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Edit: I may be misunderstanding your question. All three of the shapes you are proposing are "flat bottomed", right?
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Yes. I put 'half body of revolution' in the title and showed full bodies in the illustration. In my defense I posted at 4 am. I realized at 2 am I wasn't going to sleep, so I got up and prepared the models. By 4 am, I was sleepy and didn't truncate them properly. I thought I scaled the square sectioned one in all three dimensions, but the length looks the same, so ??????
What I was getting at was if the frontal area is the same, and there is no air movement except out and then back into the center (i.e., no lateral movement that would lead to vortexes), would compound curves be necessary? Or would the simplified construction of the (half) square section carry an aerodynamic penalty?
What strikes me is that even though the superellipse is half way between the square and circle, it looks closer to the circle. That may be because I didn't subdivide the square section equivalently. There are a whole class of superelliptic curves, some would be very close to a square with radiused edges.
I understand that the underbody is a whole separate can of worms, until they re-merge at the rear.
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dang you! I came on here to post my pics of my latest CFD testing.
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ERTW -- Thanks for sharing. That is precisely on-topic. Consider it a preview and do your own separate post if you like.
Is the line at the bottom a ground plane or are they in free air? And if so, why do you think the stream-lines from the top cross the stream-lines from the bottom in the side view? Wasn't that a no-no in Ghostbusters?
Does anyone have a reference for the study done on a body shape with a pronounced arch to the underbody? I know I've seen it referenced here but I didn't save and can't find it now. My recollection is an Italian-sounding name in the 1960s. I wanted that for MTrenk's underbody thread, and the 'Aero concept car -- Bugatti Stratos' thread the mods spun out of that one. TIA