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I see lots of combinations for the tooth count on the rings for the front crank setup, but am confused which setups are best for flat roads and which are best for climbing.

Which is which? I really want to get into doing more and more mountains (hills in NJ), but for the life of me can never remember how gear ratios work.
 

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Shifting to smaller chainrings makes pedalling easier. Generally once the road starts tilting up, riders start shifting to their smaller chainrings.

So triples, which usually have a smallest chainring with 30-teeth have an easier gear then compact cranks do (which usually have a small chainring of 34-teeth), which in turn is easier then "standard double" cranksets, which usually have a small chainring of 39 teeth. Which one is best depends on your fitness level, what your riding goals are, etc.
 

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Understanding gear ratios

jsedlak said:
for the life of me can never remember how gear ratios work.
This is one of the simplest concepts in bicycling. The ratio of the front teeth to the rear teeth determines the gear. The larger that ratio, the bigger the gear and the harder it would be to climb a hill. You need a low gear that is low enough for YOU to get up the hills YOU ride. You can compare one gear to another simply by comparing that front:rear ratio.
 

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Avoid the temptation to overcomplicate this

jsedlak said:
Thanks for the help!

Today I realized that I never use more than 3 of my rear chain rings. I haven't even considered using the big ring on the front for the flat parts. What I need to do is find some bigger hills!
For the record, the ones in the front are chainrings, the ones in the bag are cogs, just so you're speaking the same language as the rest of us (nothing to be embarrassed about--when I started riding, I called the bottom bracket the "pedal axle" until somebody straightened me out).
For ordinary riding, it really isn't necessary to understand gearing on a deep level. Just go by feel: Put the chain on either chainring in front and then forget you have a front shifter--leave things as they are and ride around experimenting with the rear shifter only. If it's too hard to pedal, shift "down" (which means to a lower gear, but is actually UP the cassette to a BIGGER cog). If you're spinning the pedals uncomfortably fast, shift "up" to a higher gear, which is DOWN the cassette to a SMALLER cog. If things get worse instead of better, you went the wrong way, so go back two clicks. You can learn it in about five miles if you quit thinking.
Once you're comfortable with that, shift the front as necessary.
 
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