GTA
All Springer/NP/PCP Air Gun Discussion General => Air Gun Gate => Topic started by: Can-o-cide on May 13, 2015, 10:35:31 PM
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I recently acquired an umarex surge for dirt cheap. I cleaned it and broke it in well. Shooting rws superdomes and meisterkugelns, they will group under a quarter inch at 10 yards. But if I back the target up a mere 5 steps the groups open up to an inch, and basically another inch per 5 additional steps. I assume this means the pellets are going transonic. I have ordered some 10 grain pellets and hope this brings the velocity down. According to my research, I should get just under 900fps. I have two questions:
1) will the 10 grain pellets stress the mainspring too much? I will pay attention to how the gun feels and if the spring is unloading properly.
2) if 10 grain pellets will stress the mainspring too much, can you recommend a 8-9 grain pellet that tends to shoot slower than other pellets in this weight class?
thanks.
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Try a true round-nose pellet like a JSB Exact or Crosman Premier.... The RWS Superdomes are just that, domed, they have a significant corner at the back of the head and can suffer from buffeting effects when driven too fast.... I would try the Exact Express 7.9 gr. and the Exact 8.4 gr. before stepping up to the Exact Heavy 10.3 gr....
Bob
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Remember that the 1200 FPS it's rated for is probably shot with the lightest non lead pellet they can find.
With a light lead pellet you're lucky if it goes past 950FPS.
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I'll try a true round nose then. I did notice that the super domes look more like a wad cutter compared to other domed pellets. But I've mostly shot .22's until now so it all looks small. This is my first 1000fps springer .177 but for $17 on clearance i couldn't pass this gun up!
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Just got back from the range with my surge. I set up a target at 5 yards, and shot a superdome, moved target back 1 foot, shot a superdome, moved target back 1 foot, etc. I cut a near perfect spiral on the target. So the super domes are corkscrewing. I suppose this explains why after 10 yards the superdomes go haywire. I suppose also that the meisterkugelns are corckscrewing as well.
I tried 10.65gr beeman match heavy, which did poorly at any range, although the gun didn't torque as much as usual with these heavier pellets. I then tried the jsb exact 8.44gr and wow what a difference! At 10 yards, the jsb pellets did worse than the corckscrewing superdomes, which I find kind of amazing since at 25 yards the jsb pellets were supremely accurate! The jsbs were still extremely accurate at 10 yards, but just not the one hole accuracy of the superdomes.
at any range past 15 yards, the jsb pellets are more accurate than I am. It doesn't seem fair to tell the group size since that would only be a measure of my ability and not the pellets or the gun. I set up 20 empty 9mm and .45 auto casings at 25 yards, and hit each one in a row. I then did the exact same thing with .22 casings, with only a couple getting knocked down by the air wave from the pellet instead of the pellet itself. I set up 10 shotgun shells and knocked the primer clean out of 4 of them, and dislodged it severely in the other 6. I would aim at tiny pieces of clay targets, small enough that I could barely keep the crosshairs on them, and bust them into pieces time after time at 25 yards.
I just found my plinking rifle.
the surge is a little hold sensitive. I place my supporting hand with the thumb touching the second slot on the forearm from the muzzle. Supporting hand has to be flat and not touching the sides of the gun. The trigger hand has to lightly squeeze the thumb hole stock using the pinky and second finger only. Cheek just barely touching the comb. Held against the shoulder light enough so that I don't feel the recoil in the shoulder, but hard enough that the stock doesn't slip against the shoulder after firing. Even if it's not perfectly held, about the worst I'd do is hit an inch away from where I'm aiming at 25 yards.
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To go transsonic, the pellet first has to go supersonic. If it's going supersonic, you should hear a loud crack (like a 22LR rimfire). If you are hearing that, then either the 8.3 gr Superdome is going supersonic (unlikely -- specs: 1200 fps w/alloy pellets, 1000 fps w/lead pellets, and ALWAYS overrated by manufacturers), or the crack is from dieseling (detonation of petrol-based lubricant in the compression chamber, very bad -- it will ruin the air rifle in short order), or both. Transition from supersonic to subsonic, as with powder burners, occurs well down range, even with supersonic 22LRs at 1200+ FPS, not typically at relatively short distances, though I suppose in theory, it could.
The pellet is probably not going supersonic. If your rifle is dieseling, it needs a thorough cleaning and going over by someone who can remove the spring, piston, and piston seal -- the most likely problem if spring lubricant is finding its way into the compression chamber -- unless you have oiled the air rifle. It doesn't take very much oil in the wrong place to cause this problem.
Inaccuracy is more likely not coming from pellet problems. Checklist: 1) scope mounts tight, solid?, 2) scope holding zero -- magnum springers can beat inexpensive scopes to death in short order, 3) action screws -- loose action screws are a notorious cause of accuracy problems that can easily be overlooked.
Those seriously into shooting magnum springers usually end up with a torque screwdriver, degreasing cleaner solvents, and Blue LocTite (NOT Purple or Red) on hand to keep everything tight on their thumpers.
Regarding pellets: be a pervert and look up under the skirts of your Superdomes. See the hole in the back end of the pellet? That smooth, round cylindrical hole is the female counterpart of the "nose" in the tip of the breech block on most CO2 air rifles and pistols. It helps center the pellet in the breech and keeps pellet seating uniform when the bolt is closed. Superdomes also have "stiff", swaged (see the serrations?) skirts not designed to expand much. While they shoot well in many air rifles, they are ideal for CO2 rifles. Ditto for Crossman Premiers. Magnum springers, on the other hand, will usually shoot best with softer, thin-skirted pellets, like JSB Exacts. These are designed for the skirt to billow and expand under pressure more easily (like Marilyn's), sealing the skirt against the bore's lands and grooves. The downside for soft-skirted pellets is the greater potential for "dinged" or deformed skirts from rough handling. Dinged skirts can cause accuracy problems, too.
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Thanks for your comment, but I realize now the inaccuracy of the super domes is due to the pellet spiraling out of the barrel. My surge shoots jsbs at 920fps, a guy at the range was kind enough to let me shoot a few through a chrony.
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Thanks for your comment, but I realize now the inaccuracy of the super domes is due to the pellet spiraling out of the barrel. My surge shoots jsbs at 920fps, a guy at the range was kind enough to let me shoot a few through a chrony.
Under a strobe light. in the dark, I have seen a fletched arrow fired from a compound bow wobble and spiral.
I have never seen evidence that a bullet actually spirals. The Cardew brothers address this in their book, The Air Rifle from Trigger to Target.
Springers have both a two-phase recoil from the spring uncoiling and the piston "bounce" and also a rotary recoil, from the uncoiling of the spring. both cause peculiar things to happen, but not, I believe, an actual spiraled trajectory. Perhaps I am wrong. . .. I often am.
Check out these references:
http://www.championshooters.com/index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=642&virtuemart_category_id=9 (http://www.championshooters.com/index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=642&virtuemart_category_id=9)
http://www.scribd.com/doc/124074201/CARDEW-The-Air-Gun-From-Trigger-To-Target#scribd (http://www.scribd.com/doc/124074201/CARDEW-The-Air-Gun-From-Trigger-To-Target#scribd)
Brian LItz has an excellent book on external ballistics for powder burners, some of which also apples to pellets, in principle.
http://www.amazon.com/Applied-Ballistics-Long-Range-Shooting-Edition/dp/0615452566 (http://www.amazon.com/Applied-Ballistics-Long-Range-Shooting-Edition/dp/0615452566)
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To go transsonic, the pellet first has to go supersonic.
Sorry - incorrect.... Transonic refers to a range of velocities where the air is seeing the onset of compressibility effects, generally accepted as Mach 0.8-1.2 (900-1350 fps).... The effects can occur lower than that, where there are sharp corners for the airflow to negotiate, however.... Consider this drawing....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/PelletTurbulence_zps2f99ca19.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/PelletTurbulence_zps2f99ca19.jpg.html)
The upper drawing shows a round-nosed (hemispherical) pellet, and the lower one a pellet more like a Superdome (or wadcutter).... When the latter is driven fast enough, the air trying to get around the corner at the back of the head can actually break the local speed of sound (even though the pellet is well under Mach 1), and cause shockwaves, and their associated eddies to form.... You can see that along the leading edge strakes of an F-18 in a high-speed (yet subsonic) high-G pullup, where the shockwaves cause the water vapour to condense and form contrails there.... Here is what happens to the drag in the transonic region....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/G1%20Drag%20Model%20Net_zpsopno7nwx.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/G1%20Drag%20Model%20Net_zpsopno7nwx.jpg.html)
Subsonic (<Mach 0.8 ) - air is acting incompressibly.... Transonic (Mach 0.8-1.2) - air is seeing compressibility effects and the onset of shockwaves.... Supersonic (>Mach 1.2) - a leading edge shock dominates the flow regime, the angle of the shock determined by the Mach number....
