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Thread: Twisting Bullets 101

  1. #1
    Boolit Master
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    Twisting Bullets 101

    I'd like to keep this short, but probably won't. I submit the subject of gyroscopic stability in spin stabilized projectiles is poorly understood by most folks. I shall not endeavor to bestow the full dialog appropriate to the subject as it would make a book. Several in fact. Highlights follow and I will be happy to discuss any aspect in following posts if there are questions.

    It may sound terribly simplistic, but the purpose of stabilizing bullets and ball is consistency. Consistency is the basis of accuracy, or the foundation for doing the same thing repeatedly with reasonable expectation of the same result. To that end, see the definitions below:

    Center of Aerodynamic Pressure (CP): The sum of all atmospheric forces applied to the bullet while in flight, measured on the axis of rotation.
    Center of Gravity (CG): The mass balance point of a bullet on the axis of rotation.
    Pitching Moment: The linear displacement on the axis of rotation between the CP and CG of a projectile.

    The CG of conical bullets is, in nearly all cases, aft of the CP. This is the reason that conical bullets with no (smoothbore) or relatively slow rotational speed, will tumble when they leave the barrel. One exception is a Forster slug, such as commonly loaded for shotguns. Other similar designs may be dynamically stable, but for the most part, conical bullets do not have dynamic stability.

    Round Balls:

    Round balls have, for the purpose of this discussion, a co-located CP and CG. This assumes the ball does not deform when shot, and in the case of smooth bore guns and hard alloy, it is the case. Without such displacement there is reason to wonder why muzzle loaders using round balls have slow twist rifling in the barrels. Sometime after events unfolded at Concorde, the British discovered an elementary fact regarding such benefit, much to their chagrin.

    British forces used smoothbore muskets and to some extent, subcaliber patch and ball to facilitate rapid reloading with heavily fouled bores. Given their style of warfare it made sense. Their volley fire was sufficient when facing ranks of opposing forces armed in similar fashion, even though accurate fire by individuals was problematic beyond 50 yards or so. The upstart Colonials however, did not have the manpower to waste in this fashion, and to large degree had previously adopted rifled barrels for many sporting arms. You see, someone over on the Continent had discovered that grooves in the barrel greatly assisted accuracy. Even the initial application which used straight grooves helped a great deal. The reason was simple. If one set aside the need for rapid reloading, which might be appropriate for hunters, it was discovered that the ball no longer left the muzzle with random rotations on an infinite varieties of axis. Spheres in rotation will generate aerodynamic lift on one side, thus causing the ball to swerve in that direction. Vary the axis from one shot to the next and you have random dispersion...or the accuracy of a Brown Bess. The Colonials were hunters first, warriors second. By the time of the Revolution, it had been discovered that helical rifling was even better than straight and the Long Rifles of the day were fully capable of striking man sized targets consistently at ranges beyond 100 yards. The Colonial Mothers did not raise fools and their sons understood standoff was a good thing. It was expedient to let others die for their country and although the British thought this very tawdry, they let their sense of propriety lead them to defeat.

    Conical bullets:

    There is a simple reason for the development of conical bullets. They are more streamlined and they carry more weight or mass per caliber as compared to a round ball. Streamlined means they carry energy further (higher BC) and weight means they penetrate more (SD). There is some debate of who first ventured into this realm, many think of a Frenchman named Claude Etienne Minie'. It is pronounced "Men-nay". He was not the first, but his bullet design caught on for the armies of the world and thus he is known for this. His bullets were pointed and hollow based designs. Initially there was a plug in the bullet base intended to obturate the sub-caliber bullet (quick to load) to ensure it would engage the rifling. Since the moment in this design was very short, it took little if any change in twist to accommodate this bullet and the armies of Europe and subsequently America, had the first practical stabilized conical bullets for their infantry forces. It's that standoff thing again. Somewhere in that rapid evolution, some efficiency expert found the base plug was not necessary. Another struck upon the idea of paper cartridges. The freight train was rollin'........but there was much to learn.

    Now we get to the meat of it. A flurry of experimentation around the world started the formal study of ballistics. There are three disciplines, Interior, Exterior and Terminal. Different folks studied different aspects in the mad race to military supremacy. In this case, we talk about exterior ballistics, or that point from the rifle's muzzle to target impact.

