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A natural shooter

by B.B. Pelletier

I witnessed something last week that I have to share with all of you. I saw a new shooter who is a “natural.” What I mean is that I saw a shooter who did everything she was asked to do, with the result that she hit most of her targets. What made it noteworthy was that her targets were ones I would have struggled with.

In what must be a classic twist of irony, the new shooter is Crystal Ackley, a new host on American Airgunner. She’s supposed to be learning to shoot! And we’re supposed to be teaching her. But who knew she would be a natural?

I’m sure many people might think that we turned Crystal into another Annie Oakley through the magic of editing. But we’re not doing that! We don’t have to, because miss Oakley, er Ackley, is a dead-accurate shot right out of the box! In all my shooting experience, which includes running hundreds of ranges and teaching thousands of new shooters over the span of 40 years, she’s only the second natural shooter I’ve ever encountered.

Those of you who have seen the show will have seen me teaching her to shoot the Makarov BB pistol in episode six. We started at five feet from the target and gradually backed up to 20 feet. I wrote about this teaching technique in a blog in 2008. But when I watched Crystal shoot on camera, I was amazed. She was able to hold her groups as tight as any that I can shoot with the same pistol, even though this was practically the first time she’d shot a gun! I’m a 10-meter pistol competitor, for those who don’t know.

For a moment, I thought What a wonderful teacher I must be! Then it dawned on me. I’m not a great teacher; she’s a great student–a natural shooter, if ever I saw one!

This past week, she was back on the show, learning to shoot other airguns. In one scene, she was instructed how to shoot air rifle silhouette by silhouette shooter Mike Sporer. Mike is one of those great shots who seldom misses anything; but when I saw Crystal hit the first 20-yard chicken target she ever shot at, I felt like a proud parent of an honor roll student. Suddenly, those sappy bumper stickers made sense!

Then, she hit the second chicken she ever shot at, and the rest of the crew began to take notice. We all shoot a lot during the filming of the show, so everybody knows which shots are easy and which aren’t. The 20-yard chicken is not an easy offhand shot.

But it didn’t stop there. She proceeded to hit the 30-yard pig and the 36-yard turkey, as well. Oh, she did miss a couple of times, but the hits kept coming at a rate I don’t think I could have equalled.

Then, we got to the 45-yard ram. Mike, who had been cleaning the targets up to this point, missed his first shot. Then Crystal fired her .22-caliber Benjamin Discovery and launched the ram into orbit. The camera was rolling, so I had to scream silently, but scream I did!

Mike shot a second time and missed again. Then Crystal hit the second ram she ever shot at. Paul Capello, who was running the camera at the time, looked away from the eyepiece, turned to me and gave me a “What the hell did we just see?” look. Mike connected on his third shot and the scene finally ended. Then I screamed for real! I was reminded of the real contest between Annie Oakley and exhibition shooter Frank Butler, in which Annie beat her husband-to-be.

The funny part about this whole thing is that Crystal doesn’t seem to know that she is doing anything special. I get the impression she thinks we are trying to build her confidence by heaping praise on her, when in fact we are all saying that we wish we could shoot as good as she. Paul is a better offhand rifle shot than I am and even he is astounded by her natural talent.

I knew one other natural shooter. Back in the 1950s, my maternal grandmother shot archery with me one day. We were shooting at a cardboard box filled with crushed newspapers, placed about 20 yards away. I had just received a lemonwood bow for my birthday. It had a draw weight of about 25 pounds, so it was just for target shooting. I shot first and hit the box a couple of times, then I asked my grandmother to try. She said, “Where do you want me to hit?”

I answered, “On the box, grandma!”

To which she replied, “I know on the box, but where on the box?”

So, I asked her to hit the red circle of box specs that was showing on one bottom flap. She quickly drew back and put her arrow through the center of the three-inch circle.

“That must have been luck.” I said. “I bet you can’t hit the spot where all four flaps overlap,” which was the center of the box. She put the next arrow through the overlap hole without touching any one of the four flaps.

After that demonstration, I decided that shooting was over for the day. Later that evening, my mother told me that grandma had been a champion archer in the early part of the century, when archery was a popular social sport.

So, there are such people in the world. People like little Phoebe Ann Mosey of Darke County, Ohio, who scarcely ever missed what she shot at. Then there are the rest of us who labor a lifetime trying to approach the standard these gifted persons must take for granted–these “natural” shooters.

author avatar
Tom Gaylord (B.B. Pelletier)
Tom Gaylord, also known as B.B. Pelletier, provides expert insights to airgunners all over the world on behalf of Pyramyd AIR. He has earned the title The Godfather of Airguns™ for his contributions to the industry, spending many years with AirForce Airguns and starting magazines dedicated to the sport such as Airgun Illustrated.

110 thoughts on “A natural shooter”

  1. BB,

    Don't sell yourself short. There are no bad students, only bad teachers. I'm sure you've influenced her more than you realize.

    Please email me when you get a chance mchavka-at-hotmail.com.

    Michael in Florida
    Success is not an entitlement.

  2. BB

    I picked up a .22 Maurader the other day, and the only pellet I can find that shoots well through it is the Beeman extra heavy. It don't like the 14.3 grain pellets. I've not changed the factory settings. Will you give you 2 cents worth.


  3. BB
    What a great post! This is what air guns is all about! I remember as a young lad,shooting in NRA matches with 22.cal and the one opponent that was my nemesis was a young girl that tore every one to pieces. I really appreciate the fact that shows like this are making a public appearance, it is so great for the sport. Chrystal really is a natural, and I think your post will really boost her confidence and hope she continues to use the talents that God has bestowed in her! Don't forget to tell her about the Baikal 61 where she can hone in on her skills at home.

    By the way, I LOVE my Mak!


  4. An avid golfer finally convinces his wife to try out his favorite game. She stands at the first tee and asks "What do I do?". Her husband points out the little flag in the hole and says "Hit the ball as close to that hole as possible".

    So she winds up and wacks the ball. It arcs up and comes down a couple feet from the hole and lazily rolls up right to the edge of it. They both go over to the ball, and Hubby is incredulous – he can't believe his eyes! "What do I do now?" she asks. "Hit it into the hole" he says.

    She replied: "Why didn't you just say that in the first place?"

  5. There is something about that turkey that always made it a booger for me. Chickens were no challenge; neither were the pigs. The rams took holding just so but were definitely hittable. That turkey, though . . . .

    If Crystal went 5 for 5 on them then I tip my hat to her.


  6. Jane (or anyone else interested…),

    QUESTION – Could the center of gravity and center of pressure be determined experimentally using cut outs of the cross section of a pellet?

    I know that if you cut out a cross section of the pellet and suspend the cut out from a pin than a vertical string will then intersect the center of gravity. The center of gravity will also be of course along the center line of the pellet. Probably use a pin towards the edge of the skirt to give you the best angle.

    But could you do something similar for the center of pressure? Instead of cutting out the hollow out of the inside of the pellet, you just cut straight across the skirt. Then would the measure of the new “center of gravity” correspond to the center of pressure? The new measurement would fall behind the center of gravity (for every pellet but the Mendoza pellets with the filled skirts. ( I have to wonder if ANY pellet rifle or pistol would shoot these pellets well. None of mine did…)

    Calculate a “stability factor” as perhaps distance from tail to center of gravity divided by distance from tail to center of pressure.

    This wouldn’t be the end all of end all in pellet measurements, but some general predictions would seem to hold. The JSB Express pellets would be less stable tha the JSB jumbo. Eun Jins would likely be the most stable pellet. The Mendoza pellets with the filled skirts probably the least stable.

    Considering the Crow Mangum and the Predator pellets with the plastic tip, the plastic tip would seem to be a bad idea. The plastic tip is so light that it contributes virtually nothing to the center of gravity. However the plastic tip would contribute to the center of pressure and move the center of pressure forward. Thus it seems that the plastic tip would aerodynamically destabilize the pellet. The impact damage between the different pellets is an entirely different consideration.

    There is obviously more to stability than besides the center of pressure being behind the center of gravity. As the center of pressure gets further back on the pellet, then the tendency of the pellet to precess would increases. Thus for the Eun Jins you’d have to shoot them fast to spin stabilize them. Shot slow the Eun Jins would probably precess. Note that shooting the Eun Jins slow isn’t the same thing as the Eun Jins slowing down. If shot at 900fps, when the Eun Jins slow down to 500 fps they will be spinning at very close to their initial spin rate. If shot at 500 fps muzzle velocity, then the Eun Jins would be spinning slower.

    This two cut out method obviously wouldn’t work for a solid bullet. The center of precession and the center of gravity would be the same. So it is a crude method. The question is – Is it good enough to be useful?


  7. Matt,

    RE: Group size

    Stumbling around on the internet and found some data you might find interesting. A magazine was testing various ammo in various guns. Ten 5 shot groups for each combination.


    I was surprised that the difference between the best group and the mean was larger than the difference between the largest group and the mean. I thought it would be the other way around.

    The point is that you can see how much variation there is in group size for a 5 shot group. So how good a group you shoot depends to a large degree on how many groups you shoot. As the old adage goes, even a blind squirrel occasionally finds a nut.

  8. 78g,

    Congratulations on your new Marauder. Have you tried crosman premiers in the cardboard box? Almost without exception everyone is learning that these are the most accurate pellet in their Marauder's.

    It's becoming cliche when people say that crosman built a gun that will only shoot crosman ammo.


  9. 78G,

    Something is wrong. Beeman pellets are not the best in the Marauder. Have you tried JSB Exacts in any weight?

