Race Tyres
Tyres need to be speed rated to the speed attempted.
The fastest Vespa tyres are rated "P" which is 150 km/hr
Sava 3.50-10 51P MC 18
Schwalbe Raceman 3.50-10 10327541
Continental ContiTwist Race 3.50-10 M/C 59P TL
The tyres I use are Sava 3.50-10 51P MC 18 tyre Code 72761.
Speed Ratings
Most scooter tyres are rated "J" which is only 100 km/hr.
Reading Notes
Reading Tyre Technology - Tom French
Internal heat generation is a problem and the times per second a tyre is deflected contributes to this heat generation. When the tyre gets hot enough the it "can lead to total disintegration". The book talks about a typical motorcycle tyre at 100 mph having 17-18 deflections per second.
My calculations are that at 100 mph a scooter tyre has about 34 deflections per second (twice that of a motorbike!). This is based on a tyre having a circumference of about 1.3 metres.