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Education / Training How and when PA get started – Part 2

How and when PA get started – Part 2

Announcement: Pyramyd AIR has lowered the price of the Walther Lever Action rifle with scope…from $499 to $375. The combo is being discontinued by the manufacturer, so they’re trying to quickly move the remaining stock. The rifle without scope will continue to be available.

Part 1

Josh is concerned that he may be boring some readers with all the details he’s putting into his Russian trip to find marble and wood for his Japanese friend. This trip was where he got the idea to export American-made shotguns to Russia, and that was the business that ultimately started Pyramyd AIR, so there’s a tie-in. Please tell him with your comments whether he is being too detailed about the trip.

How and when PA get started – Part 2

by Joshua Ungier

I had the pleasure to travel to Russia thirteen times in a span of one year. This trip by far was the most memorable. I spent a month traveling through Siberia’s forests, marble quarries in Uzbekistan and the Ukraine for its granite. The people were the most unforgettable part of the trip, but I also got really homesick.

The flying dumptruck
After arriving at the headquarters of LesProm, the company in charge of the territory where we wanted to do business, we were flown to the forests and marble quarry by helicopter. The MI-17 is a medium-size Russian helicopter. It’s widely used in Soviet Bloc countries for transporting goods over harsh terrain. It’s a tireless workhorse, was not designed with any comfort in mind and is definitely not for tourists. It’s for transporting bulk goods or, if necessary, cattle.

This MI-17 is outfitted for passengers. No doubt it has seats, a heater and sound-deadening material. I wasn’t as lucky with mine!

The one we chartered was bare bones. It was obviously used for cargo, not people. It should have said on the door “bring your own chair.” The pilot and co-pilot had the only two seats. The four of us in back were trying to sit anywhere we could. I sat on a fuel tank by a window and took hundreds of photographs.

Apart from the deafening engine noise, the unheated “passenger” compartment, terrible vibration, and the growing need for a bathroom they didn’t have, the morning was uneventful. We were flying at a good clip for several hours when the pilot announced that he was in a landing pattern and we would be touching down very soon. Below us was a village of about two dozen log homes. On the outskirts of the village was a large prefabricated building. Apparently, it was a sawmill. Scattered for acres in every direction were mountains of timber. Each pile was at least big enough to fill a railroad car. Some piles were large enough to load a train of a hundred cars.

A warm reception
We were greeted by a village elder, who ushered us into a small hall. It was WARM! A wood-burning stove the size of a VW was blazing hot. All four of us smiled at that. The walls were plastered with propaganda posters. Some very old WWII posters hung among flags and photos of the Stalin and Lenin eras. Slogans defending the communist ideology were tucked into a corner behind a coat rack.

A breakfast consisting of a large loaf of bread, a dish of salt and, of course, a bottle of vodka (coffee was to hard to find) graced the breakfast table. When I timidly protested the early hour to start imbibing what amounts to government-sponsored moonshine with a label “Sibirskaya Vodka,” the village elder replied: “It’s okay. Siberia is timeless. She will not be angry. She is your mistress, not your wife.” He was right. It was already 7:30 a.m. and no one was angry.

You’ll freeze your *&%#@ off!
Preliminary talks were concluded inside a few hours, and by noon we were in a Toyota SUV driving toward an old forest. We drove across a large lake. A clearly marked ice road emptied into a deep valley. We were surrounded by pines four and five feet in diameter. Enormous birch trees straddled steep ridges. The car stopped. “If you want to relieve yourself, this would be a good place. No wind.”

The driver said, “What does he mean by that?” So, I asked the elder. “No windchill factor injuries, you know.” He grinned. I shuddered. It was warmer in the forest. A balmy -29C (-20.2 degrees F).

According to Jethro, my forest expert from Virginia, the wood was at its peak for selective harvesting. Russians, at least those days, did not practice selective harvesting. Clear cutting was more profitable. We spent several hours in the forest looking at the grove and went back to the village. It was getting late. We had one more stop to make that day. We gathered inside the hut and signed paperwork. Brief goodbyes were accentuated by shots of vodka with words, “Eto wam na pasashok.” It translates, crudely, “To healthy passages you face ahead.” Great people!

The MI-17 turbines whined to life. The helicopter was warming up. Rotors were engaged. Our suitcases were packed and delivered to the chopper. We were on the way to another wood-processing facility only 10 air miles away. We were to observe their process and possibly purchase their product for export to Japan. Basically, they shredded whole trees to make plywood using the bark and all. The tree goes in at one end, and plywood comes out the other end.

By this time, it was late in the evening, so we made plans to meet with the owners the next morning to talk business. The one and only “hotel” in the village was an 11-room refurbished army barracks. One shower, one bathroom, one stove. Army cots substituted for beds. Nevertheless, I was out before my head hit the pillow. We were up the next morning at 5 a.m. Outside, it was -36C (-32.8 degrees, F). Hot tea and perozki were enough to wake me up. On top of it, some joker put salt in my tea. That definitely woke me up.

But now the owners were nowhere to be found. They had left in the middle of the night and were not coming back for a while. Strange! No contract was signed there. We were done. Time to move on to the marble quarry.

The duty-free store
We were then airborne and on our way. A couple of hours by helicopter and a few hundred miles later, we landed in the middle of nowhere–right on a frozen river. The powerful prop wash revealed solid grayish-blue ice three to four feet thick beneath us. “What are we doing here?” I asked.

“We are going fishing,” the pilot replied. “It is perfect weather,” he continued. “There is no wind.” He proceeded to extract an auger from the helicopter and, about a hundred feet from the chopper, he drilled a two-foot hole.

“You can snag a ten-kilo pike here,” the co-pilot said. And he was right. No sooner was the line in the water (he used chunks of bear meat on a hook) than we had a fish. Fish after fish was hauled out and lay frozen on the ice. At -30C, fish freezes instantly. After an hour or so, we took off again, laden with a dozen trophy-sized pikes in an ice chest. “It is not good to arrive empty-handed where we are going,” he said. “Food warms up negotiations.”

The river was several hundred feet wide where we landed to fish. It was cradled on both sides by tall mountains. The pilot handed me a pair of binoculars and said to look around. “There is a lot of bad history here,” he said. “A lot of people died here.”

A very bad place
Partially denuded of trees, the steep banks were dotted by caves. Some caves were very large with gaping entrances facing directly onto the river. High above the caves there were remnants of a castle-like building. “During the reign of Jozef Stalin, people were sent into that building for interrogation,” he pointed. “Thousands of prisoners went in and were never seen alive again.” He continued, “There was a trap door in the floor right behind a chair. When the interrogation was over, the prisoners were shot with a .22 behind the ear and then dumped through the trap door, which lead down to the caves below. Dry conditions mummified tens of thousands of bodies in the caves.

“A huge flood a while back washed away half of the mountain and the bodies were floating down the river by the thousands. Locals and soldiers stationed near the town were called to dig mass-burials graves, but they couldn’t keep up. When that did not work, the government sent a train loaded with bricks and a thousand miles of strong twine. Twine was attached to the bricks and then to each corpse. The remains then sank to the bottom of the river. Bad, bad history,” he said.

