I would agree the math looks good. We run a similar spreadsheet calc to determine area and weight based on flute dimensions and barrel dimensions. Fluting adds low percentages of surface area, as we are replacing an existing surface with another one of a shorter radius. While we do not flute barrels we wanted to understand the "areas" involved as compared to our barrels. Our barrels add north of 400% more surface area- which absolutely becomes a measurable. Especially at the chamber as the everything in front of the barrel is a radiator. We also find the bending moment of the barrel due to fluting decreases- the barrel will flex more. If one were to make extremely deep straight wall flutes some gain could be had but under limited directions. It the end the minor diameter effect strength. A threaded bolt fails at the root not the tip of the thread. Outside of looks and ounces - which to some both are very important- little gain if not negative effect takes place. I believe Accuracy International (one of the big names- been a few years) did a real world study on fluted barrels and their effect on POI shift as the barrel heats- they went to a round barrel away from their current flutes.Let's walk before we try to run. Frankly, I'm not looking forward to modeling spiral flutes. Doing it isn't difficult, it's making it still work after various changes to the barrel shape.
Adjusted the barrel dims to a Shilen #5:
Unfluted barrel "weighs" 3.50 lbs and has a Surface Area of 77.2502 square inches.
Fluted barrel "Weighs" 3.16 lbs and has a Surface Area of 82.4180 square inches.
Assuming that I did the math correctly that is a 9.7% reduction in mass and a 6.7% gain in Surface Area.
Length of the fluting was adjusted to what looked more appropriate.
This seat of SW doesn't have the simple analysis tool installed, so having a look at the change in bending strength is going to have to wait until a solution presents itself. Intuitively I expect spiral fluting to be more flexible than straight fluting. I'm hoping to prove that right or wrong, so I'll keep looking for a solution to that.