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Choosing optimal gear increments

Old 07-13-21, 04:08 PM
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Choosing optimal gear increments

Previously tried out half-step gearing with most of the gaps between gears around 7% and one 12% which felt annoying right around 20-25km/h range @70 rpm cadence. The 7% felt too minuscule sometimes.
Now another option arised using 46t chainring instead of 45t one due to some unrelated mechanical problems. This would solve two issues at the same time.
With 46t one most of the gaps are 10% and few 7%, while others are way too small but still in the range of some corn cob clusters around 5%. Not sure if this option will be better for my specific terrain and reduce unnecessary shifting around 12% gap. Earlier mostly used some 7 speed shimano freewheel with 9, 10 and 11% gaps in the middle which felt adequate, but due to need for lower gearing and being stuck with limited chainring size resorted to half-step gearing.


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Old 07-13-21, 06:44 PM
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I like a 7 percent ratio progression myself. I run 45-42 / 13-15-17-20-23-26 on the Peugeot, and would add a 30 and a 34 for a 2x8 system. I am a big fan of either half-step or 1.5-step, such as 50-42 / 14-16-18-20-23-26.(... -30 for 7 speeds, etc.)
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Old 07-13-21, 09:09 PM
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the 13-15-18-21-24-28-32 sequence is fairly good.
To get from 13 to 32 in six steps, the ideal ratio of one cog to the next is 1.162.
With these cogs, the smallest ratio is 1.143, which is 98.3% of the ideal.
the largest ratio is 1.200, which is 103.3% of the ideal.
Overall, that indicates that these cogs should give pretty even steps between gears.

The issue of selecting the two large chainrings is relatively simple.
The ratio of the ring sizes should be the square root of the ideal cog ratio, which in this case is 1.162.
The square root of 1.162 is 1.078.
If you start with the 42T middle ring, then the large ring should be 42 x 1.078, or 45.3 teeth. Clearly, a 45 tooth ring is a better match than a 46 tooth ring.

This is my general process for designing a half-step system.
I didn't see a question in the first post, so I'm guessing you are just looking for some general input?

Steve in Peoria
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Old 07-14-21, 03:50 AM
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Originally Posted by steelbikeguy
the 13-15-18-21-24-28-32 sequence is fairly good.
To get from 13 to 32 in six steps, the ideal ratio of one cog to the next is 1.162.
With these cogs, the smallest ratio is 1.143, which is 98.3% of the ideal.
the largest ratio is 1.200, which is 103.3% of the ideal.
Overall, that indicates that these cogs should give pretty even steps between gears.

The issue of selecting the two large chainrings is relatively simple.
The ratio of the ring sizes should be the square root of the ideal cog ratio, which in this case is 1.162.
The square root of 1.162 is 1.078.
If you start with the 42T middle ring, then the large ring should be 42 x 1.078, or 45.3 teeth. Clearly, a 45 tooth ring is a better match than a 46 tooth ring.

This is my general process for designing a half-step system.
I didn't see a question in the first post, so I'm guessing you are just looking for some general input?

Steve in Peoria
It may sound like a rhetorical question in a sense.
In order to stay with a 45t (7075) one I have to reduce its thickness somehow from 4mm to 3mm, but the 12% gap kinda ruins everything.
I have access to milling machine and lathe which could help, but the owner says the chainring looks too flimsy to be securely clamped down in order to reduce any chances of accident while working on it.
I could file it down manually, but there is no way to do it without ruining the teeth.
39t small ring would result in more 8% gaps instead of 7%, but as I said I'm stuck with 42t one due to various reasons.
Probably will try out the 46t one to see if it discourages unnecessary shifting which ruins momentum.
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Old 07-14-21, 05:16 AM
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Originally Posted by steelbikeguy
the 13-15-18-21-24-28-32 sequence is fairly good.
To get from 13 to 32 in six steps, the ideal ratio of one cog to the next is 1.162.
With these cogs, the smallest ratio is 1.143, which is 98.3% of the ideal.
the largest ratio is 1.200, which is 103.3% of the ideal.
Overall, that indicates that these cogs should give pretty even steps between gears.