We landed at the airport of a small settlement. I don’t recall its name. There were several old biplanes with their motors running 24/7 down the tarmac aways. An attendant, a young girl, asked for our passports, and, after completing her duty, ushered us to the office of the chief. That guy could have wrestled a T-Rex! “Welcome, welcome!” he shouted. “Americans! I saw you only on TV. What a great treat. Sit!” And out came ever-present local moonshine he called vodka. Who needs an embalmer? It was just past 10 a.m.

96 thoughts on “How and when PA get started – Part 2”

  1. What a coincedince, I had a loaf of bread, a dish of salt and a bottle of Vodka for breakfast myself this morning!!

    Great story Mr Ungier. I enjoy the detail and my only hope is that we get to hear this story through to its completion.

    Thanks for sharing,


  2. Fascinating reading- nice job. The details make the story, so please continue just as you are! More photos if possible, too. Hmmmmm… is there a book in the works here? GF from Garrettsville.

  3. I agree with the others. I hope it takes a long time before we get up to date. If you wrote this into a book, I would read it.

    David Enoch

    Tell Tom I will see him at LASSO.

  4. B.B.

    I know your a fan of the 1911. Last night on the TV show Bones, FBI agent Booth was carrying what appeared to be a 1911 in a shoulder holster with hammer back and I assume safety on. See sometimes even TV can get it right.


  5. Extremely interesting story – it's been a good read so far. Nothing for Josh to feel uneasy about. I prefer rum, however, to Vodka. Tonight I'll have some salt with my bread and think of Josh. Maybe at lunch, too. Maybe rum as well.

    I work with a Russian girl Yulia – very tiny – gymnastic size. Not what you would think of typically. We all learned early on not to engage her in shot for shot drinking contests.


  6. I'll never be on an adventure like that. It is very interesting.

    By the way, flash freezing was discovered because of such hash conditions. If you freeze fish slowly the flesh gets all mushy. If you freeze it in a super cold environment, the ice crystals formed are small and don't pierce the cell walls. Hence the flesh of the fish stays firm.

  7. Not boring at all. Please keep writing.

    "It's okay. Siberia is timeless. She will not be angry. She is your mistress, not your wife."

    That just stuck with me. There's something powerful there.

    Al in CT

  8. Mr Ungier,
    You cannot be too detailed! You are in the details. Please continue as is. And, yes I will read the book, too. So, there, you have already sold two books and it's not even out yet. Hmmm….bread, salt, Vodka…I know how I'm going to read my copy of the book.

    Seriously, Russia is such a mystery to me, and your personal insights and anecdotes open up a fresh look at the real deal. Please don't leave anything out.



  9. Joshua,

    Please continue your story as you are writing it. You are letting us see the people of Russia as they are, and how they have adapted to the harsh weather and conditions, and not as our governments have labeled them.

    Your writing style shows that you would be a great author of books, so I am also waiting for the book.

    Thank you for sharing part of your life with us.


  10. “I went to Russia, then did this and that and started an air gun company” would be to the point but not nearly as entertaining.

    Certainly proceed as you have begun. My suggestion would be once you are finished to compile the story and include it as a preface in catalogs or perhaps a collectable booklet. Entertainment wise it makes Dr. Beeman's account of developing the R-1 seem like a well Vodka instead of a top shelf selection.

    On a different topic, does your new location include a store front?

  11. Volvo,

    Josh doesn't see these comments unless he reads them like you. He generally reads the blog in the morning, so I will answer the storefront question.

    They do not have a storefront in the new building. They may do something in the future, but right now it's not in the plans. A person can always arrange for local pickup, however.


  12. Hi Josh: Great job on this article. Keep up the details they are fascinating.

    Your helicopter trip reminds me of a couple of trips I once took on a Bolivian military plane, but on those the copilot offered me cotton for my ears, and there were seats.

  13. Mr Ungier,

    Considering your recent move of Pyramyd AIR I certainly appreciate the time you're taking out of what I imagine to be a very busy schedule in order to relate this fascinating story.

    Please take your time and continue telling us about this interesting adventure that lead to the birth of Pyramyd AIR. The details help us to vividly accompany you on these travels.

    Thank you.


  14. Morning B.B.,

    Very bad place. Thousands went in and none came out. After the interogation was over they were shot behind the ear, etc. We think that we know hardships, but….! The Russians, amazing people.

    Josh, please keep the details in your story. They are what gives it life.

    Nr B.

  15. Mr B.,

    It's NRA not Nr B. ;^)

    Glad to hear that you received the new scope. Blue illumination is interesting.

    I'm also interested in hearing about your comparison of magnification in the new scope to magnification in one of your other scopes. Field of view and sharpness/clarity would also be interesting comparisons once you have the two scopes side by side.

    I think Chuck mentioned yesterday about comparing mil dots. Not as important to me but stumbled across this interesting read about mil dots:



  16. Very informative and entertaining. The details add color and life to the story. Aside from having business acumen, you have the talent for writing.

    Thank you for sharing your story.


  17. Josh,

    Now, that I think of it, I don't suppose that helicopters have bathrooms. Trains, planes or cars the Russians do seem short on the creature comforts. And I have wondered what the Russians themselves think of Siberia. Glad you persevered through all of this to bring us PA.

    Purchawk, ha ha. That's a great question about comparing one 50 shot group to 25 2 shot groups with your 1377 that puts things on the line. Are they they same? My answer is that it depends on what you mean by same. Physically, it is clear that your call radius under the conditions you describe is under 1/2 inch. In other words, your shooting skill, gun, rest, and range conditions are such that you could put shots within a 1/2 inch circle forever barring some outside physical intervention. In that sense the 50 shot group and the 25 2 shot groups are the same. However, the various 2 shot groups are different from each other. Some should be on top of each other, others will be on opposite sides of the 1/2 inch circle, the rest will be at every distance and every type of orientation relative to each other. The two shot groups are different from each other in this sense. However, if you were to overlay all of your 2 shot groups–an idea from Vince I think awhile ago–the pattern should be very close to what you get with a 50 shot group, so in that sense the 2 and the 50 shot groups are the same.

    As for an ideal group size for testing, I don't believe there is a single answer. Our working assumption is that at any distance a 30 or thereabouts shot group is as large as you will get barring equipment failure. Where your call radius is so small that you do not see any density variation in your group, I would say that a small group size, like 5 should be sufficient. Beyond that, questions of group size and how many groups you want to shoot depends on how much uncertainty you can tolerate and what your purpose is. Getting back to our original question of the value of 20 and 30 shot groups for testing, I would venture to say that from a rest, for anything under 25 yards, large groups like 20 or 30 shots are superfluous because of the size of the call radius. 10 at the max should tell us what we need to know.


  18. BG_Farmer,

    Regarding a comparison of six 5 shot groups and one 30 shot group, my answer is that the size of your 6 shot groups will vary within the size of the single shot group. The variation could be described by a normal distribution in which each point corresponds to a whole group rather than a single shot. The normal curve is fully established at 30 shots or thereabouts. Six will give a rough approximation of the curve that will be much more spread out and flatter. This suggests that the largest of your six shot groups can be as large as a single shot group, but that's not very likely. As for how large the largest six shot group would be, Alan's suggestion of about 80% sounds plausible, but how often the largest of the 6 shot groups will be 80% of the 30 shot group is beyond my ability to calculate.


