How does two-rail-sweep scale/interpolate intermediate sections?

Rhino Rhino for Windows
1

Hi all. I’m working on a model glider wing mold to be CNC milled and am trying to figure out the best way to create my wing shape. In the past I’ve used both 2-rail sweeps and lofts to create wings for this purpose, but as I’ve been thinking about it more (perhaps thinking about it too much…) I’m wondering if I’m distorting my airfoils inadvertently.

The wings I’m modeling have elliptical planforms (i.e. the leading edge and trailing edge shapes are elliptical). I have multiple different airfoil shapes that are located at intervals (“stations”) across the wingspan (5 total airfoils at 7 stations). These airfoils need to be maintained very accurately at the scale I’m working in order to perform properly. The airfoil shape at any point between the defined stations should be a linear interpolation of the two foils on either side of it. For example, the foil midway between station 1 and station 2 should be a 50/50 blend of the station 1 foil and the station 2 foil. At 1/4 of the way between station 1 and station 2, it should be a 25/75 blend of the station 1 and station 2 foils, etc.

It is less critical for me to follow the exact elliptical planform (wing outline) shape than it is to ensure that the airfoils are accurate across the entire wing. However, it is desirable for me to be able to control the planform exactly.

If I do a loft of the foils (placed at the right locations, with the right rotational relationship to each other) I believe that I will get an accurate representation of mid-station airfoils, but I don’t have direct control over the planform outline (I’m not certain about the mid-station airfoil accuracy statement - any clarification on that would be appreciated). If I do a 2-rail sweep, I have direct control over both the airfoils at the defined stations and of the planform outline, but I’m not sure what process is used to obtain the shape of the sections between the defined airfoil stations, particularly in situations where the planform is not planar (often the rear of the wing rotates up near the tip to create washout). My gut tells me that it’s possible the mid-station foils could be getting scaled/blended in a non-2D fashion that could change the airfoil shape. It’s also possible that a 2-rail sweep performs linear blends of the defined section shapes and then subsequently scales and rotates those shapes as required by the rails, in which case it should create exactly the surface I’m looking for.

Any commentary on how 2-rail sweep creates surfaces, or from others who do shape-critical lofts/sweeps is most appreciated. Please feel free to ask clarifying questions, and my apologies if this is hard to follow. I can post an example file if desired. BTW I’ve just signed up for this forum and am quite impressed - it looks like a very helpful community.

Thanks very much,

-John
Seattle

2

@lowell, can you help?

thanks,

-Pascal

3

Sweep2 does not use a simple linear interpolation between sections. If it did the resulting surface would have creases at sections rather than continuous tangent and curvature.

You could do some experimentation in Rhino. Create an wing surface using Sweep2. Then use Contour or Section to examine slices between your input sections to see if the resulting sections are close enough to your desired shape.

4

If you are not interested in following the leading edge and trailing edge with extreme accuracy then I wouldn’t use 2 rail sweep to make the surface. Use loft instead. With evenly spaced profiles I would use loft with the “uniform” style.

If you want to make a lofted surface follow the edges more accurately you can create additional intermediate profiles. Use TweenCurves to create intermediate profile curves.

For instance you could divide your leading edge and trailing edge into 6 segments and create 6 tween curves. Then you use Orient command to place those tween curves at exactly the midpoint of each edge segment. You will probably find you need to use the scale3d option in orient command because the distance between edges at the midpoint won’t be exactly half the distance.
This would give you 13 stations to loft which will follow along the edges much more closely than the original 7. 13 stations will give you about the same accuracy as rebuilding the leading edge and trailing edge to 13 points.

if you want to get even closer to the edges you can create 12 more intermediate stations and loft 25 profiles. Even with 25 stations you will get a simpler better quality surface than 2 rail sweep will give you.

-jim

5

With curved leading and trailing edges, except in special cases, the shape that connects the midpoints of those edges will be rotated in plan form the shape at the root and tip, so even if the scaling is proportionally accurate in 2d in the plane of the generated shape, when you look at a section through the wing parallel to the root shape, the scaling will stretched.
It seems like you would be interested in the sections through the wing that are in planes parallel to the flight direction and not parallel to the rotated planes sweep2 finds to generate shapes.