Effect of Various Error Factors on Accuracy

[rsterne]

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....



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....



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....



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....



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

[Ribbonstone]

Seems right to me. The range. the target size, and how well the gun(and shooter) shoot.  Can add in, how well the estimate of the range/wind (and the farther away the target, the less likely to guess the wind right).

Maybe it's human nature to worry/test the things we can control (like velocity variation) simply because we can control that.

While I do still keep the numbers (shot strings, targets, variations, etc) have come to rely on them less and less in the real world.  Just kind of a guide, giving an idea of when you are stacking the deck against yourself.

[Motorhead]

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

There is MUCH irony to that statement 

[shorty]

Good stuff Bob.

Since we don't have control over wind drift and gravity is constant, It's strange to hear that those factors play a larger role than ES% (our only controllable factor). Unless I am misunderstanding, if you set up to run 2% ES you should be able to hit a target out to 100 yards with less than .5" CTC (with accurate range identification).

I have been asking about accuracy based on ES and bouncing it back and forth in my head. If you can control the ES (firstly) and measure the factors of accuracy, you should be able to hit bulls eye every time.

So to me, ES would be number one since you can control it. Every thing else is the Luck.

Not too many guns get that 2% or less ES without regulation. I have been asking a lot about ES because I am starting to think electronic valve control may have an advantage over regulation and possibly be the beginning of an all in one paper shooter and hunter all in one.

[pllagunos]

Awesome work Bob!

I have two questions... it has not much to do with the topic but what way do you find best to estimate wind? Lets say from 2mph to 10mph? I am trying to stretch legs with my at44 out to a 100 yards. Using the 17 shots I have at 2% (30 ft/lbs JSB 18.1), ranging at less that 1% (either with mil-dots or range finder) and estimating my wind correctly, do you think the rifle will perform out to 100 yards in the field, in a 2" kill zone?

[michaelthomas]

I appreciate you taking the time to quantify these things, Bob.   

Mike

[rsterne]

At 950 fps, with BCs from 0.03 to 0.06, a 2% ES at 100 yards should have a maximum C-T-C vertical dispersion of 0.68" or less (about 5/8 MOA).... Virtually any unregulated PCP will deliver that ES if you restrict yourself to a few shots (sometimes quite a few) at the top of the bell curve.... As you and Ribbonstone point out, the ES you settle for is the only thing in your control, so it makes sense, if you are shooting for group size, to want that as small as possible.... until it gets lost in the noise of the basic accuracy of the gun itself (which is MOA for a good gun in ideal conditions).... On the other hand, what I was pointing out was that there is little point in getting anal about it, when in the real world range estimation and even a tiny bit of wind will be a much larger problem....

It is interesting to note that .22 LR target ammunition (Eley Tenex 1055, one of the best in the world) has a ES of only about 25 fps over a box of 50 shells, which is 2.5%.... That translates into a vertical dispersion at 50 metres of 1mm per 3.9 fps, which means that over a box of 50, the vertical dispersion at 50 metres is 1/4".... Thinking that we need to have (or can achieve over 50 shots) an ES of less than 2% may be wishful thinking, mixed with theory and some VooDoo thrown in....

Bob

[rsterne]

The best way, in the field, to get a rough idea of windspeed is to get used to the effects of the wind on common objects, as described in the Beaufort Scale, developed by the Royal Navy in 1805....

http://www.spc.noaa.gov/faq/tornado/beaufort.html

Beaufort Scale values of Force 0 (Dead Calm <1 mph), Force 1 (Light Air 1-3 mph), Force 2 (Light Breeze 4-7 mph) and Force 3 (Gentle Breeze 7-10 mph) are the ones to study.... Anything Beaufort Force 4 or over, you can forget about shooting at long range and hitting anything on the first shot, IMO.... At 100 yards, with a good pellet at the optimum velocity, you can figure about 1" of drift per 1 mph of windspeed....

As far as any given rifle having the ability to hold a 2" group at 100 yards, even in perfect conditions, there are so many variables.... with the ones most likely to bite you being pellet quality/damage and barrel harmonics/movement.... If the pellet is damaged, or if the barrel is in full swing and not near a vibratory node, at the moment the pellet exits, all bets are off.... Fortunately, harmonics are one of the things we can tune around, and damaged pellets, if you are serious about hitting things way out there, should never reach the chamber.... Pellet weight just ends up being a part of the ES....

Bob

[pllagunos]

The best way, in the field, to get a rough idea of windspeed is to get used to the effects of the wind on common objects, as described in the Beaufort Scale, developed by the Royal Navy in 1805....

http://www.spc.noaa.gov/faq/tornado/beaufort.html

Beaufort Scale values of Force 0 (Dead Calm <1 mph), Force 1 (Light Air 1-3 mph), Force 2 (Light Breeze 4-7 mph) and Force 3 (Gentle Breeze 7-10 mph) are the ones to study.... Anything Beaufort Force 4 or over, you can forget about shooting at long range and hitting anything on the first shot, IMO.... At 100 yards, with a good pellet at the optimum velocity, you can figure about 1" of drift per 1 mph of windspeed....

