I think I have figured out a good way to find a reference point biased the barrels original configuration.
If you see a problem with the theory, my equations, or estimates please let me know
Though this looks complicated I assure you it really is not, its just long-winded...
We know that the barrel (which includes the gas port) has been engineered to function properly at the standard 20" length.
The function of a properly engineered gas system is to apply the appropriate "power" to cycle the bolt/carrier assembly.
So here is the math:
The rate at which energy is added to a system (energy divided by time) is called power. (Mass is represented by "m" Velocity as "v", Time as "t", and Force "F"). With mv divided by t, power becomes force only (mv/t = F). With ½mv² divided by time, power becomes force times velocity (½mv²/t = Fv).
Now we can call most of the properties we are working with constants :
Which is to say that they are unchanged by the decrease in barrel length past the gas port.
The bolt assembly still requires the same force (F) to cycle it, the pressure in the barrel at the gas port is unchanged because the volume of available gas exceed that required to supply the appropriate mass (m) , the velocity (v) at, and acceleration of the bullet and gasses past the gas port for the duration of time the bullet remains within the length of barrel to the point where the shorter barrel terminates.
The only part of the equation we need to solve for is time (t):
To figure out the difference in time that force is being applied to the bolt assembly between the two configurations is a mater of determining the velocity and rate of acceleration of the bullet starting at the point where the shortened barrel terminates and ending at the point that standard length barrel terminates this product is the amount of time it takes the bullet to travel the difference in barrel length. This could potentially lead to a bit of math so lets take a shortcut, I have looked at a few test charts and it appears that a 4" difference in the barrel at these lengths only amounts to a about a 5% difference in terminal velocity. Where terminal velocity is only reached literally at the point that the barrel terminates and takes the entire 4" to accelerate to that point (this amounts to a negligible difference as it is within "commercial accuracy" and there is greater variation in the different ammunition the rifle is designed to fire)
What this means to us is that you can simply divide the length of the barrel that extends beyond the gas port on the shorter of the two, by the same measurement on the standard barrel (which is 4" longer) the product of this equation is the difference in the value of (t)
By decreasing the value of (t) as it applies to the difference between the shorter and longer barrel configurations we can solve the new value of (m) while retaining the constant value for (f).
Now we know how much we need to increase the value of (m) to apply the proper (f) to cycle the bolt assembly in the (t) we have available.
We could discuss port dynamics at this point, however it once again could lead to a bit of math and unless I am mistaken the variation we would find would also fall within "commercial accuracy" best of all this variation acts opposite the the one we allowed in figuring (t) (meaning they actually work together to help cancel each other out, making the end product of the two estimates more accurate not less)
Because the pressure inside the barrel at the gas port is unchanged we simply increase the aria of the port opening relative to the difference in the value of (m) between to two configurations (which is directly proportionate to the change in the value of (t))
Important note:
We are changing the value in the aria of the opening. (though this will obviously reflect as a change in diameter "aria" and "diameter" are not interchangeable in this equation) so we will have to do some math: πR² to find the aria of the opening biased on its diameter.
I ordered the barrel today so I don't currently have the diameter of the gas port handy, but once I do I will use it to illustrate the equation including the aria translation of the factory port diameter, the total aria after the required increase, and its conversion back into the new diameter.
I am going to conclude with the statement that this (in theory) should be fairly accurate however I still plan to start with a port diameter smaller than that provided by this equation, for the simple reason that if the theory or equation are flawed and you end up with too large a port you can't just make it smaller...