How would I figure out the proper gas port hole diameter for a barrel?

[pizza654]

Hi as most of you know who are in the gun community a bunch of AR 70/90 kits came into the country and theirs still no barrels or receivers in production. Since I cant find anything I decided that I'm just going to make my own barrel and I've found the measurements from a guy on reddit who lives in Italy. 

 

https://imgur.com/gallery/WUtxuAP

 

https://imgur.com/gallery/1ydhDUS

 

As I was getting the measurements a curiosity ran through my head, how do you mathematically figure out the proper diameter of the gas port hole for the gas block in the barrel?

 

Much help will be appreciated! 

 

 

[Miroslav]

You send your nerdiest engineer to go do some theoretical calculations while you stay in the workshop and mount the barrel in a press drill and put a small hole in the barrel. If you can't get the rifle to function properly, then you put the barrel back into the press drill and use a larger drill bit. Repeat until the rifle works properly. You'll be done before the nerdy engineer.

I too look forward to a theoretical answer, but in practice, fluid dynamics are very complex and I'm sure that most gas operated firearms developed during the 20th century had a lot of empirical iterative development to get the working right. Engineers are not scientists - everything is done within the scope of a development process were results are more important than a scientific lab report. It is often the case that it is more rational to find the answer by experimentation rather than theory. Of course it helps if you have some theory to start off with when you pick your first drill bit, or when you design the gas piston and cylinder that you intend to screw on to the barrel, but my bet would be that the engineer with the press drill finds the correct answer before the engineer with the calculator.

[pizza654]

Interesting response if your still curious I found this!

 

https://digitalcommons.lsu.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=4746&context=gradschool_disstheses

 

[Collimatrix]

Chinn has this to say:

 

"If it were possible, it would be highly desirable to be able to compute exactly what size and shape of orifice should be used, or to know in advance how the configuration of the passage leading from the barrel to the gas cylinder will affect the variation of the cylinder pressure with respect to time.  Unfortunately, accurate solutions to these problems and to problems of a similar nature can not be obtained analytically because of the complexities involved in predicting the flow of the turbulent and high velocity gases produced by the propellant explosion."

I suspect that such analysis could be done today with computer voodoo, but that for the vast majority of existing gas operated designs, the engineers applied some rules of thumb to get themselves close, and then iterated from there.