A really fast surface area experiment. Total guesses at all of the dims, but these are they:
24.00 long
Ø.308 cylindrical hole.
Ø1.06 X 2.00 long Tenon
Ø1.25 max diameter at shoulder, no straight/cylindrical section, tapers from there to muzzle
Ø.875 muzzle diameter, 90° flat crown
carbon steel
R.1875 flute "cutter"
Six straight flutes with 15° lead-in angle, Ø.750 minimum diameter (at bottom of the flutes), R3.00 transition radius, Straight portion of flute starts at 5.875 from breach and ends at 2.415 from muzzle, 25° lead-out angle with R3.00 transition radius.
I mention all of this detail in case someone else wants to see if they get the same results or not.
Unfluted it "weighs" 5.55 lbs and has a surface area of 105.02 square inches.
Fluted it weighs 4.45 lbs and has a surface area of 115.53 square inches.
By my math that is only a 10% gain in surface area. From messing around with these models it is very easy to make that number far lower as these flutes are pretty deep in a barrel contour that is pretty stout.
Next I looked at bending stiffness. I held the tenon fixed and put a 100 lbs downward force on the muzzle.
Unfluted exaggerated deflection diagram:
Fluted exaggerated deflection diagram:
Comparing the two peak deflection numbers the fluted barrel deflected down ~.06" more than did the unfluted barrel. That's roughly 60% more deflection!
I have not had time to perform a reality check on these results. I trust the process, these just aren't quite the numbers that I was expecting to see. Assuming that these results are valid this says that a fluted barrel is NOT stiffer than the same profile unfluted barrel. I was expecting that unfluted would be stiffer, but not by such a large margin.