„The beast in me
Is caged by frail and fragile bars
Restless by day
And by night rants and rages at the stars“
The „beast“ to tame here is not a kind of Halloween monster, but the structure of Schneewittchen.
If there is anything that makes the design of an all-wing aricraft special—besides their aerodynamics—it’s their structure. Sweep-back is a headake! When you build an rc-model, you just drop some elements into the structure, and voilà it works. When you are going to sit in that airplane and there are regulations in strength and weight to fulfill, things get really complicated. There is not a glance of being able to just drop some wood or carbon into the structure and getting it right. Either it’s not strong engough, or it’s too heavy.
A couple of postings ago I reportedt that I started to calculate the structure. Most headake has provided me sweepback and the implications of it. One of the largest problems is to account for the change in direction of the central spar. This kink in the main spar sheds a large torque, which tends to rotate it about the span axis and has to be balanced by the pilot’s weight. Sounds easy? Well not really, as this torque is considerably larger compared to the one produced by the wings. At the joint between the center section and the wings, there are merly 0.8 kN·m (590 lbf·ft) of pitching up moment produced by the wings. In comparison, the change in direction of the main spar produces a torque of -2.8 kN·m (2065 lbf·ft). The reason for this high torque is that part of the axial loads of the main spar are shed into torsion. The spar’s caps carry a huge axial load originating from the bending moment, and the kink has about 25°. Hence, about 40% of the axial load is shed into tranversal forces at the joint, while the axial load is only reduced by 10%. That’s what I call a bad deal!
Changes in direction are almost inevitable when there is sweepback. At some point the spar will have to account for the symmetry of the wing. We’ve build several rc-models and tested different structural concepts. Most notably is the structure of the Schapel SA-882 models we designed.
Large turbine acrobatic model:
Small speed model:
If you look carefully, you’ll see that the main spar is curved preventing localized changes in direction. Also, the aft spar is straight connected to the main spar, and builds, thus, a sort of triangular shape when seen from the top. This type of structure has prooven to be very stiff and strong. Take for exaple the flight of John Wright’s turbine rc-model he made from a kit we provided him with:
Or speed flights with the small one built by a friend from a kit we gave him:
So what’s all about the curved spar? Well, this is the best way to prevent strong localized changes in direction. The continuous change sheds constantly small amounts of shear which are taken up by the spar’s shear web. The aft spar adds a surplus of stiffness to the structure, in particular torsional stiffness.
The main problem with a curved spar is that it is not suited for demountable airplanes. Schneewittchen needs to be demountable and a curved spar is not feasible. The aft spar is fine. Here’s a scheme of Schneewittchen’s structure:
Essentially, the straight aft spar was kept and the main spar had to be kinked. Believe me, this kink has given me something to brood about…
The forces acting on the center section’s structure look as follows (ignoring the shell):
The change of direction sheds a large torque, which is mostly counteracted by the pilot’s weight (2×2kN) and the batteries (2×0,7 kN). The pitching moment of the wings also slightly contributes. The two beams on which the pilot sits cannot transfer a torque on the main spar, or at least they shouldn’t if we want to prevent that the joint breaks. These beams transfer up/down forces on the spars, but they also join the spars at the bottom. Hence, the main spar can be assumed to be fixed on the bottom but free to move on top. A rotating main spar is a really bad idea!
The above scheme misses that there is a rib connecting both the aft and main spar. This rib is very stiff to shear (fibres oriented ±45°) and prevents shear deformation. Any kind of rotation of the main spar would produce shear. Even more cleary seen, when we assume that there are stifferners between the spar caps.
Thus, a the torque will produce a rotation of the structures around the shear center of the section at the joint between wing an center section. The shear center is very near to the main spar, and the spars and the rib will try to rotate around a point inbetween the spar caps. This rotation means, however, that the aft spar will have to bend, as it is supported by the main spar at its ends. Violà, the weight of the pilot and the batteries pushes the aft spar down counteracting this rotation.
Let us recapitulate: If we have a shear web connecting the spars at the joint between wing and center section, the torque produced by kinking the main spar is converted into a bending moment of the aft spar and the masses in the the center section can balance the torque. Quite strange and not obvious.
So much on the theory. It’s sometimes easier to have a small model in which hypotheses can be tested. This is usual in many fields, such as in analysis of aeroelastic effects. In aerolasticity it is common to build models with realistic distributions of mass and stiffness (bending and shear). I built, thus, a scaled down version of the main structure to see how it deforms when loaded:
The video shows clearly how bending the structure produces a torque a the main spar and tends to rotate it about the lower spar cap. Torsional stiffness is also low.
Folloing the theory derived above, the structure should become much stiffer by adding the ribs at the joint:
Stiffeners were added between the spar caps to prevent these from buckling. We did not make a video of the modified structure, but stiffness increased substantially (also against torsion). Rotation of the main spar is minimal. The whole structure tends to slightly rotate about the bearing, which is good because this means that forces are flowing as expected between spars and the pilot’s mass.
We built another even more realistic mockup:
Adding shear webs to the spars made it extremely stiff and, thus, not suited for seeing how it deforms when loaded. Though not having a closed shell surrounding it, the torsional stiffness is exhorbitant. This are good news for Schneewittchen…