    The aforementioned benefits of conical bullets guaranteed their permanence in history. Round balls do not have endearing traits from an aerodynamic standpoint. Conical bullets do. Case closed. However, to harness the benefit of conical bullets it was necessary to develop the science and that took a lot of work. In the mid 1800's a fellow named James Forsyth was in the thick of this and wrote a book entitled "The Sporting Rifle and its Projectiles". It is available through Google Books online. He was not the discoverer of most of what he reports but was one of the first to make the information widely available via the press. The book is an interesting reference and is mostly valid by today's standard. And you thought our generation was the fount of all knowledge huh? Read the book and find out otherwise.

    Conical bullets are stabilized by application of angular momentum, that being imparted by rifling in the barrel. It requires less that 1/2% of the energy produced by the powder charge and only requires that the momentum be sufficient to overcome the overturning or pitching moments created by the difference between CP and CG. Stability is defined by what is known as gyroscopic stability factor (Sg) and in theory a value of 1.0 is unity and the projectile will achieve stability. In the practical world, it requires a minimum Sg of 1.1 and more realistically about Sg 1.3. I will point out here that bullet weight has absolutely nothing to do with the twist required to stabilize a bullet. Bullet Length is the litmus. Recall that round balls have co-located CG/CP. When the form is modified to a conical shape the displacement of CP is forward (with a few exceptions noted) The further the form is stretched, the more angular momentum is required to overcome the pitching moments, ergo, you need a quicker twist to achieve the required Sg. A .25 caliber bullet 1.25" long will require a 7" twist. A DG bullet on approximately the same length requires much less, perhaps a 16" twist. The reason is found in the larger radius of the bullet which provides for more velocity at the circumference and thus more angular momentum. Gyroscopes and bullets have a common aspect, that being what is known as rigidity in space. It is this momentum force that resists upset by outside forces such as aerodynamic forces, gnats and global warming. (sorry....) When a bullet or gyroscope is acted upon by an outside force it will precess 90* to the axis of rotation in the direction or rotation. Every time. The degree to which it precesses is regulated by the Sg. When a bullet is upset in this manner, the precession occurs in the form of nutations, or a wobbling motion that will, given sufficient Sg, stabilize or null in a new rotational axis. Bullets go through this process when affected by wind, imbalance, gravity and any other of the myriad of forces experienced in flight. That includes gnats. A bullet may experience as many as 3-5 modes of precession. They WILL experience a minimum of two. Save that discussion for later if there is interest.

    It is important that bullets be properly stabilized through the range of their intended application. The aerodynamic forces at play during a bullet's flight are variable. The highest drag is found at Mach 1 and this is where the .22 RF HV bullet lives. Secondarily, the flight regime for the .22 RF and most black powder bullets is in the transonic range of Mach .7-1.3. This is the place where the pitching moments are strongest for RF bullets. For those asking the obvious question, in absolute terms, drag is higher at higher velocities but most conical forms exhibit a curious reduction in coefficient of drag as Mach number increases and the absolute increase in drag is thus not of linear nature. So, where do we go from here?

    An English fellow named Greenhill is credited with a formula which defines the required twist rate for a given length of bullet. You can read a bit more here:
    http://www.mamut.net/MarkBrooks/newsdet35.htm

    The formula's age has little to do with its applicability. Those who twiddle with high velocity guns will opine a different constant is appropriate for their bullets and that is true. Others dealing with very low velocity projectiles will use yet another constant. The constants change when one has a particular agenda in mind. The basic formula is not unlike the way gun builders apply more or less standard twist rates for particular chamberings. It works for practical purposes. The formula shows the path to gyroscopic stability for conical bullets. If you need to stabilize a bullet of X length, Y rate of twist is required.

