A triple gear means that a third, smaller inner ring with typically 30 teeth, is being added to the classic two chainrings of the double crankset. Since several years, there is also the compact that aims to unite the benefits of both the triple and double.
In contrast to the normal drives, the compact uses a stitch of 110 mm. This makes it possible to use an inner chainring of 34 teeth, in addition to, e.g., an outer chainring of 50 teeth. The cassette at the back can, for example, consist of 12 to 26 teeth. The smallest gear thus becomes 34x26. However, with the introduction of the 11-speed (11 instead of 10 rings on the back gear) also very small compact gear have become possible.
The 11-speed group is a recent development. The 11-speed group is available both on the double and triple crank, but the triple is, in 2013, only available with Campagnolo, with a maximum (minimum)of 30x29. The 11-speed on a double crank can have 28 back teeth (Dura-Ace) and up to 32 back teeth on the Ultegra GS. On the Ultegra GS, cassettes can go from 11-23 up to 11-32. With an inner crank of up to 34 (smallest), you have a maximum (minimum) gear of 34x32, which should be sufficient for any climb.
Advantages and disadvantages of compact and triple
Whether you choose a triple or compact depends mainly on yourself. According to some "big climbers", a triple is for sissies. Never mind. Since the recent developments, also compact gear have very small gear and personally, we also ride a triple. On 10%+ climbs, they're merely useful. Given you landed on this page, chances are that you are there to use it for similar purposes.
In addition to knowing the maximum incline level of the harder climbs, information you can find on climbbybike, some insight in your power output and pedaling cadence (rpm) can help you to determine your choice for a compact or triple. The smallest possible triple resistance (30x30) makes your wheel rotate exactly in line with your crank, so, per rotation, you cycle the distance of the circumference of your wheel, e.g. 2100 mm for a 20-622 wheel. With the typical smallest compact resistance (34x28) your distance per rotation is 2,550 meter or 21% more than on a 30x30. With the Ultegra GS gear of 34x32 however, you come very close to the triple gear. Given your own maximum power, you will logically have a lower cadance with a compact.
Disadvantages of the triple: more weight, less precise derailleur (long cage), bigger distance between pedals
Advantages of the triple: smaller gear, more options in the smallest gears, straighter chain line
Disadvantages of the compact: possible (in)compatibility with derailleurs and shifters, less power transfer and increased wear by often inclined catenary
Advantages of the compact: lighter, more precise derailleur
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