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I never did get an answer from the several sponsors of race car tires as to why the sidewalls of race cars are so tall. From NASCAR to INDY to CART, no one runs anything close to a 3" tire profile (30-35 series on a 18" rim).
I am still curious to know if lower sidewalls actually increase handling.
Here's my opinion:
In general, shorter sidewalls increase the "sharpness" of directional changes, but they also are less forgiving at the limit of adhesion, meaning that when they pass their limits, they tend to "let go" more suddenly and with less warning than a tire with a taller sidewall.
Since cars in a race spend a great deal of time "at the limit", maybe ultra-low profile tires are just too "knife-edged" to keep at 10/10ths for the duration of the race?
Comparing true race tires to street radials is like comparing a stock LS1 motor to a C5R 427 motor. One really doesn't have anything to do with the other.
There are forms of racing that do use very low profile tires, such as AMLS, or Touring Cars.