    Is the pellet nicking the baffles?

    Remove the shroud and baffles and shoot several groups.

    A Marauder should astound you with its accuracy.


  10. Having just finished reading this blog, I can only repeat what the great Oliver Norvell Hardy would say to Stanley, "I have nothing to say".

    I hope before I leave this earth that I discover that I, too, have a natural talent like Crystal. That is, besides manufacturing my own natural propellant.

  11. I've tried the Crosman pellets, RWS domes, JSB 14.3, Gamo match, and pointed. The shot pattern is terrible with these pellets. With the Beeman extra heavies its spot on. ONE hole shots at twenty five yards and fifty was about half inch. Was busting tree rats dead on at around 35 yards. My gun just don't seem to like the lighter pellets, but I'll look at the shroud to see if it nicking the side.

    On a side note I love my disco .22 and Sumatra .020


  12. BB,
    When you post something about the show it makes me look into getting it again. The last cable company I used didn't have access to the Sportsman Channel and now I have Dish Network and they don't have access to it either. I hope you can get a more accessible network to pick up the show.

  13. Is it rude to notice that she's not only a natural shooter, but apparently a naturally smokin' hot shooter? OK, I won't then.

    As for the Marauder, mine's one more (probably futile) scope test away from going back to Crosman; after a promising start, it just won't group any more.

    I love this gun. Just can't live with 1.5" groups at 45 yards. I still believe the thing's going to take over the world.

  14. Trout Underground,

    Don't send that Marauder back!

    Remove the shroud and baffles and shoot some groups. JSB Exacts are the most accurate. Both the 16 and 18-grainers seem to work.

    If that's it, the pellet is touching something on the way out. Brit PCPs have that all the time and it is easily fixable.

    If that's NOT it, send it back and let Crosman fix the gun for you. You won't regret it.


  15. 78G,

    It is essential that you shoot the gun without the shroud and baffles. You may not actually be able to SEE the nicks because the baffles are Delrin. All it takes is a touch.

    Shoot now with the pellets you have. But buy the JSBs, because they are the best.


  16. B.B.,

    Curious – if 78g's Marauder shots well without baffles and shroud, what is the fix?

    Drill out the baffles a bit?


    PS – Geeze I keep coming back to a tough choice. Eat for the next three months or buy a Marauder? Eat or Marauder? …

  17. Just put on order some JSB 18 grain pellets. I look forword to seeing how the shoot not only in the Marauder but also in my Hunter Extreme. Had to order a new breech seal for it. Funny Gamo sells them in packets of 4.


  18. This story reminds me of my wife, she's also a natural athelete. When we were in college, I used to love to watch her play raquetball. The thing was, the only opponents that were available were men! It was an inevitable evolution of emotions demonstrated by new opponents every time. They would invariably start out with that 'I'll take it easy because I'm JUST playing a girl' manner – lazily taking a few shots and condescending to her. Then when they realized they were not getting any points they'd step up their game a little – still no luck. OK, now they were ready to prove a point and score a point. Maybe they did – sometimes, but they realized this was not going to be easy and now the game was on! They were not about to let a girl beat them. You could see the determination on their faces – my wife on the other hand was oblivious, relaxed and enjoying the game. As the game would progress, most of the time but not all she would pull ahead and still be winning the games. The men would get so frustrated and flustered. How could this little (5'-5" 115lbs.) person be killing me? But kill them she did, almost every time. I would just chuckle to myself. Then I decided to take her fly-fishing one day. She had never fished before, let alone fly-fished. And guess what – she was a natural at that too! She's out fished me every time we've gone out. Rock climing? Natural. Tae Kwon Do? Natural. Everything she's ever tried? Natural. The only thing she has trouble with is technology – She still can't operate the TV remote!

    By the way – no joke, the word verification is hoties. So here's to all the women out there who can out-compete men. Maybe they are really the superior gender. But I've still got control of the remote!

  19. Hotties,

    Yes, Crystal is aware that she turns heads. But I have never seen her project anything other than a "regular" and almost humble demeanor. Unquestionably that adds to her charm.

    Natural athletes–my aunt was one. She could beat most men at any sport. She beat me at tetherball so many times I stopped playing. I was in college at the time, so I was at my peak. She taught me to ski, but I could never keep up with her.

    I never saw her shoot, but now you've got me thinking.


  20. B.B.,

    RE: The artillery hold video at PA

    Oh, well time to give my springers another try. I was balancing, not holding, the foregrip, but
    I was shouldering the rifles!

    I'm a shotgun shooter. If you don't shoulder a
    12 gauge your shoulder quickly gets beats to a pulp. Old habits die hard…

  21. I think what often makes a 'natural athlete' is just the fact that they don't realize that what they are doing is supposed to be hard.
    In effect they never psyche themselves out.
    My 8 year old just thinks that shooting is easy. I'm always amazed at his abilities. He has the sights on his Red Ryder figured out, and he just seems to feel that it's an accurate gun and so he never second quesses how it shoots.
    He has no problem nailing a Daisy Shatterblast (those little 2" orange wafers) at 25' 8 out of 10 times.
    I tried to see just how accurate the Red Ryder is. I'll go down to my shooting range (30') and 10 shots will have a 6" spread…so how does he hit these 2" wafers, I asked myself.
    I came to the conclusion that I to down and take a shot…it high and to the left. I try and compensate but it's way low and to the right…etc, etc.
    He just goes down, expects it to hit the wafer…and it does.
    CowBoyStar Dad

  22. B.B.

    Did the shroud removal thing, which didn't accomplish much. Given the amount of lead in the barrel (even after shooting only 50-60 lubed pellets) I wonder if there isn't a burr at the breech end of the barrel, or too much choke at the other end.

    Either way, something's not right, and Crosman has made it clear they'll make it work. Good company.

  23. DISCO blues

    Great post! Thank you.
    I have a question for you and for others who have experience with the Disco.

    Ever since PA's moving sale, I have been trying to figure out the Disco. I have been unable to obtain decent groups at any distance. I have tried Premiers lights and, of course, Premier heavy pellets as well. I have tried JSB exacts.

    I have used a firm hold, sandbag rest, artillery hold, hold further on the forearm, next to trigger, etc. I have used some combinations thereof. The scope seems to be firmly attached. I have shot the Disco altenating with the Whisper and my .22 rimfire to verify my personal ability that particular day.

    While I can get a 1-inch group with the Whisper and sub-inch groups with the rimfire at 50 yds, I can't get the Disco to group less than 2 inches. Similar story at 30 and 10 yds. At 10 yd, I cannot get it to group within a quarter coin sized area. Two shots look perfect, then the third and fourth become "randomized"

    I have the power curve I shot with the CP ligths and heavies, and I can post it if you think everyone would benefit from that. I start shooting at around 1,800 psi as per the built-in gauge.

    What is happening? can it be a faulty valve? At this point, I have not tried other pellets because I think this goes beyond finding THE best pellet. Any decent pellet should give me groups similar or better than the Whisper, right?

    Thank you

  24. TE,

    I am almost certain the valve isn't to blame. But I suspect the barrel. It could be the crown or it could be the rifling.

    Try cleaning the bore and then shooting Premiers again. Use JB Paste and of course you have to clean from the muzzle, so be careful. You need a brush with short bristles to clear the bolt, or if you can remove the bolt you can clean from the breech. You still need a shorter brush.

    If that doesn't work, contact Crosman.


  25. T.E.
    My disco wasn’t pretty but out shot my gorgeous Webley Raider.
    The one strong point that Disco had was accuracy. Not such a bad thing for a rifle. Anyway, have you tried taking out all the variables?
    Start with the scope I will assume you are using and switch it out, tighten all screws, clean the barrel, etc. Then shoot from a full rifle rest. If it still won’t group, sell it.

  26. BB,

    I have a question about scope mounts for BSA's. What do you suggest, given that B-Square's 17501 is back-ordered with no end in sight? I've been thinking about a one-piece Leapers mount, and either living with some cant or machining the base a little wider to fit BSA's bastard dovetail.

    Thank you,

  27. Re: First Diabolo pellets

    Ah, like a dog after a bone…

    In book "BELL TARGET SHOOTING" which is evidently available as a PDF file at:


    There are a couple of references to pellets.

    On page 2 it talks about "cat slug" dM pellets in use in the 1890s in bell target shooting clubs in Engalnd. Doing some digging it seems that these were (mostly?) straight walled pellets. Maybe a hint of a flair at the back of the pellet?

    In 1905 it appears that Lincoln Jefferies patented a hand tool to resize such pellets. British patent # 11,002.

    What is really interesting is on page 21 of the PDF file. It shows a box of Cox and Son's pellets with a date of 1902. So it would seem the diabolo was created some time between 1890 and 1902.

  28. TE, are the shots moving vertically or horizontally?

    Mine is pretty picky on pellets. Eun Jin 32.4 points, Predators and sometimes RWS Superdomes.

    Did you try cleaning the barrel and checking all the screws?

  29. RE: Lanes Cat Slugs

    Found several references. Evidently sold in a box with a black cat getting shocked. They were no.1 CAL or .175, and shot from a smooth bore airguun.

    BBS reference:


    Link to Photobucket picture:


    Geeze, no wonder they needed a tool to reform them…

    More info on Lanes Co.


    states Lanes pellets "produced from (approx) 1901 until the 1930s"

  30. B.B.

    How interesting. Keep us updated on how Crystal does. I started out as a great natural shot myself then promptly nosedived. I think the pressure got to me and there was a maturity factor.

