It sounds like you are on to something here! We never tried larger than 1/8" x 1/8" legs. I'm pretty sure most people thought the opposite. We even tried 3/32" x 3/32" once. The idea that you make it bigger to make it lighter and stronger is somewhat counter-intuitive to most people.[/quote][quote="Balsa Man
Yeah (on the 5/32nd). For example, on our B tower, in 1/8. best stick > our design buckling strength was 1.22gr/36", w/ 110% of design BS. In 5/32, best is 0.97gr/36" w/ 120% design BS.
At the same density, going from 1/8 to 5/32 increases weight by a factor of 1.56, while "I" goes up by a factor of 2.44.
Yup, its another example of how understanding the mathematical relationships that are.... in play is the key to optimizing design; where those relationships come from, how they... work.
Looking at the 3 key factors in Euler's buckling equation - buckling strength = E x I/effective length squares
The most important one is the inverse square relationship of buckling strength to length- it tells us that if a member (under compression loading) is made a bit longer, buckling strength falls off a lot, and the other way around, shortening a bit increases strength a lot.
Then when you look at E, the modulus of elasticity, its a linear relationship, but not 1:1; if you double the density, E goes up by around 2.25, saying higher density is... more efficient. A critical factor/relationship in the data of how E varies with density (that old Forest Service study) is the variability; there is a trend, but individual sticks vary around a mean. That tells us that if you have/look at a number of sticks at a given density, some will be stronger than others. You'll see a bell curve for strength vs weight- a few really weak, most in the middle, a few really strong. The further out the 'good end' of the bell curve you get, the higher performance of the stick.
And when you look at I (second moment of inertia), which, as you know, for a square is d (where d is the dimension of one side) is d to the fourth x12, it says a small increase in d gets you a....significant in crease in I, hence in buckling strength. When you run these numbers for 1/8 and 5/32, at same density I goes up more than the weight does. (x 2.44 vs 1.56)
The limitation lies in the fact that balsa has a bottom limit in density; only so light. At the loads on towers, 5/32 at pretty darn near the minimum density balsa exists in, gives you the needed buckling strength.