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Theory on Accurate Ball Shooting

by Ed Wosika

HOW in the WORLD did some of our country's patriots, in the late 1700's and early 1800's, make reliable head and chest shots on British officers at 200 to 300 yards using patched ball rifles, thus, cutting the snake's head off, as it were?! They DID do it, with normal-for-the-period caliber and twist-rate rifles, but HOW?!

This is NOT a trivial question, as it would be when using muzzle loading rifled slugs in a faster-twist arm. My experience is that most frontstuffer patched ball loads will shoot OK out to no more than 100 yards, but, at more extended distances, will really go wild. I have had two 1:48 twist rifles (in .45 and .50 caliber) do this .......... shooting OK at 100 yards and then giving 15 to 20 FOOT wide patterns at 200 to 300 yards. Clearly, something was happening, with my loads, that was NOT happening in any of those long shots against the Brutish officers.

The deeper I dug into the problem, mentally, the greater the number of interwoven controlling factors I came up with. At one point, I ended up with the following bewildering list, all of which have a bearing on the issue:

  •  In order to get a good well-centered-and-spun sendoff, the charge must be sufficient to cause some obturation, such that the ball "waste band" expands, compressing into the cloth patch (providing sealing and torque transfer). Upon exiting the muzzle, the patch (which is a laminar sabot) separates, and the ball proceeds downrange with a narrow weave-patterned (from the patch fabric) band around its equator. Bud, this does NOT include your little 5 grain squib loads for 20 yard shots with your .32cal Seneca >>> they operate on a different principal; 
  • The ball is the only practical projectile that has no overturning moment, given that it has no "length" to allow the nose to act as a lever to tip the bullet over into a tumble. I know that the spin counters that in long bullets, creating a precession/nodding effect, but my point is that this effect does not even exist with the ball >>> no matter HOW it turns over, it still presents the same face-shape to the oncoming wind;
  • Our treasured Greenhill formula (which did not exist when our patriots were letting the air into Strutting Poppycockaded officers at long range) is a twist rate formula that addresses the elimination of the overturning moment effect for longish bullets. Therefore, either it does NOT apply to balls or, more likely, it applies in a completely different manner that is yet to be discovered; 
  • All balls have flaws (voids, sprue hump, etc.) that create an imbalance when they are spun quickly on any axis that does not pass through the flaw. Quickly? You bet. ML balls in standard loads run from 25,000 rpm, for .32 caliber ones, down to around 10,000 rpm for the biggies like .62 caliber. That is fast enough to produce significant effects! So, unless the flaw is either dead-nuts on the axis of rotation (or, less favorably, but still OK, right ON the equator), the ball will have a "heavy side" and a "light side," that want to migrate to the only safe spot available to them: the ballís equator. Given "excess spin" (and our goal, in part, is to discover what THAT means for a ball), this causes the ballís axis of rotation to move, gradually, so that the flaw is on the ball's equator. In all such cases, this shift, however slight, will result in the axis of rotation's no longer extending INTO the oncoming wind; 
  • Even if a ball is perfect, so that the axis of rotation does not suffer this shift, its very low ballistic coefficient will cause it to slow down quickly (over a short distance), causing the oncoming wind's angle of attack to strike the spinning ball from below the axis of rotation. This effect becomes quite pronounced beyond around 130 yards (for most deer-capable calibers and loads); 
  • So, the ball's form factor (i.e., the shape it exposes to the oncoming wind) changes hardly at all when the wind starts hitting it from a non-head-on-to-the-rotation-axis direction, but another, very brutal factor then exerts its effect >>>> that equatorial weave-pattern-band is exposed to the oncoming wind, consistently, more on one side of the ball and is exposed less, correspondingly, on the ball's opposite side. The dimples on a golf ball, combined with the strong backspin it gets from the club, when exposed to oncoming wind, make it a low aspect ratio lifting device (the wings of gliders exhibit a high aspect ratio and are more efficient lifting devices, but the low aspect ratio golf ball still exerts enough lift to let it fly up to 400 yards, as compared to the roughly 100 yard maximum range one could obtain with a smooth ball of the same size and density). Golf balls, when properly struck, move into the wind equator-first, whereas rifle balls start out pole-first. Nevertheless, once the wind is no longer directly onto the pole, a spinning rifle ball creates strong lift that pushes the ball off the path it would have taken otherwise. Bernoulli strikes again!!; 
  • All supersonic projectiles have a problem retaining their stability and accuracy as they experience the buffeting associated with their passing down through the sound barrier. Without special bullets, loads, and twists, standard 308Win or 30-06, which drop through the sound barrier at around 700 yards, give FAR worse accuracy (measured in minutes of angle) at 1000 yards than at 600 yards. Balls? Ha! Most deer-capable caliber balls in typical hunting loads fall through the sound barrier at around 90 yards (both a .45 caliber ball w/1900 fps muzzle velocity [MV] and a .54 caliber ball w/1700 fps MV do this at the same ~90 yard distance). Therefore, even hitting a 200 target with such a ball is like hitting a man in the chest with a standard 0.308Win at 1500 yards. Using a ball at 300 yards? Ha! Right! The "problem" is that we cannot use this as an excuse and drop the analysis, given that there WERE many such shots against the British, with deadly results. It CAN be done. The question is HOW?; and 
  • Smoothbore long guns can hit a man-sized target reliably only out to around 50 yards, so the twist DOES serve a purpose in a ball gun, but how much is too much, and how the hell would one find out what "just enough twist" means, when all the above factors are having an effect too?!!

