Patience …

… is a gift and usually pays off.

The rough XPS core of the cabin is ready to cover. I hoped to be able to use few pieces of abachi veneer to cover it, but it turned out to be impossible. Thus, I remembered a technique I’ve used several times in rc-models. The basic idea is to use small strips of wood to cover the spherical surface. Take for example the prototypes I made for the S12 (1:6), the Beluga (1:4), and Schneewittchen (1:4):

IMG_0013_s

IMG_9523_s

P1030081_s

The principle is always the same: Use thin strips to cover the surface.  If you try to cover a spherical section with a large sheet of abachi veneer, balsa or plywood, you produce huge shear loads in the sheet and most likely you’ll fail to get a good surface. The reason is that spherical surfaces have gaussian curvature. It’s very easy to cover a cylinder or a cone, because these lack gaussian curvature: Cones and cylinders are curved only in one direction, whilst the other is straight. This is not the case for the cabin of Schneewittchen, which has for sure gaussian curvature.

I used the same technique. The difference is that I have to prefabricate the curved venner sheet before it is cemented under pressure to the XPS core. This is how it looks at the moment:

There are still a couple of few square meters to cover. Though it will take a couple of days to finish, it is a nice relaxing job which is best done with some music, and of course with plenty of patience.

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Taming the beast

„The beast in me
Is caged by frail and fragile bars
Restless by day
And by night rants and rages at the stars“

Johnny Cash

 

Halloween

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:

holme_biegen

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:Struktur

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):

struktur_zeichnung_geschnitten2

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!

verbindung_holme

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.

schubmittelpunktThus, 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:

P1100347_m

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:

P1100346_m

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…

 

Long rainy weekend

„Anstrengungen machen gesund und stark.“, Martin Luther 1566

It is a grey Sunday with lots of wind and rain. Perfect for building Schneewittchen. Tuesday is the 500th anniversary of the reformation day and, thus, an exceptional holiday in Germany. Happy those like us who can take Monday free and have a long weekend. Having a couple of free days does not mean that we bum or laze around. It is pretty much the contrary: We have finally time to do a couple of things on Schneewittchen that take longer.

Yesterday was a bad day. I thought we could quickly machine a couple of pieces for the next prototype of the elevon mixer. It turned out to be a mess ending in a broken milling tool—a 4mm solid carbide one-flute and by the way one of my favorites—and another shiny new solid carbide tool clogged. You can imagine I was not amused! This is the miserable rest of the one-flute:

P1100334_m

Heartbreaking! I did not fasten the material correctly and it started to oscillate at some point. This loss is my fault, but how it came to the clogged tool is not explicable…

Anyway, I finished the pieces and adapted the elevon-mixer:

P1100335_m

In contrast to the last version, I used two spherical bearings this time (less parts and a less complicated setup). Tightening the bolt on the left in the picture, which fastens the plate on the stick, results in a tighter fit of the spherical bearings. So this setup has some more friction than the last one, although the bearings run very smooth before installation. This shows that their internal clearance is small, which decreases slackness of the controls and is good when not excessive.

Today was, besides the weather, a great day. We started to cover the cabin’s plug with veneer. It was not the surface, but the bottom of the plug:

Sanding the border is much easier when it is reinforced. This is in particular true for the thin tail, which would else be pushed away when sanding. We used leftovers of abachi veneer and glass fabrics (feels like 80 g/m²). It will have to cure at least overnight before we can trim the border.

In one of the last postings I wrote that sanding the plug is a multiscale process. I made two pictures to show you what kind of scale we are working on now:

There is a change in curvature between the canopy and the aft of cabin. This is the kind of errors that need to be corrected at this step. It’s not about getting a perfect smooth surface. This kink has a large scale and extends over 25 to 50 cm (10″ to 20″). No veener in the world would make that disappear.

Nevertheless, not only large scale imperfections need to be corrected, as the plug has also many small defects. Some can be ignored and others would affect the shape even after covering. Large defects can be improved by glueing small pieces of XPS and sanding the surplus material. The following picture shows, for example, a larger dent which was improved as mentioned:

P1100330_m

That’s good enough to be covered with veneer. The glue used was specifically designed for XPS and EPS foams (UHU® POR). There are many more similar defects on the plug, which have to filled and improved before covering. The next days won’t get boring…

 

Second prototype of elevon mixer

Many hours of hard thinking and searching the internet for standard parts are behind this second prototype. The first prototype was a good proof of concept and showed that the mixer works, but it is far from being acceptable. Most notably is that it had way too much friction. Also the linkage would have never been able to take the loads up required by the regulations. The devil is in the detail, and this surely true for the control unit of an airplane!