As far as any given rifle having the ability to hold a 2" group at 100 yards, even in perfect conditions, there are so many variables.... with the ones most likely to bite you being pellet quality/damage and barrel harmonics/movement.... If the pellet is damaged, or if the barrel is in full swing and not near a vibratory node, at the moment the pellet exits, all bets are off.... Fortunately, harmonics are one of the things we can tune around, and damaged pellets, if you are serious about hitting things way out there, should never reach the chamber.... Pellet weight just ends up being a part of the ES....

Bob

Thanks Bob, one more question how can I control the barrel harmonics/movement? I 've heard people say the AT44 barrel bands can affect accuracy but at 20yards I am getting less than .20" CTC groups consistently...

[Ribbonstone]

Think me and Beauford go back at least 48 years...it's as good a guide now as it was them, but with the horrid BC of pellets (compared to bullets) it's still just a guide.

There is a reason I try my absolute hardest to not shoot a critter past 40-50 yards.  Feel just fine about shooting tin cans, paper targets, knot holes, pine cones, cow patties, etc, but on anything that has the gift of life that I want to take away, will limit myself to 40-50yards (yeah...even vermin...won't kill anything that (1) I don't want to eat or (2) hurts the environment of the critters I want to eat).


As far as long-long range shooting:

There has got to be a 100yard shooter out there that will do 2 things (and I feely admit, I'm not that shooter)::

1. Shoot 4 5-shot targets.
2. Have the groups centered on the target's aim point.

One "freak" groups, down in the left hand corner, it's going to cut it.  I've had those, and while it's nice to post them (per-internet we'd just cut the freak "bragging group" out and carry then around)....but one freak groups is just a sign that lady luck was with you for  ashort time (and she's a fickle b....h).

[pllagunos]

Think me and Beauford go back at least 48 years...it's as good a guide now as it was them, but with the horrid BC of pellets (compared to bullets) it's still just a guide.

There is a reason I try my absolute hardest to not shoot a critter past 40-50 yards.  Feel just fine about shooting tin cans, paper targets, knot holes, pine cones, cow patties, etc, but on anything that has the gift of life that I want to take away, will limit myself to 40-50yards (yeah...even vermin...won't kill anything that (1) I don't want to eat or (2) hurts the environment of the critters I want to eat).


As far as long-long range shooting:

There has got to be a 100yard shooter out there that will do 2 things (and I feely admit, I'm not that shooter)::

1. Shoot 4 5-shot targets.
2. Have the groups centered on the target's aim point.

One "freak" groups, down in the left hand corner, it's going to cut it.  I've had those, and while it's nice to post them (per-internet we'd just cut the freak "bragging group" out and carry then around)....but one freak groups is just a sign that lady luck was with you for  ashort time (and she's a fickle b....h).

I know some long range shooters from youtube 1) Ted, from TedsHoldOver and 2) Matt Dubber, from AirArmsHuntingSA

[Ribbonstone]

Unless you have a link to a vid I haven't seen, not sure that the "4 5-shot group on target" criteria has been met.  If I missed that, post a link.

[pllagunos]

Oh I didn't meant that they shot 4-5 shot groups at 100 yards, but that they have taken a lot of doves, pigeons and squirrels out to a 100 yards

[Ribbonstone]

Have watched most of those. Impressive for what they are. But the "miracle" of video editing does come into play.  If there were not missed shots or no flapping/kicking around results, there were edited out.  Don't much care if you show 12 kills on video if they were 22 shots taken.  Might be wrong, may be a much better shot than I.

[pllagunos]

Have watched most of those. Impressive for what they are. But the "miracle" of video editing does come into play.  If there were not missed shots or no flapping/kicking around results, there were edited out.  Don't much care if you show 12 kills on video if they were 22 shots taken.  Might be wrong, may be a much better shot than I.

Agree 100%

[Oldblades]

Best post I have read in my short time here Bob. Thanks for this.

 In regards to the wind at 100 yards, thats tough duty considering what may be going on at the muzzle isnt the same at any distance all the way to the target. So how does one establish adjustment to error, if the error is not known to be controllable or not.
Hence:

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

As Motorhead mentioned, there is profound irony in that statement.

[SpiralGroove]

Hey Bob, thanks for your work 
I need to re-read this one a few times before the bulb stops flickering .
God knows, I need to spend more time understanding the accuracy factors that = better luck

I think Baxter has learned how see/read/interpret/manipulate the wind........................
Kirk

[rsterne]

When I was sailing R/C Yachts I knew ONE guy that just seemed to be able to SEE the wind.... He was the guy who tacked off from a nice safe cover, leaving the fleet to wonder why.... and then suddenly the wind would shift, doubling his lead.... He was the guy everybody called "lucky", but I know better.... Irony perhaps, but I always figured he could win sailing a 2x4 with a sail on it....

Bob

[Tomg]

We need to put sails on our bullets....oh wait yeah, those are called pellets

[Sfttailrdr46]

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

There is MUCH irony to that statement 

Bob it is not luck it is MAGIC some shooters are just better magicians than others because they practice using their magic more,