bending 1x3s SOLAR.KnowledgePublications.com

bending 1x3s
5 nov 1996
here's a little calculation that might be useful for curved sunspace design:
it finds the approximate bending radius re and helps estimate the length le of
the 2 1x3s needed to make a spaced sunspace beam. picking a length la gives an
estimate of the actual effective bending radius; 10' seems like a good radius.
much less than that, and cheap 1x3's (10 cents/linear foot) tend to snap.
much more than that, and headroom and snow loading become problems.

10 h=8'height of an approximate quarter cylinder lean-to sunspace
20 d=10.75'depth of sunspace
30 c=sqr(h^2+d^2)'length of diagonal chord (use for prebending with a wire)
40 re=c/sqr(2)'approximate radius of bending
50 le=3.1416*re/2'approximate length of 1x3
60 print c,le,re
70 la=14'actual length of 1x3 used
80 rae=la/sqr(2)'estimate of effective radius of bending
100 ra=rae'save last estimate
110 rae=c/2/(sin(la/(2*ra)))'refine estimate
120 if abs(rae-ra)>.01*rae goto 100'iterate to 1%
140 print,la,ra' note: at ra = 8', 1/3 of cheap 1x3s snap, when bent.

run

13.40009      14.8838       9.475297
              14            12.38271

a typical beam might have flat 1x3 spacer blocks every 2', screwed between 2
12' 1x3s with 2" deck screws, with the bottom 1x3 sticking out (tab a) an inch
below a horizontal purlin serving as the last spacer, with tab a tucked inside
a pressure treated 2x4 staked on edge to the ground with 3' of 1/2" rebar
through a 5/8" hole every 6'. the top tab might stick out from another purlin,
and tuck under a 2x4 screwed flat along the wall of a house, with another 2x4
under that. a slightly diagonal center purlin is useful for alignment and
racking strength. the glazing can be very clear, long-lasting polycarbonate,
at $1/ft^2 in 49" wide rolls, or 3 year uv-stabilized greenhouse polyethylene
film which comes in much wider rolls, with some nylon twine stretched over
the poly from top to bottom between each beam to reduce wind fatigue.  

dr. erdos might have offered a dime for the solution to this math problem :-)

nick

dr. paul erdos died of a heart attack this spring at age 83, while attending
a conference in warsaw. he lived a celibate, monkish and nomadic life devoted
to mathematics. he had no home, lived out of a single suitcase and traveled
the world attending conferences and visiting mathematicians. above average
mathematicians might publish 20 papers in their lifetimes; great ones might
publish 50. erdos worked on mathematics for 19 hours every day, and was the
author of more than 1500 works. he received the immensely prestigious world
prize, at $50,000 the highest-paying award in mathematics. despite a spotty 
income, he gave most of it away, offering $10 prizes for easy unsolved
mathematical problems, $100 for hard ones, and $1000 for impossible ones.
he defined the word "mathematician" as "a machine for turning coffee into
theorems." told by many colleagues to slow down, he always replied "there'll
be plenty of time to rest in the grave." he was 5'6" tall and weighed 130
pounds, with white hair, glasses and an unruly beard. he lived on a diet
consisting largely of caffeine, antidepressents and amphetamines. he was
a master of the japanese board game go.