The funny thing about this is that most ballgun shooters run along blithely, completely unaware of these issues because they almost NEVER take a shot beyond 100 yards. After all, why SHOULD they, given that the ball is, by that distance, subsonic, providing only marginal stopping power for game? Well, I am sure you can understand that I felt that the problem's resolution was valid, but was beyond me. I could obtain NO progress toward a solution. So, one day, on the way to work, I "talked to" my subconscious, handing the problem over to it to solve. On the following morning, on the way to work, I "talked to" it again. I then put the problem out of my mind. That was about six weeks ago.

Finally, several days during the past seven, I got the usual "HEAR YEE THE FOLLOWING!!" notices from that lovely between-the-ears computer, at various times during several working days, and once during a nice cigar after work. I noted each revelation carefully, but still could not extend that into a solution. Then, on Wednesday night, my subconscious woke me up out of a very sound sleep and, suddenly, put all of the components together in the only order that is amenable to rational solution. I was so excited I could hardly get back to sleep. Hang onto your shorts ....... here is the scheme it laid out for me:

1. Clearly, by trial and error, many, if not all, the patched-ball rifles of that period worked for this sinister-yet-intriguing application. Their calibers ranged from around .47 (48 balls per pound, as then described) to around 0.54 (31 balls per pound) and, within that range, their twist rates varied from 1:48 to 1:70. For my purpose, the low end of the caliber range is .45, given that modern .47 caliber barrels are mostly unavailable. Keep it simple, it told me, by sticking to these twist and caliber limitations, for you KNOW that there is a solution lurking in there somewhere, especially in the slower-twist end. Once you have the solution, you can extend it to larger and smaller calibers and create a more general theory; 
2. Every such rifle will have two "sweet spot" velocity ranges: 1) the velocity above which the charge exerts enough acceleration to obturate the ball; and 2) the velocity below which the ball has enough, but not too much, spin to avoid the axis-spin-shift effect; 
3. In most rifles of the above caliber and spin range, these two ranges overlap, but, at the faster-twist end (1:48), they may not do so. This does NOT apply to calibers below the study caliber range (.45-.54), given that, for example, in .32 caliber, the 1:48 twist is close to ideal; 
4. To work up an accurate long range (for a) ball load, first determine the minimum charge the rifle needs to obturate the ball into a tight patch fit. Loads below this level give poor accuracy. As one proceeds up through that charge level, the short range groups start to "go through one hole" (on your 25-to-50 yard target); 
5. If the obturation sweet spot is narrow, this shows that you are having gas leakage/cutting problems with the patch. Try a wad with 1/2" of corn meal over it to eliminate the gas-patch-damage effect completely. The obturation sweet spot should now be broader, extending up quite a ways above the beginning of the accuracy-charge range. If the wad and corn meal effect helped, keep using it for the next steps too; 
6. The obturation sweet spot relates ONLY to short-range accuracy, but it also controls long-range accuracy! IF a long range load exists for this rifle, it MUST be within the load range width of the obturation sweet spot, given that an inaccurate short-range load will NOT provide long-range accuracy. The obturation sweet spot load range is an INTERNAL BALLISTICS question. You must solve IT before moving to the long range accuracy question, which is an EXTERNAL BALLISTICS question; 
7. Most ball load problems come from too fast a spin, so, most likely, IF the rifle has a good long range load, it will be at the lower end of the obturation sweet spot. Therefore, once you have the obturation sweet spot load range nailed down, switch to 200 yards and try out the lowest obturation sweet spot load, using a mark on the bare backstop as your target; 