  19. On the subject of the 5/30 64% ratio of group sizes, I think the underlying question is what is the statistical distribution underlying this prediction. If it's not the normal distribution, then what is it? A look at the criteria for applying the normal distribution–a collection of random variables, distribution of trials around a mean value–suggests that shot groups are not only eligible but a fairly ideal candidate for modeling with the radial normal distribution. More to the point, the paper in question models group size with the chi distribution and the lognormal distribution. So, what are these two? They are both variations of the normal distribution with the chi distribution applying to smaller group sizes and the lognormal applying to larger groups. To ask if the chi and the lognormal are the same as the normal distributions is like asking if orange is the same as red. Not exactly, but close depending on your standard of precision.

    As for whether indeed the ratio 5/30=64% for groups sizes at all distances is true, I'm not able to say. I had a look at the various tables and found them highly ambiguous. It appears that their purpose is more to test the correspondence of randomly generated set of computer data with a mathematical model rather than compare the size of groups to each other. There's particular ambiguity surrounding the sense of standard deviation. Does it refer to the radial distance associated with a group or the variance of the curve?

    I'm not able to say one way or the other just what the various tables and procedures are doing, but I tend to doubt the constant 5/30=64% ratio for a couple of reasons. First, a simple calculation. The area under the normal curve is the probability of appearance. Total area equals 1 or 100% and this is associated with a 30 shot group which fills up the total area under a curve. A five shot group should fill up 5/30 or about 18% of this area occupying a vertical band symmetrical about the mean. Is the radial distance associated with 18% of the area under the curve 64% of the total? It doesn't seem likely.

    Secondly, the paper does not address at all how the normal curve might change at different distances. There are all different kinds of normal curves. The bell curve is just the standard normal based on one standard deviation. Other standard deviations will make the curve narrower or fatter. And there are many other flavors–chi, lognormal, chi-square and on. For each of these curves of different shape the relation of various group sizes should be different. It seems to be a significant question of whether the curve changes over distance which this paper does not address at all.


  20. Matt61:

    I think I follow what you said and that essentially what I did is valid.

    You left me with "call radius," which I can't find a definition for easily on Google. (I'm an historian and editor and illiterate in math.)

    I experimented a little more this AM and found I could just as easily put three pellets into the half-inch circles as two, and I probably could do it indefinitely. I did get one uncalled flyer.

    When I look at the final target sheet, your comment about superimposing all the circles makes obvious sense.

    In fact, looking at the target gives the very strong impression that what I asked has to be correct, regardless of the actual math. The physical evidence is compelling: all the circles are the same size, so they would clearly all fit on top of one another and the pellet holes would all be inside the diameters of the circles.

    By the way, I usually make my own targets with simple publishing software, but this time I just drew lots of circles using the center of a CD as the template.

    Thanks for commenting.

  21. PurcHawk,

    I was trained to be an English professor and a librarian. 🙂 Call radius is a term that I picked up from David Tubb–all-time great rifle shooter. It refers to the circle that you can keep your shots inside of at a given distance. Yes, your method makes sense to me.


  22. Matt61:

    For an English major, you certainly manipulate mathematical language well!

    I really appreciate your comments and Herb's. This seemed simple and to make sense to me, but you guys made it appear to be valid.

    Since, for me at least, it is much easier to shoot twice each at 25 different targets than to shoot 50 times at one target–you can see what you are doing, if nothing else–this approach will help me in the future in judging a gun's accuracy.

    The trick will be to predict what size the circle should be in order to pronounce a gun "accurate."

    I suppose you could draw one-inch, minute-of-angle circles for shooting at 100 yards in order to verify some of the claims manufacturers and gun magazine writers make.

    If we ever get decent weather again, I'll try one-inch circles with my old Mossberg 144 target rifle. I bet it will do it.

  23. By the way: great writing, Josh. You have the hard-to-come-by abilities to isolate the telling detail and articulate your experiences. I'd love to edit your memoirs.

  24. I agree with everybody else, please keep the story going. As a US Soldier, it's interesting to picture what it must be like for a Russian soldier under such conditions, especially after the USSR fell apart around them! Maybe we were enemies, but I think a lot of soldiers feel a bond with every other soldier, regardless of nationality. He could be me after all…

  25. This is a great story, made so by the details.

    I don't like much about the government, but I don't believe that America has labeled Russians as bad people. The Russian government on the other hand has been one of the most sinister entities to work its evil in man's history. I think that warrants the ire of our previous leaders.

    I have found the Russians I have met to be tough, hard working people with a great sense of humor. I guess you would have to be, if forged in those conditions. I think most Americans draw a distinction between the government and it's people. We're not all bigots and hateful as our own media makes us out to be.

    While we're on the subject, there is an EXCELLENT video on youtube from PyramydAir on the elusive Russian-made IZH 61! For some reason it's not on the PA site, but easy to find on youtube. Dig that funky soundtrack.

    This is the ugliest rifle I absolutely must have.

    Mr. Ungier, maybe you could make another quick trip to Russia so I won't have to wait another month and a half to get my IZH61!

    Slinging Lead in Powder Springs

  26. Powder Springs,

    The video on youtube isn't from Pyramyd AIR. It was one of the submissions for a Pyramyd AIR video contest, which required that all submissions must have the PA logo.


  27. Stroke of genius, requiring the PA logo. Pyramyd would be well advised to hire this DWMono guy to do some more videos for them. Besides Paul's great reviews there is nothing even close to the quality of this as far as airgunning videos. (Notice both are affiliated with PA) Also he is apparently willing to work for prizes!

    Slinging Lead

  28. Matt,

    I agree that you are doing very well on the statistics, but there is one thing that I think I can help clarify for you. It was triggered by your comment on the shots filling part of the area under the curve.

    The "normal curve" depicts the theoretical probability distribution for a particular kind of variation. A sample size of 30 or more is considered to be large enough to accurately represent the performance of when that data is statistically analyzed, most commonly resulting in determining the mean and standard deviation (or "sigma") values. This is not the same as saying that if one takes 30 samples, that person is guaranteed to have found the extreme capability of the system – only that they can fairly reliably (within defined confidence intervals) calculate what the extreme capability of the system is. That is found by calculating sigma and performing some analysis on the results. For a normal distribution, approximately 68.3% of events will be within plus or minus one sigma of the mean; 94.5% will be within plus or minus two sigma (four sigma total); and 99.7% will be within plus or minus 3 sigma of the mean. There is still 0.3% of the events outside of plus or minus 3 sigma.

    So if you picture the normal curve, realize it represents the probability of an individual measurement (or shot) of having that particular value. It is not about having the area fully represented by any particular number of shots. The odds of any one shot landing in any spot are the same for each shot, at least once the system is stable. The more shots, the more the data "stacks up" to look like the picture you are used to seeing of normal curves.

    If you think of the distribution of shots across approximately 1" CTC (for a very large group of around 100 or more) about 68% of the shots will land within 0.33" of the mean, another 26% percent will fall in the band between 0.33" and 0.66", and only about 5% will fall in the band from 0.66" out to 1" (there will also be 0.3% outside of the 1" ring, as I assumed that to be plus or minus 3 sigma). But as Herb has pointed out, you wouldn't actually see this on a target because all you would have when you are done would be a hole about 0.8" in diameter with some ragged edges and few things that might look like close fliers – most of the data is lost.

