best chamber to barrel ratio

okay I have not built a cannon yet as such, as I am going to make my first one awesome but I've done some research and found the golden ratio for efficiency for chamber-barrel size, assuming the chamber is always the same volume a chamber is 1.6, now I'm guessing a bit from now on but it seems that that maximum efficiency is approximately 1.61803399 or the golden ratio that keeps appearing in our world, I just thought you guys would like to know for the design stage as this is what I'm going to be using when I make my gun. also is it worth spending extra for a high flow blowgun over a normal one for the pilot valve to my 1" sprinkler or wont it make a noticeable difference P.S. if my calculations are wrong please, if you know more ( I'm only 13) please correct me. I have worked this out from pneumatics, not combustion's or hybrids. expect to see my gun soon!

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Lftndbt8 years ago
No a high flow blow gun will not help much. It is only a very small volume of air you are venting. So no.
Lftndbt Lftndbt8 years ago
In regards to you post. Assuming you are only going to 70PSI your formulae is adequate. However I operate a cannon which has a chamber size only half that of the barrel. At 70PSI it does not function optimally. Yet at 170PSI it is another story completley.
cheeseboy (author)  Lftndbt8 years ago
thanks I will spend the money I save double sleeving the chamber, thanks for confirming my maths.
NachoMahma8 years ago
. Intuition tells me that chamber pressure will have an effect on the optimum ratio. Maybe not.
cheeseboy (author)  NachoMahma8 years ago
this is the max efficiency for 2 chambers of the same pressure and volume of air at 70 psi say you had a 1" barrel and 3" chamber it wouldn't be as powerful as a 1" barrel and 1.5" chamber but the chamber being longer so as to have the same volume, thanks for the comment I should add that I found this at 70 psi and have yet to try efficiency for higher or lower pressures because I was only going up to 70psi as that is when my safety valve starts regulating the pressure, I would take it higher but my parents wont allow it