    In the world of the .22 RF there are many bullet designs and few twist rates. The 1:20 will stabilize bullets typical of the .22 Short and 1:16 will do the same for Long Rifle bullets...or shorter. This leads to another subject: what twist do I need and why do they only make a certain twist for .22s today? What twist you need is defined by the longest bullet you intend to shoot in your rifle. The day's standard for production .22s is 1:16". It will stabilize all .22 RF bullets with the possible exception of the Aguila 60 grain SS round. I say possible because some report acceptable performance with the 16" twist. I say also, there are variables at play and you never quite know until you try it. As an example, I have a .358 Win. w/ a 16" twist that stabilizes 250 grain spitzers very well. It is a rare exception, most require at least a 14" twist for that and some opt for 12" twist rates. So, is there any adverse effect found in "over stabilizing" a bullet, such as using a 16" twist for shooting .22 shorts? While a bench rest competitor may be able to ascertain the answer to that, I cannot for short range work, ie. less that 600 yards. The theory is that rifling imparts deformation on bullets, and the faster the twist, the greater the deformation. I will go a step further and state this is a fact. What is difficult to evaluate is just how much impact this has. Hardcore CF bench competitors will shoot bullets and barrels matched to each other, with the minimum twist required to stabilize the bullet from muzzle to target and not an inch further. If they do their calculus for competition in Denver, Co. their gun will not shoot for sour grapes at sea level. I don't know the converse to be true. When science does not provide solid answers, superstition steps to the fore. So far as practical application, the difference between a 16" and 20" twist for shooting shorts is not apparent to me. My T/C carbine shoots consistently in the MOA range out to 50 yards with a 16" twist. So far as I'm concerned, case closed. A friend has a Rem. Model 24 (chambered for shorts only) that shoots nearly as well and I believe it has a 20" twist. He is a pragmatic fella...and cares not a whit what the twist rate is.

    A word of caution. It is a common misconception that one may compensate for slow twist by using higher velocity. The concept is valid only to very small degree. Very small. On the other hand, a great deal of benefit is gained by quickening the twist rate a small bit. No, I'm not going to do the math, but you can. A 12" twist at 3000 fps vs. a 10" twist at 3000 fps....pull out your calculator and do the math to determine RPM. Once that is done, figure the difference between a 3200 fps bullet w/12" twist and compare to the 3000 fps bullet at 10" twist. I think after you've done this exercise you'll get over the higher velocity theory of bullet stability. It works, but the gain is VERY small.

    What all that means is that it won't hurt to "over stabilize" a bullet, but it will be a small disaster to do it the other way around. If you want to walk off the beaten path, do a lot of homework before you order that barrel with an odd twist rate. The large gun manufacturers do what they do to achieve certain economies of scale and production in order to make a profit. Their approach may not always be the absolute best for a given application, but they do pretty well for a range of applications. They do well and you might do better...but you'll have to do a lot of research, or rely on another's expertise if life without guard rails appeals to you.

    Well, that constitutes a scratching of the surface without a lot of painful math. Accept it or do your own research. If you want further discussion on the subject, fire away with the questions. I might not know the answer, or you might not agree with the answer. It's a DEEP subject though, this thing called Exterior Ballistics; Subchapter B: Spin Stabilized Projectiles.......

    Dan
    Last edited by Digital Dan; 03-19-2017 at 12:45 PM.
    I have danced with the Devil. She had excellent attorneys.

  2. #2
    Boolit Master

    44man's Avatar
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    Very good and the over stabilization does no harm is where I live.

  3. #3
    Boolit Bub
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    Excellent post- especially like that you highlighted that it is bullet length, NOT weight that determines stability criteria. The guys shooting extreme long distance with turned bullets can attest to that.

  4. #4
    Boolit Master
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    44Man, I agree that over stabilization is not an issue for normal hunting applications at "normal" ranges. It does however carry some baggage at the distance increases.

    I know most have witnessed a well thrown pass in the game of football, wherein the ball arcs gracefully, nosing over as it begins returning to earth. What you see here is described in technical terms as the characteristic of tractability. Likewise, it is common to see a punted football not nose over and begin its descent nose high. A vigorous kick puts more spin on the ball than a quarterback's hand most days. The punted ball is "over stabilized" and, well, who cares? It's only football.

    Well, bullets will behave in similar fashion and at long range when descent angles begin to steepen, it can lead to a loss of stability and the bullet will tumble as a result. Such are the things that make long range shooters a bit different from you and I. The circumstance is simply that a bullet pitched nose high experiences increased drag and those forces promote gyroscopic precession at right angles to the applied force. It can only go so far before the aerodynamic moment exceeds the stability factor, and those moments increase substantially as velocity approaches Mach 1.
    I have danced with the Devil. She had excellent attorneys.

