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Credit: Jim Baumann
Author - "Air Rifle Ballistics"
http://www.airgun.co.uk/Airgun_Accurracy.html
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Understanding Accuracy - Part 1
"When we think of accuracy in relation to our airguns; we think of punching several tiny little 5 or 10 shot groups on paper at fairly long ranges. This is not what accuracy is; but, this is what accuracy enables us to do. Accuracy in its simplest sense, is nothing but consistency.
To put it as concisely as possible; we could say that airgun accuracy is the ability for our airgun to launch a pellet at, say 800 FPS, and have it arrive at our target at, say 600 FPS. Now, if every shot we take does exactly that, and it is not deflected by wind or something else, our pellet is capable of shooting through the same hole shot after shot after shot. Most shooters assume; if every pellet leaves the muzzle at exactly the same velocity every pellet will hit the target at the same terminal velocity; but, it really does not work that way. If it did, we would have absolute accuracy.
Also, sometimes we put two pellets into the same hole at 50 meters; but, how often does that really happen? Sure, we get small groups at long ranges; but, why and what causes this? Better yet, what causes a seemly perfect pellet to be the one nasty flier in the group? Why do all the pellets cluster together, on the target; but, one has to go and ruin it?
We have all heard this story, or we have experienced it first hand. We have two guns that were made by the same gun maker. They are the exact same make and model, but one will shoot tiny groups with pellet X; while, the other shoots the same pellet all over the place. You are about to find out why and how this happens.
To fully understand accuracy we must understand what really happens to our pellet between the time we put it in the barrel and it hits the target. To understand accuracy, we must understand both internal and external ballistics.
We know that high powered rifles are accurate at very long ranges; it is nothing for the best of them to shoot tiny groups at 300 meters or even much more. Then why does our airgun accuracy fall off at such close ranges? Accuracy for ten meter guns, and Field Target range guns is not quite the same thing. First off, ten meter guns shoot better at rather low velocities, and shoot quite well or even more accurately with flat nosed, wad cutter type pellets. These guns are great at what they do; but, as our range increases so does the need for power.
The a-for-mentioned ten meter match guns shoot what are probably the finest made pellets; but, you never hear of anyone winning a field target match with those pellets. The reason has to do with ballistics, or the ballistic coefficient of the pellet. The ballistic coefficient is the pellet's ability to maintain a higher velocity down range. Simply put, the higher the ballistic coefficient of the pellet, the further it will shoot accurately.
While the reason that high powered firearms can shoot accurately for such long ranges is partly do to brute force; but, there is more to it than that. If we look at the design of a high powered rifle bullet; we can see that there is a great deal of difference between its design, and that of our airgun pellet.
A quick look at our high power rifle bullet tells us that it is very aerodynamic; but, lets take a closer look. The fact of the matter is that the back end of this bullet is much heavier than the sharp pointed front end of this bullet. If you were to shoot this bullet out of a smooth bore barrel it would be less accurate than an old pumpkin ball, shot out of a 12 gauge shotgun.
Twist Rate
What enables this high tech boat tail bullet to be aerodynamic, and very accurate, is the rifling in the barrel, that it is designed to be shot from. These rifles usually have a fast twist rate; in fact, they have a very fast twist rate. This causes the bullet to rotate very, very fast. Without this fast rate of rotation, our high tech bullet would probably flip end over end, and it would, of course, not be worth much in the accuracy department.
Rotating our pellets, through the use of rifled barrels, helps give them stability; so, they do not flip end over end. One of the questions that we need to address, is how fast do our pellet need to spin? Airgun barrels come in twist rates from, as slow as, 1 turn in 20 inches to 1 turn in 12 inches. How do we decide which is best? And does it really matter?
Without going into a bunch of theory about which twist rate is best; lets look at what works, and why it works. The object of the rifling is to rotate the pellet, and what we are really interested in, is the pellets rotation rate. To understand rotation rate, we need to look at some math. Rotation Rate = (12 / Twist Rate) * Muzzle Velocity, in feet per-second. The number 12 comes from 1 turn in a foot, or 12 inches; since we are using feet per-second. This gives our 150 grain 30 caliber rifle bullet a rotation rate of 174,000 revolutions per-minute, or 2900 revolutions per-second. Now, that’s what I call spinning!
We don't have to do this math to realize that the faster we shoot our pellet, the faster it will be rotating. While, I am going against modern ballistic theory; I will say that this theory does not have to deal with shooting the same pellet/bullet out of the same barrel at 500 FPS, and 1000 FPS. When you combine that with air gun barrel twist rates ranging from 1 turn in 20,1 turn in 18, 1 turn in 16, 1 turn in 14, and 1 turn in 12; somebody has got to be wrong somewhere!
