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In a 21 speed bicycle, which is the fastest gear ratio.
Smallest on front and largest on back or vice versa?

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    One way to look at is is chain feed. A bigger front feeds more chain in one revolution. On the rear a smaller will turn the wheel one revolutions with less chain. – paparazzo Oct 21 '15 at 17:43
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    Why the down votes folks? If a person doesn't know, there is nothing wrong with asking. From what I see we do not have an explanation of this. It may be basic knowledge for most of us, but there's always plenty of people who hear about something the first time. – andy256 Oct 21 '15 at 21:51
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    What surprises me is that I can't find a duplicate, only near-misses like how can I increase the highest gear ratio which does suggest the asker has failed to even try the search box. – Móż Oct 21 '15 at 23:47
  • I guess the downvotes are because this question is very easy to answer - if you have a bicycle, just check and see. Also, it's a missed opportunity to actually ask what (numerically) the fastest ratio is. – anatolyg Oct 22 '15 at 11:53
  • BTW maybe this question is really asking "What is the definition of fastest gear ratio?". It's possible to edit the question to clarify, but I guess OP will never do it. I'd be happy to be proven wrong. – anatolyg Oct 22 '15 at 11:57
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It depends on your cadence (number of times you're turning the chainrings). If you fix the cadence, largest chainring (gear in the front) and smallest cog (gear in the back) will be fastest.

In practice, you will not be able to keep up the same cadence on all gear combinations, so depending on the cadence you can keep, a smaller chainring in the front and a larger cog in the back may end up being faster (since you can use a higher cadence) than a larger chainring and smaller cog (which, if you could spin at the same cadence would be faster, but you can't).

You can use this calculator to see what speed you get for a given cadence for the chainrings and rear cogs on your bike.

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The 'fastest' combination of gearing will be the largest chainring in the front to the smallest cog in the rear.

For a simplified example of why this is so consider a front chain ring with a diameter twice that of the corresponding rear cog. For every full rotation of the front ring the rear cog will experience two full rotations, and since the cog is attached to the wheel you will travel two full rotations of the wheel. If the rear cog was one quarter the size of the front ring, it would travel four roatations for every single rotation of the front ring.

In this manner it can be seen that increasing the size of the front ring in relation to the rear cog, or decreasing the size of the rear cog in relation to the front ring, will result in more rotation of the wheel and a larger distance traveled for each pedal stroke. Therefore, it is possible to travel faster for a given cadence (rate of pedalling).

Of course, in practice if you try using your 'fastest' ratio to go uphill you won't get very far because you'll be unlikely to produce the necessarry force on the pedals to achieve roation.

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the fastest gear ratio is largest front and smallest rear, usually 44 front 11 rear means the wheel turns 4 times faster than the crankset. Smallest front and largest rear is slowest, only for climbing big hills

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