8. If that test long-range load is all over the backstop, then your rifle may have too quick a twist, such that, by the time the ball is going fast enough to have experienced adequate obturation, it will come out the muzzle turning too fast for long range accuracy; 
9. IF that load hits in a smallish impact area, then try moving the charge up in increments. If it gets more accurate, keep trying more and more of a charge until it begins to open up. Your accuracy load is either the lowest obturation charge or the one above that which gives you the smallest 200 yard groups. Once you have your long-range ball load, shoot for grouping on paper, then use that load forever-after as that rifle's patched ball load, even though stiffer loads will still give short range accuracy; 
10. The likelihood of being able to go to a higher charge, with accuracy, than the minimum obturation charge is more likely the slower the twist (e.g., a one-turn-in-75-inches [1:75] 50cal barrel, rather than a 1:60 one); 
11. I should expect the Greenhill formula to work bassackwards for balls, compared to how one uses it with long bullets. For long bullets, the formula (decimal-caliber x decimal-caliber x 150 / bullet length) yields the SLOWEST twist that will work for a bullet of a given length. For balls, the formula (which simplifies to decimal-caliber x 150 for balls) delineates the FASTEST twist that one can have at some minimum velocity (probably in the 1500-1900 fps range) and still have the ability to hit at long range. That round ball Greenhill velocity range is something I need to pin down. For now, let's call the lower end of that range the "Greenhill Velocity" (GV) and, for discussion purposes, assume that it is 1800 fps; 
12. After finding this GV (which, I anticipate, will apply across the caliber range), one can determine, easily, the likely long-range ball-load muzzle velocity for a barrel that has a faster- or slower-twist than indicated by decimal-caliber x 150 formula. The optimal velocity formula would be: (barrel twist x GV)/(decimal-caliber x 150). For example, if GV turns out to be 1800 fps, then a .54 caliber 1:48 twist barrel would likely have its long-range load at a velocity of (48 x 1800)/(0.54 x 150) = 1066 fps. That is the MV at which the ball would have the same rate of spin as would a ball from the ideal (1:80) barrel twist, when fired at the GV (1800 fps?). So, in our example, that barrel is so fast, on its twist, that it could not give a long range ball load with a MV much above the speed of sound, and THAT low an MV is unlikely to involve a charge that is strong enough to get it into the lower range of the obturation sweet spot. So that the rifle is hopeless for long range ball loads and you might as well up the charge to be good speed (1500 to 1800 fps) and then limit it to shots within 100 yards, at which distance it will have just passed down through the speed of sound and will be beginning to take a wildly divergent angle to parts unknown; and finally, 
13. The axis-of-rotation shift effect is random, in that it can cause the ball to move in any direction away from the path that it would take otherwise. This effect is eliminated by using a load developed as described above. The slow change that the effect of the ball's progressively faster fall has on the wind's angle of attack to the ball is NOT random, given that it repeats consistently from shot to shot. Although this will cause the ball to move to one side (the lift force is DOWNward, but the rotation causes the force to manifest at 90 degrees to the axis of rotation on any such spun-up-gyroscope-like object ,,,,,,,, so, the ball moves sideways), the consistent effect allows one to compensate for it with Kentucky windage. Nooooo praaaaablem!

I will admit that the above thought-chain may have some flaws, but, at least it provides me with a rational, understandable framework for trying to understand HOW on EARTH those old-time ball-rifle shooters popped those officers at such outraaageous (for a ball load) distances.






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