This is a message which I originally posted to the Green Gear Yak forum. It discusses benefits of the 3x7 hub compared to using triple chainrings and a front derailleur when attempting to obtain wide range gearing on a bicycle with 20" wheels.
The 3x7 has gears of 1:0.73, 1:1 and 1:1.36. You can figure out the virtual chainring sizes based on this. So assume that you have a 46t chainring, then you have gears of (46 * 0.73), 46, and 46 * 1.36. These are 33.5t and 62t. You can then plug these into your gear chart spreadsheets. The general gear inch formula is (front chainring / rear cog) * wheelsize. I have an Excel spreadsheet for doing gear charts at http://www.phred.org/~alex/bikes. One other 3x7 advantage that was not mentioned by others is the complication in having a wide range triple chainring system using 20" wheels. There are two factors working against one on a 20" bike. One is that the wheels are smaller, meaning that the difference between chainrings needs to be larger to achieve similar overall range. On my singles I run with roughly a 2:1 ratio between the largest and smallest chainring (50/40/24 and 48/36/24 are two common chainring setups for me, and on one bike I run with 46/36/20). A 20" wheel requires larger chainrings overall, which means that the difference between the largest and smallest chainring needs to be much larger to get the same range. For instance on our Tandem Twosday we might like 60/48/30 chainrings. However there aren't too many derailleurs out there that work well with a 30t spread between chainrings. The 60/50/36 chainrings that the bike came with have a much lower overall range (1:1.75 roughly). I was able to push this to a 60/50/34, but going farther would mean lowering the top gear, and 60/11 * 18.5 is already a pretty low top gear for a tandem (about 100"). 18.5 is the size of our wheel and tire in inches ((406 + 32 + 32)/25.4) The other thing working against the front derailleur capacity is the chain angle. On a bike with larger wheels the bottom bracket height is lower then the center of the hub. Additionally the granny gears use front chainrings which are smaller then the rear cogs. This means that the chain leaves the crank at an upwards angle, gaining some clearance before the front derailleur cage. On a bike with ~20" wheels the chainrings are still larger then the rear cogs, even when in the granny. The hub is below bottom bracket level, so that chain leaves the chainring at a downward angle. This reduces the effective capacity of the front derailleur. While the 3x7 hub doesn't have a range of 2:1 (its range is 1:1.86) it is wider then is obtainable with standard triple drivetrain components, and none of the components are pushed out of spec. You can see above that the virtual chainrings produced by the 3x7 hub with a 46t chainring (62/46/33) have a wider overall range then what I was able to achieve with a front-derailleur equipped bike (we have 60/50/34). If I had thought this through before buying our tandem I might have considered going for a bike with the 3x7 instead. It is not a big enough of an issue that I would go to the expense of swapping out components on our existing bike. Hopefully this message makes sense, and sorry for the high technical detail for those who aren't interested. alex