  5. #5
    Boolit Master popper's Avatar
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    Practically, the boolit does't 'nose-up', the path just changes direction and CP changes.
    Whatever!

  6. #6
    Boolit Master
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    Yep, that's pretty much what I alluded to with the punted football. Conceptually speaking, the over stabilized bullet becomes rigid in space.
    I have danced with the Devil. She had excellent attorneys.

  7. #7
    Boolit Master

    Wayne Smith's Avatar
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    Thank you. I have been reading at this for years, and now (possibly because of repetition) I understand why it is the total length of the boolit, not the length in contact with the rifling that matters.
    Wayne the Shrink

    There is no 'right' that requires me to work for you or you to work for me!

  8. #8
    Boolit Master

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    I watched a lot of bullets through spotting scopes. IHMSA and BPCR. Under spun bullets would only be good to the closer ranges, then wander way far off target at a certain point. It is a strange thing to watch.
    The .44 from the model 29 was over spun with 240 gr and there is a corkscrew rotation around the flight path, 1 in 18-/34" twist. The Ruger did not do that. By just going to a 250 gr in the 29, flight was stable.
    With my pre 64 mod 70 in 220 swift using a 60 gr Hornady, I could never shoot a group at 100 yards. I had a Balvar 24 scope on it. I never used it close so sighted at 350 yards where I shot a 1/4" group. I head shot chucks to near 700 yards. I did not like the 22-250, twist was slower and lighter bullets were needed, not as good at long ranges.
    I over spin with my BFR 45-70, 1 in 14" twist, it has done 1/2" at 100 many times and my best group was 5 shots in 2-1/2" at 500 yards. All the BFR's have fast twists and all shoot.
    Anyway I lean to a faster spin. If you want to shoot closer, just slow the velocity. Bullets DO go to sleep, never seen one tumble and got round holes to 1000 yards.
    Use too long a boolit like the nutty 405 gr in the .44 or the 700 gr in the .500 and you get sideways holes at 50 yards. They tumble and go off course in wet phone books.

  9. #9
    Boolit Master


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    I concur with Bryan Litz who states in his very fine book on ballistics that there is no such thing as "over stabilization". A bullet is either stable for it's intended flight or it is not. If you watch bullets wander off down range before reaching the farthest target then they were not stabilized for the intended range.

    Bullets can be "over spun" on the other hand. That is giving the bullet more spin than is necessary for stabilization across the intended range. While over spinning, with a quality bullet that is very balanced on exit many times does little harm if the bullet has a jacket strong enough to withstand the centrifugal force. The accuracy of all bullets, jacketed and cast, is more adversely affected by any imbalances in the bullets the faster they are spun. It is the primary reason why we shoot groups instead of all the bullets going into the same hole.

    As an example; we know the accuracy of bullets used in most military "ball" ammunition is not nearly as good as the commercial bullets for reloading we have. That is because the quality of the military ball bullets is lacking in jacket thickness and bullet weight uniformity, especially as compared to our common Speer, Hornady or Sierra cup/core bullets. Taking the same lot of 7.62 NATO M80 ball ammunition and shoot 10 shot groups at 100 yards out of quality bolt action rifles with 10, 12 and 14" twist barrels having comparable accuracy with match ammunition (moa or better). If the barrels are the same length the average velocities of the 3 rifles will be close. We will find the accuracy 10" twist barrel ok and certain acceptable for military use. We will find the accuracy of the 12" twist rifle to be better. The 14" twist rifle will give the best accuracy of the 3 rifles with that M80 Ball ammunition.

    Why is that when the bullets out of all 3 rifles were perfectly stable? Using the Miller stabilization formula where and Sg of 1.0 is unstable and 1.4 is stable lets compute the Sg's (stability factors) for the 3 different twist rifles. lets say the velocity of the M80 ball was close to 2850 fps for all 3 rifles. The bullet Sg for the 10" twist barrel is 2.52, for the 12" twist barrel the Sg is 1.74 and for the 14" twist the Sg is 1.28. Remembering that the RPM of the bullet is a prime factor in stability with a higher Sg meaning more RPM we see we are over spinning the bullet in the 10" twist which is the cause for the inaccuracy. Yet in all 3 twists the bullets were perfectly stable flying point forward with no indication of instability.

