Flat pattern
I'm not sure exactly what you're asking. If the reddish dashed Arcs are to indicate that the ends are circular, and if you're talking about rolled-out-flat sheet-material shapes for the surfaces of this kind of thing:
then the top and bottom sections should not be too hard, with a sine-wave edge where they meet the middle section, the same as with a 90° elbow. But the "conical" middle section is not just conical. It's an elliptical cone [I made the 3D version by LOFTing between Ellipses at the bends, drawn on the faces of Sliced Extrusions from the circular ends].
Is my assumption about what you're after correct?
Here's a process for creating the deleopment pattern for the truncated elliptical cone.
Start we a 3D solid model of the cone and create sections every 15° for one quarter of the shape.
Create 3DFACES (of 4 vertices each) from the sections.
Mirror the 3dfaces to yield the full elliptical cone.
Use align to place the entire "faceted" shape so that one panel (cyan) is flush with a rectangle. Then use align to reposition all but the first (cyan) panel such that the second panel is coplanar with the rectangle. The process is repeated but with one less panel for each alignmnet. Here's the model after 3 panels have been algned.
After 8 panels have been aligned it looks like this.
After all the panel have been "rolled out" it looks like the following.
Fitting a spline through the edge vertices we have the final development.
I had some time this morning to do some checking on my last post that I did late last night.
Here are the templates for the development.
The developments for the truncated cylinder have a sine function profile for one side. To simplify the construction I have a 180° sine curve drawing file with a period of 1 and an amplitude of 1. It has 4 CVs and is very close to a true sine curve. It looks like this.
To use it I create a block from it and then scale it in x and y to meet the requirements of the drawing. For the bottom pattern the period is x = radius * pi = 1 * 3.14159... , and y = 2 , (2.81 -0.81).
The development for the truncated elliptical cone is pretty close. The width at the major ellipse axes is right on at 2.39. The width at the minr axes is sightly off with a value of 2.35. This should be closer to 2.32. The development was create from panles that were inscribed wthin the solid shape. Better results could be achieved by using panels that used an effective value between inscribed and circumscribed elliptical radii.
This was an interesting challenge.