However, since the actual rate of rotation is controlled by both velocity and twist rate; these twist rates are not really that far off the mark. However, airgun pellets have bigger problems built into their design.
A Case Of The Wobbles
Sometimes, when bullets are not properly made, they can suffer from something called static or dynamic unbalance. This is usually caused by the bullet having a hollow spot or spots inside. The key word here is unbalance. When a bullet is unbalanced; it quickly loses stability and accuracy goes in the crapper. This is a very rare occurrence with most modern high powered rifle bullets. The bullet makers put a great deal of effort into building their bullets, and having a bunch of bad fliers, would not keep them in business very long. While this is interesting information; all we care about is the fact that a bullet or pellet can be unbalanced.
- bullet2.jpg (5.9 KiB) Viewed 1249 times
When we look at the picture, above, we can see that our airgun pellet has a great deal of air space around it, and inside it, when compared to our high tech bullet. This lends itself to the pellet's weight not being perpendicular, or centered with its line of travel. In any real sense this design leaves itself open to the a-for-mentioned static and dynamic unbalance! Again, the key word here is unbalance; any lack of balance can and will cause our pellet to wobble. That is to say, it will not travel in a very aerodynamic fashion.
If you have ever looked at the pictures of air flow around pellets you will see that the air flow does not hit the tail. The air flows around the head in a perfect aerodynamic fashion; but, the sad truth is that this almost never really happens!
If we look at the picture below; we can see this perfect air flow; but, for some strange reason, there are NO RIFLING MARKS ON THIS PELLET.
- pellet-drag.jpg (6.9 KiB) Viewed 1249 times
It looks as though we have just found another problem; wind tunnel test are fine; but, they don't really tell us anything about the effects of rifling or what effect the groove marks have on the head of the pellet. Besides, large test models don't have the tool and die marks on them that are caused by stamping cutting and/or casting.
Aerodynamic Unbalance
Enter another problem, and that is something I like to call Aerodynamic Unbalance. Simply stated, Aerodynamic Unbalance is caused by pits, die marks, and deformation in the head of the pellet. You won't see many high powered rifle bullets with pits, dents or die marks in their head; but, this is quite common with airgun pellets.
Aerodynamic unbalance can also be caused by the rifling in the barrel; what can happen, is that coarse rifling will cause tiny chunks of lead to be pushed outward giving the head of our pellet a fan blade like appearance. Needless to say, that this is not good for the aerodynamics of our pellet. While this fan blade type of deformation is rare; all of the barrels with coarse rifling tend to do this to some degree. However, if you get rid of the rifling; you would also get rid of accuracy.
The simple fact is that our pellet always has some degree of wobble to it; and this causes the tail of the pellet to increase air drag. This is a fact, and with all of my testing, I would say that everything works exactly the way it should, less than 1/2 of 1 percent of the time. In very good guns, with the best of pellets; stabilization reaches only 75 to 85 percent. In other words, our pellets lose 15 to 25 percent of there potential; because, of extra air drag on the tail of the pellet do to a slight wobble.
This may horrify many of you; don't worry about it; because its affect on accuracy is quite small. Remember, consistency is accuracy, and as long as this wobble is nearly the same every shot; the pellet will go the same place. Why does it matter then? It matters because, it shortens the range, and limits the accuracy of our guns. The worst part, however, is that, it causes wind deflection to be very hard to predict. Shot to shot wind drift can double, and even triple, with no change in wind speed or direction!
Under ideal conditions all the pellets will hit at almost the same place on the target, even though the exact wobble changes a bit from shot the shot. The thing is, that the terminal, or target velocity can vary quite a bit, without shifting the point of impact. However, when we add wind, what happens is that the differences in velocity at target, or terminal velocity cause the slower moving pellets to be pushed further off course than the pellets that arrive sooner do to their losing less velocity. They lose less velocity; because, they wobble less.
It is hard for most shooters to understand that each and every pellet can leave the muzzle of their gun at the same velocity; but, the velocity at the target can and will vary a lot. I have clocked guns that while they had only a 5 foot per-second spread at the muzzle, they had as much as a 60 foot per-second spread at the 50 yard mark. While this terminal velocity spread does increase group size somewhat; almost all of the pellets would go into a nice tiny little group, until the wind would start to blow......
