Math Question

[pipehand]

Does anyone have a tutorial for figuring out the diameter of three balls or circles or rings nested within a larger circle, if the inside diameter of the larger circle is known?
I know that the traditional OO buck load without shotcup is supposed to use .330" balls. I would like to order a mould that throws the ideal size for use in shotcups. I have heard of #1 and O being used, but is it just trial and error?
I'm a pretty fair hand at trig and geometry, mostly due to my trade, but the circles within circles thing has me stumped. Tried breaking down the configuration into two 30-60-90 triangles, but without one known side, I was stumped. Any suggestions?

[UNIQUEDOT]

The inner circle diameter would change with different wads anyway as they are different (petals) thicknesses. I use #0 .320 diameter buck inside shot cups and before i got this mold i was using .319 diameter as well as .313 .315 .311 and .310 from my blackpowder molds inside shot cups. #0 in .320 size works well in many different wads.

[pipehand]

Thanks for the reply UNIQUEDOT, but it doesn't really answer the math question. It goes beyond " what works" for me. I just came up on a problem I couldn't solve on paper. Don't even know what to enter in a search, but I do know that there are a lot of people on this board that have all sorts of arcane knowledge.

[gsdelong]

Your question intriged me the last post in this thread has a link to a drawing that shows the theory of solving the problems based on triangles.

http://www.google.com/url?sa=t&rct=j&q=largest%203%20circles%20inside%20a%20circle&source=web&cd=2&ved=0CGAQFjAB&url=http%3A%2F%2Fforums.anandtech.com%2Fshowthread .php%3Ft%3D1766375&ei=Bfa2T6WzFMH6ggeDp4mqCg&usg=AFQjCNFV0GKyjFaR_o0H4644OE-mgsVs7A

[pipehand]

Gsdelong- The .46x r thing is real close per the link. Now i want to know why.

[gsdelong]

Read the very last post. Click on the link inside of it that brings up the diagram. Blue THIS. The diagram show the problem broken down to triangles. By doing that you can write the equation.

[pipehand]

OK, I'll try it, but not this late.

[nanuk]

you can find your answers HERE!!! (http://www2.stetson.edu/~efriedma/cirincir/)

[oso]

pipehand, trial and error is more effective than math since buckshot diameters are not that consistent and your calculation might result in a bulged shell that won't chamber if the actual size of the buckshot is larger than supposed. Then you may end up having to cut the petals off your shotcup.
What gauge are you loading and for what intent?
I like card and fiber for buckshot loads for my style (max number of big pellets) so help me understand your preference for shotcups.

[220swiftfn]

If you're after 12 ga. in a shot cup, then #1 in layers of three or #2 in layers of four fit reliably in a petaled cup.....

Agree with the above for 00....


Dan

[pipehand]

Thanks,All. Went to the site Nanuk linked and the formula is backward. It gives the radius of the circle around the 3 balls. When it is inverted to give the radius of the shot, the number is .46425. The reason I wanted to know, is that not all hulls, wads, and shotgun barrels are the same, and Skiesunlimited has buckshot moulds in .010 increments in the nominal sizes useful in a 12 gauge. As was mentioned, storebought buck may vary, but cast roundball shouldn't by very much.

[Blammer]

I kinda like number 19!

[pipehand]

#19 sure is pretty, but I don't think I want to be casting shot that small.

[Cap'n Morgan]

Not a mathematically correct answer, but more than close enough. Divide the outer circle with 2.16 to get the diameter of the ball:

Bore (.724) divided with 2.16 = .335

To find the smallest diameter that will hold a cluster of three balls: Multiply the diameter of the ball with 2.16

To find the values for a five-ball cluster, just use 2.70 instead of 2.16

[tommygirlMT]

http://forums.handloads.com/uploads/tommygirlMT/2012-05-20_084338_Buck_Shot_Stacking_Formulas.GIF

[tommygirlMT]

With some big bore guns like the 10 and 8 bore guns with small size buck there is also a layers of seven arangement --- with a circle of six with one in the center of the circle which is unique in that the outer six in the layer stack more compactly then the center column --- it is possible to do a 3D math model to calculate how many pellets get left out due to the center column not stacking as compactly but I aint going to derive that one just for the heck of it unless someone pays me to do it

Also --- as to the original question of the OP --- you will probably actually need two sizes for most shot cups that have tapered petals in a 12 bore to get a perfect stack inside a shot cup --- Namely 310 ball size for the bottom layer or two and then 320 ball size for the layers above --- or at least that best triple stack combo I have seen for most lead shot type wads in 12 bore

[Bloodman14]

It would appear that Miss Tommygirl is the math guru among us! I have copied that formula set for future use (hope you don't mind, Miss Tg!).

[pipehand]

Thanks again. TommyGirl- was wondering the same thing about the taper. Will be buying some different wads to measure while they are inside Remington hulls, and in the barrel of my shotguns. And petal thickness at the base and end. Should br fun!

[nanuk]

Cap'n Morgan has the inverse correctly from that page I referenced.

I posted it, and assumed you could work backwards from there....

[pipehand]

You assumed correctly. I spent a whole afternoon trying to come up with that from scratch, but to no avail. Suffice it to say that I may have delayed the onset of Alzheimers by an hour or two by exercising previously dormant parts of my brain.

I knew that if I posted the question to the board, it would be answered. Thanks again.