Author’s note: this article has been heavily revised since its original publication on this website.
I really enjoy cycling. It’s been really good to me, as a hobby - I stay fit, I get outside, and bikes themselves are a tinkerer’s dream. They have all the of the fun mechanical parts (bearings, gears, chains, pulleys) while being relatively attainable and easy to work on.
I definitely consider myself a car enthusiast, but it’s much more realistic for me to acquire a project bike than it is a project car.
I’ve got three bikes:
- The ‘74 Raleigh single-speed conversion pictured above,
- a 2021 Cannondale Topstone 4 (the subject of this piece),
- and a 2019 Trek Marlin 5
The Topstone was the first “road bike” I ever purchased. Yeah, it says “Gravel” on the tin, but “Gravel Bike” is a bit subjective. If you ask 4 different people, you’ll get 4 different responses. For my Topstone, it basically means it’s a road bike with a front fork and rear seatstays that can fit wider tires, and gearing that resembles a mountain bike’s.
To that last point - one of the concessions that Cannondale’s engineers made when equipping this bike was the 1x10 mountain bike drivetrain. The drivetrain spouts impressive range - the rear cassette goes from 11 teeth up to 48(!) teeth at the high end.
This setup should provide the best of both worlds - low gears for tackling higher grades and winding trails, and high gears for paved surfaces. The lack of a front derailleur also eliminates complexity and weight1, and (in theory) makes it easier to pick the correct ratio when traversing quickly changing terrain.
Of course, the reality is slightly less rosy. Consider that the drivetrain has a somewhat low number of gears with which to provide that excessive range. This leads to situations where it’s not easy to find a comfortable gear near the top end of the range (the smallest cogs).
Theoretical degree in Physics
Understanding why this sucks requires us to think about this theoretically.
The mechanics of maintaining a given speed on a bike are simple: you’re trying to balance the force of your legs propelling you forward via the rear wheel, against the force of everything else. That “everything” is mostly comprised of:
- Wind resistance
- Friction
- Gravity
Say I’m riding along, and the gradient of the road I’m on increases from 1% to 2%. This increases the gravity component of the “everything”. For the sake of argument, say that this increases total pull by 5%.
“Just pedal 5% harder!” is the obvious response, but it’s wrong. I don’t need to pedal 5% harder - I need to increase the force the tire exerts on the road by 5%. This is where mechanical advantage in the drivetrain starts to work against me: the 5% increase in force at the wheel is multiplied by the advantage the wheel has over my legs. Therefore, small increases in “pull” at large gain ratios produce large changes in pedaling effort required to maintain speed.2
This matters because the human leg is not an uncaring machine. In physics, Watts are Watts, but anyone who’s spent any serious amount of time on a bike will tell you that 200W @ 60RPM feels different than 200W @ 90RPM. This is because of weird bio-mechanics things that are way above my pay grade. Take my word that maintaining a comfortable cadence and pedaling force is an important part of not tiring yourself out too quickly.
What this boils down to is: at higher gain ratios, large gear-to-gear differences are bad, because changes in pedaling force get multiplied by the gain ratio. This leads to situations where there may be no gear combination which allows you to pedal at your most comfortable combination of pedal force and cadence - the smallest cog may be too high, and the next largest cog may be too large.
Quantifying the Problem
Now, just because we feel like a problem exists, does not mean that it does exist. Let’s do some math!
I was looking around for a calculator to punch in some gear combinations, which (naturally) led me back to Sheldon Brown’s site. That’s how I stumbled onto the article about Gain Ratios..
I can’t possibly do the original article justice, so here’s an excerpt:
This number is a pure ratio, the units cancel out. I call this a “gain ratio” (with thanks to Osman Isvan for suggesting this term.) What it means is that for every inch, or kilometer, or furlong the pedal travels in its orbit around the bottom bracket, the bicycle will travel 5.58 inches, or kilometers, or furlongs.
For a mental shortcut, we can think of the Gain Ratio as the amount of effort required to move the bike from a standstill. Higher gain ratio, more effort. This isn’t wholly accurate, but it’s a good mental model that’s intuitive if you’ve ever ridden a bike before. The difference from computing the raw gear ratio is that the Gain Ratio takes crank arm length and tire size into account.
The site has a calculator, but I found it finicky on modern Firefox. It’s one of the parts of the old web that hasn’t aged so gracefully. So, I went and recreated it in a spreadsheet. Let’s see what that looks like for the factory Topstone 4:
The numbers clearly reflect what I’ve been feeling on the bike: the jump from the 2nd-smallest to smallest cog is a 15% hike in ratio! In fact, the whole cassette is really bad. The smallest jump is 12.5%.
Proof in the pudding
Anyways, now that we have our calculator, we can start fiddling with the numbers. More importantly, we can go about plugging in the values of cassettes designed by people who spent more time thinking about this kind of thing than I ever will. Let’s do that!
Here’s the Shimano 105 11-30 tooth cassette on Cannondale’s 2023 CAAD13 105, which has a 52/36 front chainring:
The difference between the four smallest cogs are all under 9%. Significantly lower than the 15% of the stock Topstone!
For giggles, let’s swap a couple-generations-old Ultegra 12-30 cassette onto our Topstone.
A pattern emerges, which represents a clear acknowledgement of the problem I’ve been experiencing. High gear-to-gear difference at high gain ratios: bad news.
Discovering this was really exciting! It’s fun when you can validate mental models you’ve built, empirically. It’s like debugging, but for physics.
Building this tool was so insanely helpful during the process of choosing the parts for my Topstone’s upgrade. Bike fitting might be an art, but gearing is a science and I want to help that science in any way that I can. I’m making my gearing calculator available on Google Sheets, and via a download here on the site. Excel should be able to open ODS files, but if yours can’t for some reason, you should download LibreOffice.
If you read all of that - thank you!
Footnotes
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The weight is probably a wash. Front derailleurs are like 150 grams, and you’re easily adding that weight (and then some) to the massive steel gears on the cassette. Chainrings probably aren’t much of a crankset’s weight, either. ↩
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This was such a pain in the ass to explain and I still don’t think it’s as clear as it can be. This is also why everyone argues about horsepower and torque on car forums. ↩