Bob
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Thank you rsterne. That's exactly why I titled my thread the way I did. I knew that the shape of the pellet affects the local air speed around the pellet, and I believed that my surge is shooting them fast enough to be a problem. The chrony results with jsbs and your numbers confirms this I think. I always thought that a pellet that went transonic would begin tumbling. I have evidence that they are spiraling. I know it is quite possible for pellets to spiral, I have seen slow motion videos clearly showing spiral trajectories.
I find it amazing though that the super domes spiral in such a consistent way at close range. Kind of a controlled chaos...
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Spiraling is a result of Dynamic Instability, and is most often caused by too fast a spin rate.... Tumbling is caused by insufficient spin rate (Static Instability - too slow a twist).... Since the forward velocity of a pellet slows down faster than the spin rate, pellets can become Dynamically Unstable as they travel downrange....
If the pellet is launched consistently on every shot, and the initial yaw is caused (for example) by the movement of the muzzle, the spiral starts in the same place, and if consistent, the pellet will hit in the same place.... That is one of the weird parts about spiraling, it doesn't necessarily spoil the group size, particularly at close range.... but if can cause a wandering POI....
Bob
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Perhaps my comments extrapolated from ballistics of firearm projectiles are lacking for the aerodynamics of the flight of pellets. Precise definitions of gyroscopic stability, dynamic stability are indeed important. Spin, or angular velocity affects gyroscopic stability. Linear velocity of the bullet decays faster than angular velocity (spin) such that a gyroscopically unstable (under spinning) bullet leaving the muzzle can stabilize "some call it go to sleep" down range as the linear velocity drops off. Conversely a stable projectile at very high initial linear and angular velocities, as it loses linear velocity down range, can "overspin", causing the bullet to yaw -- the axis of the projectile's spin no longer matches the axis of the down range trajectory. Drag increased dramatically and bad thing happen to accuracy.
You illustration reminds me that the laminar flow over the smooth surface of a typical bullet is different from the air flow over a diabolo pellet. I stand corrected on that point. But perhaps I misunderstand the usage of "transonic":
transonic refers to the condition of flight in which a range of velocities of airflow exist surrounding and flowing past an air vehicle or an airfoil that are concurrently below, at, and above the speed of sound in the range of Mach 0.8 to 1.0, i.e. 600–768 mph (965–1236 km/h) at sea level. This condition depends not only on the travel speed of the craft, but also on the temperature of the airflow in the vehicle's local environment. It is formally defined as the range of speeds between the critical Mach number, when some parts of the airflow over an air vehicle or airfoil are supersonic, and a higher speed, typically near Mach 1.2, when the vast majority of the airflow is supersonic. Between these speeds some of the airflow is supersonic, but a significant fraction is not.
(http://i306.photobucket.com/albums/nn270/tcups/P1010850.jpg)
Cardew & Cardew (both engineers) wrote what is still, I believe, by most to be the definitive scholarly work on air rifles, pellets and pellet ballistics.
The Airgun from Trigger to Target. Though out of print, it can still be found used and as a pdf file on line, I believe, including entire chapters on Pellets and Pellet Testing (Chapter 18, p. 167-188) and The Pellet's Flight (Chapter 19, p.189-218). They extensively test, photograph and reproduce with models the shock waves occurring as the result of "forebody drag". Similar to your graphic, but obviously not the same, the shock waves formed by forebody drag have been amplified and photographed on a water table. They also did extensive testing on pellet trajectory including a section on "Spiraling" (p. 186-189). They tested critically to see if spiraling trajectories occurred as they wrote: "However, we put the "spiral phenomenon the test because if it were really true there would be little future in serious airgunning." The were unable to demonstrate any true spiral trajectories. You can read about the multiple thin tissue screens set pat regular intervals and grid coordinated that were precisely aligned between the air rifle, the pellets and variables tested.
(http://i306.photobucket.com/albums/nn270/tcups/P1010860.jpg)
(http://i306.photobucket.com/albums/nn270/tcups/P1010852.jpg)
(http://i306.photobucket.com/albums/nn270/tcups/P1010852.jpg)
(http://i306.photobucket.com/albums/nn270/tcups/P1010853.jpg)
Brian Litz, an aerodynamics engineer (rocket scientist) and champion long distance shooter also writes extensively in his text about ballistic coefficients (G1, G7), projectile trajectories, drag, gyroscopic stabilization, dynamic stability, yaw and bullets transitioning from supersonic to subsonic velocities. Refer specifically to Chapter 10, p 135-147: Bullet Stability, and in particular, to the section on Dynamic stability for spin stabilized projectiles, pages 144-147. Dynamic instability at transitions around Mach 1 cause the dramatic change in the drag coefficients, and the G1 and G7 Ballistic Coefficient curves as in this graph
(http://i306.photobucket.com/albums/nn270/tcups/P1010857.jpg)
Noticeably different from this in the range of velocities typical for air rifles and center fire rifles:
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/G1%20Drag%20Model%20Net_zpsopno7nwx.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/G1%20Drag%20Model%20Net_zpsopno7nwx.jpg.html)
Notice, though where the slope of the drag curve you posted is greatest? At about Mach 1, but most or all of a typical pellets linear velocity is subsonic, and described by the flat part of the curve.
Forebody drag, if I understand the term is, as in your illustration and description, a "transonic" condition due only to differential, non-laminar flow over the sharp edge of the pellet traveling at subsonic velocities, so it would seem to me that differential air flow, and therefore, the dynamic instability it causes, might persist over a much longer portion of the flight of the pellet, not just at a single transition velocity of the pellet itself. The the broad, sloped drag curve shown in your illustration is indeed much different from the sharp slope of the G7 and G1 BC curves at Mach 1, showing an abrupt degradation of the BC as a rifle projectile goes transsonic also illustrates the difference.
So, while I acknowledge that it is possible I am "incorrect", I again offer my references to anyone with a serious interest in the subject I don't believe pellets spiral. I believe that the leading shockwave cause by forebody drag turbulence of a diabolo or pointed pellet is more of a continuous degradation of the pellets BC, or tendency to maintain its initial velocity, over a broad range of velocity and not technically synonymous with the abrupt phenomenon of dynamic instability at transonic speeds near Mach 1 for a rifle projectile, at least as known to long distance shooters.
Also, can you please provide your source references? Always interested in learning something new, especially if I am wrong or don't understand something as well as I though. Thanks.
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Well when you can see them spiral it tends to make a believer of you...
In just about all my pumpers the Daisy points .177 and .22(poor cg pointed with a raised ring around outside edge of the head) tend to suddenly do a 6" crescent at about 15-20 yards...
There are Ytube vids that you can watch that show a pellet spiraling...
I knocked off some of the nose of the Daisy pointed and got rid of the ring and they stopped spiraling by the way... still could only get 1"-2" groups at 20 yards...
I tried all the way down to about 500 fps and stock they where still spiraling...
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Here is a recent thread on pellet spiraling, with references.... http://www.gatewaytoairguns.org/GTA/index.php?topic=86818.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=86818.0)
In particular, you may find the following interesting.... They show animations of nutation and precession, which are the cause of spiraling....
http://www.arld1.com/nutation.html (http://www.arld1.com/nutation.html)
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/yawmot_zpselkjyair.gif) (http://s378.photobucket.com/user/rsterne/media/Ballistics/yawmot_zpselkjyair.gif.html)
Here is one of the best explanations I have seen on the subject of bullet stability....
http://www.nennstiel-ruprecht.de/bullfly/index.htm#Contents (http://www.nennstiel-ruprecht.de/bullfly/index.htm#Contents)
In particular, this quote from the summary....