    Even out of a 30 shot group, one would only expect (on average) about 1.5 shots to land in this outer band, so the odds of having 2 shots directly across the mean from each other is extremely unlikely. I would bet that a 30 shot group measured in the 1" scenario above would only measure about .7-.8" or so, maybe even less.

    I hope this helps.


  29. Wet scope,

    Quality scopes today are sealed and filled with nitrogen. so they don't fog on the inside. I have been in conditions where they would fog on the outside in a matter of seconds. But that should not affect their zero.

    Heat is what affects a scope's zero. However, there can be ancillary affects when the stock on a rifle swells with moisture. I have seen rifles change zero and even seen their wood stocks crack after a few hours exposure.


  30. Staying a bit liquored up keeps you from having to move so often due to mild dehydration. Maybe that is one reason they have vodka with every meal up there when they have to undergo lengthy truck and helicopter rides with few facilities and no TP.

  31. General question on the expected accuracy of a tuned Quest 800:

    I posted this late last night, and I thought I would try again today so that I might have a chande at more answeres over the weekend. Sorry for the duplication:

    I have a tuned Quest 800 (TurboTune by Gene in SC with a Tarantula XL spring, new Apex seal and custom machined guides – done in attempt to make my venture into a springer as accurate as possible after the mainspring broke), and I’m wondering what kind of accuracy I should be working to achieve in terms of group sizes at 20 yards with this gun. While it is still no high end gun, I still expect it is probably more capable than I am. I would just like to get a feel for how much more I need to improve.

    My best 5 shot group has been about .6 inches with Beeman FTS pellets (it does not like JSBs, yielding only about 12 ft.lbs. vs. 14.5 and more accuracy with the FTS), but I frequently still get some that are an inch – which as BB stated is not at all accurate.

    I love the tune – the firing characteristics are so much better now – but would love to know how much I should expect to improve while I practice and save up for a Marauder.


  32. Josh,
    Keep up the story. It seems like it may document not only Russian Siberia but also the last big days of capitalism in our own country.

    Alan, Matt, and Herb,
    Thanks for the help on the 6 5 shot group versus the 30 shot group. I think I see what I missed in my conception — that even the largest of the 5 shot groups may not have the maximum dispersion. I also think I'm starting to catch on to what you all are talking about. Its obvious now why statistics are so useful/powerful but also why so many people distrust them:).

    I'm sticking with 3-shot groups for c/f hunting rifles, five shots with target rifles, esp. .22's, and air rifles.

  33. For all of the high-velocity fans, this week rocket-scientists, (and others), mourn the passing of Richard T. Whitcomb, who died Tuesday at age 88.

    Mr. Whitcomb solved the most perplexing aviation engineering problem, that, despite being obviously adequately powered, aircraft design prior to 1951 could not achieve supersonic flight.

    Wind resistance approaching supersonic speeds was so vexing that engineers took to calling it the "sound barrier".

    Whitcomb solved the problem, proved that there was no "barrier", had US interceptors flying supersonic within 2 years, and every jet aircraft since then has some of his fingerprint on it…..

    May he rest in peace..

    Jane Hansen

  34. RIP, Mr. Whitcomb.

    I love your story, Josh. Please keep it coming, and don't leave out the details.

    I think I solved the scope slippage problem on my new Crosman Storm. The included scope mount (two piece) has a pointed pin that extends down into a hole on the reciever. I tried to drill out the pin and discovered it was threaded! but still too short. I replaced it with a 3/4" long 5/32" roll pin. I haven't tried it yet, but the stock pin just gouged a groove back in the top of the receiver.

    I'm new to the forum, trying to get into some better quality airguns. Right now, I have a Daisy Red Ryder, two Daisy 880's, a Daisy 856, a Winchester 600X, a Beeman 1763, and the Crosman Storm.
    I like shooting springers, they are a real challenge!

  35. Josh,

    Great story!! Please continue! We've all been waiting a long time for these installments. I agree with woguph's comment earlier. Details are good! I'd read the book if you wrote it!


  36. I'm looking to get air rifle recommendations, I need something very quiet and accurate only to 20 yards for backyard plinking in a populated area. I was thinking a low powered break barrel but I'm open to anything.

    Thanks for the hlp


  37. decibels,
    Quiet means lower powered or shrouded. PCP is always more quiet than a springer of the same power. Shrouded barrels make any gun quieter.

    PCP cost more than springer and require a pump or air tank. Shrouds add to the cost of a gun too.

    So… it comes down to low power or higher price. Pick one these two choices and then zero in on the other features you’d like to see on your gun.

    The Daisy 953 is quiet, has a modest price tag, and is reasonably accurate out to 20-yards. It is of course low powered… to low for reliable kills for anything except maybe rabbits at close range.

    Have fun selecting an airgun,

  38. Jane Hansen,

    Thank you. Mr. Whitcomb was apparently a giant in his field. Thanks for bringing him to our attention since his work has touched all of our lives. We just didn't know it.


  39. Matt,

    You are starting to understand how statistics works. I hope this will help.

    There is only one "normal distribution" or "normal curve." It is also called the bell curve, and the Gaussian distribution. However the "normal distribution" is only one of the many types of "probability distributions." You mentioned the chi, chi-squared, and log-normal which are other "probability distributions."

    Any type of measurement value which is "normally distributed" can be transformed (mathematically manipulated) into the basic "normal curve."

    For let's assume that the height of a man is normally distributed. So there is some average and a standard deviation. To get the "basic" normal curve, you subtract the mean height from each man's individual height and divide that result by the standard deviation of the men's height. You'll then get the "basic" normal distribution.

    The benefit is that probability tables for every combination of mean and standard deviation aren't needed. Thus all of the different types of "normally distributed" measurements can use the same set of probability tables.

    Now for group size…

    The underlying assumptions I have outlined before.

    Let's assume that I measure the horizontal and vertical difference to the aim point.

    (1) The horizontal and vertical errors are independent.

    (2) The standard deviation of the horizontal and vertical errors are the same.

    (3) That both the horizontal and vertical errors are normally distributed

    The hitch is that "group size" won't be normally distributed because of the quirky way in which the group size measurement is made.

    Let's go back to the average height of a man. Let's say that a man's average height is 6 feet and that the standard deviation is 0.5 feet. Let's also say that the average woman is 5.5 feet in height with a standard deviation of 0.4 feet. Now what is the difference in height between the average married heterosexual couple?

    The average difference in height will be:
    6.0 – 5.5= 0.5 feet

    The standard deviation for that difference is:
    SQRT(0.5^2 + 0.4^2) = 0.64

    In this case all of the math works out nicely.

    Back to group size….

    When you calculate group size for a 3 shot group, the measurement is a bit quirky. The error propagation of the horizontal and vertical errors can't be combined in any simple way like I did for height. There isn't any mathematical formula for the "3-shot group size distribution." The only way that is known to get the required measurement is to simulate a 3 shot group over and over again until you build up enough data to form the distribution.

