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I'm thinking of not covering the engine compartment area
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you'd be missing out on a good opportunity to reduce drag.
here's an article (free preview; paid reg'n required) about a 1st gen prius which reduced hwy fuel consumption by 10% with
just the front undertray. you could always include a trap door in the front pan to make oil changes easy (that's what i'm planning).
as for cooling airflow, don't forget, you need to leave a fairly large cut-out to permit lock-to-lock steering of the front tires. the openings are large enough for air to escape from the engine bay through there.
one of the interesting things i've learned about aerodynamics is to keep in mind when you're looking at those cars that there are actually 2 opposing aerodynamic theories at play. one is to reduce drag for higher speeds, the other is to
increase drag to create downforce for better handling at those higher speeds.
the underbodies of high-end sports cars and F1 type cars, while smooth, are designed to create a low pressure zone the car that creates downforce. it actually takes more power to propel a car with that kind of underside. rear wings are the other way downforce is created while also creating more drag - talking high-end sports cars here. (the max-mpg vw bug is an exception - its wing helps correct an otherwise aerodynamically poor shape and makes it more efficient.)
don't get me wrong, smooth underneath is good. you'd have to shape the underbody in a very specific way to cause downforce as a result - we won't cause that by putting belly pans on our regular cars.