typically used at.... If you are shooting in 10M competition, the velocity is typically about 500-600 fps, and wadcutters are used.... This means that if you have a 2% ES, the vertical dispersion is about half what is shown in the table above, or about 1/16".... Therefore, you won't want anything over a 10 fps ES at the most....

In my next post I hope to present some graphs showing the maximum ES vs. range for a few common examples, to obtain a given MOA of vertical dispersion.... I hope you find this information useful....

Bob

These graphs are taking a while to generate, so I'll just post them one at a time.... This one is done with a BC of 0.030, and I used an allowable Vertical Stringing of just 1/2 MOA.... This would be typical for shooting at relatively small targets at longer ranges, where you want the ES to be small enough to be just about negligible.... ie less than half what you are likely to shoot on a good day....

http://i378.photobucket.com/albums/o...psepwassf5.jpg

Some noticeable benchmarks, for fussy shooters, are:

900 fps at 100 yards, 1% ES.... at 55 yards, 2% ES.... at 37 yards, 3% ES.... at 30 yards, 4% ES.... at 23 yards, 5% ES....
800 fps at 82 yards, 1% ES.... at 42 yards, 2% ES.... at 31 yards, 3% ES.... at 22 yards, 4% ES....
700 fps at 65 yards, 1% ES.... at 35 yards, 2% ES.... and 23 yards, 3% ES....
With a non-PAL (<500 fps) airgun, even a 1% ES (just 5 fps) will cause over 1/2 MOA stringing past about 35 yards....

If you are satisfied keeping your Vertical Stringing to within 1 MOA, you can double the allowable ES at every range, they are in direct proportion.... Note that at 900 fps, with a 4% ES, you would be just under 1 MOA Vertical Stringing at 50 yards (about 0.44")....

Bob

Here is the second post, this time looking at shooting a Wadcutter with a BC of only 0.010.... I only plotted 500-700 fps, because you aren't likely to use more than that when shooting them, and 50 yards is the maximum that makes sense with these pellets at these velocities.... I stayed with the 1/2 MOA Vertical Stringing, as most of the guys doing this seriously will want to stack the pellets pretty much hole on hole.... At 10M, 1/2 MOA is just 0.058" (2 mm)....

http://i378.photobucket.com/albums/o...psbhlciqxo.jpg

So for shooting at 10M (11 yards), at 500 fps, a 3% ES (15 fps) will keep the stringing under 2mm.... At 600 fps, the ES could be 4% (~ 25 fps) and still keep the stringing to just 2mm.... To get that down to 1mm dispersion, (1/4 MOA), you need about a 1.5% ES (8 fps) with a 500 fps gun, and about 2% (12 fps) with a 600 fps gun.... Pretty much any target rifle will do better than that.... In fact, any regulated PCP should hold a tight enough ES to produce under 1mm Vertical Stringing at 10M....

Incidently, looking at the graph in the previous post, but thinking about it for 25M benchrest shooters, who typically use pellets with a BC of 0.030 or better.... once again any regulated PCP that is working properly should pretty much do the job.... At 25M (27.5 yds), 1/4 MOA is 0.072".... If we look at velocities of 800-900 fps, we get the following.... In a gun shooting 800 fps, a 1.5% ES (12 fps) should shoot less than 1/4 MOA dispersion.... If the gun is shooting 900 fps, that could expand to a 2% ES (18 fps)....

Bob

Here is the third graph, this time for you long range bullet shooters.... This time I used a BC of 0.100, and looked at velocities of 800-1000 fps and ranges of 50-250 yards.... The criteria for Vertical Stringing is still 1/2 MOA....

http://i378.photobucket.com/albums/o...psqy6yloe5.jpg

Here are the points to note....

At 100 yards, at 1000 fps you can get away with a 1.5% ES, but by the time the muzzle velocity has dropped to 800 fps it needs to be under a 1% ES....
At 200 yards, cut those numbers for the acceptable ES in half.... At 900 fps, you need a 0.6% ES (5 fps) to shoot within 1/2 MOA Vertical Stringing....

Looking at this from this perspective, you can see how important it is to get the ES as low as possible when you are reaching out 200 yards.... Remember, 1/2 MOA at that distance is over an inch.... The BC makes hardly any difference at all in the Vertical Stringing at these ranges and BCs.... less than 0.05" at 200 yards if the BC doubles to 0.200.... You can see why a lot of the long range guys tether their guns to a regulator, to keep the ES to a minimum....

Bob