Understanding Gears, or Aww man, More Math!

My, what big teeth you have...
My, what big teeth you have…

So, you’ve been riding around on your double, triple, mid-compact or compact double for a while now. You know to make a big change, you shift the front, a smaller change, the back. You know that your front small ring in combo with your rear big gear is like riding a stationary bike – lots of spinning to get nowhere. Whereas your big front ring and your smallest rear gear makes your legs feel like you have to move a sofa bed into a 5-floor walk-up.

If you’re the type who looks at baking measurements for a recipe for homemade cookies, and then heads to the store to pick up a package of Betty Crocker, don’t read on. Cause this could get messy (just kidding… sorta).

The Concept

Here’s a quick demo to get our minds on the right track: take a pencil and lay it on your desk. Now, flip the pencil end-over-end once. The pencil has now moved one pencil length. This is like riding a single-speed or fixed-gear bike.  The distance from end-to-end of the pencil doesn’t change, no matter how many times you flip it over.

But what if you want to change the distance it moves without changing the length of the pencil itself? Find two straws (or cut a straw in half), and stick one straw on either end of the pencil. If you flip the structure end-over-end, the total distance has increased, but the pencil itself is the same size.

The pencil in this example is taking the place of your cranks (the arms attached to your pedals). If you only had one gear on your bike, the distance your bike moves for each revolution of your crank will always be the same. That’s where gears come in. They act like the straws, artificially increasing/decreasing the length of your crank arms.

Another way to think about gearing is to consider torque. To keep it simple, we’ll use a wrench and bolt example. If you have a very long-handled wrench and use it on an easy-to-turn bolt, you barely have to apply any force to the wrench to turn the bolt. That’s like using the lowest gear on your bike to ride on a flat road. It’s very easy to spin the rear wheel (very low torque). But if you have a short-handled wrench and a really tight bolt, you need to apply a lot of force to turn that bolt. This is like trying to climb a steep hill in your highest gear – you’ll barely be able to turn the crank because the torque required to turn the rear wheel is too high.

So you need to find a balance: long-handled wrench on tight bolt = low gear on steep hill. You’re reducing the torque needed to turn your rear wheel. Short-handled wrench on loose bolt = high gear on flat road. You’re pedaling less and going fast. Some people don’t get the torque concept because it requires translating a twisting force into generating forward motion. We’ll stick with the distance stuff for now to keep it a little simpler.

The Behavior

Without gears, this would suck.
Without gears, this would suck.

After you’ve ridden your bike a while, you’ll start to find sweet spots – gears that work very well for your particular cadence, the speed you want to travel, the terrain, etc. You’ll also find that some combinations of gears are eerily similar to others, making you wonder why they are the same.

Well, turns out that there are some combinations of gears that are almost identical. On a bike with a triple chain ring, one combination of the rear cogs and large chain ring come very close to matching the revolutions of one of the combos on the middle ring – and one of the combos on the small ring – for a given speed. Learning these overlap points can be useful for figuring out when you’ll need to shift your chain ring versus your cassette cogs (front or rear). And the more efficient you are at shifting, the easier your ride will be, and the better prepared you’ll be for climbs.

The Calculations

Okay, I didn’t mean to scare anyone off with math, so I’ve employed a calculator from Sheldon Brown’s website. I find his concept of gain ratios to be one of the easiest ways to compare various gear combos on a bike, or even one bike to another.

A gain ratio takes into account your wheel/tire size, your crank length, your chain ring sizes (front), and your cassette cog sizes (rear). Crunching all those numbers, we come up with a ratio between the linear distance your crank travels versus the distance your bike travels, and the difference between each combination of gears. Imagine a frisbee describing the outer-length of your crank arms (the diameter of the circle your crank arms make). If you have a gain ratio of 5.0, and that frisbee rolls one foot, the entire bike will have traveled five feet. The unit of measurement doesn’t matter (inches, feet, miles, etc.) because it’s a ratio.

The Comparison

Here’s an example: we have a bike with a 52/42/30 triple chain ring, and a 12-25 cassette (8 cogs). Quick note: the numbers (52/42/30) indicate the number of teeth on a cog or chain ring.  So a 52/42/30 means three chain rings, the largest has 52 teeth, the middle 42, and the smallest 30.  The “12-25” means the cogs on the cassette (each “gear”) will range from 12 teeth (the smallest cog) to 25 teeth (the largest). Here’s what the calculator comes up with:

52 23.8 % 42 40.0 % 30
12 8.4 6.8 4.9
13 7.8 6.3 4.5
15 6.7 5.4 3.9
17 5.9 4.8 3.4
19 5.3 4.3 3.1
21 4.8 3.9 2.8
23 4.4 3.5 2.5
25 4.0 3.3 2.3

What do all these numbers mean? Well, let’s say you’re on your smallest chain ring (30) with your largest cog (25), the gain ratio is 2.3. That means that for every foot your crank travels, your entire bike travels 2.3 feet. Same goes for miles: remember, the ratios are unit-independent (meaning it works for any unit of measurement).

On the other end, your big chain ring (52) with your smallest cog (12) gives you a gain ratio of 8.4. For every foot your crank travels, your bike travels 8.4 feet. That means your bike travels about 3.6x further per revolution of the crank (8.3 / 2.3) on your highest gear than on your lowest. Another way to think of it: it’s 3.6x harder to turn your crank on your highest gear than your lowest.

