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The turning rate describes the rate at which the car changes direction. It increases by up to 0.2 per tick, for a maximum of 1 (to the right, i.e a steer value of 65536) and a minimum of -1 (to the left, i.e a steer value of -65536). 0 means the car is not turning.
Turning rate does not affect the car in the air, as only the direction matters during a countersteer.
Every car in TMUF has a set turning rate, with the exception of Coast. The Coast car snaps directly to the desired steering value with no gradient.