Part 1. Revisiting unorthodox automotive designs
Frontal area is said to be a key factor influencing a car's aerodynamics. Sometimes there are outliers — e.g. BMW M4 GT3 — but in general we assume a car with less frontal area will experience less drag if we leave everything else equal. For instance, if we sawed off the A-pillars of a Ferrari 296 GTB, lowered the enclosed rooftop, and let the driver take up both seats lying sideways, then compared it to a regular 296 GTB: the former should go faster. I believe most people would agree on that.
Venturi ducts are a debatable feature when it comes to improving aerodynamics. In many cases they do help increase downforce, depending on placement. However, whether they help reduce drag despite reducing frontal area is uncertain. The answer is more likely negative, but it also depends on the structure.
The 1967 OSI Silver Fox was built with a huge center duct to break the 24hr Le Mans record, but never got effectively tested because the company went bankrupt. The performance of the WMC250EV — also with a center duct — seems to justify the concept.
S-ducts are more common these days, especially on hypercars. While the Lotus Evija stands out as one of the most aggressive, it had lower stats (top speed, Cd value, etc.) compared to other hypercars around the same era — despite tremendous downforce and 2,039 hp.
The conclusion: while the pressure difference created by s-ducts may increase downforce but worsen drag tolerance, a large enough center duct might have been beneficial for reducing drag and achieving higher top speeds. There is a lot of work in terms of converting the structure — the main reason we don't see modern quads with this technology.
Inspiration behind EPCX
There were two (debatable) automotive features I was looking into before I ever wanted to build an automobile, both in high school. One was adding a HALO to a road-legal go-kart; the second was prone seating for street-legal 4-wheelers.
I guess a fair reason for some people applying to Princeton was that the Princeton Racing Electric had overall better aesthetics compared to many other Formula SAE cars. It might be more fun to modify the body and add a HALO, to make the "not-so-street-legal" car street-legal. Apparently, BAC Mono and KTM E-Bow do a better job at this for a production version. The following was a reimagined rough sketch from what I submitted along with my application in 2021:
A car with a kneeled seating structure — where three prone seats are placed the same way as the McLaren F1/Speedtail, with one additional seat behind the driver's seat — doesn't sound very smart. But I did submit an annotated sketch (now lost) along with my application to the University of Chicago back in Jan 2021. Hennessey's Project Deep Space had a roughly similar layout but with regular seats; now seems to have gone south.