Modeling the Center Wing

On the first glance the SBD center wing section seems to be a simple rectangular (i.e. constant chord) wing, with modified leading edge (Figure 18‑1):

Figure 18-1 Center wing section — the basic shape

However, the landing gear openings visible on the photo can be difficult to recreate in a mesh smoothed by the subdivision surface modifier.

Additional photos from one of the SBD restorations made by Vulture Aviation in 2012-2013 reveal that the fuselage was mounted on the top of the wing (Figure 18‑2a):

Figure 18-2 Center wing section — further details

A part of the upper wing surface was simultaneously the cockpit floor. Note the rectangular cutout in the middle of the leading edge. The SBD had a small window on the bottom of the fuselage, in the space between the two root ribs.

On the photo of the bottom of this wing (Figure 18‑2b) you can see that these root ribs had a modified airfoil shape: it bottom contour has a straight edge from the leading edge to the main spar.

I started to form the center wing section by preparing the single curve of its external rib (Figure 18‑3). (I copied it from the root rib of the wing reference object, which I used during modeling of the outer wing panel):

Figure 18-3 Copying the basic airfoil shape

I think that creation of these large landing gear bays (as in Figure 18‑1) will require a lot of modification in the wing mesh. Thus I decided to separate the mesh fragment that contains these openings (from the leading edge to the main spar) into a separate object. (It is always easier to modify topology of such a medium-size mesh part, than the whole wing). To ensure a smooth, invisible seam between this forward and the rear part of the wing, I had to accordingly prepare the control polygon of the initial airfoil. I added an additional point on each side of the vertices located above and below the spar line (Figure 18‑4):

Figure 18-4 Preparing the root airfoil for splitting the wing mesh along the main spar

What’s important, such three points have to be collinear. The resulting subdivision surface “touches” the middle point of such a fragment of the control polygon, and it is tangent in this point to these two adjacent control polygon segments. (This is just one of the mathematical properties of the Catmull-Clark subdivision surfaces, which are implemented in Blender).

However, these four new control points altered the shape of the airfoil curve. Now I have to fit this shape to the original NACA-2415 airfoil of the outer wing panel (Figure 18‑5):

Figure 18-5 Fitting the modified curve to the wing airfoil

Fortunately, the Catmull-Clark curves/surfaces have another property similar to the NURBS: so-called local change. Their formula ensures that influence of a single control point does not exceeds two subsequent segments of the control polygon (two segments in both directions — see Figure 18‑5, right). It is easier to focus on the modified mesh fragment, when you know this rule.

Once the initial rib shape fits the outer panel, I can extrude it forming the center wing section (Figure 18‑6):

Figure 18-6 Extruding the initial airfoil into center wing section

To shape the leading edge I had to stretch a little bit the forward part of this mesh. As you can see (Figure 18‑6), I placed this new edge loop in the place of the wing root rib.

However, comparing the resulting object with the photos I discovered that the leading edge of the center wing section should have constant radius (at least approximately — see Figure 18‑7):

Figure 18-7 Constant leading edge radius (observed on the photos)

In this way I have found another error in my reference drawing: the wrong      shape of the root airfoil (Figure 18‑8):

Figure 18-8 Another inaccuracy in my drawings: leading edge at the wing root had different shape

The tangent direction at the wing spar differs from the direction estimated on the drawing, thus the bottom, straight segment of the root airfoil has a slightly different slope. The leading edge is much thicker than I draw on these plans.

Adapting the well-known von Moltke’s sentence: “no plan survives contact with the enemy” to this situation, we can say that “no scale plans survive contact with their 3D model”.

I created a first approximation of the main wheel (it lacks the details) to check if it fits into the space between the leading edge and the main spar (Figure 18‑9):

Figure 18-9 Separated part of the center wing section

When I was sure that the shape of the wing is OK, I separated the forward part of this mesh (by splitting it along the main spar). As you can see (Figure 18‑9, right) these two parts join in a seamless way. It was quite simple to prepare such an effect in the initial curve by adding additional control points (see Figure 18‑4). It would be much more difficult to introduce similar modifications into the extruded mesh.

If you want to learn more about properties of the Catmull-Clark subdivision surfaces, as well as the details of the modeling workflow, see Vol. II of the “Virtual Airplane” guide.

In this source *.blend file you can check all details of the wing presented in this post.

In the next post I will create the opening for the landing gear.