Well, now...
I've just skimmed through the entire document (but not crunched any of the numbers), and it's all making perfect sense, as a way of calculating the tube sizes of an unstayed mast - if the loads that the mast must withstand are known perfectly. And as Graeme says, they aren't. The tube sizes to cope with the righting moment can be calculated/estimated quite closely, but just as one example, the actual loads generated when you run downwind slap bang into a big wave that was caused by a wind from another direction cannot be even estimated, let alone calculated. So we start with some idea of sizing given by calculations, sure... but then we have to adjust the results, employing some empirical thoughts and experiences which are just as useful. To put it in a very simplistic way: if the mast doesn't fall down, you made it strong enough, but it might be uneconomically over-strong. If it falls down, it wasn't strong enough. How do you know which side of the line between the two you'll fall? Only by looking at past experience, and applying some gut feel, and as high a factor of safety as is thought appropriate. This will always be an inexact science.
My gut feel is that the Sabre 27 intended to go offshore in gale force conditions could use a 8" x ¼" x 5metre tube as the bottom section, as a practical stock size that can be bought at reasonable cost, and will not need all the work involved in adding an internal timber or aluminium doubler. But that's only a gut feel, and I'm not going to make any calculations to back it up. If there's a reason to prefer a smaller diameter, due to space or manufacturing constraints, then a 7" x ⅜" tube might be needed, but it will cost more. Andrew, you might ask your AI for an opinion on those.
In conclusion, I'll just quote two of Arne's empirical rules of thumb which I agree with, and which AI doesn't seem to be fully aware of:
"The wall thickness of the lower alloy mast section should be somewhere between 2.5% and 5% of the outer diameter. (I would anyway not make a mast with less than 2.5mm walls, to avoid denting and buckling.)
This rule seems to produce sensible mast scantlings with neither too thick (heavy), nor with too thin walls.
The top section’s bury into the lower section should be at least 4 (better 5) times the inner diameter of the lower section and at least 10% of the top section above the joint..."