The last couple of weeks have been hard: I had to revise the calculation of the loads and adapt the structure. I started with integration of the distributed loads to get the primary stresses in the spar and the forces at the joint of wing and center section. It sound easy but it isn’t!
As mentioned in my last blog entry, a huge problem is the sweep back of the wing. It makes integration of the loads more difficult to conduct and has some potentially problematic side effects on the structure. I have in particular changes in direction of the spar caps in mind. More on that later …
Sweep back has as a consequence that a portion of the torque is transformed into a bending moment. Thus, knowledge on the position of the elastic axis—also known as shear center—is a must. Below we see a graph with the position of the main spar and the shear center (yellow) assuming a usual D-box structure:
When a shear force is applied at the shear center, the wing does not twist. It is also the center of torsion, which means that the wing tends to turn around that point when a pure torque is applied to it.
From the above figure, the shear center is slightly in front of the spar in a D-box structure. The reason is that the nose is a shear web which stiffens the structure shifting the shear center slightly off the main spar.
That’s alright for some wings, but the structure of Schneewittchen is slightly more complicated:
It is a multispar structure with several shear webs. This has as a consequence that the shear center shifts slightly aft:
The reason is simple: The other spars have also shear webs which add some extra shear stiffness. It sounds strange, but torsional stiffness increases merely by having more than one spar. Anyway, having the shear center moving aft is good, because the main spar is more or less on the ¼ chord line— also known as aerodynamic center—for which torque is mainly produced by the pitching moment of the airfoil. The above figure shows also the position of the neutral axis (in orange), under the assumption that shear webs do not resist bending. The neutral axis is free of bending stress, and hence, is used as a reference for calculation of bending stresses.
The whole process is iterative, as the size of the spar caps affects both the position of the shear center and of the neutral axis, which in turn affect the amount of torque and of bending moment. Doing it a couple of times delivers following distribution of shear, bending moment and torque:
The bending moment creates bending stresses in the spar caps, which produce axial loads in them:
So, finally I have some values to work with. The axial loads in the spars are shown up to the joint between center section and wing, because this is the place where the main spar makes a kink and loads have to change direction:
Spar caps resist only axial loads, which means trouble at the joint. Consider the extreme case of a 90° change of direction: The full bending moment is transformed in a torque. This is how a wrench works! Not to forget, the main spar is subjected to a bending moment of much more than a couple of Nm: It is rather 18’000 Nm (13’300 ft lbf). Such a high torque would be very difficult to resist. The good news are that the kink is only about 25° and it produces a torque of “only” 2’800 Nm (2’000 ft lbf). This is trouble enough, as it results in transversal loads of ±7’600 N (1’700 lbf) at the main joint …
This loads are equilibrated by the mass of the pilot and structure. For this to properly take place, the structure needs to be suitably designed. First things first, one needs to have a good load plan:
I’ll probably be busy with this scheme and with the layout of the structure the next weeks …