The issue of selecting the two large chainrings is relatively simple.
The ratio of the ring sizes should be the square root of the ideal cog ratio, which in this case is 1.162.
The square root of 1.162 is 1.078.
If you start with the 42T middle ring, then the large ring should be 42 x 1.078, or 45.3 teeth. Clearly, a 45 tooth ring is a better match than a 46 tooth ring.

This is my general process for designing a half-step system.
I didn't see a question in the first post, so I'm guessing you are just looking for some general input?

Steve in Peoria
Steve, I also don’t see a question from the OP, but I completely agree with how you created your 2x7, or is it 2x7 plus granny? I put the same method into an Excel spreadsheet starting a bunch of years ago, but I can never manage to explain it so simply.

To design the cog set you are trying to find the best match to an ideal sequence of 5 to 11 ratios. The ratios are precisely calculated, but to build the closest matching cogset we use real gears which can only be sized in whole numbers. You cannot build a cogset with fractional teeth!

In my spreadsheet I built in a few checkpoints:

> are the tooth jumps constant or increasing as you go from smaller cogs to larger? They should not in general get smaller ac the cogs get bigger. This is just based on subtracting the number of teeth on cogs that are next to each other.

> check the percent error of the ratios, as Steve did. They should all be in a narrow band around the ideal band. The smaller the band is relative to the ideal, the “better” the cassette, freewheel or whatever, u it s for a half-step.

> check the standard deviation of the ratios of adjacent cogs to the ideal ratios (normalized ratios). Some error is always present in the real-steel results. This function is built into Excel and easy to use. For this number, the closer to zero the better. It is bigger if all of the the ratios have error, or if only one of them is big. One way you can use it is to see if making a small change is an improvement from a half-step point of view. For example, would there be anything objectionable to modifying a 7sp 13-26 to a 13-30, to get a little more climbing leverage?
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Old 07-14-21, 05:46 AM
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Originally Posted by sysrq
It may sound like a rhetorical question in a sense.
In order to stay with a 45t (7075) one I have to reduce its thickness somehow from 4mm to 3mm, but the 12% gap kinda ruins everything.
I have access to milling machine and lathe which could help, but the owner says the chainring looks too flimsy to be securely clamped down in order to reduce any chances of accident while working on it.
I could file it down manually, but there is no way to do it without ruining the teeth.
39t small ring would result in more 8% gaps instead of 7%, but as I said I'm stuck with 42t one due to various reasons.
Probably will try out the 46t one to see if it discourages unnecessary shifting which ruins momentum.
Sysrq, how does the thickness of the chainrings become a problem with setting up your gearing increments? I’m not sure I see what problem you are concerned about at the moment.

If you want to make a half-step with 9 cogs or more, you will need a chain that is narrow enough to work with an indexing control, or a friction shifter. This narrow chain in turn will be best with a set of chainrings spaced for the narrow chain and a suitable front derailleur. This is a real mechanical problem, but it doesn’t have much to do with how you choose the half step front and rear cog/chainring tooth specs. If you can’t find appropriate hardware, that’s another story and you may need some new hardware or some compromise in your goals.

To thin a chainring sounds like a machining challenge! It might be better to look at modifying the spider arms which hold the chainrings, to put the existing rings in the correct locations, if you can decide where those positions are.

I built a 2x10 friction-shift using a Sram 11-32, a KMC chain, and a IRC 46-30 chain set. It works great. I think the downtube shifters are old SunTours, but I don’t recall clearly. I would only have to locate a suitable 44 (or whatever is correct) inner ring to make it a half-step. In this case the whole gear train is based on narrow lateral spacing between cogs.
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Old 07-14-21, 06:09 AM
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Originally Posted by Road Fan
Sysrq, how does the thickness of the chainrings become a problem with setting up your gearing increments? I’m not sure I see what problem you are concerned about at the moment.

If you want to make a half-step with 9 cogs or more, you will need a chain that is narrow enough to work with an indexing control, or a friction shifter. This narrow chain in turn will be best with a set of chainrings spaced for the narrow chain and a suitable front derailleur. This is a real mechanical problem, but it doesn’t have much to do with how you choose the half step front and rear cog/chainring tooth specs. If you can’t find appropriate hardware, that’s another story and you may need some new hardware or some compromise in your goals.

