- Oct 18, 2003
- Saline Michigan
Yes, you apply the torque to the stiffness centroid. But finding it can get fussy in a composite structure.But at which point it is applied ? Or shell i apply it to stiffness centroid ? ~ at main spar .
The fussy part? In a structure all made of the same material, yc = Sum(Ay)/Sum(A). In structures with varying E's, yc = Sum(EAy)/Sum(EA)... In UNI Glass spar caps, E is about 4.4M, while the +/-45 skin is about 1.8M. Want to work with Graphite caps, the disparity doubles. The easy way to look at it is any unidrectional elements look like they are a multiple of their actual areas. Let's bite it off one piece at a time:
Most of our wings have things cut out of the trailing edge - flaps and ailerons - so the wing skins go from about 0.00C to about 0.75c, with the lower skin wrapped back up to the bottom of the top skin as a drag spar and to close the aft edge. Under those circumstances, I have done piecewise calcs of my Riblett 37A315 and found the skin centroid to be 0.38c aft of the leading edge and 0.02c above the chord line (as stated in post 254 above).
Spars typically have caps of unidirectional material and wraps and webs of +/- 45. Symmetric rectangular spars have their centroid about their middle. I prefer symmetric caps and channel shapes, so mine have the neutral axis in the middle of spar, but the fore-aft line will be shifted to the web side. Good first estimate for a symmetric spar will be to just use the visual center of the spar. Some folks find asymmetric spar caps to be appealing, in which case a downtown job on all this will first require finding Sum(EAx)/Sum(EA) in both axes for the spar.
Most of us working in composite wings are working in Laminar Flow foils. Max thickness runs in the .35c - 0.4c range. The Riblett 37A315 has max thickness at about the centroid of the skin, and conveniently, also the place where you could fabricate your lightest spar. Hmm. I suspect that for running basic models to see what is possible, you could just call it 0.375c aft and 0.02c up. If ,however, you are running a more traditional foil with the spar at 0.25c, you will have to do the Sum(EAx)/Sum(EA) to find total centroid. This also requires some spar sizing to get in the ballpark. I have discussed this elsewhere on hba.com. Rule of thumb: size caps to carry bending moment; Size web to carry shear; use your favorite multiplier greater than 1.6 on the web and cap areas; Make sure everything is wrapped in two plies. This will probably do for the current exercise, but for final design a more thorough check of failure criteria, iteration for low total weight, and manufacturing ease are all in order.
Some folks find using an equivalent G to be convenient. J for the wing section with a spar is then Sum(GJ)/Gskin where Gskin is the shear modulus (Q66 in composite parlance) of the skin material and the other G's vary with the material and fiber orientation. After that, yes, tau = Tr/J, and r is how far the point being looked at is from the centroid of the composite system. When you first get started, composites can make you nuts, but after a while it becomes normal for you, and your friends just think you are nuts... Oh, and Excel is your friend in all of these calcs. If you want I will check your math. Send functioning Excel spreadsheet files. We can communicate on PM.