An estimate shows that the axial load on the linkages is up to 1.5 kN (340 lbf) including a safety factor of 1.5. This load derives from the regulations, which assume that a pilot applies—probably in panic—up to 35 daN (80 lbf) of force on the elevator’s control stick. The force required for ailerons is smaller (20 daN, 45 lbf), but as we have both functions on the same linkage, the worst of both cases is decisive. Knowledge of the force is a must to properly choose the parts: spherical bearings, diameter of linkage, clevis, and so on. Originally we thought of using plastic parts by Igus GmbH, but we had to discard this idea soon, at least partially…

Igus GmbH has some neat parts, which are great for some applications. I’ve used some of their parts in rc-models, in particular their bushings. However, there are other applications, where their products are not the best choice: high loads and low friction spherical bearings. I learned a lot on these parts the last couple of days, and I would like to share with you the experience made.

Let’s start with their bushings. They are great as long as the fit has not to be too tight. They are easy to use and strong materials are available (iglidur© G1 with 90 MPa / 13’000 psi). These bushings could be great for bearing long control linkages (to prevent buckling) or to support small forces (e.g. at control levers).

P1100316_m

 

Clevis joints are the next pieces that are interesting for airplane controls:

P1100317

These joints have the usual shape defined by DIN 71752, but are made of robust pastic. They are very light and are maintenance-free. Depending on the size, they have a strength that is very well suited for our application (M6 size has 1.3 kN or 290 lbf). The depth of the opening is something you really need to consider. The standard defines two types: 12 and 24 mm (roughly 0.5 “ and 1 „). This might be somewhat tight, at least for us it isn’t enough. The bolts of the clevis have standard dimensions with good fit and can be combined directly with standard (spherical) bearings. Other companies sell similar aluminum or stainless steel joints. By the way, custom clevis joints can be very well machined of AW-7075 aluminum with a CNC machine.

Now we come to the spherical bearings. I my opinion the weak spot for our application. The bearings look great:

P1100319_m

P1100318_m

…but good looks is not everything. From the specification provided by Igus GmbH, they should be perfect for our application: rotating, oscillating and linear movements. After purchasing these, things look differently: The friction of the ball against the housing is high. It takes quite some force to change the direction of the ball. This is not really what be want for an airplane control, which should run as smooth as possible. So where’s the contradiction? Well, this parts are made for „rotating, oscillating and linear movements“ inside the bore of the ball. The ball itself is thought for compensating static differences in angle, not for bearing dynamic changes in angle. For our type of applications, one should stick to standard steel bearings:

P1100320_m

P1100321_m

These run very smoothly and are available in maintenance-free variants with PTFE membranes. The shperical bearings GE6UK above are maintenance-free, while the rod end bearings shown need maintenance (grease fitting). You should keep an eye on the maximum allowable movement angle. This is around 13° for M6 parts, whichi s not much when it comes to a control stick of an airplane. The angle can be extended by using thin bushings above and below the ball.

So, I guess you understand now why the second prototype took so long get ready: purchase a piece, wait for the surprise, purchase a new piece, nect surprise, etc. Anyway, we modified the first prototype to achieve a smooth runing mixer:

P1100322_m

Load testing will have to wait for another prototype with a wider stick!

 

Sanding the plug of the cabin

Besides optimizing the control mixer and working on a second prototype for load testing, I’ve been working sporadically on the plug of the cabin. The rough shape is there, but many necessary and essential steps follow.

The video on making a molded fuselage by The Arnold Company  is very inspiring and shows very well how much work there is behind a good plug:

I follow essentially the same steps, but decided to cover the surface with veener instead of glass fabrics. It’s going to be the same procedure as last time for the center section’s plug. The reason is that veneer smoothens somewhat and filling the surface should be easier. Enough abachi veneer is ordered and should arrive soon.

Before covering with veneer, the XPS core needs to be sanded. Finishing a plug is a multiscale process, in the sense that you start with a rough shape and in each following step you increase the quality of shape and surface. At the current step it’s not about achieving the best surface quality, but rather about getting the right shape without kinks in curvature. Surface quality is achieved later by sanding the veneer and filling.

