Half-Step Gearing Question
 

I recently purchased a vintage bike with what I have come to learn is a half-step gearing with granny set-up. The triple up front is 50-45-24 with a seven speed freewheel of 13-14-15-17-19-21-23. My question: Is this an appropriate half-step arrangement? Thanks for for your input!

that is half step gearing. I don't think it's a very useable gear setup for most riders in "average" fitness condition.

what kind of crankset and dee-railers are you rockin ?

/markp

You need a different FW. Plug your equipment teeth numbers in here.

https://www.sheldonbrown.com/gear-calc.html

Basically, you want to zig zag down the big chain ring columns to change your gear inches. Each zig or zag cuts the change of going straight down in half.

I'd get a 5 speed FW to really explore half step plus granny.

The crank is a Sugino AT but I’m unsure if the 50 chainring is Sugino. The front derailleur is a Suntour Mountech the rear is a Suntour Accushift 4050 Edge.

all right, Classtime suggestion is a good starting point, choose a freewheel with a large cog of 28 or 30 T

your rear derailleur should handle that, maybe splurge and get a new chain too ?

also on any newly purchased bike, make sure the brakes are correctly adjusted and the tires are safe and properly inflated

/markp

https://cimg4.ibsrv.net/gimg/bikefor...2af1e4cfd0.png
The % between each cog should be about twice that of the % between the two big rings with no gear inch duplicates.

Much appreciated, Classtime and mpetry912.

https://cimg1.ibsrv.net/gimg/bikefor...6aee475c0f.png
Notice the difference. But change the 13 to a 14
I’m a big fan of 1/2 step plus granny. I need to get another bike and set it up so.

... and also what freewheel is mounted? My guess is a Suntour. There's a possibility I can assist with regearing your freewheel.

24t small chainring to 45t middle chainring ?

Unfortunetly, this is not a half-step gearing pattern. The 24t chainring does give you gears down into 23 gear inches. But there should be a zig-zag pattern of large chainring - small chainring - large chainring - small chainring as you move up (or down) through your cogs on the freewheel. That is the part that is missing. This works ok but there are overlaps and repeated gears.

https://cimg5.ibsrv.net/gimg/bikefor...91075f1613.png



Do you want half-step gearing? Some of us like it, some don't.

Here is the same chart with @Classtime 's gearing. You will notice there are only five cogs on the freewheel but even with less gears you have a nice shift pattern and better ratios.

https://cimg2.ibsrv.net/gimg/bikefor...c2463c13bf.png


You can see how evenly spaced the each gear combination is and that the shift pattern is relatively easy to figure out. And Classtime kept your chain rings so you would only need to get a 5 speed freewheel.

Honestly, how can anyone answer this question without an understanding of what you mean by "appropriate"? Please explain your application, how you plan to use the bike or the terrain over which you ride.

I say that because, unlike the others, I think it is a great combination. I use a set up like that for most of my riding.

However, when going to the mountains, in order to get the low end ratios your set up offers, I have to change freewheels, rear derailleur and inner front chain ring. Now, that is not a problem and does not actually take very long to do but yours offers those ratios without any mods.

Still, I'd like to understand your use case. I think it will help everyone to better understand your question.

I like this calculator as it's real time changeable.
https://www.gear-calculator.com/?GR=...&DV=gearInches
As you see, not very effective choice of FW and rings.

I used to run a 26/44/48 with a 13,15,17,20,24,28,32 FW and it was perfect. I could ride in either ring and only change rings when I wanted to fine tune the gear.
The FW these days with a 13.15.17.19,21,24 are so great for HS.

Sunrace currently makes a 7sp MFM300 FW with 14,16,18,21,24,28,34 cogs that'd be great with say a 30/44/48 combo.
https://www.gear-calculator.com/?GR=...&DV=gearInches

short answer: the freewheel has a pretty consistent step size from cog to cog, which is important for half step gearing. The downside is that you'd only have two teeth separating the chainrings, such as 50-52. Since you are starting with a narrow range freewheel like a 13-23, you already know that you are getting a narrow range of gearing.

longer answer:
To evaluate a freewheel for suitability for half step gearing, you'll want to see how even the gear steps are and how well the ideal step size maps onto physically available cogs.
In this case, with a 7 speed freewheel, if you had even step sizes from one cog to the next, the size of this step is X.
The first cog is 13 teeth. The second would then be 13 x X, the third cog would be 13 x X x X, or 13 x X^2, the fourth cog is 13 x X^3, etc.
The final cog is 13 x X^6, which we know is equal to 23.
This lets us solve for X: X = sixth root of (23/13), or (23/13) to the (1/6) power.
Running this through the calculator shows that X = 1.0998.
If you now calculate what the ideal cogs would be, you get this: 13 - 14.3 - 15.72 - 17.3 - 19.02 - 20.92 - 23
Practically, to build this, you'd pick 13 - 14 - 15 - 17 - 19 - 21 - 23.

