Square aeroplanes

Almost all aeroplanes have round cross-sections. This doesn't seem to be the best shape for optimal use of the interior space. In particular, it means that there isn't much headroom above the window seats. On my most recent flights I found that could not even stretch my arms above my head.

I don't think the reason for these round cross-sections is an aerodynamic one - if I recall my fluid dynamics correctly, drag is a function of turbulence, which is caused by chaotic vortices being shed from the trailing edge. I don't think that would be affected by a square cross section.

I suspect that the real reason is that with our current materials, it's easier to make planes strong enough if they're round - a square cross section would have weak points at the corner edges and might lead to parallelogramming. I wonder if future advances in materials science might be able to counteract this.

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