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I have a 20x1.75" 6-speed folding bike with 52x14-28t drivetrain. Even with the gearing at 52x14, ~3.71 ratio, I can still pedal uphill.

I also have a 700x25C fixed gear with 49x17t gearing or ~2.88 ratio. I have yet to try riding it on uphills so I'm not sure if it's going to be difficult to pedal with that gearing.

I know that the gear inches depend on the ratio multiplied by the diameter of the wheels. Given that, I know that the gear inches of my folding bike is at around 74 while the fixed gear is at around 79. But which one actually determines how hard it is to pedal, the gear ratio or the gear inches? If it is the gear inches, would 5 inches higher be that significant? If it is, I'm thinking of getting an 18t or 19t cog.

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    Definitely gear inches, which is the fully calculated gear ratio, since there's effectively a "gear" between the rear tire and the road. Other factors, such as tire size and bike geometry, may affect bike handling and hence the overall ease of cycling, however. – Daniel R Hicks Feb 17 '17 at 12:39
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    The grade is relevant too - there's a 15% near me I can ride up fine on a road bike but my folding bike is pure torture on the edge of balance, due to frame design and balance, even in the same gear-inches speeds. – Criggie♦ Feb 17 '17 at 22:06
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Gear inches. Gear inches are, for better or worse, the most commonly recognized way of making the kind of comparison you're trying to make here, which one is harder to pedal. Gear inches are simply how far one complete rotation of the cranks moves the bike forward. The higher the number, the harder it is to turn the cranks.

You hear people make reference to ratio all the time, but usually it's within a niche where the wheel size is implicit, i.e. cross racers talking about 46/11 on a 700 or BMXers and 25/9 on a 20". Gear ratio independent of wheel size is meaningless.

Gear inches are actually a deeply flawed concept because it doesn't account for crank length. Sheldon Brown's proposed Gain Ratios system solves this and is pretty easy to argue as the best system possible for describing bicycle gearing. It's based on the movement of the pedal and not the crank.

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  • I see. What about my other question about the difficulty of 5 gear inches? Actually, using that calculator, the difference is now 6.6 gear inches (69.4 vs 76). – dork Feb 17 '17 at 9:29
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    "Deeply flawed"? I'll accept "flawed" but I'm not sure it's deep, and that may be why people still use gear-inches. Common crank lengths are basically 172.5mm +/-7.5mm, which is 172.5mm +/-4%, which doesn't seem like a huge difference. – David Richerby Feb 17 '17 at 11:08
  • 5 gear inches isn't much but it certainly is relevant. It's more than many of the jumps on modern cassettes, or all of them on an 11-speed road cassette. And I will stand by "deeply flawed" 100%. Systems for quantifying and comparing gears have one job, and by disregarding crank length, gear inches don't do it right. Gain ratios are an obvious, better, and more elegant solution. – Nathan Knutson Feb 18 '17 at 1:14
  • Gain ratios are not without their drawbacks. Starting from a stop I agree there are good indicator how difficult it would be to pedal, but in a performance context (e.g., time trial) for the same gain ratio I find a shorter crank relatively easier as I do better with a faster turnover rate. In this situation gain ratios can be a bit misleading. They do a good job summarizing mechanical advantage but biomechanics is a bit more complex. – Rider_X Feb 18 '17 at 3:14
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    No one is saying gear inches or gain ratios or whatever are the final word on biomechanical efficiency. – Nathan Knutson Feb 18 '17 at 4:22
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How hard it is to pedal depends on every piece of leverage within the system:

  • your legs are using the cranks as levers against the crank axle;
  • the crank axle is using the chain ring, chain and rear cog as a lever against the rear hub;
  • the rear hub is using the wheel as a lever against the ground.

The gear ratio is essentially the middle term, so you can't consider only that. Using longer cranks makes the input side of the crank lever longer, so makes it easier to pedal; using bigger wheels makes the output side of the wheel lever longer, so makes it harder to pedal.

Gear inches includes both of the last two terms, but ignores the cranks. Since there's not a huge variation in crank lengths (popular sizes are, essentially, 172.5mm +/-7.5mm, which is +/-4%), ignoring the variability of crank length is a probably a reasonable approximation.

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