My two cents...
Sumner, I really enjoyed your miscellaneous ramblings on lsr, particularly the section on aero. I am the furthest thing away from a mathematician, but have always wondered about a couple of concepts I have not seen developed in lsr.
1) Supercavitation ~ I quote from Wikipedia for a definition better than I could write:
"Supercavitation is the use of cavitation effects to create a large bubble of gas inside a liquid, allowing an object to travel at great speed through the liquid by being wholly enveloped by the bubble. The cavity (i.e., the bubble) reduces the drag on the object and this makes supercavitation an attractive technology; drag is normally about 1,000 times greater in water than in air."
Does that mean that using a perforated body skin on a streamliner with the right amount of air being pumped out of the car in the right places could have a big enough role in reducing drag? Having not probed the depths of the rulebook (my bad) I don't know if there's a stipulation about on-board engines/motors needing to be involved in vehicle propulsion only (maybe to prevent a Chaparral 2J fiasco) but if so, maybe a wheel-driven pulley could spin an air pumper that...
2) Vortex Generators ~ again I quote from Wiki:
"The purpose of the generators is to stick out of the stagnant air near the surface of the wing, and into the freely moving air outside the boundary layer. This layer is typically quite thin, but dramatically reduces speed of the airflow towards the rear of the wing. The generators mix the free stream with the stagnant air to get it moving again, providing considerably more airflow at the rear of the wing and thereby providing the control surfaces with more power. This process is typically referred to as re-energizing the boundary layer."
(Me again) In lsr I would think that having a tidy airflow at the back of the car would be as important as the front. I've seen vortex generators on only a few race cars, an old Indy Eagle, and on the back deck of one John Force's floppers.
Maybe these two concepts provide not enough gain for the trouble, or wind tunnel $ is best spent on other bigger issues. For interest, I found a picture of a shark's skin; it's vortex generating surface results in a more slippery body that I would guess needs less energy to go through the water...
www.filmstream.com.au/ extraordinary.html
Thanks for enduring my own ramblings ...