Pulley Progress and Static Stress observations and worries
I've built more pulleys and inserted ball bearings in them. That took a long time on my mini-lathe, but it was fun learning how to custom-make cutting tools and trying to be precise. FWIW, I overshot on boring one pulley and ended up putting in a larger bearing. That's what happens when you lose count of your thousandths.
Meanwhile, I've been breaking things in the name of learning. I decided I should quit pondering wing stress with my flap modification and do something about it. I had to go to basics. Beam theory, statics, and then material stress analysis. Etc.
I read a lot and found myself wishing I had gone on beyond the 2nd year in engineering school instead of switching to Soil Science and Music. But my fossilized brain started to catch on.
First, I decided to use the standard rectangular beam formula on various pieces of douglas fir I had laying around. I calculated the Moment of Inertia of each piece, stuck it in a big vice, and used a fish scale to bend them until breaking. Then I calculated the bending moments and bending stresses to compare them to the table in ANC-18. Pretty cool. Every piece I tried broke right around the modulus of rupture listed, plus or minus 10%. The pieces ranged from 1/4 x 1/2 up to 3/4 X 3.5. I did this to see if I understood how the formulas worked.
Interestingly, I tried it also on some 1/4 X 1/4 spruce scraps I had laying around. Both had some leftover epoxy on them, so that is a confounding variable. They actually broke at nearly 2X the listed fiber-stress limit in the table.
So, with that under my belt, I thought, "OK, let's look at these wood spars."
Ugh.... Front spar is .75 x 6.25. Rear spar is .75 x 4.5. I ran numbers different ways--tried point source loading, equal distribution loading, assumed center of lift at 20% chord, then 30%. Ran an Excel spreadsheet. Etc.
WagAero lists this 2+2 as having a 2200 pound gross weight. When I use that figure (one-half per wing), the numbers don't work unless I go with a 2.7G load and no factor of safety. It's supposed to be 3.8G with FOS of 1.5.
Scratching my head here, but all along I suppressed suspicions. The wing looks like a J3 wood wing, except the N-brace offers some rigidity. The numbers work out fine for a Gross Weight of around 1450.
To be clear, I was doing a very basic static load analysis--something I should have learned how to do long ago, but here I am.
Also, I'm starting to run numbers on aluminum spars and the larger ones from Carlson look encouraging. Still, I'm wondering if I'm falling into "fake engineer trying to analyze things" syndrome.
For the engineering minded, the basic problem is that at 3.8 G and 1.5 FOS, the bending moment at the lift strut is around 70000 inch-pounds. Using a moment of inertia for the 3/4 x 6 1/4 wood spar, [(a)h^3/12], I get 15.26. Then using the bending formula Bs=M Y/I, I get a result of between 10,600 to over 14,000 psi depending on where I put center of lift.
Spruce's fiber stress limit is listed at 6200. So, depending on angle of attack, etc., I think I'm over 2 times ultimate load at a 2200 gross weight.
Hmmm........
Not making me feel confident.