BCD and smallest possible chainring

[Alberto]

Hi!
I repeteadly see 38T as minimum teeth count for 5-bolt 122 BCD chainrings, the only issue is there actually are some (rare) 37T or 36T chainrings, I even have a 36T one.
What are the maths to determine that minimum?

 

[BikeGremlin]

Hi!
I repeteadly see 38T as minimum teeth count for 5-bolt 122 BCD chainrings, the only issue is there actually are some (rare) 37T or 36T chainrings, I even have a 36T one.
What are the maths to determine that minimum?

Hi,

You've got a keen eye and you do have a point!
In fact, I was hoping you caught a mistake in my BCD article so that I could correct it, thank you, and call it a day. However, it is more nuanced than that. Let's dive into it:

A brief less long answer​

38T minimum is often cited (on my site too) as the minimum for 5-bolt 122 BCD chainrings, it's not an absolute. The smallest possible chainring is limited by two factors:

1. Bolt Circle Diameter (BCD):
   The 122 mm BCD determines the smallest diameter a chainring can achieve while still leaving enough room for bolt holes. Theoretically, you could go down to about 36T, which you've seen, but the design starts getting tight for both material and strength.
2. Structural Integrity:
   Chainrings with fewer teeth, especially below 38T on a 122 BCD, become harder to manufacture without compromising durability. This makes 38T a practical minimum for most manufacturers, but niche or custom parts can sometimes push those boundaries.

So, while 38T is commonly accepted, the existence of 36T options (as you've noted) shows that it’s achievable with careful design, but it’s less common.

For a bit more details, you might find this article useful: Chainring Standards & BCDs. For even more details, read on.

The numbers and the formula​

A bicycle chain's pitch is 0.5" (12.7 mm). The chain sits on the chainring like this (the outer circles depict a worn, elongated chain's meshing with a chainring):



So, to get the diameter of the circle marked with the blue arrow in the pic. above, we would use this formula:

Diameter = Teeth_count x Pitch / π

So, for 36 teeth, that would be (let's call it "Dc" for chain):

Dc = 36 x 12.7 / 3.14 = 145.6 mm

Of course, the mounting bolts could not hang in the air, they would need to be close to the chainring's centre. Let's try to calculate the diameter of the circle where the teeth start (as the absolute outer limit past which our bolt-mounting hole would gape open) - call it Db (for mounting bolts):

Db = Dc - chain_roller_outer_diameter

Technically, we need to substract one half of the chain roller outer diameter twice.
Chain roller's outer diameter is just under 8 mm, so that would give us a max. outer chainring diameter of about 137.6 mm.

Db = 145.6 - 8 = 137.6

This is what I'm talking about:

Now, let us finally consider the mounting bolt holes. Their diameter is 10 mm on Shimano chainrings (and I haven't seen other manufacturers make larger holes).

So, with our 36 tooth chainring we would need to stay inside 137.6 mm (Db). If our holes are 10 mm wide, we must drill them with a centre that is 5 mm inward from that, making the whole circle be 10 mm smaller, which is 127.6 mm.

With a 122 BCD, this would give us the following margin:
(127.6 - 122) / 2 = 2.8 mm.

That is a similar margin to using 38 teeth on a 130 BCD chainring, but 130 is often seen on road cranks and used to mount a 39 T chainring (not a 38 T one).

I'll probably leave my article as it is, but link to this discussion for a full(er) info/answer.

Relja

 

[Alberto]

Hi! Thanks for your detailed explanation!

In the meantime, I discovered my 36T is just a BCD 74 machined to fit into BCD 122 cranks, and really the bolt holes lie so close to the teeth that it could became a structural issue. I wonder how close to the limit is 39T for BCD 135.

Anyway, it seems there are some genuine 36T or 37T BCD 122 chainrings (e.g. Sakae SR and Red Clover Components) and also Stronglight made some 37T for the 105 Bis crankset, as seen in the 1980 catalogue.