P1100255_m

This picture remebers me to Ed Sheeran’s song Shape of You:

„Girl, you know I want your love
Your love was handmade for somebody like me
Come on now, follow my lead
I may be crazy, don’t mind me
Say, boy, let’s not talk too much
Grab on my waist and put that body on me
Come on now, follow my lead
Come, come on now, follow my lead

I’m in love with the shape of you
We push and pull like a magnet do
Although my heart is falling too
I’m in love with your body…“

 

 

 

 

Prototype of a control mixer

Having a cardan joint for the control stick, a mixer for the elevons was the next consequent step. There are several points to consider when designing a mixer:

  • proper deployment angles of at least ±20°
  • correct direction: „up“ and „right“ should deploy the right control surface „up“
  • comparable elevator and aileron angles (good starting point for a maiden flight)
  • negligible differentiation between up-down and left-right (differentiation should be set near the control surface up)

After a search in the internet, and in particular RC-Groups which had some posting on mixers including Fauvel- and Mitchell-wings, I came with following mixing principle (looking from top to bottom, up is front and top is aft of airplane):

steuerung

The movement of the control stick (top center) is translated to rotation of two levers (bottom left and right). The angle, distance between control stick and levers determines the kinematics. The behavior is non-linear, as a circular motion (lever roation) is coupled to a prescribed distance between control stick and joint at lever. Choosing the right layout is not obvious, but can be done using, for example, a CAD program by playing around. Just in case you are wondering, the angle between control stick and levers is pretty near but not equal to 45°. As I wrote, it’s not obvious…

So much on the theory. Last time we made the cardan joint for the control stick. This time we finished a prototype for the mixer. We started by looking for suitable parts in our workshop: a couple of standard radial bearings and some Igus GmbH plastic spherical bearings:

P1100245_m

The CNC-machining of AW-7075 aluminum worked like a charm! The complete mixer works as expected and looks like this:

P1100248_m

The proper mixing is exemplified in the following video. Note the symmetric rotation of the levers on „up“ and „down“ and the asymmetric rotation on „left“ and „right“:

Cardan joint works

After some problems with the spindle, we managed to finish the prototype of the cardan joint. The thread of the tool holder of th spindle was damaged and we had to get a one… Anyway, we learned a lot regarding the production of such a complex part: It needed more than 16 steps and some didn’t work out as expected. The result is more than good enough for playing around and testing a mixer:

P1100147_m

Here’s a video of it at work:

 

Next step is making a prototype of the mixer. The material for the levers is ready and waiting!

Back again: Machining a cardan joint!

The controls of a Horten are slightly different than those of a usual configuration. The ailerons are used for both pitch and roll. A consequence of this is that control inputs have to be mixed. There are several mixers around, but the one I like most is very simple:

Mischung_Steuerung

The movement of the control stick is converted by levers into either symmetric (pitch) or asymmetric (roll) movement of the control surfaces.

In usual airplanes the control stick is supported such that pulling/pushing acts directly on the elevator, while moving to the left/right pushes rods that are connected to the airlerons. This presupposes that the center of rotation of the stick is above the pushrods of the ailerons, which is easy to realize. See for example the ULF2 build log of Matthias Zahn:

http://zahn.flugmodellbau.de/holme/hlmbrken.html

For Schneewittchen’s mixer, the situation is slightly different. The connection between the pushrods and the stick is above the bearing. It has to have a small footprint to keep everything compact and small. So the callenge is to have a small cardan joint at the bottom of the stick. I designed a prototype for testing:

kreuzgelenk

 

Today we started to produce the first piece of the joint:

 

Last foam pieces on the plug

Two complex shaped foam pieces were missing on the plug. We used our new CNC machine to mill these:

Though the machine makes most of the work, a good sketch is always needed. And this isn’t easy. This is even more evident when  three dimensional pieces are milled. We used a mixture between QCad and FreeCAD to design the parts (both open source programs).

The piece at the front of the cabin was straightforwad to draw:

P1090155_m

P1090207_m

 

The piece at the aft has a very complex shape: It has on the top a cone shaped section, which is merged to something that looks more like a trailing edge of a wing. Drawing a good transition between these two quite different shapes is challenging. We, thus, decided to keep the piece simple but still providing the basic shape. We will sand it to its final shape:

P1090209_m