Summary
Bullets fired from handguns follow general rules of physics and behave like gyroscopes. The angular motion of these bullets can be understood as a superposition of two oscillations, most easily be demonstrated by a two arms model (the animation above).
Practically all handgun (short) bullets are statically stable, many pistol and revolver bullets (and pellets) even have excessive static stability.
However, dynamic stability is not automatically guaranteed. Some bullets are dynamically unstable at the moment they leave the muzzle, others may loose dynamic stability during flight after being decelerated (eg. increased pellet spiraling with distance).
At the moment no reliable method exists, except experimentation, to foresee dynamic bullet instability, especially at long ranges. Some highly sophisticated computerized procedures (numerical solutions to the Navier-Stokes equations) to attack these problems are just being developed by ballistic researchers.
While the Cardew's may not have been able to measure spiraling, and I am familiar with their work (I have both their books), I can assure you that it is a proven phenomenon.... Perhaps this is because their tests were conducted at only 30 yards.... All you need to do is watch a few videos of pellets at high velocities to see it for yourself.... However, not all pellets spiral, and some spiral only when driven above a certain speed, and past a set range, as the pellets become "overspun" as they slow in their forward velocity.... This is a classic case of Dynamic Instability.... The last link above bears careful reading to understand this phenomenon....
The G1 Model I showed in the graph looks only at the part of the flight regime of interest to airguns, and that is the primary reason that the increase in drag in the transonic region (Mach 0.8-1.2) appears to have a much shallower slope than the diagram you gave for the Berger bullet (simple scaling of the X-axis).... Here is the complete drag curve for the G1 Model, along with the G7 model, and a sphere (GS).... These plots of Drag Coefficients are available from multiple sources, and are very well established.... As you are I am sure aware, the "G" models are the standards by which all projectiles are measured.... Chosing the right one for the projectile in question is, of course paramount.... You will note that the Berger bullet is a near perfect match for the G7 profile, not surprising as the G7 Model is a spitzer boattail design....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Drag%20Coefficients_zpsmvh8fg13.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Drag%20Coefficients_zpsmvh8fg13.jpg.html)
Our Diabolo pellets do not match any of the existing G profiles very well.... For many years, pellets were assessed against a constant Cd of 0.20, which was ridiculous, as it didn't take into account the huge increase in drag at the "Drag Discontinuity Mach Number", which is around 0.8 for most projectiles.... Recently, it has become common practice to use the long standing (oldest) G1 profile, and ChairGun, the most commonly used Airgun Ballistics Program now uses a profile they call "GA", but it still is a very poor match for our pellets.... They have a MUCH larger increase in drag in the Transonic region , more like a five-fold increase instead of a three-fold increase.... I am attempting to gather data to develop a new Drag Profile, and you can read about the efforts, and results so far in the following thread....
http://www.gatewaytoairguns.org/GTA/index.php?topic=84534.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=84534.0)
Here are some graphs of some of the data collected so far, plotted with the G1 profile shown, and showing how much more the drag increases for our pellets than the G1 model in the Transonic region....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/New%20Drag%20Baseline1_zpslpxixjnu.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/New%20Drag%20Baseline1_zpslpxixjnu.jpg.html)
The dotted black line is a preliminary suggestion for a new Drag Profile to represent the best pellets currently available.... but note it is very much a work in progress....
Bob
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Here is a great video of pellets spiralling from Ted's Holdover.
http://youtu.be/8z8aFP2TVyA (http://youtu.be/8z8aFP2TVyA)
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Bob
Frankly, G1 is too low from 750 on or is that GA? If your curves are accurate you would be better off just tracking a straight line from 750 into the trans-sonic region and having done with it.
Your graph says this is not that complicated. You want a model that fits a lot of different pellets. I'm going with a line because it is simple and fits the data you present.
I mean we might want to pretend this is rocket science but it really isn't. Here is your model. There is an argument to be made about complicating the model and how well any model fits to multiple candidate projectiles. Unless you have done thirty or forty pellets your model will favor the projectiles you selected.
In my mind, we use the models we have available AND THEN if we want more precision we shoot over our own chronographs with our own guns and our own pellets.
It is cool what you are trying to accomplish. Certainly any measurements you make will add to the knowledge base.
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Trying to model a non-linear function with a straight line, to me, doesn't make sense.... Sure, you can model a SECTION of the velocities that way.... but what do you do if the pellet starts out at 900 fps and slows to 600 over 100 yards (which is typical).... Which straight line do you use then?.... Have a look at the G7 Model, how would you model that as a single straight line?.... You can't....
None of the existing "G" models are straight lines, for the simple reason there is a discontinuity in the drag in the transonic portion of flight.... Below Mach 0.8 the drag is relatively constant, above Mach 1.2 it is again relatively constant, but between the two the drag increases by a factor of 3 to 5.... Could we use three straight lines?.... sure.... but it wouldn't represent the change in drag as closely as an "S" shaped curve....
I do agree that since every pellet is different, we can't have one model that will work for everything.... However, the closer the model is to reality, the less the BC will change over the entire range of velocities when you use that model.... Right now, if you calculate the BC of pellets using the G1 (or GA) model you will get vastly different results subsonic and supersonic.... Using the old linear drag model (CD=0.20) the values were totally ridiculous.... The BC on a JSB Exact would start out at 0.04 and drop below 0.01 at supersonic speeds.... Therefore, you couldn't use one BC over the entire range and get anything that even remotely resembled how the velocity decayed with distance.... If we can come up with a model that is closer to reality, then using that model will more accurately predict that velocity decay.... That is my goal....
Bob
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tosses this out there for review...
smooth bore?...no precession,"diabolo" shuttlecock profile projectile, center of drag behind center of mass...
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My thesis advisor once told me "for every problem you can't solve, there a millions of simple problems that you still can't solve". I could pursue the mathematics of spiral trajectories, but *(&^ I can't even build a useful model to determine optimal barrel length in an airgun. For me, I'm quite content shooting jsbs and saving the super domes. There. Problem solved.
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Trying to model a non-linear function with a straight line, to me, doesn't make sense.... Sure, you can model a SECTION of the velocities that way.... but what do you do if the pellet starts out at 900 fps and slows to 600 over 100 yards (which is typical).... Which straight line do you use then?.... Have a look at the G7 Model, how would you model that as a single straight line?.... You can't....\
There is an argument for that. It is as relevant as shooting one hundred yards at pigeons.
None of the existing "G" models are straight lines, for the simple reason there is a discontinuity in the drag in the transonic portion of flight.... Below Mach 0.8 the drag is relatively constant, above Mach 1.2 it is again relatively constant, but between the two the drag increases by a factor of 3 to 5.... Could we use three straight lines?.... sure.... but it wouldn't represent the change in drag as closely as an "S" shaped curve....
True in as much as we have not quantified what the details mean. I contend that a straight line will model many, many different pellets between 800 and 1000 FPS so accurately that your "S" curve is not really significant.
I do agree that since every pellet is different, we can't have one model that will work for everything.... However, the closer the model is to reality, the less the BC will change over the entire range of velocities when you use that model.... Right now, if you calculate the BC of pellets using the G1 (or GA) model you will get vastly different results subsonic and supersonic.... Using the old linear drag model (CD=0.20) the values were totally ridiculous.... The BC on a JSB Exact would start out at 0.04 and drop below 0.01 at supersonic speeds.... Therefore, you couldn't use one BC over the entire range and get anything that even remotely resembled how the velocity decayed with distance.... If we can come up with a model that is closer to reality, then using that model will more accurately predict that velocity decay.... That is my goal....
Bob
Really, I think a simple model that gets the job done within definable limits would be more useful to you and others. I still contend that you need to test thirty pellets before your curve becomes relevant. At that point, sure...
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Between 800 and 1250 fps the straight line model is just fine.... Below 800 fps, you can use the G1 Model.... I agree 100%.... I ask again, what do you suggest for a pellet starting at 900 and ending at 700 fps?.... An example would be a JSB Exact at 60 yards....
