This document is copyright &#169 1995 by Tom Holub.  It may be freely
redistributed as long as this notice is retained.  It may not be sold.


In the last installment I discussed the role of maintaining proper
cadence in improving cycling enjoyment and endurance (if you missed it,
it's in ~tom/bikestuff/advice).  The purpose of a bicycle gearing
system, as with an automobile gearing system, is to keep the engine
operating within a certain range of RPM (for a car, 2000-5000ish; for a
bike, 80-100). Because the RPM range on a bike is much more restricted,
bicycles need finer gradations between gears, and because of other
engineering considerations, bike gearing is harder to use than car
gearing.  For this reason and others, many cyclists never learn how to
use their gearing system (even those cyclists who buy mountain bikes
because they have "21 speeds").  But really it's not that hard, and
since bike components have improved markedly in the past 15 years,
shifting is easier now than ever, especially on inexpensive bikes
(unless they have Shimano under-bar shifters, but that's another rant).

First, we need to get some terms out of the way, then I'll add a bit on
how gearing works from a rider's view, and then a more technical
discussion of what goes into a gearing system and how to set up your own
(non-geeks can skip the last part).

DEFINITIONS:

The chain runs on the CHAINRINGS in front and the FREEWHEEL in back (the
FREEWHEEL is so called because it floats freely on the hub, allowing you
to coast or pedal backwards; early bikes couldn't do either).  The
freewheel is made up of five to eight COGS (most modern bikes have
seven, though 8 is becoming more popular.  I'm going to assume 7 for
this document).  The FRONT DERAILLEUR moves the chain between chainrings
by pushing on the tense (top) part of the chain.  The REAR DERAILLEUR
takes up (or lets out) slack in the chain, and moves the chain between
freewheel cogs by moving the slack (bottom) part  of the chain
underneath the desired cog.  The SHIFTERS are levers that move the
derailleurs by pulling on the DERAILLEUR CABLES.  The notation for the
current gear involves a character denoting the chainring and a number
denoting the cog.  The small chainring is usually denoted L, the large
usually H, the middle, if it exists, M.  The largest cog is  denoted 1,
so L1 is the smallest chainring, largest cog. 

OK, now down to basics.  What your gearing system does is change the 
ratio between your pedal revolutions and wheel revolutions.  "Low" gears
have a small number of wheel revolutions per pedal revolution (the
lowest gears on bikes with 3 chainrings can go below 1:1 ratios).  High
gears have more wheel revolutions per pedal revolution; the highest
gears get up to about 4 wheel revolutions per pedal revolution.  The
gearing system is able to change this ratio by changing the effective
size of the wheel and the cranks (by moving to larger or smaller cogs or
chainrings).  Smaller chainrings make for lower gears because they
reduce the length of chain that is pulled around in a pedal revolution. 
Larger cogs make for lower gears because they require more chain to be
pulled to turn them.  So you are in your lowest gear when the chain is
on the smallest chainring and the largest cog (inverse for the highest
gear).  In the notation discussed above, this is "L1."

Many people believe (incorrectly) that their bike has two sets of gears:
"low" ones when the chain is on the small chainring, and "high" ones
when the chain is on the large chainring.  In fact there is considerable
overlap between the two, and each bike has a calculable ideal shifting
pattern that requires at least one crossover between chainrings (many
shifting patterns require more).  For details on calculating the
shifting pattern of your bike, see below.

However, it's not really necessary to calculate and remember your
shifting pattern to get more out of your gearing system.  Just remember
three things: One, you need to cross over to the large chainring
somewhere in the middle of your freewheel; that is, if you climb a hill
in your lowest gear (L1) and want to shift up after the hill ends, you
can shift to L2, then L3, then maybe L4, but before you get too far you
want to get onto the large chainring by shifting to H2 or possibly H3
(that's a double-shift to a larger chainring, larger cog).  You can 
actually get by shifting directly across (L3 to H3) but should be
careful not to let your cadence drop too much.

Two, if you have a triple chainring, your smallest chainring is probably
what is called a "granny"; very low gears for big hills.  With a granny
you use only the biggest 2 or 3 cogs (L1, L2, L3); if you need a higher
gear you should get back on the middle chainring.  L1 and L2 are usually
far lower than M1, L3 is usually pretty close to M1.  If you go much
above the third cog on the smallest chainring, you will probably throw
your chain.

