actually the first type r was a motorbike... The CBR was a sports bike made by honda, but when they decided to put race piston in and modify the engine they renamed it the CBRR. RR standing for race replica.
This is straight from wikipedia:
"The Honda CBR models are a series of sport oriented motorcycles, several of which (400RR, 600RR, 900RR, 929RR, 954RR and 1000RR) are marketed as Race Replica, hence the suffix "RR" after the engine size designation. With the exception of the single cylinder CBR125 and CBR150, all CBR motorbikes have inline engines (as compared to the V engines in the VT, VTR and VF/VFR series). Less sporting models with inline engines make up the CB Series."
"A race replica motorcycle is a publicly available retail vehicle that resembles a competition race bike either in performance or appearance.
The classification is imprecise and varies from bikes derived directly from a racing prototype (such as the Ducati Desmosedici) to production bikes that are considered heavily influenced by a manufacturer's racing experience (such as the Aprilia RS125 or Kawasaki ZX-7R). It does not extend to retail bikes competing in race series that require an existing production bike be used (such as the Honda CBR1000RR).
The term is often applied by manufacturers to market motorcycles and scooters that resemble a racing prototype (such as a similar paint scheme) but are not actually derived from racing vehicles. Some of the performance race replicas are offered with sponsor decals so that it may completely resemble a professional race bike.
Some enthusiasts may incorrectly consider true race prototypes that have subsequently been privately sold as replicas (such as the Yamaha YZR500)."
The reason the first type r was made, was to take an 'órdinary' car and make it into a race car. The nsx r actually started off as just an nsx but then later became a type r to comete with its big brothers. The 'type r' has always been about increasing the performance of a stock car/bike
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