You are also 100% correct that if you want the information for YOUR gun, and YOUR pellet at YOUR velocity, then get out and do the testing, at all possible ranges you might shoot.... That is absolutely the best way, and in fact the only way, to get 100% accurate results.... Since every pellet is different, we may as well just continue to use the Drag Models that were developed over a century ago for artillery shells as try and improve on that model.... I mean after all, our pellets don't look too much different than this, right?....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/g1_zps09zm9zd2.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/g1_zps09zm9zd2.jpg.html)
If you have three different models for subsonic, transonic, and supersonic, then you have three different BC's.... All I'm trying to do is come up with a model that is an improvement over what we have now, and still covers all three velocity ranges.... Maybe I'm completely wasting my time.... but then on the other hand, it's my time to waste.... Perhaps the real waste of time is trying to share?....
Bob
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If everyone thought the same, there would be no new ideas. If the interest is there, do it. I desperately want to figure out the optimal barrel length problem.
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"Optimum" barrel length is longer than would ever be practical to pack around for anything except low powered pneumatics or springers.... For most PCPs, the longer the better, certainly if you're going for power.... and the math to model that isn't that difficult....
Bob
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I was doing the equations for springers. Here is what I have:
compression chamber has length L, radius R. Barrel has radius r. Coefficient of friction in compression chamber/piston is C, and barrel/pellet is c. Mainspring constant is K, and has uncompressed length k*L where k>1. X is the location of the piston head in the compression chamber, x is the distance traveled by pellet in barrel. M is mass of piston, m is mass of pellet. Then we have the system of differential equations
MX"=-\pi*R^2*P-CX'-K(X-kL)
mx"=\pi*r^2*P-cx'
where
P=P_0*L/(L-X+x*[r/R]^2)
(P_0 is the ambient air pressure)
with initial conditions X(0)=L-\epsilon,X'(0)=0,x(0)=0,x'(0)=0
with the basic assumption being that the pellet begins moving at time 0 at the moment the piston head hits and stops at length L-\epsilon where \epsilon is small. To answer the question, one needs to find the value of t_0 such that x'(t_0) is maximum, and then the optimum barrel length is x(t_0).
I wrote some matlab code to numerically solve this system of equations. Playing with the numbers is interesting. I started out with some measured numbers from my broken hatsan, what numbers I couldn't measure I played around with. With these values, all of the plots had x' rising sharply to a peak, and then slowly decaying. Also, x started out flat and then became approximately linear. My equations predict the optimal barrel length to be within one inch of its actual length, btw! Playing with the unmeasured numbers doesn't affect the graph much. I think most manufacturers use a barrel that is slightly long, since it's the "safe side" of the maximum.
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Starting to read this thread and am desperately trying to absorb all of this fantastic information.
I'll probably need to read it 2 or 3 times ;D,
but with that said,
I think it would be a good idea to have a close look at the crown to see if possibly some of the inconsistencies in the POI could be attributed to that ? ?
and also start with the basics...
Check the breech seal for any leakage (tissue test)
Check the stock mounting screws for tightness.
Polish the contact surfaces in the trigger group
Consider doing a soft bedding with closed cell neoprene
Check the pivot screws for proper tightness, and shim if necessary
Check the scope mounts for tightness.(If using a scope), verify the scope is not the problem, (try a different scope)
Practice different holds to determine if this can also be contributing to the problem
Are you shooting from a rest ? Bags?
Most springers don't do well from a rest, but many here have found the "paint roller rests" to provide good results.
Try moving the rifle to different points for CG while rested
Eliminate the "Mechanical" possibilities first, so you are not "Chasing ghosts" for your POI.
High powered springers are the most difficult to master, and can be very frustrating.
then after all of that, it's Practice, Practice, Practice.
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I believe that the fantastically good results im getting with the jsbs rules out any and all issues with my shooting technique. It is purely superdomes and my particular surge.
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Math has nothing to do with springer barrel length, in the sense of effecting power....once the air flow through the transfer port maxes out there no more increase in projectile speed....approximately 9" is enough
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I wouldn't have a clue where to start on barrel length for a springer, other than the bigger the chamber and the smaller the caliber the longer it needs to be.... I'm would think the basic governing factor would be the relationship between chamber volume and barrel volume.... The 9" rule of thumb for older springers just has to go out the window for the new magnums, assuming that velocity is your goal.... It is also possible that a different hold technique may be required for different pellets as the chamber fit, and pressure to start them moving, could act differently....
Bob
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rsterne:
Thank you for the references. Obviously I am not up to date on my reading. It has been some years since I was regularly shooting and studying air rifles and their projectiles carefully. This both because empirically, one finds a pellet that shoots well and sticks with it, and because only after switched to 223 and 308 centerfire target shooting with hand loads over the last 6-7 years, did I have to learn more about it. Hence, my reference to Brian Litz, G7, etc.
My brother, Jerry, has developed a new pellet gage that he has asked me to help test. That, and the recent sad events of Gene Curtis' passing away have brought the GTA and air gunning back into focus for me.
It is always interesting to learn and even more interesting when you have to un-learn something you only thought you knew.
I did notice the difference in the graph scales -- but only after I posted. So, is it correct to say that while the non-laminar air flow occurs at all velocities, it accentuates the transonic dynamic instability both at around Mach 1, and over a broader, lower velocity range of the drag curve because the non-laminar flow prolongs the transonic dynamic instability into the subsonic projectile velocity range for pellets, especially with angular surfaces, and much less so for smoothed diabolo surfaces?
Is the "shuttle cock" morphology of the diabolo contour acting somewhat as might a finned projectile and accentuating the tendency to spiral more so than a standard bullet shape? I think probably not, since, in effect, it's only a single "fin" that of itself, imparts non angular force on the pellet. I see a few pellets with straight swage marks on the skirt -- I wonder if anyone has ever tried swaging superficial angled fins onto the skirt?
Is the "shuttle cock" shape of a diabolo pellet primarily to help stabilize the projectile (as the Cardew brothers seem to suggest), or more so to provide a better seal in the bore for the pellet? I am thinking it must be the primarily the latter, since similar bulletn configurations are not used with powder-driven projectiles, presumably because powder driven projectiles can have a much tighter fit in the bore and a much higher operating pressure driving the bullets.
Is there any printed reference to the different twist rates used by the various manufacturer's air rifles? I don't know that I have ever seen much reference to air rifle twist rates, but it's probably because I never went looking for them before I switched to reloading and shooting centerfire seriously.
Thanks again.
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While there is turbulent flow over all diabolo pellets behind the head, it is the separated flow, localized shockwaves, and eddies that can cause yaw forces to be greater in a pellet with a non-hemispheric head.... at least that is why I think that pellets with a hemispheric nose have better accuracy at long ranges.... Wadcutters are a classic example of the opposite effect, their accuracy tends to degrade with range, and their BC deteriorates rapidly as you push them faster.... ie their Drag Discontinuity Mach Number (the velocity where the drag increases drastically) is lower....
Dynamic Stability is almost impossible to model or calculate, so I can't really answer the question whether the diabolo design is worse or not.... However, they can be remarkably stable in even a smoothbore (as noted by Cardew), and that may be the reason that the FX Smooth Twist barrels work so well, even though they produce a spin rate as low as 1 turn in 13 FEET... My personal opinion is that most of the barrels we use have too high a twist rate for diabolo pellets, causing Dynamic Instability and spiraling as we push the velocity....
The skirt certainly has two functions, drag stability and bore sealing at the relatively low pressure we see compared to a PB.... I am not aware of a good reference on the twist rate of airgun barrels, although certainly there is information available on individual ones....
Bob
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My equations do explain some situations where people mod their airguns and get results opposite or not as good as expected. While the equations are too difficult to answer the optimal barrel length problem because of all of the parameters, playing with the numbers and seeing how it affects the end result often leads to new insights that can be explained without using math, which is the true benefit of using math.
so I think the existence of spiral trajectories is well established. I think the mechanics of a spiraling pellet is well described using the two arm model. I think my experience rules out, in my particular case, the shooter and the crown of the barrel as the cause of starting a spiral trajectory. The remaining question is what causes a pellet, in my case, to spiral. And I think that the only logical answer is the profile of the superdome, driven at exactly the speed my surge shoots it, causes instability. The drag is barely sufficient at close range to keep the pellet from going haywire, but is insufficient to fully stabilize it. If the pellet gets turned too sideways from the instability, the drag begins correcting it, but then the momentum of the pellet causes it to overcorrect, and the pellet is essentially bouncing of the walls of an imaginary tube. At longer range, the drag loses all control of the spiraling trajectory, the pellet gets sideways and the drag cannot straighten it out, and the pellet begins tumbling (I shot a few more today at 30 yards and saw some keyholing). Furthermore, I believe that a fast twist rate is a double edged sword. On one hand it helps by establishing a stronger angular momentum that fights anything trying to turn the pellet off its axis of spin, but on the other hand, if something is strong enough to pull the pellet off its axis of spin, then the fast spin becomes detrimental by causing the pellet to bounce off the imaginary tube too frequently which ultimately, when the drag is reduced, causes tumbling. So, if my surge had a lower twist rate, I imagine the pellet would not "bounce around in the imaginary tube" as frequently, and it would give the drag a better chance to stabilize the pellet.