To thin a chainring sounds like a machining challenge! It might be better to look at modifying the spider arms which hold the chainrings, to put the existing rings in the correct locations, if you can decide where those positions are.

I built a 2x10 friction-shift using a Sram 11-32, a KMC chain, and a IRC 46-30 chain set. It works great. I think the downtube shifters are old SunTours, but I don’t recall clearly. I would only have to locate a suitable 44 (or whatever is correct) inner ring to make it a half-step. In this case the whole gear train is based on narrow lateral spacing between cogs.
I already filed down the 5 mm thick spider arms by a 1 mm which was easy thanks to some harder metal spacers which eliminated chance of reducing the thickness too much while filing.
I have already figured out the method for filing down the 4 mm 45t chainring but it's not as straightforward as spider arms due to awkward and bigger surface area.
I see some racer cassettes also have bigger gear step gaps between midrange and upper range which seems strange since it gets used the most.
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Old 07-14-21, 08:54 AM
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Originally Posted by sysrq
I already filed down the 5 mm thick spider arms by a 1 mm which was easy thanks to some harder metal spacers which eliminated chance of reducing the thickness too much while filing.
I have already figured out the method for filing down the 4 mm 45t chainring but it's not as straightforward as spider arms due to awkward and bigger surface area.
I see some racer cassettes also have bigger gear step gaps between midrange and upper range which seems strange since it gets used the most.
Or you could just buy a 3/32" 45T ring. I assume this is for a 130mm BCD crank?
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Old 07-14-21, 01:40 PM
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Originally Posted by ThermionicScott
Or you could just buy a 3/32" 45T ring. I assume this is for a 130mm BCD crank?
It's a 110mm BCD. Last time this was the only one I was able to find.
https://www.amazon.co.uk/Dimension-c.../dp/B0091GZ6G2
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Old 07-14-21, 01:54 PM
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Originally Posted by sysrq
It's a 110mm BCD. Last time this was the only one I was able to find.
https://www.amazon.co.uk/Dimension-c.../dp/B0091GZ6G2
Is there a used bike emporium or coop near you? Pretty sure that they would have LOTS of 110 BCD chain rings.

And you could post a WTB on the C&V Sales sub-forum. We probably have even more.
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Old 07-14-21, 02:22 PM
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Originally Posted by sysrq
It's a 110mm BCD. Last time this was the only one I was able to find.
https://www.amazon.co.uk/Dimension-c.../dp/B0091GZ6G2
Peter White's website shows that he carries a T.A. 110mm 45T chainring. Whether or not it is in stock is a whole 'nuther matter, as is true of so much stuff now.
https://www.peterwhitecycles.com/ta-...ngs.php#zephyr

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Old 07-14-21, 04:20 PM
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I was thinking of asking a question similar to the OP. I’m not sure if percent change answers my question. I use the same calculator, but in the flatlands we can have a narrower range as hills are minor. I won’t be going 35 mph down any hills, so any thing over 90 gear inches is not really necessary.

Asking a similar question; How many mph difference between gears do you like? In the flatlands with a closer ratio 2X7 it wouldn’t be too difficult to have mere 1 mph jumps between gears. I used to be interested in doing it that way. Now I am happy if gaps are maybe up to 1.5 mph, as anything closer feels like a shifting fixation. If it’s there I will do it, but 1.5 mph gaps seem okay, at least for now.

As an aside, I ran a 144 bcd as a half step 42-45 6 speed for awhile on my Trek and now have it as a 42-46 with a 5 speed 14-32 on my vintage Frejus.

