Bob IMO it has nothing to do with tires. Anyone with a pointed car will never feel it. It's a process of "aero" and trying to push the air out of the way and either running out of HP or only using what you need to qualify for a new licence.
About 6 years ago a gentleman came with a turbo small block Chevrolet in a street roadster and needed to go thru rookine orientation and his licensing. The car was easily powerful enough to get him in the 200 MPH club. On Wednesday when I parked next to him in impound he came over said said he almost quit during his qualifying runs. He new what RPM was needed forrunning below 149, 174, 199 so he accelerated to the RPM and held it. Guess What? when you do that you are "out of power" or your car thinks so. Being it had a 32 grille shell it started darting all over the track. Each new licence run was not under full power but no one had told him this would happen including me during inspection. His final qualifing run for the record and record were under full throttle and 2 runs were a smooth and straight and he got his "hat". He said he never realized he should have kept a mild acceleration ending the timed mile while still accelerating then it would have never happened. Since that time I have made it a point to tell new roadster drivers licensing to be prepared or accerate thru the early miles and not to just hold the throttle at a set RPM.
I'm no expert but I took that ride between the 4 and 5 on my return record run. I had qualified at 205 in the 5 still accelrating. The next morning I ran that same 205 in the 3 and was accerating at the 4 to 214. No problem. Then it ran out of HP and I let it have it's head as it moved all over the course for the next mile hoping it would not spin. I went 215 in the 5 and many drivers came up after to congatulate me but laughed when I told them what happened...No one told me either.
It's why I love stand up roadsters...................JD