My goal for this ride (aside from finishing with less embarrassment) was to see how best to take full advantage of the Di2 capabilities. I leaned one Big Thing, and one Little Thing.

First the Little Thing: It is

**fast and easy to pick up or drop lots of gears with Di2! I practiced simultaneous shifts, and never came close to a bad shift. I clicked the buttons as fast as possible to select the front and rear gears without waiting for the shift to complete, then relieved pedal pressure for a moment until the derailleurs became quiet. I can press buttons far faster than I can twist a lever, and the time to shift was amazingly short, significantly faster than I had expected, or even hoped for. I'd estimate multi-gear shifts happen nearly twice as fast as before.**

*so*Now the Big Thing: Front shifts are now the same as rear shifts! This means there is absolutely no need to stay on the current chainring and use a gear ratio that's "close enough" if there's a slightly better gear ratio available on the other chainring. This means that it is now well-worth knowing the order of the gear ratios across all chainring/sprocket combinations, and knowing how to get from one to the next.

And that leads us to the Bike Math portion of this post. Let's look at what one pedal stroke does: One rotation of the crank causes the chain to pass through the number of teeth on the current chainring. Since the chain isn't elastic, that means the same number of teeth must pass over the currently selected sprocket in the rear cassette, which in turn causes the rear wheel to rotate.

Let's take the example of my granny gear: 34 teeth in front, and 28 in the rear. How many times will the rear wheel rotate due to one full pedal stroke (one full crank revolution)? We know that the chain will have been pulled forward by 34 teeth after one revolution of the crank. When the chain moves 34 links forward, the first 28 links will cause one rear wheel revolution, and the remaining 6 links will cause just under 1/4 of a revolution of the rear wheel. The precise number of revolutions is 34/28 = 1.21 revolutions.

And that's our formula to convert front strokes to rear wheel revolutions: Divide the number of teeth in the front chainring by the number of teeth in the rear sprocket. This number is called the

*.*

**gear ratio**But how far will that one full turn of the crank make us move? We know that each full rear wheel rotation moves us forward by an amount equal to the circumference of the rear wheel. But what is the circumference of our rear wheel?

Don't worry: There's no need to measure the diameter of the rear wheel then use trigonometry or equations with Pi in them! Every tire has its "ISO size" on it, which consists of 2 numbers separated by a dash, or it may be written as a fraction. My tires have an ISO size of "23/622". And the ISO specification gives the circumference for each size, which in my case is 214 cm, or 2.14 meters, which is a hair over 7 feet. I got this number from one of Sheldon Brown's excellent web pages.

So how far forward do I go for one turn of the crank in my granny gear? We know the rear wheel rotated 1.21 revolutions, which means I moved forward 7 x 1.21 = 8.47 feet. (It sure didn't feel like that much on that last hill into Del Mar!)

And that's another formula: Distance forward per crank rotation is the gear ratio times the tire circumference.

That's all fine and everything, but what I really want to know is: How fast was I going? I know I was pedaling with a cadence of about 90 RPM, which means my crank turned 90 times every minute, which means that during that minute the rear wheel turned 90 multiplied by the gear ratio times the wheel circumference of 7 feet to give us our forward motion. So our speed was 90 crank revolutions per minute x 1.21 rear wheel revolutions per crank revolution x 7 feet per rear wheel revolution.

This is getting too hard to say in words! Let's try using an equation to restate all the above in a more condensed form:

Well, a value of 762.3 feet/minute is what comes out of the equation, given the units we've been using. Let's convert it to the more familiar units of miles per hour:

A speed of 8.66 miles per hour is very close to what my Garmin reports, so it seems the math actually works! We can't expect an exact match, since things like tire wear and inflation pressure affect the effective circumference of the tire. But this value is certainly useful as-is.

Now that we've calculated the speed we expect to see for a given cadence when using a specific chainring and sprocket, what about the other gear ratios associated with all possible combinations of front chainrings and rear sprockets? With 2 in the front and 10 in the rear, that's 20 total combinations. Let's figure them

*out!*

**all**I have a compact crankset that has front chainrings with 34 and 50 teeth. My rear cassette is an 11-28, which contains 10 sprockets with the following tooth counts: 11, 12, 13, 14, 15, 17 19, 21, 24 and 28. The speeds listed assume a 90 cadence.

__Chainring__

__Sprocket__

__Ratio__

__Speed__

50 11 4.55 32.54

50 12 4.17 29.83

50 13 3.85 27.53

50 14 3.57 25.57

50 15 3.33 23.86

50 17 2.94 21.06

**50 19**

**2.63 18.84**

50 21 2.38 17.05

50 24 2.08 14.91

**50 28**

**1.79 12.78**

34 11 3.09 22.13

34 12 2.83 20.28

**34 13**

**2.62 18.72**

34 14
2.43 17.39

34 15
2.28 16.23

34 17
2.00 14.32

**34 19**

**1.79 12.81**

34 21
1.62 11.59

34 24
1.42 10.14

34 28
1.21 8.66

Hmmm... It seems that there is some redundancy in my system of gears! The combinations of 34/19 and 50/28 have nearly the same ratio, and the combinations of 34/13 and 50/19 have ratios differing by half a percent. That means that out of our 20 gear combinations, only 18 of them are truly unique.