    My Dad knew a great natural shot in the army. The fellow held the M1 rifle all wrong and ignored the 8 steady hold factors. But not only did he qualify expert, he broke the range record. My Dad remembers the sergeant shouting this from the loudspeaker. Afterwards the sergeants went up to congratulate him and looked pretty sick because they considered him a wimp. The guy just said it seemed easy. My Dad caught up with him years later when he was a judge, and the guy told him about shooting the 1911 during advanced training as a military policeman. Apparently, he couldn't hit anything, and the instructor told him that if there was a problem, he should just throw the pistol at the assailant–a clear sign of a frustrated teacher.

    I like Ed McGivern's comment as relayed in one of the Bob Lee Swagger novels: Talent is better than hard work, but both together is best.

    Herb, I think you're right that having the mean of multiple 5 shot groups closer to the largest group than the smallest group testifies to the high variability involved. I'm still at work on a way to quantify the uncertainty between multiple small groups and a single group of the equivalent shot number.


  31. Based upon almost 50 years of shooting, I'd say that the female of the species
    1) can outshoot the guys most days, and
    2) doesn't consider this to be a big deal.

    Perhaps in the old days we should have had them do the hunting, while we stayed home to mind the kids.

    Just an (unpopular) thought.

  32. BB, there is only one explanation for Miss Ackley's skills– SHE'S A WITCH! BURN HER!

    No, but in all seriousness, I've seen it all before. People who have dedicated themselves to a pursuit only to be bested by people who have no right to be so good. Maybe once in my life I can be among the latter group.(sigh)

    Meanwhile, I have recently acquired a TX200 in .177 and can't hit the earth with it. I will have a report soon if anyone feels like scoffing.

    I have to catch this American Airgunner show. Any chance of it showing up on YouTube?

    SlingingLead in Powder Springs

  33. Matt,

    I feel like I've beat the statistics thing to death. It is hard to just jump into the middle of a discussion about statistics. Why don't you contact me at hcacree at yahoo.com and I'll discuss it with you as long as you want.

  34. Herb:

    I am not completely sure where you are going. CoG and CoP are two factors in determining how well an airfoil, (or missile, in certain lines of work), will self-correct after encountering turbulence. This "stability" calculation is not the same stability of a spin-stabilized projectile. Is IS important in drag-stabilized flight, but this is where I wonder if our spin and drag effects are working at cross-purposes.

    For pellets, we need to consider the center of pressure of the flow field on the entire vehicle with a very small angle of attack.(the bore-line launch angle, which we call the "Trim Angle").

    Rocket fins and stabilizers are the key contributors to CoP. In pellets, it's just the "tail". Fins are designed to minimize drag, not so for pellet-tails. For positive stability, the center of pressure must be further from the nose than the center of gravity. This just makes sense, we want the wind to exert a force on the body and "pivot" the pellet back into "trim". It also explains why we always make rockets nose-heavy. It is logical to assume more "leverage" and hence, more stability, if the relative distances are greater.

    Without going into the math, we can calculate several force vectors and calculate the moment that pushes the pellet back into the "trim" position.

    But here's the "rub". We don't spin rockets. Unlike a rocket, too much of this "stability" will push the pellet beyond the "trim angle", and into alignment with the flight-path. ANY force that pushes the pellet off of its axis of rotation will lead it into precession.

    On rockets, we can add all sorts of tail fins that have low drag, yet, with a small angle, can drastically shift the CoP. This is very effective, and rockets don't precess.

    The balance for us, (and I haven't envisioned how to calculate it), is to have just enough gyroscopic stability to maintain nose-to-tail alignment, but not enough to work against the stability induced by drag, (or CoP force, if we ever get there).

    My conclusion is that, the faster we go, the less spin we want, and the more centered the CoP. The pellet really needs to start looking like a bullet.

    Some other things start to become intuitive: Lighter domes, (either plastic tips or hollow-points), should be less stable than heavy domes, but not always. At some point, the lower CoP/CoG effect is going to be preferred – most likely at higher spin-rates.

    The other factor we haven't talked much of is moment of interia. This is the projectile's resistance to spin, and is detemined by where we position the mass of the pellet – towards the centers, or towards the perimeters.

    Again, a trade-off: We always want high longitudinal spin resistance, but rarely want high axial spin resistance.

    best regards,

    Jane Hansen

  35. Jane,

    I agree that stabilizing pellet is a multidimensional problem, and it is all about trade-offs. I was just trying to calculate something that seemed to at least roughly indicate stability based on the drag of the pellet's tail.

    I'd disagree with your statement: "My conclusion is that, the faster we go, the less spin we want, and the more centered the CoP. The pellet really needs to start looking like a bullet."

    The more the pellet becomes a bullet, wouldn't you need to spin them faster? A smoothbore shoots a diabolo pretty well when there is no spin at all. For a bullet the CoP is ahead of CoG. There is no skirt to drag stabilize, and the only stabilization comes from the spin. I think the answer here might be that we're spinning pellets too much with standard twist rate when shooting at 900-1000 fps. Spinning them too fast causes a yaw, and then any hope of precision is gone…

    At 900 fps with an EinJun you're shooting as fast as a 0.22 short and about as heavy a round. The rub is that a .22 short bullet would have a lot more friction in the barrel. Perhaps a "bullet" (round nose cylinder) with bands to fit rifling? That would have less waist and thus a higher BC. Less waist also means that the CoP would more forward (from tail towards front of pellet) towards CoG so that there is less aerodynamic torque to cause precession. You'd get your 0.22 rimfire then.

    As you point out the trick is to try to balance spin, velocity, drag, and precession. Spin, velocity, and the twist rate of the barrel are interrelated of course.

    Some of this has to do with how long the pellet is. For a given bore size, as the pellet weight goes up, the length of the pellet gets longer. Longer pellets are more likely to precess.

    As far as my calculation goes, as I indicated the Mendoza pellets were awful in any rifle I tried. I think it because the skirt is filled with lead. The diabolo depends on the tail being hollow to have CoP behind CoG. With skirt filled you have something more like a bullet.

    The "stability factor" that I proposed is misnamed. At first the stability would increase as the factor goes up, but you get to a point where the pellet gets so long that it precesses. So the actual stability goes down. Don't know what to call the ratio I proposed. Misnaming it is no doubt part of the confusion of my notion.

    I've been looking at the precession rate for a top and trying to figure out how to fold that into the aerodynamic characteristics of a pellet. But unlike a top, the spin rate doesn't decay. The velocity of the pellet decays, and hence the stabilizing force of the tail. You get to a point of mathematical chaos, and some imperfection unbalances the pellet and it starts to chaotically precess. Perhaps at the point of chaos the pellet isn't just precessing, but precesssing and nutating.

    Thanks for responding to my whackey idea. 🙂


  36. I read a theory once that said women are naturally better at small-muscle coordination–sewing and the like (Jane, this is not my idea!)–and therefore better at shooting. This sounded like pop-anthropology, but who knows.

    B.B. has Crystal Ackley replaced the other woman you mentioned–Heather whose last name I forget?

    Herb, thanks for the offer.


  37. Jane,

    How interesting. I was a dismal failure at the rocket equation the one time I encountered it. Let me guess. The reason rockets are nose heavy is that they will drop from their original launch angle into an orbital pathway. It looks to me like rockets are launched straight up which would be on a path radially outward from the earth and straight into deep space unless compensated somehow like being nose-heavy.

    As for the center of pressure for pellets, I'm gathering that the pressure in question is from wind resistance. How would you move the center of pressure off the nose and the axis since the pellet looks to me to have axial symmetry? Would it be a light nose and something about the drag from the tail?


  38. Jane,

    Looking around today I found a paper by Dan Miller that evidently is an improvement to Greenhill's formula.


    You could of course play with constant of 30 in the equation to move stability factor around.

    There is a velocity correction in paper.

    Also the (1+L^2) term in denominator changes for different bullet shapes. No idea what it would be for a pellet.

    Looking at the equation, the velocity correction is wrong. The velocity correction is just in the numerator, and hence as velocity goes up, the stability factor goes up. For a pellet this seems wrong. The twist of rifling is fixed. As the velocity increases, the spin rate also increases. Faster spin makes the pellet yaw more. Too much yaw and the pellet starts to precess instead of self-correcting. So it would seem that the velocityy correction would have to be modified to make it parabolic. That would mean another constant to fit in the equation.

  39. B.B.

    thank you. I will look at the bore and check if there is anything weird in there. Somehow I do not think that is the problem. It might be the crown though

    AJVenom. They move in all directions, left and right first, then who knows.

    One more piece of info. The power curve with CPs looks like a dome. With CP heavies, it starts at about 800 fps at 2,200 psi (I overfilled to make sure), and climbs steadily to 900 fps at 1,500 psi (30 shots). Then stays within the 900-850 fps range until pressure= 1,100 psi (45th shot). Within the 1,500-1,100 psi range of pressure, I do get a quick drop to 850 fps and a quick climb to 900 fps (all within 8 shots), with a final steady drop to 850 fps (45th shot). Drops steadily and rapidly thereafter.

    Sorry for the rambling and the confusion. Tried to make it as clear as possible.

    Thank you


  40. Tunnel Engineer–

    I very recently acquired a Discovery in .177 that I could not pass up due to an insanely ridiculous price, even though I could not afford it, because I had just purchased another air rifle I cannot afford, but I digress…

    Mine has the best "out of the box accuracy" I could possibly imagine.