Three, NEVER use the largest chainring, largest cog, or smallest
chainring, smallest cog combinations (H1 or L7), for two reasons. 
First, the steep angle the chain has to take causes excessive wear on
the chain, the cogs, and the chainrings.  But more importantly, these
combinations tax the ability  of the rear derailleur to deal with the
slack in the chain.  The H1 combination can immediately jam the chain if
the chain is a link too short, and the L7 combination usually puts more
slack into the chain than the derailleur is able to take up; when the
chain is too slack, any jolt or bump can knock it off the cogs.  Thrown
chains (along with flat tires) are the most common cycling problem,
mostly because people insist on riding in the L7 gear.  It's somewhat
natural, because in this position both the derailleurs are "relaxed" (no
tension on the cable) and the shifters are usually both in the same
position.  But it's a bad idea and in any case it's usually a redundant
gear that H5 or H6 can replace easily.

That's about all you really *need* to know to shift effectively.  For
the whole story, read on.

The original bicycles were known as "high-wheelers" or
"penny-farthings," the former because the front wheel was huge, the
latter because the difference in size between the front and rear wheels
was similar to the difference in size between a penny and a farthing. 
The cyclist sat high up on the front wheel and turned cranks mounted on
the axle.  As you might imagine, these bikes were highly dangerous; when
the chain-drive bike was invented (fortunately, not too long after the
penny-farthing) it was known as the "safety bicycle."

The front wheel was huge because a larger wheel travels further with
each pedal revolution.  By changing wheels, cyclists could shift to a
lower or higher "gear."  It was a cumbersome system, but one thing from
it remains to this  day; gears on "safety bicycles" are measured in
"gear-inches."  A gear of 50 gear-inches (usually written as a "50-inch
gear") has the same gear ratio (wheel turns:pedal turns) as a
high-wheeler with a front wheel 50 inches in diameter.  The safety
bicycle gives another advantage over the penny-farthing here; the
maximum gear on a penny-farthing is limited by the length of the
cyclist's legs (since he has to reach the pedals in the middle of the
wheel). Top gear on most road bikes is usually 100+ inches.

You can figure out your ideal shifting pattern by computing the
gear-inches of each of your gear combinations and putting them in a
little chart (see below).  Beware that gear-inches are on a logarithmic,
not linear, scale. The formula for gear-inches is:

number of teeth on chainring 
---------------------------- * diameter of wheel in inches. 
   number of teeth on cog

(or <gear ratio> * <diameter of wheel in inches> )

When you think about it, this makes sense.  When the number of teeth on
the chainring is equal to the number of teeth on the cog, one revolution
of the pedals produces one revolution of the wheel; therefore one
revolution of the pedals produces the same wheel motion as one
revolution of pedals attached directly to the wheel would.  The biggest
problem is counting the teeth; some chainrings and cogs have the number
of teeth etched into the side, but most you have to count by hand.  An
experienced eye can make good guesses, though.

For posterity's sake, here are the gearings on my bikes.  There's a cool
Hypercard stack, ~tom/bikestuff/Bike_Gear.sea.hqx, that will do the 
calculations for you and print out a cool graph on a logarithmic scale,
but to just generate the numbers is a fairly simple C/perl program if
someone wants to do it.

First, my Traveler, the bike I usually take on CSUA rides.  It's set up
for road riding without much extra weight; it has 2 chainrings and 7
freewheel cogs.

   L     H
_____________
| 44  | 54  | 1   The optimal shifting pattern is something like
|-----|-----|     L1-L2-L3-L4-L5-H4-H5-H6-H7.  The L5-H4 shift is a pain,
| 49  | 61  | 2   so usually I will do L4-H4 or L5-H5.  This is known as
|-----|-----|     Alpine gearing because it gives lots of high and lots
| 57  | 70  | 3   of low gears for big hills.  44 gear-inches is not a
|-----|-----|     particularly low gear but it usually suits my purposes 
| 67  | 83  | 4   for this bike.  117 inches is quite a big gear,
|-----|-----|     bigger than I really need, but it's great for Bear
| 76  | 94  | 5   Creek Road and other big descents.  This is my
|-----|-----|     recreational bike, after all.
| 87  | 108 | 6   Note that L7 and H1 are virtually duplicated.
|-----|-----|
| 94  | 117 | 7
-------------

This one is for my Voyageur, the bike I use for touring and usually
commuting (as well as riding in the rain).  It has a good rack, fenders,
sizable tires, and other features that make it good for riding with
weight.  It has a triple chainring and 7 freewheel cogs.