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1 turn in 13 feet?.....wow that's twice a round ball muzzle loader's 1 in 66"....now I want some smooth bore .218" barrel blanks!
I have noticed uneven rifling marks on occasion, didn't mentally catalog the details..just hmm those marks are pretty light on that side...
after some thought of what I was shooting at the time, these could only have come from a Benjamin Titan GPNP in .22 that had very inconsistent accuracy some times 5 shots at 20 yards would be under an inch and the next group would be 3"... much work was done both the gun and on me trying for better groups....I have since spent several hours hand recrowning it after finding a step in the rifling just before the muzzle...the rifle become much more accurate after the hand work, sub inch groups at 20 yards if I do my part, but I have not specifically looked at the rifling impressions since....
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I'll capture a few superdomes and see what the rifling marks look like. The barrel on my surge is flawless as far as I can tell, and believe me I've looked at it long and hard!
after capturing some pellets, it appears the head size is a little too small on the super domes. So now there are two theories. Its either too small a head size or the pellets profile (or both) that causes the spiraling at this particular speed.
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as I understand it (please no laughing) the pellet head is supposed to ride the lands while the skirt is supposed to fill the grooves and it's the balance between the two that governs how well a given pellet will shoot from a given barrel...
the "step" that I found in my barrel was not visibly apparent..but when I finally pushed a pellet down the barrel there was a pop-pop feeling the push rod when the pellet exited the barrel....after about 20 minutes with a jeweler's loupe, I thought I could see a faint circumferential line over about 1/3 of the diameter between .010 and .015" down from the crown edge of the muzzle...more time looking at it and it was becoming more distinct....then abit of insight and I sure it was there because I knew what it was..it was the shadow of the step trying to stand out on the polished surface with light reflecting from all over the rest of the polished inside of the barrel....
now as soon as some one says anything that could be interpreted as erratic accuracy, I recommend pushing pellets down the barrel from experience
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If you have three different models for subsonic, transonic, and supersonic, then you have three different BC's.... All I'm trying to do is come up with a model that is an improvement over what we have now, and still covers all three velocity ranges.... Maybe I'm completely wasting my time.... but then on the other hand, it's my time to waste.... Perhaps the real waste of time is trying to share?....
Bob
Sharing is good. There is no doubt about that and I always learn from your efforts. I think you are not misguided. Statistically if you are going to develop a drag model, you will need to test a large number of different pellets, or maybe develop one for flat nosed, one for round nosed, and one for pointed pellets. Even then you are going to have to test a large variation of pellets for your new models to be statistically accurate.
By all means keep the effort going and if you want, I'll ship pellets that I have laying around.
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Superdomes have a smaller head and a wider skirt than the jsbs. Pushed some pellets and didn't feel anything abnormal.
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My personal opinion is that most of the barrels we use have too high a twist rate for diabolo pellets, causing Dynamic Instability and spiraling as we push the velocity....
The skirt certainly has two functions, drag stability and bore sealing at the relatively low pressure we see compared to a PB.... I am not aware of a good reference on the twist rate of airgun barrels, although certainly there is information available on individual ones....
Bob
Excellent point, Bob.
BP rifles designed to shoot round balls usually have twist rates around 1 in 66" Muzzle velocities on these rifles is usually in the 1300 to 1600 fps range. BP rifles designed to shoot bullets OR balls usually have twist rates around 1 in 48". These very early bullet guns shot projectiles in the 900 to 1200 fps range. BP rifles designed to shoot early cartridges usually had twist rates around 1 in 24" and shot in the 1600 to 2000 fps range.
I really think you make an excellent point here. One of the reasons that rifles which were intended to shoot patched projectiles have slower twist rates was so that the patch did not "skip" along the rifling or be literally "stripped" as the projectile was accelerated out the bore.
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Mostly the incredibly long twist rates in BP guns are because of the large caliber.... What most people don't realize is that for a given shape (proportion, length to caliber,) of projectile, the required twist rate required is measured in CALIBERS.... When converted to inches, that means that larger calibers appear to have a slower twist, while relative to the diameter it's the same....
A .44 cal should have twice as long a twist, in inches, as a .22 cal, for the same length/diameter ratio bullet.... Then you have the fact that as the caliber increases, for a given Sectional Density, the bullets get shorter in proportion, as for a constant shape, SD is proportional to caliber.... Black Powder guns have a relatively low pressure (compared to smokeless), so tend to use bullets with a lower SD, with roundball being common.... That is what results in the extremely slow twist rates for large caliber BP guns.... We have the same thing happening in airguns, but intensified by the even lower pressures.... There is an effective limit on the SD that we can drive with an airgun (with decent velocity), which means that particularly in the larger calibers we need a much slower twist rate.... Unfortunately, for the most part, the airgun manufacturers have been slow to realize that.... FX has figured it out with their Smooth Twist barrels.... So did Sean Pero and I when we came up with our .30 cal barrel with only a 26" twist, which recently won the Extreme Bench Rest match.... The same thing applies to our .357 barrel, which shoots bullets up to 158 gr. perfectly with only a 26" twist....
Bob
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I had heard that Superdomes had a deep, cylindrical recess in order to "fit" the longer nose on the bolt of typical CO2 guns so that the bolt centers the pellet and seats them to a consistent depth. I also notice that the shallow, broader recess on JSB's is a good fit for the bolt probe on my BSA.
(http://i306.photobucket.com/albums/nn270/tcups/P1010827.jpg)
(http://i306.photobucket.com/albums/nn270/tcups/P1010831_1.jpg)
(http://i306.photobucket.com/albums/nn270/tcups/P1010832_1.jpg)
It occurs to me that the angular momentum of a solid disc is different from the angular momentum of a ring, so it would seem to follow that if the pellet exits the barrel on a straight axis, at a uniform rotational velocity, the angular momentum, and rotational kinetic energy in the head vs the skirt of a pellet like the Superdome will be different. Since the pellet might be thought of as a heavier disc wheel and a lighter rim wheel on the opposite ends of the same axel, and if conservation of energy and momentum holds . . .
I can't quite get my brain around that, but, something in me thinks that the skirt of the pellet might just have to begin swinging in a wider circumference arc than the head of the pellet, about the center of gravity of the pellet, if angular momentum and kinetic energy are conserved and both decay uniformly.
Or perhaps I just don't remember enough physics and mechanics from my younger years to know the the answer to that one is a simple "No!!"
If I glued a hollow, truncated lead cone on a bowling ball and then spun them up on a central axis, doesn't the cone start to precess outward until the ball is swinging the cone (and vice versa), about the center of gravity?
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I must admit to not having a full understanding of Precession and Nutation of a Gyroscope.... however, my understanding is that if the object is symmetrical about the axis of rotation, and if the CG is ON that axis of rotation, and if further that no torque is being applied to the system, then neither will occur, and the Gyroscope will neither Precess or Nutate.... The classic top (Gyroscope) starting to wobble (Precess) is caused by the fact that the bottom end of the top is sitting on a surface, and the earth's gravity is pulling on the CG, the two opposing forces causing a torque, which in turn causes a reaction at 90* to that torque, which results in Precession.... which we see as the top of the Gyroscope describing a circle (the top wobbling).... The further the axis is leaned over, the greater the torque, and the faster the Precession develops.... If you tap the Gyroscope, then it will exhibit a secondary wobbling, orbiting around the (already Precessing) axis, which will generally damp out over time.... That second order wobble is Nutation.... The reason it damps out is that the torque is not applied continually, and friction reduces it over time.... If, on the other hand, the CG is not on the same axis as the axis of symmetry, then Nutation will continue, which is what happens in an imperfect bullet/pellet (or an unbalanced Gyroscope).... For a bullet, you can think of Nutation being caused by imbalance.... and the initial Precession being caused by the initial disturbanceas the bullet leaves the bore and is subjected to a torque, causing a yaw relative to the line of flight....
