During a discussion on how most folks found BB size steel to be much more difficult to get good patterns than either B or BBB, “Black Coyote” posted he thought the fact 4 BBs across just fit in a 12ga bore, and that chokes caused shot bridging issues. It was a great idea, and I wanted to look at the numbers involved based on the theory that certain shot sizes in certain bore sizes will just fit without slop, and thus give issues from bridging if pushed through any choke constriction.
I’ve done a lot of study on how spheres of various diameters will fit together when put under pressure; the whole field of ionic crystalline structure is based on how atoms will stack in 3 dimensions when under strong forces pulling/pushing them together, what spaces will be left, etc… Went back and looked at single sphere size. They’ll form into a “hexagonal close pack”, which under pressure is incredibly solid. If the pellet diam is an exact or close factor of the barrel diam, such as .18 x 4 = .72, then they should arrive at the choke tightly packed with little room to “give” or flow and would “bridge” with little if any give going through a constriction. As you theorized, this should result in huge stresses which would impart larger sideways pellet motion than normal upon barrel exit.
However, with that large .018 diam, as you state– you can only stack one sphere surrounded by six others, and then just add an asymmetrical layer of 4 or 5 more on one side and you’ve got .720″ right there… it’s a “perfect packing” which will form a very solid structure under pressure going down the bore, and when you hit the choke there is just no extra room or unfilled interstitial spaces for any give! If they were slightly larger BBB at .19″, the dist across 4 would be .76, too much to pack perfectly and without gaps– so the mass would be “loosely compacted” in the barrel, and when it hit the choke it would have voids all over it to allow compression of the edge steel pellets into the pellet-slug-mass: it would be able to flow through the choke.
Same thing with slightly smaller pellets of B size and 0.17″, 4 across just gives .68″, lots of slop for a choke there.
Your idea on this got me looking at other shot sizes vs. barrel diameters.
If your theory is correct, we should see some issues anytime pellet size is a close factor for barrel diam, with some reduction of barrel diameter for wad thickness. Taking two example wads, the CSD118 is 0.035″ thick and the LBC43 is 0.050″ thick, according to BPI manual. Actual measurment gives thinner results for me, 0.27 and 0.35. These would be reduced upon firing, as anyone who has seen the dimpled thinning on a fired wad can attest, but would thus give a MAX bore reduction of .054″ and .070″ respectively. I’d guess these would extrude to only 1/4 their original thickness at the pellet tangential pressure points, based on looking at shot wads. So .712 and .707. Taking the thicker wad, this would mean a pellet of .176″ would stack inside there perfectly– so B’s at .17″ would fit ok, but BB’s at .18″ would be completely jammed in there, removing even the WAD as a source of “give”.
I’m going to invent some terminology to discuss this.
— When A x B = C, then A and B are called “factors”. When some integer value (1, 2, 3, 4…) of pellets just fit inside a bore, I will call that a “perfect factor” or “perfect factor pellet size”. Such as #BB shot @ .180″ x 4 = 0.72″, just fitting in a .725″ 12ga.
— “wad factor” will be the thickness of the wad that is removed from the bore size, so 2 x thickness, then reduced to a guesstimate of 1/4, as the amount of bore taken up by the wad after it’s been extruded and compressed by pellets traveling up bore under pressure. I’d expect a range of .0175″ to .030″ or so, and in extreme cases with a “perfect factor” pellet, I’d expect a higher chance of pellet pinholing the wad as they are forced through a choke.
Here’s some things I’d expect to see:
1. Larger pellets that are “perfect factors” of bore size should give more issues than smaller pellets that are also perfect factors, as their diam compared to any remaining “slop” is large and would make the bridging/compression/bell-effect worse.
2. BB in “overbored” 12ga barrels such as invector plus Brownings, .742 or so diam, should perform better than in normal 0.725– a .742″ with compacted wad thickness subtracted (.070″ /4= .175) leaves 0.724″ bore, so 4 pellets of .181 diam would fit in there– the 0.18″ BB should do ok without much constriction.
3. When a pellet “just fits” inside a bore, that is it’s size is just smaller than a “perfect factor”, such as the 4 x BB pellets in hexagonal close-pack through an overbored invector barrel, I would expect LESS CHOKE to provide a better pattern than strong choking. The pellets with IC may juust fit through without bridging and the associated rebound/bell-effect, but Mod or Full may be too much. In these cases I’d expect worse patterns with tighter chokes.
