Doesn't the angle of attack have more to do with the surfaces we're concerned with?
Yes that is one of the reasons why cross winds (even minor ones) can make such a huge change.
For example the high pressure area that forms in front of the windshield quickly disappears as the wind begins to move from a quartering angle. This means two things, one a slight cross wind can drastically change your front down force (or rear for that matter) and it can very rapidly shift the center of pressure fore and aft on the vehicle. A body that is very stable in dead quiet wind conditions can suddenly turn into a car that wants to turn away or into a cross wind and unloads the front tires when it is hit by a cross wind gust.
In Norbye's book Streamlining and Car Aerodynamics (long out of print copyright 1977) he covers this issue a bit in Chapter 5. He states that the center of pressure on a typical sedan is near the cowl area and on sports GT's it is near the front wheels. (streamlining tends to move the center of pressure forward as drag at the rear of the body is eliminated, unless measures are taken such as fins to increase the rear sail area).
On the 1963 Corvette its front down force due to the high pressure area at he base of the windshield essentially disappears at a wind vector of 30 degrees from the axis of the body.
According to Norbye, the early Ford GT 40 had 696 lbs lift at 200 mph, 528 lbs front and 168 at the rear. When the wind vector swung to 15 degrees off axis the cars lift went up to1170 lbs, 786 at the front, and 384 in the rear. This car had a static weight on the front wheels of only 766.5 lbs, so in cross winds the front wheels would come off the ground.
The problem was solved with the addition of a front air dam and a change in the shape of the cars nose. After those modifications front lift at 0 degrees angle of attack was 236 lbs, while rear lift increased to 272 lbs. At a 15 degree angle of attack front lift still was only 309 lbs, and rear lift was at 343 lbs.
Larry