An object such as you describe (a cone glued to the back of a sphere), and spun up along it's axis of symmetry, and then dropped (or launched) in a vacuum would have no such torque applied by gravity alone as the gravity will act through the CG.... If the object is completely symettrical, it would not develop Precession or Nutation.... I would suspect that the same thing would apply if dropped in air from a great height with the axis of rotation pointed at the center of the Earth.... as the drag of the air would also be symmetrical.... However, if that object was launched substantially parallel to the ground (ie at 90* to the force of gravity), then as it accelerated downwards over time (and the vertical airspeed increased), the drag of the air would NOT be symmetrical about the CG, and eventually a torque would be applied, and the object would start to precess (wobble) about it's axis of rotation.... However, if the lateral center of pressure aligned with the CG, then again, that would not occur....
That is as I understand it, however, I could easily be mistaken....
Bob
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. There is an effective limit on the SD that we can drive with an airgun (with decent velocity), which means that particularly in the larger calibers we need a much slower twist rate.... Unfortunately, for the most part, the airgun manufacturers have been slow to realize that.... FX has figured it out with their Smooth Twist barrels.... So did Sean Pero and I when we came up with our .30 cal barrel with only a 26" twist, which recently won the Extreme Bench Rest match.... The same thing applies to our .357 barrel, which shoots bullets up to 158 gr. perfectly with only a 26" twist....
Bob
Thanks for your efforts in this area. We can only hope they learn from your successes.
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RE: twist rates
did some searching and find references saying "most" are 1/16" twist.
Tom Gaylord did comparison testing for accuracy, PCP's at various power settings, ranges 10 to 50 yards for barrels of 1/10", 1/12", 1/16" and 1/22" twist. Results discussed in the 2012 blog here:
https://www.pyramydair.com/blog/2012/11/how-does-rifling-twist-rate-affect-velocity-and-or-accuracy-part-1/ (https://www.pyramydair.com/blog/2012/11/how-does-rifling-twist-rate-affect-velocity-and-or-accuracy-part-1/)
All performed well at 10 meters. Biggest differences in accuracy at 50 meters (no surprise). Haven't converted his posted group sizes to MOA at the various ranges, which would be a more interesting relative comparison than just group size, I should think.
Measured the twist of my HW-30 .177 tonight - 1/16"
RE: Gyroscopic stabilization and precession:
Posted the physics question regarding the potential differences in angular momentum, head vs. skirt, affecting precession in the Physics Forum, here:
https://www.physicsforums.com/threads/precession-of-an-air-rifle-pellet-in-flight.815987/ (https://www.physicsforums.com/threads/precession-of-an-air-rifle-pellet-in-flight.815987/)
As yet, no answers.
RE: Optimum barrel length:
Though it seems I can no longer absolutely trust the Cardew brothers, they did perform an ingenious test by drilling a barrel with multiple side holes, tightly plugged with an insulated fitting that let very small wire contacts be moved inward, slightly. into, or pulled back out of the bore, such that by inserting the wires at various lengths up the barrel, the barrel-to-pellet-to-wire contact closed an electrical circuit, allowing the time of travel and instantaneous velocity at each incremental distance up the barrel to be measured.
There results say for a .22 springer, with a limited, fixed volume of air driving the pellet, max velocity is attained at ~ 6 inches down the barrel, and that critical air flow through the port into the expanding volume behind a pellet moving down a barrel no longer accelerates the bullet. For pneumatics, as with powder burners, with much larger volumes of gas propellent available, longer barrels = higher velocity. I suspect that modern magnum springers and perhaps gas ram guns increase the potential air volume per shot and lengthen the effective barrel length.
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There is no difference in angular momentum between the head and skirt of a pellet, unless the pellet had a swivel at its waist! There is one and only one angular momentum vector of a pellet. Sure, a lead atom in the skirt contributes more to the angular momentum than an atom in the center of the head (after being shot, usually) but that doesn't change the fact that there is only one commonly accepted meaning of "angular momentum of a rigid body".
It appears that the Cardew brothers are the only ones anyone references about pellet ballistics. Even Tom gaylord mentions them exclusively. I'm fixing my broken hatsan and am going to make a carbine out of it. Part of the process will be cutting the barrel down. That's why I'm interested in barrel length. I'll do my own experiment.
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I'm fixing my broken hatsan and am going to make a carbine out of it. Part of the process will be cutting the barrel down. That's why I'm interested in barrel length. I'll do my own experiment.
You will do fine. Just take it in sections.
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There is no difference in angular momentum between the head and skirt of a pellet, unless the pellet had a swivel at its waist! There is one and only one angular momentum vector of a pellet. Sure, a lead atom in the skirt contributes more to the angular momentum than an atom in the center of the head (after being shot, usually) but that doesn't change the fact that there is only one commonly accepted meaning of "angular momentum of a rigid body".
Agreed. Only one angular momentum for a rigid body. But if the mass is not evenly distributed along the axis of a rotating rigid body (i.e., the rigid body is not a sphere) and the mass is rotating, and if the distribution of the mass on one end of the axis is spherical and on the other end is cylindrical . . .
https://www.youtube.com/watch?v=CHQOctEvtTY (https://www.youtube.com/watch?v=CHQOctEvtTY)
Then, if an axel had a disk wheel on one end and a rimmed wheel on the other, or say a spherical wheel on one end and cylindrical wheel on the other, and I put it in a vacuum with no external forces acting on it (i.e.,no wind resistance gravity, etc) and spin it, it spins on its axis and stays centered. But if I apply a force to one end or the other, is the resulting perturbation the same?
Think of it this way -- you and a friend are standing on the right and left side of a road. A road - sized barbell is rolling toward you and will hit you both at the same time. On the left end of the barbell, the wheel is a solid lead ball, diameter 3 ft. On the right end of the barbell is a spoked cylindrical rimmed wheel, diameter 3 ft. Hypothetically,both the sphere and the cylinder, as you face them, have roughly the same presenting, visible surface area. Irrespective of the center of gravity of the rolling (cylinder)--------(sphere) about to smack both of you -- the COG won't be the centerline of the road, but far closer to the more massive sphere, of course -- which side of the road would you prefer to be standing on when this thing hits both of you? And if you and your buddy, say, have equal mass, the impact is not only going to perturb both of you, but also perturb the rolling (cylinder)----(sphere), then which end of the (cylinder)-----(sphere) has the greater momentum and is less affected?
(http://i306.photobucket.com/albums/nn270/tcups/Screen%20Shot%202015-05-27%20at%2012.17.02%20PM.png)
And now, imagine the rolling (cylinder) ---- (sphere) is a JSB diabolo pellet proceeding down range at -- pick a velocity -- 800 fps in a 90-degree crosswind from the left at 10 mph. Are the force of the wind resistance on the leading face of the sphere and the drag resistance on the tailing edge of the pellet equal? I think not. Is the force of the cross wind on the side of the pellet designed, roughly we will say, to have the same surface area presenting to the crosswind? Is the crosswind force an equal vector force (lb/inch*inch) applied to the presenting surface areas of the head and skirt (roughly equal), and therefore, an asymmetrically applied force relative to the center of mass (much closer to the pellet head)? If angular momentum must be conserved for the rigid body, how does the asymmetric force perturbation affect the motion of the pellet? Does it move straight sideways, or does the force acting on the skirt push it askew more than the head, rotating the pellet on it's center of mass (like a weather vane)? And if begins to precess, such that the less massive skirt is now swinging in a wider arc than the more massive head, then wouldn't angular momentum still be conserved, even though the pellet is no longer spinning on the same axis as the trajectory? Do JSB's with their shallow-holed underskirt and more sphere-like head fare better than pellets with deeper holes? Does the secant ogive of the JSB fare better than the tangent ogive of Crossman Premier where drag and BC are concerned, analogous to the ogive's effect on a rifle bullet? Inquiring minds want to know.
