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On the race cars, it's not really to reduce drag down straights. It's for cornering. If you look at the Chaparral 2J or the Brabham BT46B cars, they have skirts that basically seal off the bottom of the car. If you take the small vaccum generated by the fans & multiply that by the surface area under a car, you get huge amounts of "downforce". It may have reduced drag a little bit, but you could go around a corner like you wouldn't believe.
Backyard aerodynamicist here.
Volumetric requirements. take surface area of rear of your car in ft^2. Multiply that by your desired speed in ft/min. This would roughly give you the cfm required to fill that hole. 55 mph is 4840 ft/min. Turns out to be a whole bunch of air.
You could try to use an electric cooling fan ducted down to the underside of the car.
Don
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