   L     M     H
___________________
| 31  | 49  | 59  | 1  This setup I made myself; the idea is that the
|-----|-----|-----|    L ring takes care of all the really low gears, 
| 34  | 54  | 65  | 2  so it's possible to have a very narry spacing on
|-----|-----|-----|    the other two chainrings (I don't really need
| 38  | 60  | 73  | 3  super-high gears when touring or commuting, as
|-----|-----|-----|    opposed to recreational riding).  The shift 
| 43  | 68  | 83  | 4  pattern is something like L1-L2-L3-M1-M2-M3-M4-
|-----|-----|-----|    M5-M6-H4-H5-H6-H7.  Again, the M6-H4 shift is
| 46  | 73  | 89  | 5  a pain and usually becomes M5-H5 or something.
|-----|-----|-----|    Because of this I think this system is suboptimal
| 50  | 79  | 96  | 6  but for my uses it is adequate.  Note that 
|-----|-----|-----|    while this bike has more "speeds" it actually
| 54  | 86  | 104 | 7  has a lower top end.
-------------------

This last one is for my MB-3.  It's a mountain bike, obviously, with
a triple chainring and 7 freewheel cogs.  It has a rack but rarely
carries much weight.

   L     M     H
___________________
| 21  | 33  | 40  | 1  Mountain bikes need very low gears to get up
|-----|-----|-----|    short, steep sections of trail with poor traction. 
| 24  | 38  | 46  | 2  The granny ring combined with a fairly large 
|-----|-----|-----|    rear cluster provides a lower than 1:1 ratio
| 27  | 43  | 52  | 3  when needed (mountain bike wheels are about 26
|-----|-----|-----|    inches in diameter).  The rest of the pattern
| 31  | 49  | 60  | 4  is known as Crossover; so called because you
|-----|-----|-----|    can cross over at basically any point. L1-L2-L3-
| 37  | 58  | 70  | 5  M1-M2-M3-M4-H4-H5 etc. or M1-M2-M3-M4-M5-H5 are
|-----|-----|-----|    fine patterns, and M3-H3 or M6-H6 also work.  
| 42  | 66  | 80  | 6  This flexibility is useful on the trail, since
|-----|-----|-----|    you often find yourself needing a higher or
| 48  | 76  | 92  | 7  lower gear quickly and without warning.  The
-------------------    tradeoff is larger average gaps between gears
                       and a smaller range (note the top end is just 92
                       inches).

The other major gearing pattern, used on some mountain/touring bikes, is 
called Half-Step Plus Granny.  It's for triple chainrings and the 
optimal shift pattern is something like L1-L2-L3-M1-M2-H2-M3-H3-M4-H4
etc. Bike magazines tend to honk on mightily about the virtues of
half-step  gearing, which is just more evidence that bike magazines
don't have a clue about how actual cyclists ride.  Sure the pattern is
easy to remember but nobody, and I mean NOBODY, does that many double
shifts.  If you're choosing gearing for a bike, look for a setup with no
more than one double-shift.  The possible exception would be on bikes
with bar-end shifters (hi kube) since they make double shifts fairly
easy if you often keep your hands near the end of the bars.  I had
bar-end shifters and a half-step plus granny system on my Voyageur when
I first got it and hated it.  But to each his own.

Anyway, the routes for this Sunday's ride are in ~tom/bikestuff/routes/
6-26-94.  We're leaving Evans at 11 AM and taking BART to Orinda.  If
the weather I had yesterday is any indication, it should be beautiful,
but be sure to bring lots of water because it will be hot.  I recommend
freezing your water bottles the night before.  The easy ride is shorter
than most but more hilly; the intermediate ride is shorter than most and
maybe a little more hilly (it's actually a fairly easy intermediate ride),
and the advanced ride is quite hilly but not too long (it's somewhat
easier than the last advanced ride through Marin).

See you Sunday.  Ride Bike!
 -Tom