Twist Rate Again
As I said earlier, I won't talk about theory; but, I will talk about what works. Many years ago the 22 rim fire rifles only shot 1 bullet, and that was the 29 grain 22 short. Later the long rifle bullet came onto the market; but, the twist rate, 1 turn in 20 inches, for the 22 short, was too slow for the new longer 40 grain 22 long rifle bullet. They simply would not shoot very well, compared to their shorter brothers. That is when it was decided that the twist rate of the new rim fire rifles should be 1 turn in 16 inches. This allowed the new rifles to shoot both the long and the short bullets with a high degree of accuracy. This twist rate was a compromise; but, it worked. I have tested thousands of pellets, and tested thousands of the same pellet in many different guns, and I can say that the 1 turn in 16 inches is probably the best compromise. I have found no ill effects on even the shortest pellets, even at very high velocities, over 1000 FPS, and it seems to be fast enough to stabilize even the longest pellets. While true stability will still elude us; having a standard twist rate, would help in deciding the actual minimum depth/height needed in the lands and grooves of the rifling. This would, also be a compromise; but, it would still put us closer to our absolute accuracy gold.
To be real blunt, I think that a twist rate of 1 turn in 18 inches is just great for ten meter guns; but, for longer ranges, the twist rate should be at least 1 turn in 16 inches.
If you only want to punch nice round holes in paper at ten meters, static and/or dynamic unbalance becomes the thing to worry about; but, as our pellet reaches further and further out. Faster twist rates mean greater pellet stability; which means greater shot to shot consistency, or accuracy. It seems that some barrel maker's think that we all shoot at ten meters, and no further..... Oddly enough one of the worlds most popular Ten Meter Match gun makers, actually use a twist rate of 1 turn in 14 inches; with out any ill effects. Go Figure! I do prefer a twist rate of 1 turn in 14 inches, for the longer pellets, like the 10.5 grain Crosman Premier, and the H&N Barracuda.
Why Does Pellet X Shoot So Well In Joe's Gun; But, Not In Mine?
The most likely cause for this difference; is the difference in the barrel's choke. Some barrels are designed to have a tight choke. This choke is a good idea; but, sometimes, the barrel gets too much, of this good thing. Before I blame the barrel maker here; let me say that, too much choke only occurs when the pellets are too large for that choke. In other words, is the barrel over choked; or has the pellet maker, made the pellets too big?
This is probably the most important factor in the stability problem. When pellets don't fit the barrel; as they should, stability and accuracy suffer. At this point I would like to point out that what we pay for pellets; is nothing near what high powered rifle bullets go for. That in itself tells us that what we shoot is darn cheap. While there is a lot more material involved in making these bullets; it is not really where the cost is, and if we were all willing to pay 7 or 8 dollars for a hundred pellets; I am sure that we could get much better quality. So, before you start to blame someone, like the pellet makers, or the barrel makers, place the blame where it belongs. Gun and pellet makers sell only what we buy; so, if there is any blame here; we are the ones it belongs too!
All airgun barrels are not choked intestinally; some get their choke when the barrel is crimped for the front sight, or while being pined/pressed into the action, while others are designed with a choke built into them. Some guns come with no choke in their barrel at all.
One of the most popular and dumbest thing airgunners do, in the US, is to buy a piston gun and proceed to lop off a couple of inches of the gun's barrel. Work like this should only be done by a really, really good airgunsmith; because, the barrel may need to be choked... Just because the gun still shoots; does not mean that the job was done the best way.
Pellet To Barrel Fit
If you have ever had the experience of dropping a pellet into the breach of a barrel cocking gun; only to watch this pellet fall straight through the barrel, and hit the ground at your feet; can you begin to understand why absolute accuracy seems so elusive. The other extreme is the one you don't see, and that is when the pellet is just a bit too large for the barrel. What happens is the head of the pellet gets squashed, and deformed, causing unbalance, and poor aerodynamics. In the opposite case when the pellets are too small; the head can bounce around in the barrel, and come out at odd angles in relation to the barrel, causing all kinds of strange fliers. Pellet to barrel fit, is simply the most critical factor in airgun accuracy; period.
This is a reason why Crosman punches all of its Premier pellets out of the same die. While a pellet maker cannot control the inside Demeter of you barrel; they try to at least keep most of their pellets the same size; by, punching them out of the same die. This works fairly well; until you change die numbers. From personal experience, and a lot of testing, I can tell you that sometimes switching die numbers is just like switching brands of pellets.
Most piston guns have some sort of choke at their breach; but, many barrels have a choke near their crown. The choke actually helps accuracy, by resizing all the pellets to the size of the barrel. However, it is a place where lead will build up, and you can pull a tight patch through said barrel, from breach to crown, and the patch will come out clean. The problem is caused by pushing or pulling the lead further into the choke. Pulling or pushing the patch the other way will help dislodge most of this lead. A good brass bore brush works even better, and sometimes it is the only way to get the lead out.