    I am a horrible shot, no modesty, and I am blinder than a deaf-mute bat with cataracts.

    With the open sights that came with the rifle, with no adjustments from me, from fifteen yards I can't miss my target.

    Have you tried the open sights? If you are ok with those, perhaps it's the scope or mountings.

    I can't comment on long range accuracy, because I haven't mounted a scope yet, and I can barely see the blur of the coke can beyond the sights with my 10 year old prescription coke bottle glasses.

    The only pellets I have used so far are the CP heavies that came in the cute little coin purse. At this point I don't see any point in using anything else.

    Try the open sights if you haven't already or stripped them from the gun before you get all frustrated and send it back.

    This is not what I would consider a pretty rifle, it looks a little-bit cheap,(at the price I got it at, it was a lot cheap) but it sure can shoot.

    Between this, and my 1377c seeming to hit its stride, I think I see a Marauder in my future.

    SlingingLead in Powder Springs

  41. SlingingLead

    Thank you. No, I have not tried open sights. I will though.

    I respectfully disagree. I really like the looks of the Disco… It is a very nice rifle and I know it should shoot better than anything else at that price range.

    I posted the power curve in my Blog. It is my very first post ever, so i am not sure if I did it correctly.


  42. Matt,

    Rockets need to have CoP behind CoG to make rocket stable. Thus the engineers design rockets that way. They could design them to have CoP in front of CoG, but if the rocket flew it would be dumb luck, not good design.

    Rockets are not shot straight up. It takes too much fuel. Think of Kennedy Space Center launches. The launch is over Atlantic from west to east. Think of launching rocket horizontally at the equator on a tangent to the earth. From west to east the spin of the earth is working for you. From east to west you have to overcome spin of earth itself, thus you use a lot more fuel.

    The CoG and CoP stay along central axis of bullet/pellet. Bullet has CoP in front of coG, pellet has CoP behind CoG.

    Since CoP and CoG are different there is a force (ie a component of the wind resistance) causing the projectile to torque if the projectiles center-line doesn't perfectly follow the path of the projectile. A little bit of torque would be stabilized by spin, but too much and projectile starts to yaw. Too much yaw and you get precession. Precession then turns into precession and nutation. (Get a corkscrew inside a corkscrew). At that point groups become patterns!

  43. Herb:

    I am far to inebriated to comment coherently, but to your first response, yes, you are correct. What I was trying to say was EITHER we need to slow the pellet rotation down as we increase the velocity, OR, the pellets need to be shaped more like bullets, (in which case we move to a totally spin-stabilized designed, and we can forget most of this CoG/CoP stuff…(almost, we then want to have a very "neutral" CoP profile, as in standard slug or boat-tail desing)

  44. My daughter-in-law is one of these natural shooters. Her husand is a top ten in the nation skeet shooter. He's ok with a rifle, even I can out shoot him with a pistol.

    On my basement range he was doing ok on a 10M target with my Izzy. His wife came down, picked up the gun for the first time in her life and just blew him away. She asked 'What's so hard about that?' We sent her back upstairs. With no practice and little experience she is way better than either of us. Go figure.

    Al Pellet

    PS. Word verification: gunning

  45. Jane,

    Enjoy your Friday evening, but don't go shooting. 🙂

    I think I now understand what you were saying about the nose-up business. I thought you meant that pellets naturally follow a parabolic flight path and that spin created a force to pull its orientation back up to the boreline. The force would also cause the pellet to precess. I now believe you mean that spin causes the pellet to remain pointed like the boreline and some force pulls the nose down to follow a parabolic trajectory–and precess. So the destabilizing force is down not up.

    (Change the pluses to minuses and the minuses to pluses…Grandfather you've done it.)

    What this downward force would be is not obvious to me. It's not gravity which would translate the whole pellet downward. It's something that rotates the pellet around a lateral axis. My guess is that it is some kind of Bernoulli force. Intuitively, I see walls of wind resistance forcing the pellet to align with the flight path. More analytically, I see differential pressures from the flow of air nudging the pellet on course. Whatever.

    Meanwhile, I've been looking at YouTube videos of football passes. It's not that easy to see what is going on, and I don't have a football handy. But I did find one video that seemed pretty clear. On the downward phase of a long bomb in a championship game, a pause to the clip clearly shows the nose pointed down. It is unbelievable that it was thrown in that attitude so the nose must have followed the flight path. BUT it is precessing a little, so it wouldn't fit your definition of a well-thrown ball. BUT, this precession does not seem to alter the trajectory at all. I think it's been an overlooked part of this discussion that precession does not imply that the flight path is altering to follow the nose of the projectile to create helical pathways. It seems that trajectories can tolerate a certain amount of precession without being disturbed.

    Without numbers, it's hard to get a sense of proportion and see how the various effects relate. I now wonder if we haven't been a little exclusive in supposing that effects which are different are also incompatible.

    My sense of the pellet's adventure now goes like this. At a small angle of elevation, a pellet exits the muzzle with no precession at all. As it nears its apex of flight, spin works against Bernoulli forces that push the nose down. But the spin is not so pronounced that it causes the pellet to diverge from the flight path and creates excess drag and instability. So, the nose comes down a little and the pellet precesses but not so much as to disturb the trajectory, and the pellet smacks home to the target.

    This target is none other than the perfect spiral long bomb. It would appear that a long bomb with nose on path and no precession is impossible. I may need a drink myself. But the gain is a Grand Unified Theory of all projectiles–artillery shells, bullets, pellets, footballs. Up to a certain level of detail–there's always more.

    If this is right, it would seem that the forces here create a fairly restricted flight envelope, and it's impossible to design a pellet with radically new properties like high speed and short range. For firearms performance, you will need to turn to firearms design.


  46. Hi folks,

    Are any of going to be in DC tomorrow for the Tea Party? If you are good, but if you're not, why not?

    Maybe we can compair notes on what were saw and how it was or wasn't reported by the media.

    Mr B.

  47. RE: Spool Rockets


    "The center of pressure (CP) of a flat disc, like a CD, traveling perpendicular to its edge is 1.33 diameters behind the forward edge of the disc. In other words, in a CD spool rocket built per the main instructions … the CP is over 2 and a half inches behind the aft end of the rocket, therefore always guaranteeing a stable CG/CP relationship!"

    How about we:

    (1) Assume diameter of discs is same as caliber of pellet.

    (2) Assume diameter of spool is irrelavent

    (3) Assume that the contact surfaces where the pellet grabs the rifling as the positions of the two discs attached to the spool. From distance between contact surfaces and the constant of 1.33 We can calculate the CoP.

    The factor of 1.33 for each surface wouldn't be exact of course. For something like a Kodiak where the head gets larger and smaller with smooth transitions, the factor would be certainly be different.

    We can calculate CoG from paper cut-out method where we do cut out the hollow bell.


    Now gist is that for a diabolo pellet with some slight angle of yaw then the the restorative force due to CoP is greater than force to create yaw due to Gyroscopic drift. So long as that is true, then the pellet is stable. But if force to create yaw is greater than restorative force due to CoP which forces pellet path back to the true path, then the pellet starts to precess and becomes unstable. The precess isn't quantized, so as the pellet slows, the restorative force gets even less, and the pellet precesses even faster, and at a greater angle. So it curves more and slows down ever faster.


    From what I can gather, if the CoP is determined by the cut out method, with the cutout cut across tail without hollow, then it is as if the pellet is flying sideways. This would present a worse case analysis of the CoP. Thus it seems that for "significant" changes in angle (yaw) that the CoP does move. For a small change in angle, then the CoP can assumed to be in one spot.


    The other extreme would be to assume that the head of the pellet is a sphere. CoP is meaningless for a sphere. Now the sphere is attached to a disc via a thin spool. Now at back end is a flat disc.

    Every real pellet should fall somewhere between these two extremes. A wad cutter would be more like two discs. A pellet like the Kodiak would be more like a sphere and one disc.


    Could some function of the BC could be used to interpolate for similar style pellets?

    Perhaps for a kodiak or a round nose we'd assume a smaller disc in front.

    Something like EunJin would seem to be a different situation. The waist is so small that it is more bullet than a diabolo pellet. Same notion of yaw and restorative force would apply, but now CoP is in front of CoG. Now the spin is stabilizing the pellet, and the CoP is trying to destabilize the pellet.


  48. Re: First Diabolo pellets and Webley packages in Bell Target shooting article



    Troubledshooter stated that "The first Webley pellets were sold in card boxes for the 'Mark 1 Air Pistol', and were marked as such." He goes on to described other packages through WWII.

    My Blue Book of airguns says that the Mark 1 pistol, Webely's first air gun, was introduced in 1924. So all the Webley tins would seem to post date the Cox and Son's Pellets by 20 years.

    Cox and Son's is not listed in my Blue Book of Airguns. (7th edition) Haven't been able to find anything on internet. Not clear if
    Cox and Son's only made pellets, or if they made some air guns too.

  49. Herb / Matt:

    Fantatstic observations. Let me throw some comments out.

    Firstly, on CoP, we NEVER look at it "head on", so the sphere and disc observations need not worry us. When we apply those equations, we are using a CoP of based on the fluid dynamics on ENTIRE body flying into the wind at a slight angle. The "angle" is important. If we only consider the CoP of a projectile flying perfectly straight into the wind, then the CoP is the center of the surface of the nose.
    The "observed" CoP is the real-life example, and representative of the deviations we want to correct, it is much closer to the tail, and, (Sorry Herb), always behind the CoG, for pellets or rockets.