4. With a “perfect factor” pellet, I’d expect a higher chance of pellet pinholing the wad as they are forced through a choke. In fact, this may be a good investigative way to determine how close to a “perfect factor” the pellet actually is under firing pressure! If wad dimples are more extruded than normal, it might be an indicator of this.
5. The range of “good amount of slop” will be pretty small, as a reduction in pellet size will quickly give a 1 pellet more “perfect factor”. For example, in a normal 12ga bore of .725 with a “wad factor” removed, we have 0.707″ left. Dividing by 4 (4 pellets juust fit across it), we get a “perfect factor” size of 0.176. So 4 x .17 B’s should work nicely, but NOT BBs. Looking at the next integer, 5 pellets juuust fitting in there, we get a perfect factor size of 0.1414, so 3’s at 0.14″ diam should work nicely, but we should have difficulty patterning 2’s at 0.15″, just over the perfect factor size. (I’ve read many times folks discussing how 2’s are very difficult to pattern, such as 10gaOkie discussing his handload).
6. When a pellet is just at or over a perfect factor size, such as 2’s or BB in 12ga, then a thinner and more flexible wad should allow more slop and extrusion give for them to fit and jostle/compact through a choke. So again with 2’s as an example, I might expect the thinner, more flexible CSD118 to give better patterns than the LBC43, and that IS a result often reported on the 10gaOkie HG load.
7. Usable steel shot sizes are probably 5 and above; the integer value of 6 pellets across in a 12ga bore with wad factor gives 0.118″, which is just larger than #6 shot (0.11″.). Therefore, I would NOT expect perfect factors based on 6 pellets to be an issue since they result in too-small shot. So pellet sizes where an integer of 5, 4, or 3 pellets fit inside the bore would be the only ones really, as 2 pellets across would be #3 Buckshot in a 28ga even– clearly too large.
8. For 12ga, the critical perfect factor sizes would thus be, for integers of 5, 4, 3: 0.1414, 0.176, and .235″. These pellet sizes would mean that #2 at 0.15″ and BB at 0.18″ should cause issues in normal 12ga, but #4, 3, 1, B, BBB should be better. The .235″ isn’t a player for 12ga, it’s #3buck size, so in 12ga only 4 and 5 pellet bridging issues are players.
9. For 12ga Invector Plus barrels at .742″, perfect factors are 0.145″, 0.181″– again #2 at 0.15″ should give problems, BUT BB’s should be ok, or at least not as bad, if they are not choked down– IC would be my plan for BBs.
10. For 20ga with a bore diam of 0.615″, and subtracting a wad factor of 0.0175″ again, we get usable bore size for pellets to fit into without bridging of 0.5975″. Perfect factor sizes are .1195, .149, and .199″. So for 20ga, #5 shot (.12″) and #2 shot (.15″) and BBB shot (.19″) might all give issues with any choking. In 20ga, only the #2 shot is a real issue; I’d deal with it by trying to make sure that my wad didn’t allow the .15″ #2 pellets to squeeze into that .149″ or so 4-across perfect pack, like using a thicker in-compressible wad like the SAM1 vs. the csd20, and I’d maybe line the wad with mylar to again keep it from compressing down. The loaded shell should give enough voids to allow choke passage so long as the #2 pellets didn’t have an easy time getting into hex-close-pack. And I would expect tight chokes to give poor results.
11. For 28ga, bore of .545″ minus wad factor of .0175 gives .5275 usable bore for pellets to stack into. Perfect factor are 0.132″ and 0.176″, so #4 shot at 0.13″ might give issues, and #B at 0.17 (if you tried that in a 28ga…). Looking just at #4, since it’s an important pellet size for the 28ga, 4x .13″ pellets bridged gives us .52″, leaving .025″ for the wad and choking only. If we assume 0.0175 for the wad factor, that leaves .0075 for the choke– clearly nothing! So I’d be shooting a CYLINDER or IC max in 28ga with #4 shot–a good solution for 30yd and less shots that #4 gives you.
12. For 16ga, bore of 0.665″ minus wad factor of .0175 gives .6475 usable bore. Perfect factors are .130 and .162. Shot sizes #4 at 0.13″ and #1 at 0.16″ look problematic. I’d plan on #3 and #2 shot for 16ga– a hard knock since #4 is about all that is commercially available. You should be able to get better patterns with #3 as well as better ranges.
Well, that was fun– hopefully someone else finds interest in these projected results when assuming that pellet bridging of 4 and 5 across through a choke might disrupt patterns. All the theorized results seem to align pretty well with anecdotal reports I’ve read on #2 and BB patterns.
Best regards,
Dave
Dave In AZ 
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