Insert/comet size

[VickeA]

Hi,

 

I was wondering how to calculate the amount of insert/comet that I could fit in a shell. Lets say i have a 3 inch canister shell (65mm id) and wondered how many 14 mm comet/stars i could fit. Have been trying too figure this one out fore quite som time. Can anyone help? Would prefer a general formula. How ever i will be happy for any help.

[flying fish]

(ID-StarD)*Pi gives you the circumference of a circle running through the center of your stars. Then just divide by the diameter of your stars.

 

So (65-14)*3.14/14 = 11.4 stars per layer (assuming my math is right...)

 

A note on inserts, perhaps I'm the only one silly enough to make this mistake, but I build a 3" shell of shells recently using time fuses sticking out of the sides of the inserts, and the time fuses were bumping into eachother. I pretty much had to forcibly cram them in, hehe. Could have been avoided by making the portion of fuse sticking out of the insert smaller or putting them off center and staggering.

[AdmiralDonSnider]

Then just divide by the diameter of your stars.

 

 

I think this is not correct because we divide the circumference of a circle by the chord of this circle, while we should divide it by the arc. I may be wrong however.

[flying fish]

You are correct, for some reason I forgot about that. I'll think about it more when I get home from work if someone else hasn't figure it out by then.

 

I would think if your stars are small enough it wouldn't make too much difference.

Edited January 9, 2013 by flying fish

[Mumbles]

The math as AdmiralDonSnider mentioned is more complicated than that. The inserts do not touch at their center points. The following math works by essentially cutting the shell cross section into pieces of a pie, and determining the diameter of the circle (insert) that touches both the external wall and the pie "cuts".

 

I'm sure it can be reworked, but this takes the number of inserts and solves for the resulting diameter of those inserts. You just need to plug in numbers until you get approximately the diameter you want.

 

N = number of desired inserts

D = Inside diameter of shell

B = 180/N

 

Diameter of insert = (D*sin()/(1+sin()

 

You might need to convert B from degrees into radians depending on the program or calculator. I made a spreadsheet in Excel to do the calculations for me, and it requires radians for what it's worth.

 

There is additional math that can be done to calculate the diameter of stars for concentric rings. This is much more complicated, and I'm not willing to go over it. If you want to know how to do that, get a copy of PGI bulletin 42 from May of 1984.

[AdmiralDonSnider]

I found a useful and pretty instinctive calculator, no matter what mother tongue you have:

http://www.arndt-bru...kreissehnen.htm

 

I was under the impression that the inserts will always touch each other at their outermost point. This point divides the chord (of a given lenght=diameter inserts/stars) in half. All those chords form a polygon depending on the number of inserts.

The problem is essentially solved the way flying fish proposed, by calculating how much inserts will fit in a circle with a radius of (Shell ID-Insert diameter)/2. This question is the same as how many times an arc corresponding to a chord of a given lenght (=insert diameter) will fit in the diameter of a circle running through the center of the inserts. Given I got this right.

 

To keep things simple use the calc (link above): it requires you to specify r and s. S is the insert diameter. r is the radius of the circle running through the center of our inserts.

To exemplify using the values of the opening post, r= 25,5mm. When you type this and s in the calc, it will say that the circumference of this circle with r=25,5 is 160,22 and b (arc lenght) is 14,18.

 

Thus 160,22/14,18, i.e. about 11.3 stars per layer will fit in the shell. When one knows the height of the shell and the lenght/height of the inserts, we can calculate how much stars/inserts will be necessary to fill the shell in total.

The result of the calculations is quite similar to the one posted by flying fish, but only because in this case the arc is not much longer than the chord of the circle, which is not the case in general, depending on the properties of shell and insert.

 

May be terribly wrong however.

Edited January 10, 2013 by AdmiralDonSnider

[marks265]

This is all fine and dandy for me but I need to consider stars after they are primed and inserts when they are finished. How often do you hear of a 7/16" star plate? Usually stars or inserts are shimmed to make up any small differences. Big differences would lend to be a bad choice most likely. Inserts alone can vary in size depending on the builder and their materials.

 

I personally don't bother with calculators. I might set out some end discs and get a good idea how many might fit. After a few builds I pretty much know what will fit in a shell, especially for inserts. A little trial and error goes a long way for me on this one. It would take me more time to figure out if the math is right or not let alone what math functions to use. If I have them in my hand I know what will fit

 

Mark

[dan999ification]

snap, draw a circle, ( or take a disk ) and lay stars on top, simples..... But not academic.

 

Dan.

[nater]

Mark and Dan, I am with you guys. In less than the time it would take to do the math, I can lay out some stars on a disc, or draw a circle the size of inside of the shell on a piece of paper and figure out how many stars or inserts will fit in each layer. It isn't precise, but how many people make exactly enough stars for a shell anyway? Assume I need 44 comets for a shell, I will probably make at least 50, most likely a few hundred.

[pyrojunkie]

If you're a member of Passfire, there's a calculator for figuring this out in the "Reference" section.

[AirCowPeacock]

But it won't tell you what size you need for a perfect fit with a particular number without copious amounts of 'guess and check.' And I certainly think math would be faster anyways, as long as you have a half decent calculator.

[nater]

With all the components being handmade, there are too many variables to achieve the perfection that you would get on paper. Prime thickness, shell and liner construction, differences in the strawboard hemis, slight OD differences in insert tubes, etc... Make your layers of stars or insterts and use shims or adjust the thickness of the lining so you get a good fit.

 

And again, who makes EXACTLY enough components for one shell anyway?

[AirCowPeacock]

But it won't tell you what size you need for a perfect fit with a particular number without copious amounts of 'guess and check.' And I certainly think math would be faster anyways, as long as you have a half decent calculator.

[Mumbles]

You're never going to get a perfect fit anyway. Trying to do so is borderline idiotic, and very OCD. Just use shim and quit trying to make things more complex than they need to be. Trying to get a perfect fit is a great way to mess stuff up and have to start over. Comets and inserts never come out with perfect outer diameters, so it's a fools errand to try to make them have a perfect fit. I made a spreadsheet, and use it occasionally when trying to plan things out. Very quickly, you learn and know just how many inserts it takes to fill a shell of a certain size. I still only use 3 or 4 sizes of inserts, and maybe 5 sizes of comets for shells from 2" to 12". It's helpful for me at least to have a rough idea how many inserts/comets I need, and to plan out complex shells where I know what I want to do. Paper and disks work fine, but I can type in 2 numbers and it spits out the answer for me, and I don't even have to put down my coffee to do it.

 

By the way, the Passfire calculator uses the same math equation I just posted up above. I can try to explain what it means physically if you'd like. Trust me, it's the right formula. All these other approximations and methods of trying to figure this out are just more complicated ways of figuring out the same thing with the same or less accuracy.

[VickeA]

Thanks for all the great help!