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Old 01-24-07, 12:25 PM   #1
rhm
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Gain Ratios for 16" wheel bikes

I have three bikes designed for 16" wheels, and their gearing is remarkably different. Since a lot of the folding bikes being discussed here --Bromptons, Strida, and the cheapo's like Kent-- have 16" wheels, I'd like to compare their gearing.

Strida
The chain is actually an automotive timing belt. I count 100 teeth on the front "chainring" and 30 on the rear, which (if I have done this right) is equivalent to a 50-T / 15-T combo, which yields a gain ratio of:
3.5.

Kent Magnesium Folding Bike
The stock chainring is 46-T that, coupled with a standard 14-28 freewheel, yields these ratios:
1.7 2 2.2 2.4 2.6 3 3.4

Raleigh RSW-16
The front chainring is 48-T, the rear is 13-T, with a Sturmey-Archer three-speed hub, for these gain ratios:
2.9 3.8 5.1

In other words, the single-speed Strida is geared for going faster than any gear ratio on the Kent; the RSW-16, though the heaviest and oldest by far, is geared for going much faster than either.

I switched my Kent's front chainring to a 52-T, which improves the situation considerably:
1.9 2.2 2.4 2.7 3.0 3.4 3.8
It is now able to go a little faster than the Strida, but still cannot keep up with the RSW-16.

Corrections are of course welcome. I'd also like to see the gain ratios on some other folding bikes, esp. the Brompton. Also, I wonder if other RSW-16's have lower gain ratios than mine?

Rudi
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Old 01-24-07, 12:37 PM   #2
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There's also the Downtube Mini that is 16" and uses the 8 speed SA internally geared hub.

You can find info in this thread: Review of Downtube Mini with internal hub

Quote from Crankypants on gear inches: I believe that the low is 24.8" and the high is 75.4".
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Old 01-25-07, 05:32 AM   #3
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The three speed Brompton and Dahon Presto have the same gearing although the Brompton is slightly higher. Although you like higher gearing, I prefer a low direct drive between 48-52 inches. The reason why this low direct drive is due to the fact that 3rd gear is too high and hardly used. The Sturmey Archer AW-3 or Sram Spectro 3 are actually 2 speed hubs.
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Old 01-25-07, 02:27 PM   #4
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No, I'm okay with lower ratios, within reason. Your suggestion of 48 inches sounds pretty good to me; but it's actually a higher ratio than the single speed on the Strida (44.9). But the gearing of the Kent is laughable; the lowest gear is 22.1 gear inches, and the highest (44.2 gear inches) is still lower than your 48-52 "low."
The Downtube Mini sounds much better, but even so, does anyone need a low gear of 24.8 gear inches? Increase that to 30 or 35, and you'd have a more versatile bike.
Playing with these numbers --and relying heavily on Sheldon Brown's Gear Calculator-- I see why 16" wheel bikes need internally geared hubs.
Let's say you wanted to upgrade the Kent's derailleur gearing to resemble that of the RSW-16. If you leave its OEM 14-28 freewheel in place, you'd have to increase the chainring to 69-T. Not a common size. And this would still be pretty conservative gearing; your high gear of 66.2 gear inches would still be way below that of a Swift (highest gear: 88 gear inches), let alone most road bikes, with a highest gear well over 100 inches.
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Old 01-25-07, 08:55 PM   #5
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Quote:
Originally Posted by rhm
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Playing with these numbers --and relying heavily on Sheldon Brown's Gear Calculator-- I see why 16" wheel bikes need internally geared hubs.
Bikes with 16' inch wheels come with hub gears because the common derailuer would be within inches of the ground. Someone posted a pic of a 16' inch wheel Bike Friday and the derailuer must have been less than an inch off the street. Not a good design at all.

