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what the maximum then 170?
Depends on how you want the bike to handle. If you like quick response with minimum lean to execute tight corners, the max is the 140/70 the bike came with. If you are okay slinging around a heavier tire, are okay with speedometer error, and feel like leaning into corners more than you have been, then the 150/70 or 160/60 might do the trick. The better option is to buy the best rubber possible in the stock size, to create max grip, quick response, and less lean angle. But... that's just an opinion.
 

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Depends on how you want the bike to handle. If you like quick response with minimum lean to execute tight corners, the max is the 140/70 the bike came with. If you are okay slinging around a heavier tire, are okay with speedometer error, and feel like leaning into corners more than you have been, then the 150/70 or 160/60 might do the trick. The better option is to buy the best rubber possible in the stock size, to create max grip, quick response, and less lean angle. But... that's just an opinion.
I’m only choosing a 150’rear with a 110’front for my stunting
 

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Not a big fan of cramming big tires under sport bikes. There is a balance between handling, efficiency and stability that is met with the narrowest profile that will provide the proper amount of grip. Just stuffing bigger rubber under a bike is often a poor choice. The rolling resistance is greater (more effort to keep moving), the diameter is greater (150/70 = 105mm, and 160/70 = 112mm, which changes gearing over the stock 140/70 = 98mm), the inertial resistance is greater (slower acceleration under the same power), the weight is higher (more mass to move), and the location of the contact patch when cornering is raised (increasing resistance to changing direction - however, this feels more stable). When you get onto the shoulder of the tires, the radius of the tread has more impact on grip when cornering, which is not dramatically increased by a wider tire. A tire too wide for its rim actually may have a smaller shoulder radius, and may even have an inconsistent edge radius profile, thus less or inconsistent cornering grip. So, when you are cornering (where grip is most important), unless there are associated rim changes, the amount of grip from narrow to wide will likely be unchanged - if not reduced in some cases.

I suggest that most of the improvement in the bikes feel when a wider tire is fitted has to do with the better tire itself (quality and construction), and the extra stability (great for touring bikes and crap chopper geometries, but antithetic to the goal of a sport bike). In fact, some level of instability is built into sport bike geometries (rake.trail, tire size), that makes them more ready to change direction. Adding tire width works against that dynamic design. Further, what works great for 300HP GP bike isn't going to work on a 600cc 100HP street machine. What works for that 600cc street machine is not work at all for a 320cc 40HP lightweight, as they all use their tires differently, and have different geometries elsewhere.

Another often ignored aspect of tire application is slip angle. What many fail to realize is that the best grip is when the tire is actually slipping a little. Add more traction that reduces that slip and the bike will handle poorly. Too much slip is not good when it happens, but no slip is bad all the time. That subtle feeling of "lightness", wiggle or squirliness in the rear under cornering that so many whine about, is actually part of what makes the bike corner so well. Take that out, and the bike will feel numb, or will understeer, or may take a lot more lean to get the same corner response.

It certainly makes sense to seek tires that optimize performance, and nothing feels better than brand new rubber.

I find comparing the tire size of a YZFR6 (120/70-ZR17 on the front, and 180/55-ZR17 rear), and applying the 120/70 front with a 150 or 160/70 rear on an R3 with far less power, and far less cornering force a dubious mod. The R3 has a lower CG, greater rake (25 for R3 vs 24 for R6) and greater trail (3.74 for R3 vs 3.4 for R6), with less weight (366 vs 401). It appears to me that Yamaha utilized the narrower tire to optimize efficiency (less power loss through the tires), and compensated for stability by increasing rake and trail, to produce balance without the heavier rubber. This produces a stable straight-line ride, with great turn-in response and edge grip, while maintaining a very responsive mid-corner character - which fat tires would only improve in increased straight line stability.

I also find it amusing when digging into tire selection. I have seen many instances of forum commentary deriding stock rubber selection from one bike - that, on another forum for a different model bike is touting what a great tire that is to upgrade to from their "bad" OEM rubber.
I agree, I have changed tires twice already on my R3 and both times I went with the stock size, first I tried the Pirelli supercorsa but that turned into overkill for street use, I got less then 2,000 miles from them, so now I put on a set of Pirelli Diablo Rosso 3's and they are awesome, almost as much grip in the dry as the supercorsa's, they work great in the wet and I think they will last a bit longer.
 

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Why do people try to put "big" tires on a small(er) bike??? All it does is detract from the handling, and add to the un-sprung/rotating mass. You might look "cool" with wider tires, but you are doing NOTHING to help help with the performance of the bike. You are actually making your bike slower, and handle poorly- If you think I'm "wrong", look at ANY MotoAmerica starting grid within the Junior Cup (R3 class).... Not a single racer at the pro level, is running anything wider than a 150 series rear, and a 110 series front... If there was any advantage of doing so, those folks would be doing it- they are NOT.....
I would even go far as saying bigger tires make it look even smaller. Thin forks, thin swingarm and fast tires make it look like a skinny clown wearing big shoes lol.
no real biker is gonna care what “big” tires are on your bike. not that anyone else’s opinion should matter on the looks of your bike anyways.
 
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