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The head tube is right out there in the breeze, and a circular cross section is really bad for your aeros. Almost anything you do to the leading edge is likely to be an improvement.
Trailing edge, surely? A teardrop shape is as aerodynamically efficient as it gets, with a rounded front end and a pointy tail. If you look at any fast road or TT bike which has had wind tunnel time, it'll have a rounded front edge on the HT and then a tapering section behind it.
The majority of the drag doesn't come from the air hitting the rounded front of the head tube - it comes from the vortices from the trailing side of a round tube which are eliminated (or at least substantially reduced) by a tapered trailing edge.
Brommers-
In which case, some sort of webbing between the TT and DT would be optimal...
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Trailing edge, surely?
Trailing edge is for marginal gains, all the hard work is done by the leading edge. A circular cross section so fucks things up that there's almost nothing you can do apart from starting again with something wider that's a good shape, that's why the best aero rims are now wider than the tyres in front of them. It's also why those 90s "Aero" tubes which grafted a trailing edge onto a round tube ended up working better when turned around, and it's why a proper Kamm tail has so little effect on total drag.
The front half (i.e. from leading edge to maximum thickness) of a minimum drag aerofoil is rounded, but it's nothing like a semicircle.
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gbj_tester
The head tube is right out there in the breeze, and a circular cross section is really bad for your aeros. Almost anything you do to the leading edge is likely to be an improvement.