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I'm tuning up a 2010 Giant TCX 2 which has Giant CR41, 32-hole rims as the only information I can find. There's nothing printed on the rims themselves either.
Right now it's using the 700 x 35c Kenda Small Block Eight folding 120TPI tyres that it came with but I'd like to change to slicks and have found some 28c's that are an amazing deal.

As per Sheldon Brown I'm likely ok putting on 28c's since they fall within the range of rim where you'd find 35c's but not always.

My ability to measure this at home is limited by my lack of a ruler. Surely this information is available somewhere.

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From what I'm seeing, those don't look like the original tires that would have come on that bike. The Giant TCR 2 is a road bike, that currently comes with 700x23 tires. This bike model came with CR41, 32 hole rims, and 25 mm tires. If these are the rims that are on your bike you'll be fine with 28mm tires, and it's likely that somebody put the largest tires they felt they could safely put on the existing rims. –  Kibbee May 21 '13 at 18:03
    
What @Kibbee says sounds absolutely true. It rings alarm bells for me too. I actually have a 2010 Giant TCR 2 Advanced. But this is a carbon-framed thoroughbred racer (shame I'm not!), no way it'd be running 35mm tyres out of the factory, in fact I'm surprised that width would fit the bike at all, as the frame is shaped around the tyre. I've always ridden 23mm. Are you sure you've got the correct name? –  PeteH May 21 '13 at 18:54
    
@Kibbee oops, TCX not TCR –  Jean-Bernard Pellerin May 21 '13 at 21:31
    
@PeteH you guys are correct, I made a mistake –  Jean-Bernard Pellerin May 21 '13 at 21:33
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If you have the rims, why not just measure them? A ruler can't be that hard to come by. (Or mark off the distance on a piece of paper and carry it to where some sort of scale is available.) With a mm rule you should be able to get within 2mm or so of the correct number, certainly close enough for tire sizing. Just remember you want the INSIDE dimension, between the rim sides. –  Daniel R Hicks May 21 '13 at 23:01

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I went and bought a ruler. It's 13mm.

I'm kind of surprised they'd stick a 35mm tyre on a 13mm rim out of the factory. I'm going to stick 700 x 28c conti GP 4 Seasons on it unless someone points out a clear reason not to. Sheldon Brown's guide says 25 should be a max for that rim, but it also grants a bit of room for error and this rim was fine with 35's...

This also means that CR41 isn't necessarily a material/feature code and it's possible the TCX and TCR use the exact same rim.

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