    Now, let's run the same test with a Speer, Hornady or Sierra 150 gr SPBT cup/core bullet loaded to the same velocity of 2850 fps. Odds are the accuracy will be very good with all 3 rifles and probably close to equal.

    So why the difference when the bullets, both M80 and commercial, were stabilized? Yes the 10" twist barrel over spun the bullets to a greater degree. The difference was because the greater centrifugal force created by the higher RPM of that "over spinning" caused the more imbalanced M80 bullets to slightly cork screw (just as 44man stated he observed) around the flight path to a greater degree than did the commercial bullets.

    Anytime you have all the bullets in a bad group making caliber size round holes in the target it means the bullets are flying point forward and thus, stability is not the issue. Over spinning is the issue.

    Larry Gibson

  10. #10
    Boolit Master popper's Avatar
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    Out of curiosity, ever notice that a 'tumbling' boolit hits sideways; not quite stabilized will give some 'tipping' at the target? CP of sideways flying boolit is still very close to CG of the boolit.
    Whatever!

  11. #11
    Boolit Master
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    Larry, appreciate your thoughts on this. Bullet imbalance is a booger and I'm being polite. I touched briefly on that initially, and that would be about all the space available for a forum post. It is a complex topic. Bullets are never perfect and the forces acting on them are numerous. Predating the rise of Mr. Litz on topic, I read a fair bit on this by the likes of McCoy, Vaughn and a few others. The gymnastics a bullet performs from muzzle to target are rather amazing in the best of circumstances and the nuance of several modes of precession a function of being out of balance, here and there, nose to base, inside and out. Epicyclic modes (not caused by imbalance) are routine and tricyclic modes (balance related) common. Bullets don't ever "go to sleep". McCoy was of the opinion that 4 to 5 modes of precession existed.
    I have danced with the Devil. She had excellent attorneys.

  12. #12
    Boolit Master


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    Digital Dan

    I agree absolutely about the "gymnastics a bullet performs from muzzle to target are rather amazing in the best of circumstances and the nuance of several modes of precession a function of being out of balance, here and there, nose to base, inside and out. Epicyclic modes (not caused by imbalance) are routine and tricyclic modes (balance related) common. Bullets don't ever "go to sleep". McCoy was of the opinion that 4 to 5 modes of precession existed. " You and I understand that as do a few others but I'd bet most of the readers went on to other topics wondering; "what heck did he just say?"

    I'm certainly not disagreeing with you at all on anything you posted. I certainly appreciated your comment to 44man of "over stabilization is not an issue for normal hunting applications at "normal" ranges. It does however carry some baggage at the distance increases". The reason for that "baggage" comes in the form of imbalances in the bullet. As it is put so simply and eloquently in the Hornady manuals (8th edition, page 28 specifically;

    "Perfect balance is perhaps the most critical factor in bullet accuracy."

    For example; let's take my M70 Winchester 30-06. We''ll load some M2 bullets over 48 gr of H4895 and, shooting 10 shot groups at 100 yards, get 3 - 4 moa accuracy. If we load some Winchester 150 gr power points or Remington CLs made 50 years ago over the same load we'll get 1.5 - 2 moa accuracy. Same load over the same bullets made today and we'll get 1 1/4 - 1 1/2 moa. Load todays Speer, Hornady or Sierra 150 gr SPs and we'll get right at 1 moa accuracy. Same load with 150 gr Sierra Match Kings and that M70 will shoot sub moa. So what's the difference in accuracy? Is it that all the nuances you mention only effect milsurp and older bullets? No, it is simply because the commercial bullets made today are much better quality with much more uniform jackets and cores. That adds up to much better balanced bullets which are more accurate. The same holds true for older milsurp rifles; the better quality bullets of today shoot much better.

    The difference is simply the bullets of today are better balanced, ergo they are more accurate, especially at longer ranges when over stabilized. With cast bullets over stabilization is a killer of accuracy. at a much lower level of velocity and RPM than it is with jacketed bullets. The reason being it is much more difficult to cast a perfectly balanced bullet and launch it still balanced. We have to mind our "P"s and "Q"s and control the RPM.

    I am enjoying you discourse as it is indeed spot on.

