Sachs 3x7 vs Triple Front Chainrings on 20" wheeled bikes

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

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.


I have more bicycle information on my main bike page.