News New Math?

Bareb0nes

New Member


with the luff and foot spars at roughly 13'8" each , the leech could not be over 12'2.52" in order for the sunfish sail to have an area of 75 square feet, unless the area of a triangle is no longer 1/2 bh (base x heighth). Most of the diagrams of the sunfish sail show the leech to be about 1.08 (x) the length of the foot(or luff, being the same),for a length of 14.76', which would put the actual area of a sail at around 84.94 sq.ft. My question i guess would be: is the calculation for the sunfish sail area determined by some new math?
 
You are correct that the formula is 1/2bh. However the height is determined by length of the altitude - a line that
is perpendicular to the base. So, it is incorrect to multiply the length of the foot by the length of the luff.

A Sunfish sail is probably an equilateral triangle or close to it. That formula is ((3^(1/2))/4)*S^2. Where S is the length of any side of the triangle. See this link:
http://www.mathopenref.com/trianglearea.html
 
Also, when you lay out a racing sail (not sure about a recreational sail), you will see that none of the edges are straight which will cause the use of any triangle formula to give an incorrect value. Regardless, to use a triangle formula, the height must be calculated based on the altitude to the base.
 
i didnt multiply the sides.......i dropped a perpendicular down from the head to the leech..actually area is area regardless of where you drop the perpendicular......if the luff and the foot are both 164", and the leech is 1.08 times that, (roughly), that makes the leech 177.12, which divided by 2 comes to 88.56. 88.56 squared plus the heighth of the perpendicular squared should equal the luff squared. the luff squared is 186.78'. Subtract the square of half the leech.(54.46')=132.32, the square root of which is 11.5' that is our perpendicular. one half the leech times the perpendicular is 84.87 square feet........am i wrong?
 
additionally , if anything ,the area in reality should be MORE. as the leech is the only negatively rounded side and not to the degree that the positive round percentages of both the luff and the foot contribute, i'd imagine
 
Well the leech length takes AWAY from the area. It IIRC curve toward the luft which would decrease the area.
Sunfish recreational sails have measured in at 75 Square foot since the first sails were bought by Alcort from Old Town that were used on their sailing canoes back in the early 50's.
Racing sails measure in at again IIRC about the 84 sq ft you figured. But it's a function of the draft of the sail providing more area not just it's "flat" area.
Maybe someone from a sail loft will drop by and do a technical explanation of measuring in sails.
 
Thanks Mike, that's really all i needed to know. I'm actually a sailmaker, and draft, camber, round ,etc, are actually measured by use of integration, or by manual use of a planimeter <archaic, and now by computer. My purpose here was to illustrate to those unaware, that the sail area described in every sunfish specification sheet is indeed wrong. In order to have the modern sunfish sail be 75sq.ft. one would have to cut a chunk of cloth 3'x3' out of it to make it that.
 
lol, dusts off my old planimeter to measure leech hollow and luff/foot rounds.......better yet...use the old simpson's rule(not homer)., as an easy way out of painstaking integral calculus!
 

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