It gets worse: The range of ratios on the large chain ring have substantial overlap with the range of ratios on the small chain ring: The upper 7 ratios on the small ring overlap with the lower 5 ratios on the large ring! With the overlap removed, we are left with no more than 15 non-overlapping gear combinations!

However, this overlap is to be expected, given the wide tooth range on my rear cassette. A cassette with a minimal tooth range, such as 12-23, is called a "corncob", and will have much less overlap, sometimes none at all, depending on the front chainring selection.

Fortunately, not all the gear combinations in the overlap zone are wasted: Several of the overlap ratios on the large chainring fit nicely between those on the small chainring. Let's sort the above table by ratio and see how it looks. I'll also add the sprocket number for later use.

__Chainring__

__Sprocket__

__Ratio__

__Speed__

50 11 (1) 4.55 32.54

50 12 (2) 4.17 29.83

50 13 (3) 3.85 27.53

50 14 (4) 3.57 25.57

50 15 (5) 3.33 23.86

34 11 (1) 3.09 22.13

50 17 (6) 2.94 21.06

34 12 (2) 2.83 20.28

**50 19 (7)**

**2.63 18.84**

**34 13 (3)**

**2.62 18.72**

34 14 (4)
2.43 17.39

50 21 (8) 2.38 17.05

34 15 (5)
2.28 16.23

50 24 (9) 2.08 14.91

34 17 (6)
2.00 14.32

**34 19 (7)**

**1.79 12.81**

**50 28 (10)**

**1.79 12.78**

34 21 (8)
1.62 11.59

34 24 (9)
1.42 10.14

34 28 (10)
1.21 8.66

This list shows why I picked the chainrings and cassette I did: I get to have a great granny gear (34/28) while still having one top-end gear above 30 mph (50/11). Well, I didn't quite pick them that way: That's just how they turned out, since I picked the widest front and rear tooth-count ranges that the Ultegra Di2 derailleurs can accommodate. There are wider cassette and chainring ranges available, but they aren't Di2-compatible.

Sorting the list places the redundant ratios next to each other, making their similarity easier to see. Notice too that, except near the redundant ratios, the overlapped ratios ping-pong back and forth between the front and rear chainrings.

The overlap zone ranges from a speed of 14.91 mph up to 22.13 mph. This happens to be the speed range I spend the vast majority of my time in. Let's see what it would take to use these gears.

Let's say I'm hammering at nearly 24 mph in gear 50/15. (Hey, that

*hammering for me!) I'm starting to tire, and I'd like to ease up just a bit. The next lower ratio is 34/11, which is on the other chainring, and 4 rear shifts away. And if I tire a bit more, the next ratio down has me switching chainrings again, then doing 5 rear shifts.*

**is**With a manual shift system, that would certainly be way too much shifting for way too little gain, but with the Di2 it is just a total of 5 button clicks for the first and 6 clicks for the second. And that's as bad as it gets: The other gears within the overlap are fewer shifts apart. Let's make a table of the front and rear shifts needed to get through all the ratios in-order,skipping whichever redundant ratio makes for less shifting:

__Chainring__

__Sprocket__

__Ratio__

__Speed__

50 11 (1) 4.55 32.54

*Shift: 0 1*

50 12 (2) 4.17 29.83

*Shift: 0 1*

50 13 (3) 3.85 27.53

*Shift: 0 1*

50 14 (4) 3.57 25.57

*Shift: 0 1*

50 15 (5) 3.33 23.86

*Shift: 1 4*

34 11 (1) 3.09 22.13

*Shift: 1 5*

50 17 (6) 2.94 21.06

*Shift: 1 4*

34 12 (2) 2.83 20.28

*Shift: 0 1*

~~50 19 (7)~~

**2.63 18.84**

**34 13 (3)**

**2.62 18.72**

*Shift: 0 1*

34 14 (4)
2.43 17.39

*Shift: 1 4*

50 21 (8) 2.38 17.05

*Shift: 1 3*

34 15 (5)
2.28 16.23

*Shift: 1 4*

50 24 (9) 2.08 14.91

*Shift: 1 3*

34 17 (6)
2.00 14.32

*Shift: 0 1*

**34 19 (7)**

**1.79 12.81**

**50 28 (10)**

~~1.79 12.78~~

*Shift: 0 1*

34 21 (8)
1.62 11.59

*Shift: 0 1*

34 24 (9)
1.42 10.14

*Shift: 0 1*

34 28 (10)
1.21 8.66

It is interesting to see that minimal shifting is obtained by dropping the redundant ratios on the large chainring.

So, I now have a shift list, and since it looks pretty random and hard to memorize, I'll want to have it with me while riding, which means I'd probably want to tape it to my handlebars or wear it on my wrist. A small hassle, but certainly do-able.

But there is one other factor to consider: I always need to know which rear sprocket is in use! Since there is no gear indicator, that means I'll either have to remember, or more likely I'll have to take a look back before deciding which shift is needed.

I'll give it a try to see if it is worth the effort.