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Old 07-14-21, 09:22 PM
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Originally Posted by sysrq
It's a 110mm BCD. Last time this was the only one I was able to find.
https://www.amazon.co.uk/Dimension-c.../dp/B0091GZ6G2
It's not the most aesthetically pleasing, but you can get 110/130 combo BCD chainrings in that size: https://www.amazon.com/Origin8-BMX-S...8-8&th=1&psc=1


I remember one guy doing a 45/42 half-step with one of these rings, can't remember the username now, though.
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Old 07-15-21, 05:40 AM
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Originally Posted by sd5782
......
Asking a similar question; How many mph difference between gears do you like? In the flatlands with a closer ratio 2X7 it wouldn’t be too difficult to have mere 1 mph jumps between gears. I used to be interested in doing it that way. Now I am happy if gaps are maybe up to 1.5 mph, as anything closer feels like a shifting fixation. If it’s there I will do it, but 1.5 mph gaps seem okay, at least for now.
.....
on my touring/commuting bike, I've got a half-step-plus-granny that uses 46-49 big rings. The seven speed cassette is 13-30.
When carrying a load or dealing with a headwind, the small step between the chainrings is useful. I'm not sure I could use a smaller step, i.e. a two tooth difference, though.

Steve in Peoria
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Old 07-15-21, 10:53 AM
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Originally Posted by sysrq
I already filed down the 5 mm thick spider arms by a 1 mm which was easy thanks to some harder metal spacers which eliminated chance of reducing the thickness too much while filing.
I have already figured out the method for filing down the 4 mm 45t chainring but it's not as straightforward as spider arms due to awkward and bigger surface area.
I see some racer cassettes also have bigger gear step gaps between midrange and upper range which seems strange since it gets used the most.
Well, we started out talking about how to compute and select parts for a halfstep pattern, but in reality you can choose sprocket steps any way you like. They would not then be half-step, they'd be "Joe's gears," or "Mario's gears," or "Sean's gears."

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Old 07-15-21, 11:03 AM
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Originally Posted by steelbikeguy
on my touring/commuting bike, I've got a half-step-plus-granny that uses 46-49 big rings. The seven speed cassette is 13-30.
When carrying a load or dealing with a headwind, the small step between the chainrings is useful. I'm not sure I could use a smaller step, i.e. a two tooth difference, though.

Steve in Peoria
If you were going to make that change you'd have to see what ratio is between the chainrings, square that and then calculate out your 7 or 8 speed cassette ideal ratios, integerize them and see if it results in any parts you can buy. I suspect the total gear range is going to be inadequate seeing as how we're used to a certain amount of granny push, in the windy midwest.
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Old 07-15-21, 02:17 PM
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Originally Posted by Road Fan
If you were going to make that change you'd have to see what ratio is between the chainrings, square that and then calculate out your 7 or 8 speed cassette ideal ratios, integerize them and see if it results in any parts you can buy. I suspect the total gear range is going to be inadequate seeing as how we're used to a certain amount of granny push, in the windy midwest.
well, the comment was made without regard to the cassette. I just don't think that using 46T-48T rings would be useful. My current 46T-49T is roughly a 3% change, which is plenty small for me.*

Steve in Peoria

*edit: sorry... a change from the 46 to 49 tooth ring is a 6.5% change. Still pretty small for my non-competitive use.

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Old 07-15-21, 03:32 PM
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Originally Posted by steelbikeguy
well, the comment was made without regard to the cassette. I just don't think that using 46T-48T rings would be useful. My current 46T-49T is roughly a 3% change, which is plenty small for me.

Steve in Peoria
Yeah, essentially I was obliquely trying to say the jumps are going to get smaller than would be useful.

You did not intend to involve the cassette, but if you change the 2 tooth chainring separation to 1 tooth, the front increment will be smaller. The cogset increment is the square of the chainset increment and it will be smaller. To have 14 separated and hence useful gear ratios (the key benefit of the ½), you 'd have to stay within the ½ step math model. The rear increment is the square of the front increment, and that front increment decreased from what it was. Your rear spread will inevitably be narrow because a ½ step tightly couples the sprocket or chainring specification (tooth count) at the back to the design choices made at the rear. That may be too obvious a point, but that's all I was trying to say.

Sorry.
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Old 07-31-21, 01:07 AM
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Dicided to stick to the 45t by adding some 0.6 mm spacer in a specific location. 45t also seemed to shift better than 46t.
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