calculating traveller/sheet loads for square sails

[DeAnander]

I have been trying to figure out the force on the mizzen boomkin for my three masted traditional (square sailed) vessel, to spec a replacement spar.

Googling around I found Brion's article at the Harken site, which included a "traveller car load calculator" for Marconi rigs. that formula, if I've transcribed it correctly, is

(E**2 * P**2 * .00431 * V**2) / (sqrt(P**2 + E**2) * (E - X) )

where E is boom length, P is luff length, V is wind speed in knots, and X is the distance from the AFT end of the boom to the mainsheet attachment point.

anyway, I figured this was written for a Marconi triangular sail, so for my rectangular sails I should multiply the luff length by 2 (doubling the area so it approximates my square sail of the same boom length).

I ran this model for my 125 sf mizzen with a 12 foot mizzen boomkin, the object of the exercise being to figure out the force on the boomkin mount point (your basic cantilever beam problem).

I was surprised by the magnitude of the numbers I ended up with -- I was getting more force on the mizzen boomkin than on the mast at the partners, which doesn't seem right. surely the load on the boomkin can only be a fraction of the load on the mast...

I'm not good enough at the physics to figure out where the .00431 constant is coming from or how to tweak this formula for rectangular sails, so I appeal to wiser (or at least more mathematically literate) heads -- how would you rewrite this formula for squaresails?