    The CoG becomes the pivot-point, the CoP is the effective lever-end.

    I'm not sure I understand Herb's yaw and restorative force, but I think of it like this: The yaw, (the angle off-axis), is put there by us – it is the bore-line angle.
    If the pellet actually followed the boreline, there would be no angle an no yaw. It does not, however, gravity, (not Bernouli), pulls the trajectory off the bore-line, and this is when the aerodynamic forces become in conflict with the gyroscopic forces.

    I worry about "restorative" forces, (by restorative, we mean force trying to correct the angle to align with the flightpath, and away from the boreline), because this is what induces precession.

    The goal of spin-stabilization is to defeat all of these forces and remain in "trim".

    We need to choose between the "unguided missile" (for example – a "dart"), and a bullet, (or football).

    Bullets and footballs, (if thrown with enough spin), hold their trim angle constant throughout flight.

    Darts and missiles use aerodynamics to adjust their attitude to constantly be in aligned with their flight-path.

    Matt's conclusion is as mine – to fly as fast as bullets, we need to start looking like bullets…

  50. Jane,

    I'd agree from Nose, the CoP is behind CoG for rockets and pellets with a tiny yaw. But for bullets with a tiny yaw, the CoP is in front of CoG. Right?

    Yep forgot that nasty bugger gravity.

    The point that I was trying to make about spin stabilization is that a small amount of spin is good for a pellet because it averages out imperfections. But too much spin for a pellet causes a yaw which causes the pellet to precess. Since the CoP is in behind the CoG for a pellet, the drag force stabilizes any yaw of the pellet causes by gravity and spin.

    Since the CoP is in front of the CoG for a bullet, spin is always good. It the only thing that stabilizes the bullet against the yaw caused by gravity and the drag force. To little spin and the bullet starts to tumble. Too much spin and the bullet drifts excessively, but it doesn't tumble.

    Guess the other difference is that when destabilized bullets tumble end over end and pellets precess.

  51. Matt,

    Crystal has been invited to become a host on American Airgunner. Viewers will see that in episode 7, which airs in a week, I believe.

    Heather Parsells, the first female co-host we introduced, has a busy acting job in New York City that she cannot get away from long enough to be with us on the show.

    The trailer that you see on


    now shows Crystal Ackley as a co-host. She will be with us for the rest of season one.


  52. Herb,

    That spool rocket thing you found has been proven in bullet design for a half-century now. Maybe I will tell the story behind one of the most incredible experiments I was ever witness to, that happened at the big bore match at Damascus, MD.


  53. Gazza,

    Living outside the U.S. isn't as great a hinderance to seeing American Airgunner as you would think. I live in Texas and appear on the show and I have never once seen it broadcast live (in real time). I rely on tapes sent to me from the editor to see what the episodes look like.

    We do have plans to make a DVD of all the episodes and sell it. But right now we are so shorthanded that we are struggling just to film and produce the episodes on time. However, our staff is growing. I think by the start of 2010 we should have a DVD ready to sell.

    As for our website showing content, that is in the works. That will happen sooner than the DVD, though the entire episodes will not be available that way. But spillover footage certainly will, and there is a TON of that stuff!


  54. BB,

    I'd love to hear about the experiment.

    When I found the spool rockets it gave me a better way to look at rockets, bullets, and pellets. Most rockets are much longer than they are in diameter. Spool rockets, pellets and bullets have diameter and length which are more on par.

    There is a whole subculture in the model rocket community looking at stubby rockets like the spool rocket.

  55. Dino,

    Your question is a difficult one to answer. B-Square is going the way of the dodo, so forget waiting for them. But there are new makers, including BKL that just emerged from the ashes of a former business failure.

    I will look into this for you, but please keep bugging me, as I tend to forget things these days.


  56. TE….mmm well I'm no expert, but removing all variables like a scope etc…cleaning the barrel and checking the screws is about all I know. It seems like like you've done a good job of finding the sweet spot in your fill band. I know CP Domes haven't been the best pellet for me, but they should do better. Checking my indoor target sheet now.

    10M .22 cal. approx. 8 to 18 ftlbs I can clover all the pellets I've tried with my discovery inside a quarter. I do have a second barrel band about an inch to the end of air cylinder don't run at max power.

    I wonder if you took some electrical tape and wrapped around the cylinder and barrel to see if it changed anything. The expanding air tank may shift your POI a little, but just an experiment to see if the barrel is moving.

    As for crowning, some have taken a brass straight slot screw with a rounded head and installed into an electric drill to recrown their barrels. If I find the article, I will post it here.

    If nothing else, try the Crosman PCP forum in the yellow airgun forum. I'm sure BB and others here can help or find someone who can. You may even want to contact Crosman. I've knew one guy who had recieved a free check up and tune, just for the cost of shipping even after the warranty expired and no reciept. Although, he could have just been lucky too.

    As for Ed McGivern, I need to finish reading that book. I can shoot pretty well with my Daisy 622x. After the first day of practicing with it, I found it easier just to just point and shoot than to try to figure out every aspect of shooting it correctly. Once you have a feel for it, it is pretty amazing what you can hit, but I'm no natural, it's all practice and trial and error. I do sometimes sight it up properly, but my groupings are nothing to write about. I do want to see if there are any tips in Eds book that may relate to shooting a pellet pistol.

  57. RE: Pellets and Gyroscopic drift (Spin drift)

    OK, as I understand it gyroscopic drift is caused by a coupling of spin and gravity. So with a right hand barrel twist, a projectile will drift to the right.

    If the following discussions let's assume that the pellet reaches its apex before hitting the targets, regardless of distance. Thus the scope is always zeroed with the pellet falling not rising. This will keep whole discussion of POI shift due to gravity simple. Otherwise we have to divide the discussion into cases.


    Now if you shoot a pellet out of a smooth bore gun, then there is no spin. No spin, no gyroscopic drift. So as you increase the muzzle velocity, the POI will climb vertically on the target at a given distance.


    But if you shoot a pellet out of a rifle, the pellet will be spinning. If you have just a bit of spin, then the POI will mostly climb on target for a given distance as well.

    But if you have "too much" spin, then the pellet will drift "too much" to the right. Now "too much" drift to the right is subjective. If the projectile is spinning at all, then it will drift at least some infinitesimally small amount.

    The other point here is that too much precession will cause the pellet to corkscrew not to just to drift to the right. So at different ranges the pellet will move in odd directions. You may or may not be able to sight in at different distances.

    Scope Alignment Problem

    The other nasty bugger in all of this is that the scope may or may not be exactly in the vertical plane which contains the boreline of the rifle. If not, then the scope will induce a horizontal variation at different distances.

    If you could measure the angle between the sightline and the boreline to 9 significant figures, I'll guarantee that you'd find a difference. So we really talking about "good enough" not perfect. In the real world, you apt to have both of the problems. For 10 meter shooting alone it doesn't really make any difference. You're only shooting at one distance, so you just zero at that distance. But if you change distances, then it does matter. Hence range charts for field target shooters.

    If you look at Chairgun 2 for example, the program just calculates drop. There is no drift correction. So for projectile drift or scope misalignment, you're own your own.

    Precession rate and muzzle velocity

    I'm assuming in all of this that the precession rate for a given yaw increases as the muzzle velocity increases. As the pellet slows, the precession rate gets even greater. That is why I believe that a higher muzzle velocity is so determential to a pellet. To high a muzzle velocity and the pellet starts to precess immediately.

    Again to 9 significant figures, no pellet shot from a PCP gets 2 inches past muzzle exactly on the boreline. There is a lot of muzzle blast. (If the muzzle blast isn't important, then why is crowning such a big deal? It isn't that the muzzle blast accelerates the pellet, it is that the muzzle blast pushes the pellet off center.) So the pellet depends on something to stabilize its flight.

    Hmmm… Perhaps it isn't that the precession rate increases with the muzzle velocity of the pellet for a given pellet yaw, perhaps it is that the yaw from the muzzle blast increases with increasing muzzle back pressure in the barrel. By "back pressure" I mean the pressure right behind the pellet as it exits the barrel. More back pressure a bigger muzzle blast. Bigger muzzle blast more yaw.

  58. RE: Experiments to detect spin drift with rifle

    Shoot at two sides of the target!

    It occurred to me that if projectile is drifting right, then there is an easy way to check. Shooting from both sides of the target ought to show the problem.

    Have bull on both sides of the paper centered over the same spot.

    Shoot say from the west to the target located due east. If pellet is going to drift right, then from the front (first side shot) I'm actually aiming to the left of the bull.

    I now switch sides. The target is on the west end of the range, and I'm shooting at the backside of the target from the east. Now when I shoot, the projectile will drift in the opposite direction. Half of the horizontal difference between the two groups is the amount of spin drift.

    No difference – no spin drift!

    Since the distance is the same for shooting each side, any scope alignment problems would cancel out.

    Hmmm… my computers are on one end of my indoor "range." 🙁

    Experiments with balls & pellets

    I had tried something to measure this more or less directly for a given power. I tried shooting lead balls and pellets. The horizontal average POI with a ball should be "true" zero. The vertical POI compared to some other pellet would differ because of pellet weight, BC, barrel friction and a zillion other factors.

    The trouble is that the lead balls shot a pattern. So you have to shoot a lot of them to get a good average POI.

    For pellets somewhat of a different problem. To get the most out of each shot, you want to measure horizontal and vertical error for each shot. So a 10 shot, one hole group isn't good! You need to shoot at 10 different bulls so that you have 10 clean holes and thus you can measure the position of each shot.

