The object of this exercise is to figure out (in advance or post facto) how strong to build a mast or when to reef. The assumptions are: unstayed masts of circular cross section, junk rig (or lug or gaff or square rig) sails of approximately rectangular form, and worst case (sail jammed across the wind, unable to ease the sheets). You can change the mast diameter, wind velocity, mast wall thickness and mast height; you can make the mast tubular or solid. And you can set the wind velocity.
After defining the parameters of the mast, sail and wind speed, press the button to calculate the stress (in psi) on the mast material at the partners. This should tell you how close your mast material is to failure under these worst-case conditions.
CAVEAT I am not a marine architect, nor a mechanical engineer. I consulted mechanical engineers in the course of solving this problem for myself, and there's a reasonable consensus among us that the math is 'fairly good.' However I make no warranty express or implied, that this calculation is accurate, nor do I recommend that you use it to spec a mast or make other critical engineering decisions based on it, without doing the math yourself from first principles (which you'll find in mechanical engineering handbooks) and/or consulting a professional engineer (which is cheaper than replacing a mast).
This page is just for ballpark, back-of-envelope thought experiments, so you can explore questions like 'would it be reasonable to have 800 square foot of lugsail up on a 9 inch diameter Doug Fir grown pole if I could expect 30 mph gusts?' How much laundry you want to fly and soon you want to reef is your judgment call, but this computational model may help to inform your judgment :-)