Snetterton is a long track, if you are breaking 2:40 on road tyres in a road car you are peddling well. If you want to keep temps down then you can be on it by the time you come to Bentley Straight and then 3 further laps is already going to see you over 10 minutes.
And I can assure everybody that road tyres do roll at low pressures and so you need to put whatever pressure is required, even if that is 50, to keep them off the sidewalls, especially if it is life you are after.
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The reason why you need to support the shoulder is because there is virtually nothing under the tread. I have piles and piles of "sports" tyres that have 80% of their tread on most of the tyre and nothing on the shoulder. Just look at the pictures of the cut up one. The steel belts end at the shoulder and there is very little tread there to start with. If you run the tyre soft you roll and the wear goes to the very edge and the tread will start to peel. These tyres are from a car launch. I had 60psi in the fronts just to make them last most of a day.
Pictures