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Do UCI rules prohibit airways within the frame? Could take high-pressure air from near the headtube and duct it back behind the seatpost...
By implication, kind of. The regulatory model is solid, a duct makes the thickness of the regulated solid the wall thickness of the duct, 25mm minimum. Not that it matters, because the drag in the duct would be so high that it would cancel out any relief of high pressure on the nose cone or filling of low pressure behind the seat tube.
UCI bikes are regulated to a thickness of just over 30% of chord length measured perpendicular to the tube's long axis. Measuring chord the aeroplane way parallel to the direction of travel, that's about 25% for the head and seat tubes and about 15% for the downtube. Because the downtube has a lot of sweep in aeroplane terms, it creates what would be spanwise flow if it were a wing, so thickness:chord measured in the direction of the flow field could be under 10% at some points if the basic tube shape was as thin as is permitted.