  59. Jane and Herb,

    Yay, we're in total agreement with the precession business. What cannot be overcome by the PA blog machine!

    I must say, though, that I'm fairly crushed that the Bernoulli force is not the force that pushes the nose of a pellet down from the boreline to the flight path. My reasoning is as before. Gravity translates things downward, right? Why would it rotate a pellet around a lateral axis (CoP, CoG?) dropping the nose and raising the tail? Is this where nose heaviness comes into play?

    And why wouldn't the Bernoulli force play some role? The way I imagine it, if one were perched on a pellet there would be a terrific wind rushing past at 600 mph. This would impose a tremendous drag and punish severely anything sticking out into the air stream. Gravity forces a ball thrown at an angle to follow a parabolic trajectory. If that ball were replaced by an elongated projectile like a bullet, pellet, football that shape would move out of alignment with the flight path. What other mechanism could there be than wind resistance to force the projectile into alignment thus dropping the nose and raising the tail?

    Jane thanks for the business about CoP off the nose. That was driving me nuts.

    B.B. I'd say you could hardly do better with your new host. She brightens up the show, and she can shoot. What's her background? Is she an actress? The trailer was quite a revelation. Not too long ago all those guns would have seemed like a different world. Now, I believe there was not one that was unfamiliar to me.


  60. Matt,

    RE: Bernoulli force

    Fluid dynamics wasn't my field of study.

    With that being said, I think you're more of less right. But science is organized into using models to make predictions. We use different models for different things. A model is also used to simply things and roll other things that are small perturbations together.

    So there must be changes in air pressure at various points around the pellet as the pellet flies through the air. But this is all rolled into the empirical measurement of the "drag" of the pellet. So experimentally, different drag values are measured for different shaped pellets.

    Now if you wanted to model a pellet shape and calculate a theoretical drag for a given geometric shape, then the calculations would have to consider the differences in air pressure caused by the shape. Different angles of the pellet also cause pressure changes.

    Perhaps a better way to think about this is the lift of an airplane wing. The lift of the wing is calculated using the Bernoulli effect. But you don't have lift and the Bernoulli effect. The calculation of the lift of the whole airplane rolls all of the factors associated with the Bernoulli effects of the various parts of the plane into one factor.

  61. Blogger eats comments. The following was completely wiped out just as I was about to push the publish button. 🙁

    Herb, yes fluid dynamics is more complicated than I've made out. I seem to remember the term "shape constant" from somewhere…. My sense of the Bernoulli force is that the velocity of a fluid is related to the sideways pressure it exerts. I think of the 600 mph wind along a pellet beating any shape into alignment with the flight path.

    All, well, I had a look at my Idiot's Guide to Statistics and, sad to say, it is quite over my head in terms of answering my question about the relative reliability of six 5 shot groups and one 30 shot group. The t-test, p-test, variance, and endless tables of numbers quite made my head spin.

    But, I think I’ve been making this too difficult. If you consider ten thousand 5 shot groups, most will be of a size you expect. Some will be smaller, some very small (“I’m really getting it now.”)” Some will be larger and some very large (“Fliers…must clean the bore.”) The distribution will follow the normal, Gaussian distribution or bell curve. In other words, most will cluster around an average value and diminish as you go to either side. (In shooting terms, as the groups get larger or smaller.) The process of taking an average weights individual data points by their frequency. So, whether you average ten thousand groups or six, the contribution of outliers will be the same—the bell curve.

    This suggests to me, as I might have mentioned before, that the probability slate is wiped clean with every five shot group in a series. The uncertainty/reliability of each group (in the sense that a 30 shot group is totally reliable) does not combine and has no relation to any other five shot group regardless of how they are collected. Or as B.B. said long ago, a five shot group is a good predictor of…a five shot group. I could have saved myself a lot of trouble. Another point in favor of this theory is that the reliability of a five shot group is not the same as a 24, 20 or any other size group. Reliability and size remain tied together.

    This all implies that the American Rifleman procedure of calculating the average of five 5 shot groups does not accomplish much. It does not have the extra certainty deriving from a 25 shot group. A vast misconception has been perpetrated on the shooting community! ☺ The average of five 5 shot groups just tells you if one of your groups was aberrant, which you could see anyway by looking at the groups individually. Otherwise, it offers nothing beyond a single five shot group except to tell you whether that group is wrong because of an equipment failure or because of a very, very unlikely run of luck.

    I’m calling in powerful reinforcements to verify this and will let you know what I learn. But I’m feeling better about this all the time.


  62. Re: Shoot at two sides of the target!

    Ought to think before I type! 🙁

    Shooting both sides of a target won't work. Had to draw this out to be sure I had it right this time.

    My annoyance is that I've shot different pellets and with same setup and had the POI move over an inch horizontally in 10 meters. Trouble of course is that round balls make a lousy "gold standard." What do you pick otherwise?

  63. Herb,
    I thought so, and hoped you weren't presenting this as experimental proof:).

    Your discussion of gyroscopic drift is shaping up, although any one of the factors you named plus a few others (e.g. Magnus) is bound to be off and cause precession (or worse) if the spin rate is significant, which would seem to be all the time right now.

    It seems to me that you're almost starting to think that muzzle blast induced angular displacement is the main reason to spin a drag stabilized pellet, or am I reading too much in the subtext? As far as "averaging out imperfections", I think that spinning can exacerbate that problem (imbalance) and makes the pellet vulnerable to other effects.

  64. Re: Group size thing

    Ought to mowing yard, but this is more fun… 😉

    Ok. I have a group size for 25 shots. It is 3.26 inches.

    If I shoot another group of 25 shots, how big will it be? In other words how REPEATABLE is my measurement?

    Now I shoot five 5 shots groups.

    Now for the 5 shot groups I can calculate a mean, a standard deviation, a standard deviation of the mean, and say a 95% confidence interval.

    Now I have at least some idea how reproducible shooting 5 shots groups will be.

    Using the normal curve isn't actually correct. Look at the shooting data I pointed to earlier. The low and high values are skewed around the mean. But it does give you someplace to start.

    The "normal curve" has a mean of zero and a standard deviation of 1. I can convert my measured data to the normal distribution by subtracting the mean and dividing the result by the standard deviation. Another way to massage the data is to calculate the relative standard deviation, and relative standard deviation of the mean. Take two standard deviations and divide it by the mean to get a percent.

    The standard deviation tells me how much an individual value will vary. The standard deviation of the mean tells me how much the mean varies. Given that N is the sample size, and s is the standard deviation of the individual values, then the standard deviation of the mean is:
    s/SQRT(N-1) or s/SQRT(24)

    If I have 20 groups of 5 and 20 groups of 30 then:
    (1) Average of 5 will be smaller than average of 30
    (2) Relative standard deviation of the mean for sample size of 30 will be smaller than that of 5.

    The point is that the group size for 30 shots is more reproducible than the group size for 5 shots.

    Look at data at:

    again. For ten five shoot groups the Smith and Wesson 52 with the Hornady ammo varied between 1.49 inches and 5.50 inches. Thus the "group size" of five shots varied by a factor of nearly 4. One can only assume that the variation is pure chance.

    The problem is that we all go out to the range and get the 1.49 inch group of which we are especially proud. we then brag that we have a 1.49 inch gun. We've just thrown the other 9 groups away. Now our "precision" measurement is heavily based on only two shots out of 98!! We, for the most part, threw the data on the other 98 shots away. There are all kinds of bad statistical implications for this.

    Now you go out on another day and shot one 5 shot group. What are the chances that you'll get a value as good as 1.49 again? Not likely. But you'll always remember it. You're just having an off day, or the ammo is bad, or the sun was in your eyes today, or…

    If you want to take this to the next level we can talk about the Weibull distribution. 😉

  65. Matt:

    RE: discussion of gyroscopic drift

    I do believe that some spin is good. So I do believe that rifled barrels are "better" than smoothbore. If smoothbore barrels were better I'm sure that all the 10 meter shooters would have figured it out…

    What spinning does do is average out slight imperfects in the pellet. Nose isn't quite smooth, weight distribution a fraction lope sided and so on. but a pellet doesn't need "gyroscopic stabilization."

    The problem is this. Assume twist of 16 inches and the target is 10 yards away. No matter how faster we shoot'em the pellets rotate 22.5 times on the way to the target. Now the spin rate of the pellet does depend on how fast we shoot the pellets. Precession would depend on spin rate, not how many times the pellet rotated on its way to the target.

    There are all sorts of nasty things that happen when you just crank up the power. For instance on most pellets at 900 fps a PCP would blow the skirt out from its original dimensions. The EunJin is a getting towards bullet not pellet. There isn't a whole lot to blow out. CPs are hard, so they don't blow out so easily.

    So you first have to figure out what, then why. If you had two barrels of equal quality, then it would interesting to see what would happen in Jane's guns when twist rate was cut in half, then again to a quarter of its current value. If you cut the number by four, then the pellet would only be making about 5 turns on its way to the target. Enough to do some good, no doubt, but would it be better than the current spin rate?

    All of this also gets back to how do you figure out if two barrels are "equal quality"? So there are just layers and layers of intricacy here…

    Off to mow the yard 🙁

  66. I feel like the village idiot with my education level and aptitude reguarding physics and fluid dynamics.that being established,have you folks given any consideration to the "flying barbell" shaped pellets some of the big-bore owners are shooting?with such intelligent minds at work here,I would wonder if that is close to Herb's spool rocket theory?? Matt61:I found the ceramic rod I promised you…is adress the same?