The Usage

Now let’s look at where these gears combos overlap. First, check out the numbers in green above. If you’re in your big chain ring, you can’t slow down your speed without slowing your cadence, because your cassette is as far down as it’ll go (note: when I say “down” for a cassette, that means lowest gear, which is the biggest cog). So if you see the terrain is going to incline ahead, and you know you’ll have to down-shift, you can prepare by shifting to down to your middle chain ring (42).

If you do this, you’ll immediately notice that you have to pedal faster to maintain your speed. That’s because your gain ratio went from 4.0 to 3.3. To avoid having to pedal that much faster, shift up to two cogs on your cassette. Notice that by shifting up two cogs, your gain ratio is going from 4.0 on the big chain ring to 3.9 on your middle chaing ring – very close. What this does is allows you to maintain your current speed and your current cadence (or at least, keep it close to what you were doing) while giving your room to go down to smaller cogs should it be necessary.

Likewise, if you’re in your middle chain ring and you see a very wall-like hill ahead, you can down-shift to your small chain ring, and up-shift your cassette by three cogs to maintain the same cadence/speed you’re currently at (by maintaining the same gain ratio), but get you ready for that big hill by giving you more gears to drop to.

The numbers in blue are another useful overlap point for this particular group set, albeit for higher speeds. You won’t need to remember the numbers while riding, just the feel of those overlap points. The numbers here just demonstrate why those overlap points exist, and give you a visual of the distances between them. The big thing to remember is that you don’t want to waste your momentum. So: shifting down a chain ring? Shift up a couple of cogs. Shifting up a chain ring? Shift down a couple of cogs.

The Compact Double

Next up, here’s the numbers for a very common setup, the compact double (50/34 front, 11-28 back, 10 cogs):

50 47.1 % 34
11 8.8 6.0
12 8.1 5.5
13 7.5 5.1
14 6.9 4.7
15 6.5 4.4
17 5.7 3.9
19 5.1 3.5
21 4.6 3.1
24 4.0 2.8
28 3.5 2.4

You can see some important differences here from the triple setup. First, the differences between each cog for each chain ring (column) is usually larger than on the triple. This is especially true of the large chain ring (50). And the gain ratios are a little harder to match up from one chain ring to the other. This makes early shifting and understanding your gears very important in order to use them efficiently.

Let’s say you’re in your big chain ring (50) and your 2nd lowest (largest) cog (24). That gives you a gain ratio of 4.0 (green). The closest ratio on your small chain ring is 3.9, three cogs up (17 teeth, also in green). Because of this, it’s trickier to switch from the big ring to the small ring and maintain your cadence. Here’s a tip that works for me. If you’re going from big chain ring (50) to small (34):

  1. Go up one to two cogs on your cassette first, applying slightly more pressure to maintain your speed as your cadence drops.
  2. Shift your chain ring down (make sure to let up slightly so the chain doesn’t slip/jump).
  3. Once the chain catches, continue shifting up your cassette up to match your previous cadence (usually one to two more cogs).

Practice this on your own before trying it in a pace line or while climbing a hill (where it can be very challenging). A stationary trainer is deal for practicing chain ring shifting. To go from small to big:

  1. Shift your cog down on, and increase your cadence to maintain your speed.
  2. Shift your chain ring up (again, lighten the pressure slightly to make the shift cleaner), and anticipate it getting very hard to pedal for a brief moment.
  3. Increase pressure once your chain catches the big chain ring to retain your speed at the lower cadence.
  4. Immediately start shifting down your cassette until you hit the desired cadence, easing up on pressure so as to not speed up while you’re in those higher gears.

Warning: if you are shifting up on your cassette at the same time you’re shifting down on your chain ring, you could get the chain caught between the chain ring and the front derailleur. This is because as the rear derailleur pulls the chain to the right, your front derailleur is moving to the left. So make sure your rear derailleur isn’t moving when you’ve clicked for that front derailleur to drop. Practice the sequencing. NOTE: this isn’t a problem for electronic shifting. But let’s face it: if you have electronic shifters, you should know all this already. :p

The Conclusion

Shift early, shift often.
Shift early, shift often. Your legs will thank you.

As you might get from all the above (or not), this means you’ll be shifting your gears a lot. I mean, a LOT. The good news is, that’s what they’re designed for! You’re supposed to be shifting to match the cadence, speed, and terrain. If you’re not, you’re either specifically training (pushing larger gears to build power or pushing smaller gears to work on a faster cadence), or you’re just riding inefficiently.

Riding is all about momentum conservation: use your energy to get up to speed, and then use the energy that’s in your forward motion (your momentum) as efficiently as possible. Going forward uses up some of that momentum naturally, and you have to replace it with some more energy from your body. So the more momentum you conserve, the less energy you’ll have to use to replace it. If you down-shift too far on a hill, your cadence will be too high, and you won’t be able to put enough energy into the bike to retain your momentum. You’ll lose speed, and you won’t get it back without putting in even more energy. If you don’t down-shift enough for a big hill, you have to increase your power output (more pressure on the pedals) to maintain your speed as the steepness increases.

There’s a balance you have to strike when shifting your gears, and it’s different for everyone based on their capabilities, their bike’s capabilities, and the terrain being faced. In other words, the best way to understand and become more efficient at shifting gears – more than all the numbers combined – is to shift gears.