If you want to know if your barrel is choked, or how tightly choked it is, simply push your favorite pellet through the barrel with a cleaning rod, and a patch. If your barrel has a tight choke; you will find it.
This is why land and groove depth is so important. It is part of this fit. One of the problems that we run into, with this, is that all pellets are not the same caliber. The lands and grooves inside a 177 caliber barrel need to be much smaller than they do in a 22 caliber barrel. Think about it.
One of the main reasons that the 22 caliber pellets hold their velocity better than their 177 caliber parts; has more to do with less deformation, and the fact that the same sized tiny pits, and tool and die marks have less of an affect on the balance and the aerodynamics of the larger pellet. And all this time you thought is was just the weight difference; well, think again!
The problem that we run into when we increase the caliber of our pellets, is we create more air space. Look at the amount of air space around a 7.9 grain Crosman Premier, then look at the amount of air space around a 25 caliber Diana Magnum. You can almost stick the little Crosman inside the hole in the back of the Diana. Why does this matter? Remember the static and dynamic unbalance that I mentioned earlier!
No pellet maker can make a pellet that will shoot well in every gun. However, they could if they were to make a all of their pellets in several sizes, and in increments of .0005. This would be very costly, and I doubt that most shooters would be willing to pay the increase in cost.
Before you try to shoot a new pellet in your gun, try pushing a few through your barrel with a cleaning rod. How do they fit? do they slide through with almost no resistance? or do you hit a spot where you feel like you need a hammer to drive it through the barrel? How does the rifling marks look on the pellet? Are they even, and is the depth the same all the way around? Has the head become deformed?
While some gun designs make doing this next to impossible, several others make trying this quite easy. This is one way of looking before you leap, and it can tell you a whole lot about how a new pellet will perform, especially if you compare it to the pellet that you are shooting now.
Critical Factors For Accuracy
The Ballistic Coefficient
A wad cutter pellet leaves the muzzle at 1050, and it only has 506 FPS left by the time it reaches 50 yards; while our little 7.9 grain Crosman Premier can leave the muzzle at only 780 FPS and still have 600 FPS left at the 50 yard mark.
Pellet Stability
Pellet stability, is important to accuracy; because, without a fair amount of it; say at least 75 or 85 percent accuracy will suffer. The greater the wobble, (pitch, and yaw) The more likely it will be deflected, even under conditions that appear to have no wind.
Shot To Shot Consistent Stability
Without this; even a slight amount of wind, can and will cause large differences in deflection. In other words, if a pellet decreases from a stability of say 95 percent, to 75 percent from one shot to the next; wind drift can double, or even triple. This makes it impossible to guess where to aim! If you have ever wondered why you had trouble shooting groups in the wind, even when the wind seemed constant, now you know why.
Faster Twist Rates
According to Rinker's book, "Mathematics can show that both static and dynamic unbalance can be improved by a slow twist. On the other hand, the stability factor is improved by a faster twist." What Rinker appears to be saying is that while the slower twist reduces the unbalance; a faster twist increases pellet stability. Any increase in the stability factor increases consistency, which is accuracy. In other words as long as we don't go nuts with our twist rates; accuracy will be improved with a higher rate of twist. Or to be more precise a faster rate of rotation. We can increase the rotation rate by increasing our muzzle velocity; however, in the UK this can be breaking the law.
Lands and Grooves
Why do we care about land/groove depth; because, if it is too much it will deform our pellet. If it is not enough it will not grip our pellet, and we have all seen fliers that come from shooting Peewees, or sub sized pellets. However, what is too coarse for our 177 caliber pellet, is not for a 22 caliber pellet. Some research, leading to some design changes could decrease pellet deformation, and increase accuracy.
Stability, Stability, Stability, and Stability
Stability is the most important factor in accuracy, period! All of the various characteristics and factors that I have mentioned mean nothing without pellet stability in flight.
Every gun and pellet combination that I have chronographed had one thing in common. If they shot accurately, they had a high degree of pellet stability, and those that shot poorly had a very low degree of pellet stability. In some cases pellet stability was so poor, that even when chronographing them at 10 yards, velocity spread was over 100 FPS; yet muzzle velocity was quite consistent.
Consistent pellet stability is controlled by pellet to barrel fit; that is to say that the head of the pellet must be large enough to engage the rifling; but, not large enough to cause any deformation. The tail of the pellet must also be large enough and flexible enough to give a good air seal, without deforming. Lubricants, like FP-10, Lube 1, and many others can and do help in reducing deformation, and actually increase shot to shot pellet stability, and actually increase the ballistic coefficient of the pellet being shot. This increases down range velocity and more importantly, it increases accuracy. After all that is all we really care about."