And I don't know -- I am only speculating and asking questions, but I would bet 50¢ that diabolo pellets are inherently dynamically unstable when spun, and that conservation of energy and momentum, about the center of mass far forward of the skirt vs. asymmetry of typical ballistic external forces affects head and skirt much differently; that diabolo pellets vs. bullets are much more likely to be affected in odd ways by external forces -- wind, air resistance, drag, and maybe even gravity, compared to a more uniform cylindrical solid. I think that diabolo pellets must have to pay a significant price in rotational stability (in the ballistic sense) for having to have a skirt that is necessary for a proper seal in an air rifle and drag in excess of the head. But again, I've been wrong before and may be wrong now.
It appears that the Cardew brothers are the only ones anyone references about pellet ballistics. Even Tom gaylord mentions them exclusively. I'm fixing my broken hatsan and am going to make a carbine out of it. Part of the process will be cutting the barrel down. That's why I'm interested in barrel length. I'll do my own experiment.
Excellent! We learn by doing. You will have to re-crown the barrel carefully and decide if losing the barrels choke (if any) is a significant problem.
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I think each pellet has its own very complex mix of aerodynamics , Center of gravity, alloy/specific gravity and length so that once out of the barrel causes it to ask for a certain speed range at X twist rate. I feel very small details can make a big difference...
The RWS Superdomes have that ridge(parting line?) around the edge of the head I think it has a huge effect on the .177s and not so much on the .22s... on the .177 it compared to the size of the pellet is large causing a much larger area of low pressure and to lower speeds...
so at high velocity it sheds velocity very quickly and it goes from acting more like a gyroscopically stabilized bullet to a drag/gyroscopically stabilized pellet rather quickly...
why do I think it acts more like a bullet at high speed... because the skirt is riding in a low pressure area created by the head... physics says
double the speed quadruple the drag also... so the flatter the head and the higher the fps the more abrupt the transition to drag stabilization at the skirt... effectively a shift in the apparent COG towards the rear of the pellet...
then there is the twist rate the faster you spit the pellet at the higher the initial rpm of pellet...
I have been getting .5-.75 groups at 30 yards with the .177 superdomes out of a 20" 1:15 twist barrel (trying to catch lulls in the wind) and I think it has to do with both of the above...
Why?
I think the ~430 fps the Daisy 953 sends them out at keeps the skirt in a condition where the it's drag is consistent and though the Stability calc (SF of about 4) say it is way over stabilized there is no shift in apparent cg... and the cq is forward enough to prevent wallowing..?
and
sending it at 430 fps imparts a spin of about 21,000 rpm out of a 1:15 twist barrel...
where as
sending it at 850 fps imparts a spin of about 38,000 rpm out of a 1:16 twist barrel... and that makes it more susceptible to any imbalance in the pellet (caused by the barrel, production or handling ).
and of course I think it is more complex than the above in reality... ;)
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I think each pellet has its own very complex mix of aerodynamics , Center of gravity, alloy/specific gravity and length so that once out of the barrel causes it to ask for a certain speed range at X twist rate. I feel very small details can make a big difference...
The RWS Superdomes have that ridge(parting line?) around the edge of the head I think it has a huge effect on the .177s and not so much on the .22s... on the .177 it compared to the size of the pellet is large causing a much larger area of low pressure and to lower speeds...
so at high velocity it sheds velocity very quickly and it goes from acting more like a gyroscopically stabilized bullet to a drag/gyroscopically stabilized pellet rather quickly...
I was looking critically at several pellets last night, critically, with a lighted magnification. The separation line you refer to implies a cast bullet, correct? That was what I thought when I saw it. it also appears that the Superdome skirt may have been swaged onto a mandrel to form the cavity for the bolt tip, whereas pellets with a more conical skirt cavity seem in most cases to have been drilled or reamed. The Superdome's heads also appear to have been polished (possibly a simultaneous operation with skirt swaging?), but the finish on the rest of the pellet is indeed somewhat rough.
Had a rather odd idea last night, and I am going to try it out tonight -- dropping a handful of pellets into my now little-used vibratory tumbler (switched to a wet, rotary tumbler) with some corncob media to see what happens if I try to polish some pellets that way. It may ding the skirts too much, don't know yet. I suspect that it would depend on the number of pellets in the tumbler at one time and how long they were left tumbling. In the past, I have also added NuFinish car wax to cotton patches and put them in with the tumbling media to give brass a really shiny finish that doesn't tend to tarnish when stored. Wondering if a wax job might lubricate the pellets and potentially do some good as well. If I get really industrious, I will measure the test pellets before and after, and shoot some test groups.
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Me I am stuck on playing with twist rates right now and need to get busy getting the work done...
I have all the parts for a budget 900+ fps w/7.9g cphp at 20 pumps MK1377
I have 3 different twist rates to try on it : Daisy 10 land/groove 1:15 twist, Crosman 10 land/groove 1:16 twist and a Lothar-Walther 12 land/groove 1:17.7 twist(choked)
I wish I could find a Broken BSA Meteor to scrounge the barrel from I found a AoA pdf that says they have a cold forged 12 land/groove 1:19 twist barrel...
Scroll down a bit
https://www.google.com/search?sourceid=navclient&aq=&oq=&ie=UTF-8&rlz=1T4ADFA_enUS508US508&q=bsa+meteor&gs_l=hp..6.41l253.0.0.0.213156...........0. (https://www.google.com/search?sourceid=navclient&aq=&oq=&ie=UTF-8&rlz=1T4ADFA_enUS508US508&q=bsa+meteor&gs_l=hp..6.41l253.0.0.0.213156...........0.)
Cast .177 not likely imo just to hard to avoid voids and such...
I also have thoughts about tweaking the specific gravity #s to account for the missing mass/weight(compared to bullets) when using the twist rate calculator...
http://www.geoffrey-kolbe.com/barrel_twist.htm (http://www.geoffrey-kolbe.com/barrel_twist.htm)
in the end ya got what ya got though and just trying different pellets till you find the one that works best for a given powerplant/barrel gets the job done...
but it is very enjoyable to try and figure the whys...
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TCups.... that is an excellent explanation of Moments of Inertia, but as mentioned previously, in a rigid body, all the moments add up to produce ONE moment of inertia acting through the CG.... If the sideways aerodynamic drag acts through the same point (the CP), then there is no torque applied to cause an upsetting yaw.... The sum of all the forces acting in a crosswind and likewise be considered to act through a Center of Pressure, a concept familiar to sailing or flying.... If you read through the link I posted the summary from on page 1 of this thread, you will find the following regarding the interaction of the Magnus Force, acting through that Centre of Pressure, and the Center of Gravity, which causes the "Magnus Moment"....
http://www.nennstiel-ruprecht.de/bullfly/fig11.htm (http://www.nennstiel-ruprecht.de/bullfly/fig11.htm)
The key part of this is the following statement....
the Magnus moment will have a stabilizing effect as it tends to decrease the angle of yaw d.
It can be easily shown that this is only true, if the centre of pressure of the Magnus force CPM is located behind the CG. The Magnus force destabilizes the bullet and increases the angle of yaw, if its centre of pressure is located ahead of the CG, which may come true in a specific velocity regime.
What I get from that, is that if the CP is behind the CG the bullet should be dynamically stable (yaw damps out), but if the CP is ahead of the CG it will be unstable.... I would rather assume that Diabolo pellets are designed to have the CP behind the CG, so should be tending towards stability.... but this may come unglued at certain velocities and rates of spin....
Bob
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This is a tangent, but it relates: Did you ever make one of those 2 liter soda bottle rockets, powered by water and compressed air? It will be most stable if the addition of fins and other doodads puts the cp behind the cg by 1/2 bottle diameter.
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Bob:
I confess I still haven't read all of your references, yet. Busy day at work, etc. I will. and I will come to grips with the vector graphic animation posted. I seem to think the 2-D animation shows the principle, but thinking about it in 3-D, I believe I can now more clearly see how and why pellets DO indeed "corkscrew" downrange. Actually, as it turns out, I explained exactly why and how pellets might fly in a spiral trajectory in my second post on this thread, without realizing it:
"Under a strobe light, in the dark, I have seen a fletched arrow fired from a compound bow wobble and spiral."
and the second statement in that post is probably also still be correct:
"I have never seen evidence that a bullet actually spirals".
