Effect of Various Error Factors on Accuracy

There is always discussion about the importance of the Extreme Spread of velocities (ES) and how important it is to accuracy.... Obviously, the smaller the ES the smaller the possible group, although most rifles, and most shooters, are not capable of seeing the difference as long as the ES is reasonable for the range.... In addition, if there is any wind at all, and remember that even a 2 mph wind cannot be felt on exposed skin, that will quickly outrank the ES in it's influence on group size.... The other factor is how accurately you can estimate (or measure, with a laser rangefinder) your range, as once you are beyond your Point Blank Hold range, that becomes of paramount importance.... I looked at a pellet with a BC of 0.036 (typical for a JSB 18 gr. Heavy, or 25gr. King), leaving the muzzle at 950 fps, from a rifle where the scope is 1.5" above the bore, and the desired Kill Zone is 0.5" (0.25" above or below the line of sight).... and I used ChairGun's recommended far zero of 38 yards, which gives a PBR of 13.5-42.4 yards.... Here is what happens when we look at various sources of error.... The green line is an error of 1 Minute of Angle, for reference.... and the error graphed is the total (high to low), not just for one side of the vertical POA....

http://i378.photobucket.com/albums/o...psyjgic01f.jpg

First of all, you should notice that just a 2 mph crosswind has more effect than a 4% ES.... from 55 yards and out, it will drift you over 1 MOA off your Point of Aim.... Out to about 77 yards, the next most important factor is the ES, but after that if you make just a 2% error in estimating the range, that becomes more important than a 4% ES.... A 2% error is 1 yard off at 50 yards (ie 49-51 yards), or 2 yards off at 100 yards (98-102 yards).... At 77 yards, they both have a potential range of error of 1 MOA.... If we look at what happens when we combine the two uncertainties (ES and range estimation), we get the following limits on the trajectory, out to 50 yards....

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

For all practical purposes, until you are past your far zero (in this case 38 yards), an error in estimating the range makes no difference, and a 4% ES only starts to show up as a difference in where the pellet falls out of the intended 1/2" Kill Zone, which could be anywhere from 40-45 yards, instead of the theoretical 42.4 yards.... By the time you get to 50 yards, with a 4% ES and just a 1 yard error (long or short) in estimating the range, your pellet could be anywhere from 0.65-1.20" low, and that assumes your rifle is perfect.... Add your group size to that margin of error.... So what happens if we tighten up the ES and our ability to estimate the range accurately?.... Well, if we cut both sources of error in half, and also reduce the wind to just 1 mph (even smoke rises vertically, no way to judge it), as you would expect, all the deflections from the POA are cut in half as well....

http://i378.photobucket.com/albums/o...psolpi6d5u.jpg

So now were are dealing with just a 2% ES, and we have the ability to measure the range to within 1 yard at 100 yards (as good as any laser rangefinder, and better than the repeatability of most).... While each individual source of error is now less than 1 MOA, at 100 yards they range from 0.67 - 0.92".... Even cutting the ES down to just 1% means a possible vertical error of 0.34".... Interestingly, the Ballistics Coefficient doesn't affect that much, any BC from 0.03 to 0.06 gives the same vertical stringing at 950 fps.... If we look at the combined vertical error using a 2% ES, and only a 1% error in reading the range, we get the following range of trajectories....

http://i378.photobucket.com/albums/o...pss9n09olr.jpg

At 100 yards, your shot could land anywhere within a 1.5" vertical window, plus whatever group size your rifle is capable of in perfect conditions when tethered at constant pressure.... Even if you can get your rifle to shoot within a 1% ES (and most regulated PCPs struggle to do that), your vertical dispersion is 1.15" and the wind deflection is 0.93".... In other words, you are really lucky to get within 1 MOA of your Point of Aim on the first shot, even using a laser rangefinder.... Now if you are shooting at a known range, or an unknown one where sighting shots have given you the ability to determine holdover and wind drift, all this goes out the window.... If your rifle is tethered and holds a near constant velocity, and the wind never varies, then sub MOA groups become possible.... However, in a field hunting situation at unknown ranges, under real world conditions, even at 100 yards a great deal of luck comes into connecting with that first shot.... I would rate your ability to connect on the first shot to be first of all affected by the wind, secondly by an accurate determination of the range, and lastly by the ES....

Of course, the more you practice, the luckier you will get....

Bob