    The authors of the paper that I referenced did ten thousand simulations of 3 shot groups to define the distribution. These calculations were done 35 years ago. Now there is much more computer power and a much greater sample size could be used.

    They assumed that the centroid of the group was the X-Y origin, and that the standard deviation of X and Y were both 1.

    To transform any "real" data set of 3 shot group to this "standard surface" (3-D now not 2-D), you subtract average X and average Y, then divide X error by X standard deviation, and Y error by Y standard deviation. So one 3 shot simulation is good for all 3 shot groups of any size.

    The resulting group size for 3 shots has an average value of 2.406 from Table 1, column 2. The listed standard deviation is 0.887.

    But the group size measurement can't be less than zero. Zero is only:
    2.406/0.887 = 2.71
    2.71 standard deviations from the mean. So the 2-D curve for group size will be skewed. It will not be a nice "normal distribution."

    Now as the number of shots in the group increases, the mean moves away from zero more, and relatively (compared to the mean) the standard deviation gets smaller. So by the time you get to thirty shots, then the normal curve fits much better.

    I won't push this any more unless someone asks me a question directly.


  40. decibels,

    Re: need "something very quiet and accurate only to 20 yards for backyard plinking in a populated area"

    There are a lot of airguns, rifle and pistol, that can be accurate at 20 yards with the right pellet, right hold, etc. When you're done with them you're mildly satisfied and the resale value (read: potential buyers of your airgun) reflects the ho-hum reputation of your choice.

    There's only one springer (self contained, just cock it an fire, accurate and quiet for a springer) I can recommend. A Beeman R7.

    It's good out of the box, reasonably priced for the german engineering, fine finish german guns are known for and if you get hooked on this airgun thing, it can be tuned into a gun that you will never sell and will always be happy to shoot. You have to shoot 700 pellets through a new R7 in order to break it in and know what a great gun this is. If you disagree after its' break in period, there are always buyers for an R7. They sell within 24 hours if they're priced right.

    HERE'S THE WARNING. If you buy this gun thinking you're just going to plink in the backyard and have a little recreation you're dead wrong. If you buy this gun it will hook you on the very reason that many of us get consummed by pellet guns and start buying many more and trading up into crazy costing pcp's, etc. etc. This gun can and has hooked many people into this hobby. Do yourself a favor and just buy a gamo at your nearest outlet store and continue to be dumbfounded by these idiots that collect hundreds of accurate and fun airguns.


  41. decibels,
    Hammerli 490 is quite accurate to 20 yards and very quiet. Mine has had several thousand pellets (I've lost count) through it and shoots better than ever. The trigger can be a little stiff at first, but proper lubrication and wear makes it pretty nice. Perhaps not the equal of an R7, but it is a nice little rifle at a good price that should do what you want. BB did a multi-part review of it on the blog, so just search for it.

  42. Purchawk,

    The universal standard for accuracy with firearms rifles is 1 minute of angle which is a one inch diameter circle at 100 yards. I strongly suspect that the standard for air rifles is actually slightly lower. Consider that super-elite Feinwerkbau target rifles as described on the PA site are rated at about .5 MOA. This is very good for firearms rifles but you could get the same performance by going down to a considerably lower level of rifle than the equivalent of the FWB. My match-up with Wayne will tell more on this subject. >:-)

    Thank you for your comments about my science work. It has been an ongoing interest. It was greatly assisted by the former chairman of the math department at Oberlin College, Professor Susan Colley, who tutored me remotely through her entire textbook sight unseen. I have never met her. But what a fantastic teacher–a mathematical B.B.

    Alan, your point is very well-taken that the area under a normal curve is the probability of occurrence, not a physical event. So, the area covered by a 30 shot group is a little less than that covered by the associated probability curve. I considered this distinction a case where one doesn't need to sweat the details, but it's important to acknowledge it.

    Herb, I suppose that what one calls a normal curve is somewhat a matter of semantics. The bell curve of school days is the standard normal distribution based on one standard deviation. If you alter just the underlying standard deviation, you get curves of the same shape which are broader or narrower. Which one of these is the normal curve? By other tweaking, you can deform the curve much more than this while retaining basic properties. I've heard of the normal distribution as a family of infinite curves related by adjusting various parameters in the equation, and this seems a useful way to think about it.

    I don't see why the normal distribution can't be used to measure group size when every single article on this subject that has been referenced is based on the normal distribution, and the Aberdeen Proving Ground itself says that it uses it as a model. I do understand that groups of less than 30 shots are not well-described by the normal curve which appear only around 30 shots or thereabouts. However, if the smaller groups are understood as incomplete manifestations of an underlying probability distribution it makes sense to me to use it as a model.

    I have a great idea which is B.B.'s idea of a few days ago. Why not test all of this by actually shooting? We don't need a million trials. The working assumption is that one 30 shot group is more or less descriptive. Applying the same logic, thirty 5 shot groups should give us a reliable number for the size of a 5 shot group. This is a total of 180 rounds which is easily done. At the end of it we take the ratio of the 5 and 30 shot groups and see how it compares to the 64% predicted.

    I just received my RWS Hobbys today from PA, and the fabulous Black Hills ammo was not more welcome. I'm going to celebrate by running my test tomorrow. In the meantime, why not liven up the proceedings with a little prediction. Applying my quick and dirty method of comparing areas under the standard normal curve for 5 and 30 shot groups and their associated radii, I get a ratio of 5/30=10%. This seems a little low. So, I will invoke my conjecture that the probability distribution might change with distance and double the figure to 20%. My range is 5 yards, and I'll be shooting offhand with the IZH 61. By the end of the day tomorrow Pacific time, the data will be in and the targets posted on photobucket.


  43. Jane,

    That's pretty intense about Dr. Whitcomb. So, how did he solve the problem of breaking the sound barrier??? I'm guessing that the answer had something to do with the planeform. I know that for WWII fighter planes encountering compressibility that an extra flap or dive brake allowed them to escape the effects of compressibility although it did not allow them to break the sound barrier.

    Don't feel pressured to answer, but I'm curious if you're the Jane Hansen who designs jets for the military. I'm waiting for the weather to clear to launch the maiden flight of my new $350 radio control Corsair fighter plane. May it not nosedive into the ground on launch.

    On the subject of Russia, I find it a place of incredible extremes–enormous cruelty, deep religious faith, amazing brilliance, total social chaos. As one example, I hardly knew what to think when I embarked on studying the martial arts of the Russian special forces. I had supposed that the practitioners would be like James Bond villains with robotic, violent techniques. The reality was very expressive, excitable people, prone to spontaneously hugging each other. The style itself was very fluid and natural and more like Tai Chi than anything else, but boy were they good.

    Regarding the darker past of the Soviet Union, I read a book about a Polish soldier captured by Soviet forces in the early part of WWII. He was subjected to interrogation which involving getting a 2 inch diameter circle shaved on his head. Then, a long line of Russian soldiers would walk past, and each would tap the shaved part of his scalp with a finger. It doesn't sound like much, but it was supposed to make you long for the .22 described in today's post. Anyway, the guy finally escaped the gulag in Siberia and walked all the way to India 30 miles a day.


  44. Matt,

    RE: "Which one of these is the normal curve?"

