This question comes up a lot on the bicycle lists and just came up again today. I figured I'd save my response in the blog so that I can easily find it and reference it in the future.
On Tue, 19 Jul 2005, John Gruber wrote:
> Correct me if I'm wrong. The cages work for different
> numbers of teeth on the rear cassette. More teeth =
> bigger cage.
This is not accurate. The geometry of the parallelgram defines how large of a cog the rear derailleur can work with.
Cage length determines how much chain the rear derailleur can wrap. You can compute the amount necessary by adding the difference of your large and small chainring along with your large and small cog.
So if you run a typical Shimano crankset with 44/32/22 chainrings and a 12-32 cassette you need a rear derailleur capacity of (44-22) + (32-12) = 22+20 = 42t.
If you replaced your outer chainring with a bashguard you could get away with (32-22)+(32-12) = 30t. That would let you use a GS cage derailleur instead of an SGS cage.
If you are good about not using the smallest cogs with the small chainring you can get away with using a shorter cage rear derailleur. I don't recommend this practice on mountain bikes (where remembering what gear you are in can be trickier) but I do it all the time on road bikes.
As an example my road bike has 46/31 chainrings with a 12-32 cassette. Doing the math above I would need a (46-31)+(32-12) = 35t capacity. The older GS cage XTR rear derailleur that I use has a 28t maximum capacity. I can use this if I avoid the smallest cogs on my rear cassette. The cassette gearing is 12-14-16-18-21-24-28-32. I need to gain 7t, which is 12+7 or 19. To play it safe I should only use the 31t chainring with the 21-24-28-32 part of the cassette.
If you cheat like this and accidentally shift into the 12 or 14 nothing bad happens, the chain just rattles against the rear derailleur and makes a lot of noise. If you cheat in the other direction (making your chain too short so that you can't use the large chainring and large cogs) you are likely to trash your rear derailleur or derailleur hanger or both. I've been there and have done that and it isn't much fun.
Shimano only makes the GS (shorter MTB length) cages at the XT and XTR levels. This is too bad because I like using a short cage derailleur on my MTB (where I have a bash guard instead of an outer ring) but would be fine with running a cheaper LX or Deore rear derailleur.
There was this followup discussion about using road GS cage derailleurs (such as a 105 triple) with a wide range mountain bike cassette:
On Wed, 20 Jul 2005, Justin Vander Pol wrote:
> Good write up Alex. A lot of us run the cheaper Shimano 105 road
> rear derailleur in a GS cage to get a mid cage and keep costs down.
> Shimano says it won't work, but it runs great with a dual ring/bash
> up front and standard 11-32 cassette in back. You can find 105
> derailleur for fairly cheap on ebay since a lot of roadies are
> ashamed to run mid-level gear on their bikes.
I don't like doing this because it requires a large chain gap in the smaller cogs, which makes the shifting less precise. The only real functional difference between the "road" and "mountain" rear derailleurs is the geometry of the parallelgram. The road ones ones are designed for a tight ratio cassette. If you max out the B-tension
adjustment to use a 105 GS cage derailleur on an 11-32 cassette then you'll have a small gap between the upper jockey pulley and the 32t cog, but a large gap between it and the 11t cog. For the best shifting you really want a roughly 1" gap here and you want it to be pretty consistent across the cassette.
For a 12-28 cassette the road GS cage derailleurs work well.
> Also, what raodies call long-cage, we call mid-cage, so make sure
> you look at the model. Like Alex said, SGS is long, GS is mid, and
> SS is short.
Yup. I always go by the cage code instead of the abitrary terms "long, medium, and short".