roughly 60% of the entire drag on an Indy car is the tires hitting open air making for the ramp up in Cd (Drag Coefficient)
Here are some typical drag coefficients from the March 2006 HOT ROD magazine:
Flat plate ......................................... 1.15
Indy car .......................................... 0.75
“Bad” production sedan ...................... 0.50
“Average” production sedan ................ 0.43
“Good” production sedan .................... 0.35
Late ‘80s C4 Corvette ........................ 0.32
NASCAR Cup superspeedway car ......... 0.30
Perfect sphere ................................. 0.15
LandSpeedRacing streamlin................ 0.11
Airfoil ............................................ 0.05
Now we are talking about a 40" tire, wait I mean four 40"s tires. That is some serious resistance and takes mega HP to go faster, but that doesnt mean anything if you cant control it due to the wind pushing the car around as it slices the air.
My experience:
I have an open wheel landspeed car F/BFRMR (29" slick tires), I've been in the high 200's with it. At 275mph its like driving a cadillac in the slow lane. 100% control, no buffetting, no breaking rear traction as you would as you push on the wind resistance "The Wall" as you max out your aero package. So that means one thing I havent yet reached the limits of my aerodynamics. I'm just out of HP.
Now take my old C1/U4 the Unicorn. This examples from pavement as I never went over 132mph on dirt. Anything over 120mph the car would begin to buffett ever so slightly in the rear. You could feel the car slipping left and right, by 130mph the nose would start to slowly follow suit. 135mph and the car had some pronounced left and right shifts. Somewhere just over 140mph the entire car would finally come into its own of feeling light at all 4 corners. I hit 144 and my balls said no more. Gearing and HP were still there, just couldnt control it enough to feel safe pushing further. Drinking beer later we probably could have pulled the headlights and side fiberglass, and laid some lexan on for a windshield and gotten a few mph better but...that was just some f-ing around.
So yes, if you could do something to help your tire aero, anything would be something. Might look like those Europe mudflap/tire covers, or just look at Dakar.....