    The normal distribution is defined in virtually every statistics book. You can see the mathematical formula in equation 1 at the following website:

    Other probability distributions have different mathematical formulas, and there are a multitude of formulas. The MathWorld site has dozens of them. However there is not a defined mathematical formula for "group size."

    Writers have used the normal distribution when talking about group size because they either didn't know the difference, or they couldn't find the appropriate tables. I had a very difficult time in finding the appropriate tables.

    Who shoots 30 shot groups?

    Impose on Professor Colley on more time. Give her the reference and ask her if using the statistical tables in the reference provide better estimates than using the normal distribution.

  45. Quest 800 at 20 meters about half an inch 5 rounds ctc is about all I can do. I have good luck with JSB Jumbo Express, RWS Hobby and H&N Baracuda Match aka Beeman Kodiak extra heavy.

    I use an extremely light hold.

  46. An interesting story on breaking the sound barrier. Some 9 or 10 years ago, I was at a conference in Hawaii which had General Chuck Yeager as the featured speaker. Talk about a story teller – with that Virginia drawl and his folksy manner, he held us enthralled. Among the many areas of flight he talked about was his breaking of the sound barrier. He took credit (that's what my memory recalls) for figuring out that the reason the aircraft of the day were losing control as they approached the barrier was the shock waves coming off the wings and fuselage of the plane. The dirty air negated the controlling affects of the rudder and horizontal stabilizer on the tail (I don't know if I'm calling this by it's right nomenclature, not being a pilot). But from this, what's called the "flying tail" was developed. If you look closely at those early supersonic planes, you'll note that the horizontal stabilizer on the tail moves in it's entirety, not just the rear edge of it.

    Another neat story from the General – when a US pilot had a ME109 on their tail, they would break into as tight a turn as they could. The high g forces would cause them to lose vision as the blood drained from their brain. The theory was that if the ME109 pilot had followed them into the turn, then they had lost vision as well and couldn't aim to shoot. At that point, the US pilot would break in another direction which would give them enough time to recover their vision and continue the dog fight.

    Incredible. No wonder they deserve the title, "the greatest generation".


  47. Decibels,

    Some fine recommendations so far, but can I ask what your budget is? Also you make no mention of pest elimination, would it be correct to assume that the rifle would not be used in that way?

    Depending on these answers you may be satisfied with the Daisy 499 BB gun. It is a single shot and billed as the most accurate BB gun in the world. Mine seems to be hotter than normal and shoots at about 320 ft per second.
    I am able to get ragged one hole groups at 40 feet, and have shot it well beyond that range. It is entertaining in a small space because of the accuracy and low power. You will need slight hold over at 60 feet.

    On the other side of the coin the R-7 is exceptional, but will not be challenged by the distance you mention. It would be a great pick if pest elimination is in the equation. I have not owned the 490, but it would appear a nice economical choice.

    I have a sound meter and both the 499 and R-7 test very low. Only a fully shrouded and moderated PCP will test significantly lower than these two.

    B.B. has a series on the 499 that you can read and also published sound testing numbers.


  48. Matt,

    There is another consideration in all of this that I should have explicitly mentioned. The tables in the reference that I provided also provide estimates of the variability of the measurement from even just a single measurement of group size. You couldn't do that if you used the normal distribution. You'd need multiple measurements to calculate a mean and a standard deviation.

    Example 1A

    If you just shoot one group of 30 say and get a group size of 0.80 inches, then you have no idea how much that group size will vary if you use the normal distribution. From the table 1,
    Mean = 4.788

    From Table 2 a 95% CI
    = 3.678 to 6.170

    3.678 – 4.788 = – 1.110
    6.170 – 4.788 = + 1.382

    Relative CI
    3.678/4.788*100% = 76.8%
    6.170/4.788*100% = 128.9%

    So if you shoot another 30-shot group, then the 95% confidence interval is:
    0.768*0.80 = 0.61
    1.289*0.80 = 1.03
    or 0.61 to 1.03

    So if you shoot another 30-shot group, you would expect that the second 30-shot group would have a group size between 0.61 and 1.03 inches 95% of the time.

    Example 1B

    Table 1 also gives the standard deviation. For a 30 shot group the number is: 0.635

    0.635/4.788 = 0.1326

    0.1236*0.80 = 0.099

    +/- 1.96*StdDev gives the exact 95% confidence interval for the normal distribution. Using a normal distribution approximation instead of using table 2 gives this:

    0.80 +/- 1.96*0.099
    = 0.80 +/- 0.194
    = 0.61 to 0.99

    The exact 95% CI from the tables was given above as 0.61 to 1.03. So 30 is a big enough sample size so that there is only a small difference for the exact results and using the normal distribution approximation. The difference occurs because the distribution for even 30 shots is skewed.

    Example 2A

    In order to pool measurements with the tables you would need to use a normal distribution approximation for the standard deviation of he mean. (Averaging makes even a non-normal distribution more like a normal distribution.) Let's say that my 0.80 group size for a 30-shot group was the average of 5 measurements. The standard deviation for the average of 5 measurements will be the standard deviation divided by SQRT(5) or:
    0.635/SQRT(5) = 0.284

    1.96*0.284 = 0.557

    4.788 – 0.557 = 4.231
    4.788 + 0.557 = 5.345

    4.231/4.788*100 = 88.4%
    5.345/4.788*100 = 111.6%

    So the 95% CI for the average (0.80) of the five 30-shot groups will be:
    0.80*0.884 = 0.71
    0.80*1.116 = 0.89

    So If you shoot another five 30-shot groups, then the average will be between 0.71 and 0.89 95% of the time.

    Example 2B

    Now let's calculate the expected results for 5 30-shot groups using the normal distribution.

    RSD = 0.635/4.788 = 0.1326
    0.1326*0.80 = 0.106

    Because the 0.106 was determined from the measurements themselves I'd loose a degree of freedom. So the standard deviation of the mean is:
    0.106/SQRT(4) = 0.053

    Now since the std dev was based on 4 degrees of freedom, I look up the value in the Student's T table for the factor which is 2.776 for a 95%CI (2.5% on either side). Now my 95% CI is
    0.80 +/- 2.776*0.053
    0.80 +/- .15
    or from 0.65 to 0.95

    If you'll look at the Student T tables, as the degrees of freedom goes to infinity, then the factor goes to 1.96. The factor gets smaller because you are averaging over more values. The Students T tables "penalize" you heavily for having few data values. In order to get the +/- 0.09 confidence interval that we got from the tables in the reference, you'd have to shoot 11 30-shot groups instead of 5 using the normal distribution.


    Using the tables gives a more sensitive tests than if you use he normal distribution approximation. That is why you should use the tables in the reference.

  49. Anonymous,

    Do you wish to hunt with this? If not I recommend the Daisy 953 Target Pro or any other Daisy or Avanti built on that powerplant. Very quiet, very accurate and inexpensive.

    But it is not a hunting weapon. It will only kill sparrow and mice sized game.

    If you wish to dispatch larger game then go with the Talon SS or the Benjamin Marauder. Both are a bit expensive with the pump or scuba tank and all but both are very quiet and powerful.