The second reason these bikes come with hub gears is the wear and tear in a derailuer due to winter commuting or bagging.
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Old 01-30-07, 11:46 PM   #6
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I think you have to be careful when simply looking at the gearing while ignoring the wheels. Large gain ratios exacerbate differences in wheel size. Remember that the final gear inch calculation involves multiplying the gain ratio by the wheel size. Since the gain ratios for small wheeled bikes are large, the wheel size is being multiplied by a large number. More importantly, the deviation from 16" is being multiplied by a large number (remember the distributive property of multiplication x*(y+z)=x*y+x*z).

Three common 16" wheel sizes are 37-305, 50-305, 35-349. Assuming the tire is a perfect donut these correspond practical diameters of 14.9", 15.9", and 16.5", respectively. Using a gain ratio of 3.5 yields gear sizes of 52.1", 55.7", and 57.8", respectively. A whopping 11% spread, which is almost as big as shifting one gear on the bikes cited above.

Then there is the length of the crank, which seems like it should be just as important as the size of the chainring, but people generally seem to ignore it.
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Old 01-31-07, 11:05 AM   #7
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Good point, a wider tire means a bigger wheel, and if you're starting with a very small wheel like 16", the difference can be significant. My comparisons between the RSW-16, Strida, and Kent all assume the same tire size. If I had taken the time to account for stock tire sizes, the RSW-16 --which had the highest gearing in my survey-- would have had an even higher gearing, since it originally came 2" tires (though I wonder how many of those white Dunlop tires are still on the road).

I am not sure how to factor in crank arm length, even after reading Sheldon Brown's essay on the subject. I have ridden with 165, 170, 172.5 and 175 mm crank arms, and I honestly cannot tell the difference. I understand intuitively that long crank arms will give you more leverage. This will make it easier to pedal at low cadence, which is an advantage when starting from a stop or going up a steep hill, especially in a high gear. But the longer crank arms will become a disadvantage at high rpm's. If a bike is geared very low, and the rider needs to spin like mad, short crank arms will be more efficient. That is perhaps the reasoning behind the very short (152 mm!) crank arms of the Kent (though one still wonders about the small chainring).
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Old 01-31-07, 12:15 PM   #8
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Quote:
Originally Posted by rhm
Good point, a wider tire means a bigger wheel, and if you're starting with a very small wheel like 16", the difference can be significant. My comparisons between the RSW-16, Strida, and Kent all assume the same tire size. If I had taken the time to account for stock tire sizes, the RSW-16 --which had the highest gearing in my survey-- would have had an even higher gearing, since it originally came 2" tires (though I wonder how many of those white Dunlop tires are still on the road).

I am not sure how to factor in crank arm length, even after reading Sheldon Brown's essay on the subject. I have ridden with 165, 170, 172.5 and 175 mm crank arms, and I honestly cannot tell the difference. I understand intuitively that long crank arms will give you more leverage. This will make it easier to pedal at low cadence, which is an advantage when starting from a stop or going up a steep hill, especially in a high gear. But the longer crank arms will become a disadvantage at high rpm's. If a bike is geared very low, and the rider needs to spin like mad, short crank arms will be more efficient. That is perhaps the reasoning behind the very short (152 mm!) crank arms of the Kent (though one still wonders about the small chainring).
Yeah, I think the crank arm thing is complicated by the fact that your legs need to stretch further when using longer crank arms. The difference in leverage isn't the whole story. Sheldon's "radius ratio" implies that changing the crank length is the same as changing the gearing, but this obviously isn't the case. For example, if you had really long crank arms, but had to pedal with your tippy toes then you obviously wouldn't be able to pedal efficiently (even if you had the same torque/leverage/"radius ratio"). Alternatively, if you had really short crank arms then your muscles would not be fully extending and you would again be lacking in efficiency.

It seems to me that the optimal crank length would depend on your leg measurements. Perhaps when you deviate from this length the difference in torque/'radius ratio" is negated by your legs' inability to effectively circle at a radius equal to the crank length? After all, if crank length really made that much of a difference then why would the usual gearinch-type measures be so widespread and so enduring?

Last edited by makeinu; 01-31-07 at 12:54 PM.
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