Spirals is probably the wrong word -- technically all rifle bullets spiral, but don't usually corkscrew.
I think I have the right concepts here, if not the right technical terminology:
The heavy head and hollow skirt produce a moment of inertia that tends to wobble the long axis of an air rifle pellet. In my mind, I think of a swivel office chair. With legs extended, take a spin, then pull your legs in -- you rate of spin increases, like an ice skater tucking into a tight spin. Energy and angular momentum are conserved. Angular velocity changes.
Now, think of a double decker office chair on a single, long pedestal -- if you and I start out at the same rate of rotation, on the same axis in each of the chairs, you above and me below, but now, suddenly, you tuck in and I throw my legs out, what happens? We cannot spin at different rates (angular velocity). We haven't changed the center of gravity or the total energy of the mechanical system. But each of us has changed our moment of inertia. Something has to give. The pedestal (axis) has to begin to wobble to conserve angular momentum.
At nominal velocities, even without spin to stabilize a pellet, skirted pellets fly a relatively straight trajectory, because, like that arrow, the skirt acts like the fins of an arrow to stabilize the trajectory. .
If the pellet's skirt tries to swing outward and wobble while the pellet is still flying fast enough, it just gets pushed back in line by wind resistance. But as, down range, the linear velocity decays faster than the angular velocity, then the pellet can begin to swing it's skirt outward, and the pellet wobbles - precessing about it's center of gravity, and yes, at one and only one angular velocity, and at one and only one total angular momentum, but to conserve its total angular momentum, the moment of inertia (is that the right term for the vector force that tips the axis of precession?) is not constant.
Even wobbling, the pellet is still flying down range, and still flyiing with its skirt, wobbling or not, acting like a finned projectile -- an arrow. And the rotational precession of the pellet's "fin", its skirt, steers the direction of the pellet's flight.
For a finned projectile, spiraling yaw (precession) + fins = corkscrew trajectory
For an un-finned projectile, spiraling yaw occurs, too, but the bullet projectile's center of pressure, forward of the COG, makes the bullet tumble and keyhole, and yes perhaps even spiral slightly, but nothing like a finned projectile.
Down range, spinning bullets tend to "go to sleep", become more gyroscopically stable and behave well in most cases.
Down range, spinning pellets tend to "wobble" and fly like a wobbling finned projectile -- in an ever increasing spiral, as forward velocity decays and angular momentum begins to dominate, inducing a rotational torque on the skirt that overpowers wind resistance against the skirt and steers a corkscrew trajectory.
It seems to me that the farther and faster air gunners try to shoot skirted pellets, the more the get screwed.
PS: Here's an counter intuitive afterthought. If one were to swage a LH twist rifling into the skirt of a pellet flying out of a RH twist barrel, then as the linear velocity of the pellet decays, and the skirt begins to yaw and swing outward into the air stream, steering a corkscrew, might the counter twist on the skirt begin to increase drag on the skirt, and to slow the angular velocity of the pellet's spin, helping to reduce the tendency to yaw, and helping to minimize corkscrewing, albeit at the cost of a faster decay in terminal linear velocity.?
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The pedestal (axis) has to begin to wobble to conserve angular momentum.
Sorry, don't see it.... if the total change in moment of inertia is zero, nothing changes.... If the MOI increases, the angular velocity decreases to conserve angular momentum, and vice versa.... This is because the axis connecting you and I is rigid, and the body (in either state) must be considered one rotating body.... If there is no external torque applied, why would it wobble?....
I'm not so sure of your definition of spiraling not being corkscrewing.... I would agree that wobbling (precession and/or nutation) is not corkscrewing, but once the CG is describing a helical path, I would call that both spiraling or corkscrewing, I would use the terms interchangeably....
I think your generalization about (all) pellets spiraling more downrange while bullets do not is vastly oversimplified.... You really need to read and study that reference and the diagrams showing varying modes of Dynamic (In)Stability.... and in particular the part that say that for the most part it is not possible to predict it because many of the variables are difficult or impossible to measure or predict....
Bob
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Yes, on my reading list for this weekend, I promise. But isn't angular momentum a vector quantity? Even if the total angular momentum is conserved, its vector can change -- has to changes -- if an external force is causing a deviation of the original axis of rotation. No more posts hijacking the thread for now. Sorry. I have a lot of reading to do, so I may be a while getting back. In the final analysis, though, yes, pellets do spiral and seem to behave, potentially, like a wobbling, finned arrow in flight under the right circumstances. Thanks.
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Let me ask the obvious here. What if a pellet is not concentric on it's axis? What if the skirt is say 0.001 shorter on one side than the other? What if the central axis of the skirt is two degrees different from the central axis of the head? How much actual distance is that? IRL (In Real Life).
We have problems with pellets. It might cost those of us who care five cents a pellet to fix these problems, but WE DO have problems with pellets.
I am probably about to be bludgeoned here... so just count this post as the rambelings of an idiot and continue to march.
There are really only two reasons why they can fly poorly. Either they are poorly stabilized, or the vendors are giving us pellets which will not fly. It could be both.
All of the rest is icing on a cake. The cake is where we need to work. In my mind we should eliminate the variables which have anything to do with stabilization first. That might be by addressing rifling rates. That might be by addressing the quality of our pellets. But these two areas come to the top of the list. Fix one first, does not matter which, then fix the other.
This is how industry works. It is somewhat like science but CHEAPER. First solve the CHEAPEST problem. If that does not result in a satisfactory solution then solve the more expensive problem.
This is just an opinion. Nothing more.
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I agree 100%.... The less perfect the pellet, the more chance it will be Dynamically Unstable if it's spun too quickly.... So, you can either convince the pellet manufacturers to up their game and produce perfect pellet (which might easily cost 10 - 100 times as much).... or try a slower twist.... Benchrest shooters have know this for years, they were flirting with slowing the twist down to the verge of unstable for the Static Stabilty.... The Military use a Stabilty Factor of 1.5 - 2.5, and the BR guys were flirting with 1.2 (1.0 or below is unstable).... Then they found out that when you go below 1.5 the bullet, although it isn't keyholing, is wobbling enough that the BC is reduced.... JBM has a calculator on their website that deals with that.... Current thinking is that we should be as close as possible to that 1.5 SF as we can.... When the SF gets up into the 3.5-4.0 and over, then we can see Dynamic Instability occurring in SOME bullet designs, and it certainly starts to emphacize any imperfection in the bullet....
None of the available Twist Calculators are set up for Diabolo pellets.... The best you can do is use the dimensions for a round nose bullet of the same length and caliber, and possibly make some correction for the reduced weight.... Even that is very difficult to use, as the calculators assume a uniform bullet density.... so how do you determine the rotational Moment of Inertia of a pellet (with a waist and a hollow skirt) and compare that to a solid round nosed cylinder?.... At what stability factor is a pellet overspun, and therefore more susceptible to Dynamic Instability?.... Would that be at 3.0 and above?.... 2.0 and above?.... 1.0 and above?.... or is the answer to spin the pellet extremely slowly, like the FX Smooth Twist barrel, where I have seen spin rates listed of as low as 1 turn in 13 FEET?.... If the cure for Dynamic Instability and pellet Spiralling is too fast a twist rate, then the Smooth Twist barrels should never show it, WITH GOOD PELLETS, regardless of range of velocity....
I don't have all the answers by any means.... However, my gut is telling me that if you see Pellet Spiralling developing at longer ranges you have too fast a twist rate for that pellet....
Bob
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or is the answer to spin the pellet extremely slowly, like the FX Smooth Twist barrel, where I have seen spin rates listed of as low as 1 turn in 13 FEET?.... If the cure for Dynamic Instability and pellet Spiralling is too fast a twist rate, then the Smooth Twist barrels should never show it, WITH GOOD PELLETS, regardless of range of velocity....
I don't have all the answers by any means.... However, my gut is telling me that if you see Pellet Spiralling developing at longer ranges you have too fast a twist rate for that pellet....
Bob
I don't know but I think it would not hurt to test a lot of different pellets in the FX barrel. If the data suggests that we are vastly over stabilizing then we have an answer. If it doesn't then we have an answer. =)
Either way, I thank you for your work. It really is brilliant.