    I am not aware of ANY springer which is "quiet". I tried the Gamo Whisper and it was still too noisy for back yard use with neighbors nearby.

    Ditto CO2 unless you are using a shrouded gun which will cost you extra to get done.

    One other option would be the multi – pump pneumatics. With say three or four pumps these can be quite silent and accurate.

  50. Thanks for the quiet Air gun recommendations.

    I should have mentioned I own a Diana 48 but it is totally overkill for my backyard, although i can use it to dispatch the occasional squirrel without the cops showing up. So the purpose here is silent backyard practice for when i get to the range with the 48 so i guess it makes sense for it to be a springer?. It would also be good if it was quality enough to bring to the range for friends. I could go as high as 400 for this but I'd really rather not. but my 48 made me realize these guns are worth the $$

    right now the R-7 or a 10 meter target rifle sounds like the way to go? As a point of reference my 48 is way too loud so i need something dramatically quieter.

    thanks and keep it coming.


  51. PCP4Me,
    You bring up a good point. I thought of the 1377c because I like it so much. But the Crosman 760 is a good choice and PA has them for about $30 (reconditioned).

    This are mid-powered rifles that shoot BB or pellets. Really designed for kids but adults can derive a whole lot of fun from one. I know I shot my Crosman 766 for many many years.


  52. decibels,
    Springer and a good budget. Lots and lots to pick from.

    TX200 is quiet for a springer and accurate too?

    On the lower price end the IZH-61 and IZH-MP512 both have been getting rave reviews.

    No doubt you'll get a few other suggestions.


  53. Fred,

    I have an anecdote about Chuck Yeager too. There is a family friend who is a retired Marine Corps General in Hawaii who has made a nice business for himself writing up a history of the Pacific War and selling it at Pearl Harbor. When he met Chuck Yeager, our friend gave him a free, complimentary copy of his book whereupon Yeager said (rather ungraciously), "What the hell am I supposed to do with this?" Our friend responded, "Well, you can stick it up your ass if want," then turned on his heel and walked away. Generals….

    Anyway, who's to say who the real Chuck is–the folksy storyteller or the obnoxious person. I can say that some of his claims in this talk are odd or erroneous. It seems highly unlikely that a throttle jockey fighter pilot surpassed the best engineering minds in America in figuring out the problems of compressibility. In fact, there are documented records that the first class team that developed the P-38 Lightning and the designers of the F4U Corsair analyzed and solved the effects of compressibility long before Chuck showed up. The P-38 used a dive brake and the Corsair used a trim tab on the horizontal stabilizer–solutions in concept that are similar to Chuck's movable tail. Maybe Jane will tell us what Dr. Whitcomb did to solve the problem for good.

    Hitting a break turn against an ME-109 until you almost pass out is a strange solution. I suppose it worked for some but the odds are not with it. The ME-109 turned tighter than many American fighter planes. More importantly, how could you be sure that you wouldn't black out before the other pilot, especially when you started your turn first? Saburo Sakai, great Japanese ace, records using this tactic in air battles over Guadalcanal against an excellent American Navy pilot. With both planes locked in tight turns, the narration reads something like: "A gray film covered my eyes. I felt like I was going to pass out, but I gritted my teeth. If the American pilot could take it so could I." As it turns out, the American pilot pulls out first which exposes his plane and he gets shot down. It's my private theory that this was the end of Col. "Indian Joe" Bauer, Medal of Honor winner who went missing over Guadalcanal. Remember you heard it first from me. The episode is part of Sakai's excellent memoir, Samurai. My Dad and brother met Sakai right before his death, and their impression, that comes through in the book, is that he was an extremely nice guy.

    Yeager, as I think he even says in his autobiography, got most of his victories through his incredible eyesight–something on the order of 20/10 which allowed him to see airplanes before anyone else could and shoot them down before they knew what hit them.


  54. Fantastic stories about Yeager – I read his book. He was also an avid hunter and had a most disheartening accident with a gun when he was younger.

    Interesting stories of Russia. I was never there, but some time in Alaska exposed me to some of Russia when Alaska WAS Russia. There are still Russian churches and buildings, and genuine Siberian Russians, (their families were allowed 1 year to either stay or go back across the Bering sea, and many stayed).

    Matt: Whitcomb developed the "Whitcomb area rule", which guides the sculpting of the fuselage to deal with wind rsistance. (and, regrettably, I am not allowed to comment on my employer or my projects)..

    best regards,


  55. Decibels,

    Strike my first suggestion based on your additional information.

    Order the rifle below:


    The mechanicals are the same as the R-7 and the stock is actually better if you’re right handed.
    You’ll have to copy and paste the link.

    Happy shooting


  56. Jane,

    Thanks for the info about the Whitcomb area rule. Understood about security. The shroud of mystery becomes you.

    Herb, yes your tables have a lot of detail and various capabilities. My purpose is to test the different statistical models and their methods of calculation against each other and, most importantly, against a real shooting situation instead of a computer scenario.

    B.B. and all, a drum roll please. How exciting. I haven't felt like this since my last scientific discovery which is that if you're riding a bike over bumpy ground if you wiggle your front wheel rapidly back and forth you will inevitably get a smoother ride. Astounding I know but true, and I even have a theory to back it up. Anyway, to the matter at hand. As promised, I shot thirty 5 shot groups and one 30 shot group with my IZH 61 at five yards offhand with results as follows:

    5/30 = .63 in. (ave.)/1.5 in. = 42%, this is actual group diameter, not CTC

    Data of individual 5 shot groups arranged suggestively in a normal distribution is as follows in units of inches.

    X1 .44
    X6 .50
    X5 .56
    X8 .63
    X6 .69
    X2 .75
    X1 .88
    X1 1.00

    (Note, BG_Farmer, that I’m shooting about 8 MOA. That’s what you can expect from me next month, hopefully a little better. :-))

    Photos of targets are below. A 6 inch ruler is placed with each as a reference for size.




    Impressions: I was surprised at the consistency of the 5 shot groups. I expected them to jump around, but they were clustered fairly close to the mean. I was also surprised at how rapidly the 30 shot group converged. After about shot 8, it was quite stable except for the occasional outlier; perhaps these were the flaring of the bell curve. I really lived the normal distribution.

    Discussion: This is the part as I remember from the detested lab reports of school days where you describe all of the screw-ups in running the experiment. The main problem here is that the target paper was tearing. I suppose this was a combination of the low velocity of the IZH 61, the robustness of the paper, and mostly that the paper was not taped securely enough. This could be construed as a reason to throw out the whole experiment. The Aberdeen Proving Ground probably would. As they told Roy Boehm, founder of the Navy Seals: “Since you are not an approved testing facility, your report on the AR-15 was placed in the circular file” to which the response was “G—d— bus—crats” and a certain amount of office damage. Anyway, my response was to ruthlessly measure all breaks in the paper whether it looked like a puncture or a tear and hope that things evened out. Also, no fliers were called. Everything counted.

    To be continued…

  57. Experiment contd.

    Analysis: I admit that 42% was higher than I expected. My original calculation of 10% was way low. 20% is better but my rationale for the increase is suspect as we shall see. The 64% estimate is in the ballpark but on the high side. Another data set is contained in a paper referenced earlier.


