Rapid warm-up tire

A tire for a motor car or a motorbike for use on an asphalted surface, the tire comprising a tread surface comprising one or more continuously-smooth parts, and the or each continuously-smooth part comprising:

• a plurality of recessed portions, each recessed portion of the plurality of recessed portions comprising a recessed-portion bottom;
• and
• a plurality of raised portions each raised portion of the plurality of raised portions comprising a raised-portion top,
• wherein the recessed portions and the raised portions are arranged in such a way that, when the or each continuously-smooth part rolls along a surface, a mean top-of-raised-portion pressure Pb exerted on average by the surface on the raised-portion tops of the raised portions is strictly greater than a mean bottom-of-recessed-portion pressure Pc exerted on average by the surface on the recessed-portion bottoms of the recessed portions, the mean bottom-of-recessed-portion pressure Pc being nonzero, and
• wherein the pressure exerted by the surface on each recessed portion and on each raised portion is measured in a contact patch of the or each continuously-smooth part, the tire running at a speed equal to 100 mm/sec with substantially zero slip and camber angles, and the tire being inflated to a reference pressure equal to 1.6 bar, and subjected to a reference load equal to 5000 N in the case of a car or the tire being inflated to a reference pressure equal to 1.8 bar, and subjected to a reference load equal to 1500 N in the case of a motorbike.