  67. Herb,
    I don't know that many of these effects would be significant in only 10M. Doesn't it seem like they would really start to present problems at longer distances? For me, a lot of pellets seem to degrade rapaidly past 25 yards, perhaps because their velocity decreases much more quickly than their spin rate. At any rate, 10M accuracy does not require much improvement from what I've seen.

    I'm not sure how to relate roundballs, but we do know they benefit from a very slow twist, and won't shoot well at all out of a rifle twisted for conicals. This is on my mind, since I'm headed for Friendship tomorrow — should be lots of roundball experts:).

  68. Herb / Matt…

    This is starting to get more like a day of work…..

    The "rocket business" uses complex models, (most developed in the 80s, so the old-timers need to go back to school), to determine the summation of forces on projectiles. These days, the predictions can be tested with radar, so we're closer than we were in the previous century.

    These are the things we DON'T need to worry about:
    1. Gyroscopic Drift. This is not precession, it is "spin drift" as Herb said. It will push a huge, (400grain) bullet less than 1/2 of an inch in 1000yards. Small pellets at 50yards will never see even a tiny bit.

    2. Poisson Effect. This is called roll-off. As a bullet/pellet flies at its upwards "trim angle", it is building a cushion of air below it, and will occasional "roll off" the cushion. This may be the cause of the occasional "flyer" of higher-speed, longer-range, shooting,(but I doubt it).

    3. Coriolis drift. As you send a spinning projectile over a spinning mass, (in our case, the earth), the two induce relative forces. Since the pellet can't move the earth, the earth moves the pellet, hopefully very little..

    4. Bernoulli effect. The idea that as air flows over a curved wing, the air on the top moves faster than the air on the bottom, thus exerting a lower pressure, and voila, a 900,000lb 747 takes to the air. Not so – the Bernoulli effect, (a real effect, for sure), is now measureable, and much less than we thought. The air molecules on the top of a wing really have no compulsion to go as fast as their brethren on the other side of the aluminum….there are some other neat forces that actually lift the old Boeing

    5. Coanda effect. This is a complex interaction of two or more fluid flows. I don't even like to think of it.

    The ones I do think about are:

    1. Magnus effect – the airflow effect that curves baseballs, will move a pellet, particularly in a side-wind, or if the "trim angle" is steep.

    2. Gyroscopic forces. The much-discussed tendency of a spin-stabilized projectile to spiral in response to what we've earlier called "restorative forces".

    3. Aerodynamic drag. This is the most obvious, particularly in drag-stabilized pellets. These effects actually create the "restorative forces"

    The inter-relationship works like this. Higher speeds = higher aerodynamic forces = higher restorative force.

    Higher spins = higher resistance to restorative forces, (and thus, greater response = greater spiral).

    Soooo, in general, faster pellets should spin slower.
    Slower pellets should spin faster,

    At what point should we shift the balance between spin-stabilization and drag-stabilization? That depends on the pellet, and (this part I hate!), the "trim angle". The "yaw of repose" as it's also known, is not constant. The farther away our target, the higher angle we are going to set the barrel.

    Obviously, we can't change the twist rate of the barrel as we change the distance.

    We can, however, adjust the muzzle velocity, (with the right PCP)…..BUT, that would change the angle. Oh Bother!!

    Maybe the physics books are best used as wheel chocks!

    Best regards,

    Jane Hansen

  69. BG_Farmer,

    Agreed, the further out the worse all of this gets.

    At this point I'll try to go back and get some real data to talk about instead of my perhaps faulty memory.

    I have some cheap multipumps in 0.177. At first I had a Crosman 760 smoothbore and a Daisy 880. I played with them quite a bit. THen I bought an Remington Air Master from local WallyMart. I have about 20 different kinds of 0.177 pellets.

    Overall my memory was that not only were there vertical changes in the POI with the 880, but significant horizontal ones too. That really surprised me. I had expected just group size and vertical shifts. I was shooting 10 shot groups.

    My conjecture was that the 880 was flinging the different pellets in such a way that there was some significant perturbation. Different pellets responded in a different way to the perturbation.

    At first I thought that it was intrinsic to the pellet. But pellets behaved differently in the Daisy 880 and the Remington 77. So it became clear that you couldn't pick one pellet as the "gold standard." My notion at first was that you could find a "gold standard" which could be sued to zero each different gun. Then the different types of pellet would shift in predictable ways around "gold standard" pellet. Ha!Ha!Ha! I have this bridge in Brooklyn…

    It was just basic shoot'em and see where they go…

    RE: Round balls as gold standard.

    Dah… I've sliced enough golf balls to know that you can spin a round object and get it to curve. So a rifled barrel could very easily cause a spin which would cause a POI impact shift from the "true" vertical plane of the boreline. A smootbore would seem to be less problematic. The smoothbore should average out closer to the true vertical plane of the boreline.

  70. I'm traveling again so as time and motel wifi permits I play catchup on the blog.

    BB, you don't know this but you have been keeping me company during my travels. I have been playing all your podcasts on those long mind numbing interstates. I wish I had more of them (podcasts not interstates). I'm on my second time through them.

    You mentioned in the one on bigbore guns that you can't pump one up from zero pressure with a hand pump so one thing you can do is pre fill a little with CO2 first to shut the valve then pump the rest of the way up.

    My question is is it alright to mix CO2 and air in a PCP like that and if it is why would one need a de-gassing tool? If the CO2 and air mix pressurize to 3000psi does it matter what the ratio is?

    Also, you spoke, in one of your blog comments recently, about not ordering some scopes for PA to sell because they were not worthy. Were they the the ones with the level or were they another?


  71. Jane,

    Thanks for the lucid terminology lesson and explanation. Sorry about turning this into work…. I have really enjoyed your sharing expert knowledge. It is fun to learn something new.

    Instead of trying to explain why I'm confused, let me just ask the question. Then try clarify a few points that seem to be crystallizing in my pea brain.

    Would you lump precession into Gyroscopic forces, one of the three that you do care about?

    The other part of this in my mind is that the precession rate will be much slower than the spin rate. In 10 yards, a 16 inch twist only spins a pellet 22.5 times. If the precession rate is 1/10 of that, then the pellet precesses only about 2 revolutions, assuming that the precession starts out of the barrel…

    If the pellet precesses significantly (ie has a large yaw), then it will decelerate even faster. Less speed means that there is less aerodynamic drag to re-stabilize pellet due to diabolo shape. So the pellet yaws even more and the precession speed increases. It of course isn't about how many times the pellet precesses, but what the angle of yaw is at any particular moment. As you point out, the angle of yaw isn't a constant for a zillion reasons.

    I'd agree that the real sticky part is between spin stabilization and drag stabilization. My perception is that most of the writings on exterior ballistics are about firearms. It seems that with the CoP in front of the CoG that a destabilized bullet very quickly starts to tumble. Then all the writings throw up their hands and say who knows where it is going… But since the CoP is behind the CoG for a pellet, a pellet can't tumble – it precesses. Well at least the pellet can't tumble until the velocity gets really low. (I'd be really curious if a pellet could tumble at terminal velocity, or if it would be drag stabilized…)

    After all your effort I hope that I'm getting warmer. For now, I think I should delay my application to study for a Master's degree in ballistics. 😉


  72. Herb,
    I don't doubt you saw horizontal displacement with different pellets or different power levels. I've seen it myself (also in .22LR's), and have to admit that I thought it was probably tied to spin, although Jane's characterization of spin drift makes me wonder now.

    Regarding range, Jane may have hit on the critical distinction — angle of elevation. Perhaps spin isn't that critical (may even add stability) at short ranges because of the low angle, whereas longer ranges require a higher angle of elevation and thus the angle of flight forced by the drag stabilization diverges more from the boreline/axis of spin. I don't think pellet velocity is a primary factor, except as it influences the trajectory and spin rate.

  73. CJr,

    Yes, a chemistry question!!!! This I have cold.

    RE: My question is is it alright to mix CO2 and air in a PCP like that and if it is why would one need a de-gassing tool? If the CO2 and air mix pressurize to 3000psi does it matter what the ratio is?

    First it won't hurt anything to mix air and CO2.

    The problem is really filling reservoir with CO2 when there is pressurized air in the reservoir. CO2 goes into reservoir as a liquid, with some headspace that is a gas. The air mixes with the CO2 in the gaseous headspace. This prevents you from getting a "full" fill with CO2. As CO2 is shot, it takes some of the air out each time. So on the second fill, then you'd get a "full" fill.

    Also if you had 3000 psi in rifle, then the pressure in the rifle is greater than the pressure in the CO2 bottle. So you could not put any CO2 into the rifle.

    The degassing tool just keeps you from having to dry fire all the pressurized air out of the reservoir, before you start filling with CO2.

    You could for example, fill gun with CO2, then pump air into reservoir to get to 3000 psi. Since the air is in the gaseous phase, you'd get a couple of high power shots until air was purged from CO2 gas. At that point you'd drop back to CO2 pressure only.

    So long as there is liquid and gas, the pressure of the gas depends on the temperature of the liquid phase. As you shoot the CO2, then CO2 in liquid phase "boils" into gas. That cools the liquid.

    I'll skip a discussion of the supercritical phase of CO2 above 89 degrees F. 😉

    Geeze I love giving Dad answers… I'd spend 5 minutes explaining something to my daughter, whereas my wife would simply say "Yes" or "No". The running joke with my daughter was "Do you want the Dad answer or the Mom answer?"