    This one, based on the normal distribution, contains a graph, towards the bottom, of group size vs. number of shots. Unfortunately, it only goes up to 20 shots. However, the ratio of 5/20 is about 60%, so 5/30 will be even less. How much less? Extrapolating the curve and considering the flare at the bottom of the bell curve, 50% seems as good a guess as any. Given that my experiment is more thorough than most shooting situations, any one of these values—42%, 50%, 64%–can probably be expected for the ratio of 5/30 shots in the real world. 50%, as an easy number to remember, is probably a useful rule of thumb.

    Conclusions: I think it is useful as mentioned in the health reform debates that in the statistical panorama developed so far, the areas of agreement far outweigh the areas of disagreement. So, in the style of a conceptual call radius, a review of the areas of agreement is as follows. In shooting at a given distance, there is an associated call radius outside of which you will not shoot except for a failure of equipment or shooting technique. This radius corresponds closely to a 30 shot group. Inside the radius, the distribution of shots follows a probability distribution. At this point, I withdraw my proposal that the statistical model changes with distance. My reason for thinking so was that as the distance shrinks, the 30 shots that define a call radius have to be stuffed into a smaller area. However, the minute of angle geometry (ballistic cone) will do this without any need to alter the statistical model. The model is constant over distance which makes for a simpler and more pleasing universe. As for what the probability distribution is within the call radius, the alternatives that have been advanced are different members of the normal family of curves, the chi distribution, and the log-normal distribution. My position is that I don’t really care. Whatever it is will look more or less like a bell curve with radial symmetry around a central value, rapid initial growth outward until shot number 5-8 followed by slow growth out to shot 30 which is the call radius.

    There has been a question about how to handle fliers. These fall into two categories. The called fliers are the failures in equipment or technique. The uncalled fliers could be either failures of equipment or technique that aren’t perceived or random statistical variation. These are intimately connected and really impossible to disentangle although calculating confidence intervals could help do this. I think this addresses most of the issues that have come up, and answers them as far as I'm concerned.

    The question of what all this has to do with anything is more than fair. My opinion is that BG_Farmer’s field expedient method of using 3 or 5 shot groups will do the job for most shooting situations. Otherwise, by regular shooting of a gun, I expect that one should gain an intuitive knowledge of the physical laws described by statistics. I will end with a description of a fictionalized Ed McGivern shooting it out with bad guys at the end of his life. Ed, who probably did not have much formal education, is described as “instantaneously doing hundreds of deflection calculations based on shooting millions of rounds” as he twists around and, without looking, plugs a guy sneaking up from behind.


  58. HK P30,

    You are the second person to ask for this review, so I will do it. Why do you think this is a well-made gun? Because the price is so high?

    Umarex usually makes very good air pistols. I have already reviewed both the HK USP and the Makarov and both are fine pistols. I'm, sure you can trust that the P30 will be a good one, too. Don't wait for my review.


  59. Matt,

    your thoughts on Yeager pretty much follows mine. Regardless of how he behaves to people who want to meet him (and I'm sure he has gotten hundreds if not thousands of strangers coming up to him at all times requesting autographs or wanting to shake his hand or interrupting his meals)I still consider him one of the last American Heroes of his generation, along with every soldier who participated in the D Day assault.


  60. Matt,


    One weakness in the experiment is that you only shot one 30 shot group. Statistically even a 30 shot group should vary. The theoretical calculations were a std dev of about 25%. Since you shot 30 5-shot groups the average 5-shot size ought to be very good statistically. What the data indicates to me is that your 30 shot group is too big compared to theory. It seems like it ought to be more like 1 inch.

    Out of curiosity, was the aim point within the circle? That might be the cause of the group getting so large.

    After you put the first hole in the target, the next shot can only nibble away at the paper, it can't add paper, so as you shoot more, the hole can only get bigger. How fast doesn't matter. An infinite number of shots is a very very very lot of shots.

    I'll calculate the std dev of your 5 shot groups a little later. I'm curious to know how it compares to the theory.

    I need to look at the Long-Family paper again. I have been befuddled by their conversion to MOA. There should be some correlation between the two papers.


  61. Matt,
    That was a lot of work, but I see you are multitasking:). You do seem to come very close to a normal distribution. Your consistency offhand is pretty impressive as well — I'll have to practice seriously with my smoke pole.

    MOA is a very useful convention for the reason you cited and fortunately easy to use because 1" approximately = 1MOA at 100 yards. I think the conversion is 1MOA = 1.0472" at 100 yards.

  62. Matt,

    OK curiosity got the better of me. I did the calculations. It was simple enough. First since you measured "actual" group size as opposed to c-t-c, I subtracted 0.177 from all of your measurements to get to c-t-c.

    Plugging your data into Excel:
    Mean = 0.45
    std dev = 0.119
    rsd = .119/0.45 = 26.4%

    The theoretical prediction was:
    0.828/3.066 = 27.0%

    Doing a F-test
    (27.0/26.4)^2 = 1.02

    F-Critical(0.05,inf,29)= 1.63

    Since 1.02 < 1.63, there is no statistically significant difference at the 95% confidence level. So, at the 95% CL, your 5-shot group sizes were as consistent as would be expected.

    Looking at the theoretical 95% confidence interval for individual 5-shot groups

    0.45/3.066 = 0.147

    The 95% Confidence interval from table 2 in the reference is:
    1.611 to 4.832

    1.611*0.147 to 4.832*0.147
    0.24 to 0.71

    So the one group that you reported as 1" is an outlier could be discarded. If you do so,

    mean = 0.44
    Std. dev = 0.098
    RSD = 22.2%

    F-Test (27.0/22.2)^2 = 1.48


    Subtract 0.177 from 1.5 yields 1.323

    0.45/1.323 = 34%

    That is a lot lower than expected. Since there were 30 groups of 5-shots, the average of the 5-shot groups should be pretty good. That would seem to indicate that a 30-shot group (c-t-c) should be about 0.45/0.64 = 0.70 inches.

    On the target I saw, there was no aim point. Was the aim point on the other side, or were you shooting at the hole? To get a good result it would seem that you'd need to shoot at an aim point that you weren't chewing away.


  63. Volvo,

    My eyes are tearing up. Please tell me that's not the gun you ordered.

    I know I'm shallow but I love nice metal and woodwork. That is gorgeous. If that were an aftermarket stock it would be at least $500.00 finished. The pictures make it look like exhibition grade. And stainless to set it off??? My gawd.


  64. Kevin,
    As you know my quest for a single Springer has pulled me in many directions. A new HW35L with a nickel finish and a walnut stock was on my short list. (they are not stainless) You cannot get these in the states, so I placed the order with a Canadian dealer, but it needed to come directly from Germany. I grew tired of the waiting game and after speaking with Derek he said not to worry about it (I’ve ordered a few rifles from him over the years, so I cancelled with his blessing.) The fact that the rifle was on the shelf when this guy got it and Derek does not stock that version, leads me to believe my luck for 2009 is holding out.

  65. Volvo,

    Well…you made someone very happy. Wish it was me. Your Karma is intact so you've got that going for you. 😉

    Reminds me of the cliche', "No good deed go unpunished."

    Can't wait for this economic downturn to pass.


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