    Larry Gibson

  13. #13
    Boolit Master


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    Tagged. Fascinating subject.

  14. #14
    Boolit Master
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    Some years back I made a bold assertion that there was no reason (in theory) that cast bullets could not be as accurate as their jacketed cousins. This was on a forum inhabited by more than a few well known BPCR shooters. They thought me quite the fool. I stand unrepentant but admit it is a serious challenge.

    I suspect my optimism is fueled by my love affair with hammer swages, pure lead and paper patches.

    All that is necessary to achieve guilt edge precision is that one learns how to choreograph chaos in the same fashion each time you jerk the trigger.
    I have danced with the Devil. She had excellent attorneys.

  15. #15
    Boolit Master
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    An online resource that explains much thru graphics and (ugh) a splash of math.

    http://www.nennstiel-ruprecht.de/bullfly/
    I have danced with the Devil. She had excellent attorneys.

  16. #16
    Boolit Master

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    One of the strangest boolits I ever watched was from my 30-30 Contender. I used it for IHMSA with the RCBS 308-165-sil. Using a scope to work loads I could hit pennies and nickels at 100 yards, ran out of checks once and shot without them. All turned sideways at 50 without the check so I seen how important the extra drive length was. Recovered boolits showed good engraving with no skid so it had to be fit to twist. Boolits were hard.
    I sold it to my friend and spotted for him. The boolit did not rotate and looked good but it would angle to the right until it was heading for the next 200 meter ram, then it came back to hit the one being shot at.
    I never did figure that one out.
    Experiments with over spin with revolvers I did would show a different POI as ranges changed with good accuracy, just the amount of corkscrewing showing up with range change but then at extreme range it went away.
    The swift was different and a 2" group at 100 was tough to get so how could I get 1/4" at 350 and have stability to as far as the gun could reach? Something is going on.
    Either way close range target shooters use a slower twist to eliminate the rotation.
    Even though spin does not slow as much as velocity, I still believe bullets will settle at range if spun too fast, Just watched too many in flight to say no.
    I tested the Swift and got scope settings by shooting. A target every 50 yards from 100 to as near 700 as I could get on the property, 5 shots at each to start and then work to the bulls eye to record settings. Groups always tightened with distance.
    My standard sight in was 350 yards, never shot the gun closer, I used my BH .44 to 100 and the .222 to 350 for chucks.
    As far as bullets, I tested every brand and Hornady was always best and that was 61 years ago. Back then a quarter would get you a sample pack from all bullet makers and I bought a lot of them.

  17. #17
    Boolit Master
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    On occasion that someone gets to watch a bullet's path epiphanies are not uncommon. Years ago I got to watch tracers by the the ton. They were often fired in crosswinds of 170 knots or sometimes greater, and the ranges were long from time to time. It included .45 ACP, 5.56mm and 7.62x51mm, sometimes from M60s and other times from a minigun. Most of you fellas would not imagine what a bullet will do in such circumstances.

    That said, the most telling visual presented in the form of glimmer, or reflected sunlight from the bullet jackets, highlighted against a cloud shaded mountain side. Would give a nice piece of change for a video clip from that experience.
    Last edited by Digital Dan; 03-21-2017 at 10:44 PM.
    I have danced with the Devil. She had excellent attorneys.

  18. #18
    Boolit Master
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    I have, sitting in my safe, an early Browning BLR in .308. I recovered it,broken, from the roof of a storage shed in Hughes ,Alaska. It had a broken spring and was missing the buttstock. Some light rust. I located the parts for it in Canada. Immaterial I know ,but that is where I found them. After cleaning and reassembly, I put a leupold scope on it and headed to the range.
    At that time I did not have a means to bore sight it, so I started out at 25 yards to get it on paper. I never could get it to shoot. After 20 or so rounds there were not even any holes in the back stop.
    Finally, in frustration, I aimed at a milk jug someone had left out at 100 yards, and blew it up. After setting the target at 100, and fine tuning the scope, I proceeded to shoot it full of holes.
    To this day, I do not know what happened, but I have not tried to shoot it at 25 yards again.. Any ideas?

  19. #19
    Boolit Master popper's Avatar
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    Check the crown. Takes time for the boolit to settle into a straight line of sight path from helix path.
    Whatever!

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