  74. BG_Farmer,

    Yes it is all about yaw. But again, a pellet can't tumble. It is drag stabilized. So as the pellet yaws, it starts to precess.

    See motion demo at:

    What is critical is, why does the pellet start to precess and when? If you have a crown defect, then you might start the pellet precessing right out of the bore. Since it starts precessing at same point with same velocity, you could probably do some amount of correction for the POI. But what happens if the precession starts "somewhere" downrange? Now who knows what angle the bullet tip is at when it destabilizes.

    I really expect that every pellet precess to some small amount. I'm taking a guess that something causes the pellet to suddenly and violent change from a "stable" precession to an unstable one. think of a kid's top. the top precesses for a while, but quite suddenly it will start to wobble. It is that precessing to wobbling that I'm trying to understand.

    The other point is that as precession (intertwined with the angle of yaw) gets even worse, then pellet starts to corkscrew. Then it will get even worse and you have nutations, so you'll get a corkscrew in a corkscrew. Yuck…

  75. RE: Precession & Crow Magnum experiment

    Again, I'm going on my memory…

    I tried an experiment which I though was really really interesting.

    (1) I roughly zeroed scope with some 0.22 Crow Mangum pellets.

    (2) I then used some super glue to attach some #6 lead shotgun shot onto the top of some of the Crow Mangum pellets. The 0.177 round balls were too small to rest on the circular lip of the Crow Magnum. The #6 was big enough to rest on the Crow Magnum lip but not touch the rifling.

    (3) Shot about 10 of the things though my Daisy 22SG. I got two distinct groups. One much lower and to the left of the other.

    By putting the lead shot on the front, I increased the distance between the CoG and CoP. My assumption was that with a little imbalance the pellets when into a "wobbling" precession. This increased the drag greatly, hence lower. I can't exactly explain left-right difference. as I remember both were different (left to right, not just vertical) than the position of the plain Crow Magnums.

  76. ahhhh some nice scientific studies and experiments out there I see. Nicely done.

    I just wanted to say that I too am a natural shooter. I'm also a natural misser, ricocheter and grazer.

    You should have Paul and Crystal do a guest blog and answer questions.

  77. RE:ABOVE Exp – Precession & Crow Magnum experiment

    Ah the old memory ain't what it used to be…

    Checked pellet stash and must have used 0.177 balls with 0.22 Crow Mangum

    The #6 shot isn't quite big enough to sit nicely on 0.177 Crow Magnum, but it is the largest I had on hand. Maybe #4?

  78. I think the greatest conclusion one might draw from all of this is that one must own as many airguns as possible to make shots at different times and "shot circumstances"…..HA!….I found us some more justification!!! word verification "LUCKSTA"!

  79. RE: Lucid explanation of exterior ballistics

    Found what seems to be a paper that I can, more or less ;-), understand. It is one paper, so the termonolgy is consistent as well as terms in equations.

    There seems to be a decided emphasis on Bullets (spin stabilized) vs pellets (drag stabilized objects). Maybe looking for information on exterior ballistics for a "Spin-stabilised mortar" would clear up differences.

    Chee Meng Fann
    December 2006



  80. Herb,

    I agree with your statistical observations. It now seems to me that the original question comparing the reliability of five and 30 shot groups was based on a mistaken premise. They are different animals or apples and oranges. There is no ultimate answer that you can get from them.

    Insert a scene from Jesus of Nazareth where Jesus is facing Pontius Pilate and tells him that his mission is to deliver the truth. Rod Steiger, playing Pilate, puts his face a few inches away, bugs out his eyes, screws up his face, and shouts, "What's the TRUTH?" It's quite comical and, taken by itself, a legitimate question.

    Anyway, if you shot 5 shot groups until doomsday, the average of all of them would not be as large as a single 30 shot group. An average is just a characterization of a set of data points, so by taking an average of an arbitrary number of 5 shot groups, you are just getting a better characterization of the 5 shot group which is itself a limited tool for gauging accuracy.

    BG_Farmer's question of the value of all of this is a good one. The bell curve distribution is the foundation on which we impose all of the other causes for inaccuracy like parallax, scope quality, and the usual screw-ups of shooting technique. You would not even see the bell curve physically except for inside your call radius which is the edge of your ability. Wherever you have ability, it will override the probability distribution. There is no bell curve operating on how many times you set you foot correctly when walking. The only time you would see the bell curve distribution is out much further than we normally shoot–probably hundreds of yards with a lot of rounds–approaching 30. This is interesting enough but mostly academic. Jane beat me to the observation that whether knowledge is better in this form or as a wheel chock is an open question.

    Jane, I still don't see that gravity provides the torque necessary to rotate a projectile from its boreline attitude into alignment with a flight path. The concept of center of mass implies to me that gravity does not care what orientation something is in. If the key force is not Bernoulli's (by which I mean the definition relating fluid velocity to lateral force), then it must be one of those other exotic ones you mentioned. This is all thrown in the shade by the statement that lift is not responsible for elevating Boeing 747s. That's astounding. I'll never look at my rc planes the same way.

    B.B., well the show sounds like a great opportunity for Crystal. I have an idea for the ultimate moneymaker! PA announces a deal whereby everyone who buys a pcp is eligible for a raffle drawing whose grand prize is a field target shoot off with the PA marksmanship team a.k.a. Crystal Ackley. Heh heh. That out to get the pcps moving.


  81. 78g,
    I shoot the card board boxed .22 Crosman Premiers. I think they're 14.3gr. Are those the ones you say you don't like? They are working excellent for me in my Marauder. I have not tried the JSB Exacts yet but, in one of his podcasts, BB recommends the JSB as #1, Crosman Premiers as #2 and Beeman Kodiacs as worth trying because they might just work for your situation.


  82. Herb, Matt, Jane,
    My primitive summary of the spinning diabolo dilemma is this: The spin of a pellet tries to maintain an orientation roughly parallel to the boreline (angle of repose or yaw= angle of elevation). Simultaneously, the drag stabilization of the pellet forces a head-first attitude and an angle of orientation (also a yaw but not maintained by spin) tangential to the trajectory. While the orientation sought by drag stabilization and the angle of repose sought by spin literally begin to diverge from the muzzle resulting in minor precession, it is at the apex of the trajectory that the angles sought by the two methods of stabilization become of opposite signs, and it is likely at this point that significant precession and perhaps even nutation become major concerns. Depending on the velocity of the pellet (and thus the resultant trajectory) and the spin rate (dependent on the velocity and the twist rate), it seems likely that all drag stabilized pellets with sufficient spin will precess excessively and perhaps nutate when fired at high angles of elevation:). How many steps behind the scientists am I? At this point, my only "solution" remains to reduce the twist rate significantly and let drag stabilization do all the work, although it seems possible that may reduce absolute accuracy at close ranges.

    Just got back from the NMLRA meet in Friendship — lots of good noise and the smell of smoke and fire.

  83. Matt,

    Please, if you ant to talk about statistics anymore, please contact me off-line. I promise to answer questions till you stop asking.

    There may be lurkers interested in this, but no one else has chimed in. I feel like I'm boring everyone else…

    Suffice it to say that small sample statistics STINKS! Statistics is about large amounts of data. More data, better decision. Want an even better decision? Yup – get even more data.

    Any one measurement of "group size" is near meaningless. It doesn't give you any idea of of repeatable the measurement would be. If you shoot 30 shots, there are a lot better ways to analyze that much data than to boil all the shots down to one group size measurement.

    For instance, how do you handle what may be a "flier"?

  84. Jane's "Obviously, we can't change the twist rate of the barrel as we change the distance."

    I wonder if it would be possible to change the rifling with screw-on bbl extensions with different rates of rifling twist for different distances/pellet types?

    Word verification is 'ghter', which, as far as I know, means nothing at all (unless it's the end of 'laughter').

    G'nite all. Sleep safe.

  85. Just what I needed,

    I don't mind you blogin’ here
    and wastin' all my time
    'cause when you're shootin' oh so near
    I kinda lose my mind
    it's not the stats that you prepare
    or the blog looks like a questionnaire
    I don't mind you blogin’ here
    and wastin' all my time

    I don't mind you bangin' out
    numbers that we do seek
    it doesn't matter what you say
    as long as it was deep, yeah
    You always know just how to play
    and it doesn’t matter what time of day
    I don't mind you bangin' out
    numbers that we do seek

    I guess you're just what I needed
    (just what I needed)
    I needed someone to say
    I guess you're just what I needed
    (just what I needed)
    I needed someone today

    I don't mind you blogin’ here
    and wastin' all my time
    'cause when you're shootin' oh so near
    I kinda lose my mind
    it's not the stats that you prepare
    or the blog looks like a questionnaire
    I don't mind you blogin’ here
    and wastin' all my time

    I guess you're just what I needed
    (just what I needed)
    I needed someone to say
    I guess you're just what I needed
    (just what I needed)
    I needed someone today

    I guess you're just what I needed
    (just what I needed)
    I needed someone to say
    I guess you're just what I needed
    (just what I needed)
    I needed someone today
    yeah, yeah, so help me

    you're just what I needed
    you're just what I needed
    yeah, you're just what I needed
    yeah, yeah yeah




  86. Not only is Crystal a natural shooter, but (sorry, have to say it) she is a striking beauty.
    Nice to see that even beautiful women can be great shots, and your Annie Oakley comparison was not far off the mark at all.
    Annie herself was quite attractive.
    Hard to conceive anything more appealing than a good looking woman who can also shoot so well.

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