For a half step gearing arrangement, the step size between the chainrings should be the square root of the step between the cogs.
In this case, it should be the square root of 1.0998, or 1.049.
If the big ring is 52, then the small ring would be 49.59.
That's not a great answer, because you have to use either 49 or 50 teeth, and that's going make your gear spacing more irregular.
If the big ring was 42 teeth, then the small ring would be 40.04 teeth, which is close enough to 40. This would produce more regular gear spacing.

These calculations are a bit more useful than just plugging random arrangements into a gearing calculator, in the sense that you can look at how well a physical freewheel can match the ideal freewheel. If the ideal cogs are mostly fractional tooth counts, then you know it's not going to deliver evenly spaced gears.

Of course... when designing your gearing arrangement, the first step is to determine what gear range you want. Then you can decide whether half step or cross-over or compact gearing (or even 1x) works better.

Steve in Peoria

This was the set up on a bike I purchased. I noticed the small chainring compared to the larger two and found it interesting. I was unaware of half-step gearing until reading about it, and was curious if the set up on this bike I purchased was set up with half-step gearing. I don’t know what gearing I will eventually use for this bike. I am in the process of tearing it down an overhauling it.

Regarding half-step gearing, I think it's best to have variable steps between gears. Specifically, increasingly large gaps from the 2nd cog to the penultimate, or 2nd to last, cog. And small gaps between the 1st and 2nd cog, as well as the last two cogs.


I have a 6-speed freewheel with 13-14-17-21-26-30. It came on a bike that I purchased, and was really confused by the choice of cogs at first. But, after thinking about halfstep gearing it made total sense.

• Why increasingly larger cogs?
  • The gain ratio between two gears, as the number of teeth increases, is less. Said another way as an example, the gain ratio between 9t and 10t cogs compared to 29t and 30t cogs is very differet-- the gain ratio between the small cogs is much, much larger.
  • Thus, in order to keep the gain ratio relatively consistent, you have to have consistently larger cog spacing.
• Why small gaps between the 1st and 2nd cog, and the last two cogs?
  • Cross chaining.
    • For my given example, the current shifting progression is: 1st/1st, 1st/2nd, 2nd/2nd (chainring/cog). Or, using the actual tooth counts: 50/13, 50/14, 45/14.
    • If you swapped the 14t cog for a 16t the progression would be: 1st/1st, 2nd/1st, 1st/2nd (chainring,cog). Or, using the actual tooth counts: 50/13, 45/13, 50/16.
    • It does mean that the freewheel doesn't have quite as much range, so you'll have to decide what's most important to you.

Ignoring the granny chainring for the moment, with 50/45 chainrings the result is below.


https://cimg5.ibsrv.net/gimg/bikefor...6340abd8b8.png


https://cimg5.ibsrv.net/gimg/bikefor...87c5a3135a.png

Actually, it’s labeled a Regina Synchro 90-S.

Finding sprockets larger than 23T for that model of Regina is about as hard as finding hen's teeth. IIRC, I have one 31T and nothing in-between. However, some older Shimano three-tab sprockets can be made to fit on a Regina body.

I run a real half-step on the Peugeot: 45-42 / 13-15-17-20-23-26 (could easily go to 30T with a 7-speed freewheel or 34 with an 8-speed

My first Bianchi, a 1962, came with 52-47 / 13-16-19-23-26, which provides a 9-speed half-step, since the large-large crosschain is redundant with the 47/23, but who does large-large crosschaining, anyway?

My Fuji is pretty similar. 45/42/30 x 14-16-18-20-23-26. The 45x14 high gear only gives me around 86 inches, but that seems to be enough for me. The gearing itself is great, especially for a sport-touring, recreational road bike. Plenty of range for a medium paced, lightly loaded ride, and with only a 3-tooth gap and Suntour road double derailleurs front and rear, all shifts are fast and easy, even the double shifts.

A 9-speed 12-36 cassette with a 45/42 double gives 18 evenly-spaced gears, from 101 to 32 inches, with 7% jumps across the whole range. Or you can go 48/45, and get a 108-34 range. Might be better for group rides. All with easily-available and inexpensive parts.

--Shannon