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I don't want to be one of those naysayers (this whole thing is bonkers and I love your attitude towards this), but 2-3 mm tent poles in carbon might be awful.
Off the top of my head tent poles tend to be in the 10+ mm region. Stiffness scales a lot with diameter, so a 2 mm pole is going to be orders of magnitude less stiff than a more standard size
Those are some terrific ideas- thank you very much. Never heard of carbon tow, but it looks ideal.
As for tube width, I'm tempted to start with 2mm rod, if only for the excitement. Doesn't matter if the prototype breaks. And imagine a rack made of bits which are so thin that you can hardly see them!
I'm already mentally committed to triangles. Barnes Wallis is my inspiration. Getting compression will be a challenge. I'm no good at conceiving a design in my head. Didn't even pass Physics O level. So it'll be trial and error. I thought I might start by making something out of dowel.