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The ratios are simply math. Use the link below if you don't want to do the math.
First figure out the combination you have now and what gear inches you have (or ratios of you prefer). I find inches easier to understand but use whichever you prefer.
When you look at your ratios you will see a lot of overlap. That's unavoidable, you always have some. Depending on the setup, some combinations are probably unusable on a practical basis due to chain angle, like small/small, and large/large.
The hardest part comes now: what are your goals? Example: If you ride a lot of major hills, then you probably want some low ratios. But, to get the low ratios, you need to get some larger cogs in the rear and that will give you bigger jumps between gears, which isn't great for racing. On the other end, if you are training or training to race fairly flat ground, you likely want to have short steps between gears, so you might have to compromise the lowest gears out (drop larger rear cogs) and make the front chainwheels close. For most general riding, the ability to start on the middle chainwheel for a few gears and then switch to the larger wheel and stay there is a feature.
Note also that major changes don't shift as well and require more chain, so an old school 32, 42, 52 front will have a lot of chain flopping and require a long cage derailleur. It will also be a bit sloppier. Check the chain range on your rear derailleur before making major changes or you may find that you can't use the large front with the larger rear dogs or the small front with the smaller rear. Most front derailleurs handle a fairly wide range of triples but it's worth checking that too before you make changes that widen the front range at all.
So, look at what gears you use now. As an example, If you never use the smallest rear (12) cog and the largest front, perhaps a swap of front chainwheel down a couple teeth is a good idea. Or, you can bump the rear to start at 13 and bring the rear cluster closer together from top to bottom. If you find that you're topping out the top gear, then up the front chainwheel and/or drop the rear. Some guys like the middle and large rings in front very close so that they have nice shallow steps and can keep their speed up and use a small front for a bail out gear on hills.
If you find you use 2,3,4 and want to change, adjust ratios as needed. If you ride those ratios now, you will ride them in the future (better condition aside), so make sure you put them in a comfortable place. If you really don't use much outside that range, ever, then consider making the jumps small in the rear and the front and tie it closer to that range.
My goal is usually to have minimal steps, but have a little extra on top for when I get moving, and maybe a little on the bottom so I don't torture my knees. I like to get on the large chainwheel and try to stay there for training, but I ride fast 45 minute runs over relatively level ground... breathing hard like I am out jogging. For touring, I use my other bike with wider ratios all around - less efficient for speed, but better suited to the ride.
posted by 71.174.89...
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