3 arm cottered crank

[velomaniac]

OK retro road gurus I need help.
I have an old raleigh twenty and wanted to get a larger chainring but it needed to be a cottered crankset. I spotted some steel three arm cottered cranks on ebay going cheap and without thinking deeply enough bought them. I now find myself with a crank with I think a 102mm BCD and no chainring and it seems 116 BCD was the norm, not what I have.

So can you confirm if 102mm BCD exists for triple arm cranks or have I miss measured it. Further pointing me in any direction that might get me a chainring in this size would be helpful.

I actually quite like cottered chainsets I have decided despite the weight

 

[bm0p700f]

I have taken one of a bike today and I have a few cotted cranks set knocking about.

What chain ring are you looking for as I might be able to help.

 

[velomaniac]

Slight wire crossing here. I have a cottered crankset that needs a chainring as its a 3 arm crank that takes a bolt on chainring. I dont need a cottered chainset where the chainring is built in.
Further problem is its BCD (measurement between bolt holes) is 102mm but the common size for 3 arm cranks is 116mm BCD.
I'll find one eventually, they must exist somewhere.

 

[bm0p700f]

I'll check if they 3 armm with detachable chain ring with the right BCD.

 

[garethrl]

Perhaps I'm reading your message too literally but the distance between the two neighbouring bolt holes is NOT the BCD! You have to imagine a circle upon which each of the three holes sits and where the geometric centre of the circle is the centre of the crank bolt. The BCD is the diameter of this circle and by definition the only way in which

BCD = bolt centre separation

is if you have a two-bolt crankset, which doesn't exist.

For all other bolt patterns there is a fixed geometrical relationship between the bolt centre separation and BCD which is defined by the properties of the number of chords arising. Sheldon gives a comprehensive listing of bolt separations for different BCDs and arm patterns.

In your case, for a 3-arm crank the ratio is 1/(cosine(30)) which is 1.1547 and so for a 116mm BCD 3-arm crank then the bolt centres will be 116/1.1547 = 100.46mm apart. If your measurement of 102mm was a little too high then you might find that the ring you were looking at will indeed fit.

Sheldon's listing only refers to 3-arm cranks in 116mm BCD, which suggests pretty strongly that the vast majority of 3-armers were this size. There may be exceptions of course, but 116mm is the most common, for sure.

Cheers,
Gareth.

Slight wire crossing here. I have a cottered crankset that needs a chainring as its a 3 arm crank that takes a bolt on chainring. I dont need a cottered chainset where the chainring is built in.
Further problem is its BCD (measurement between bolt holes) is 102mm but the common size for 3 arm cranks is 116mm BCD.
I'll find one eventually, they must exist somewhere.

 

[biggs682]

posting a [ic might help as this is getting confusing.com

 

[garethrl]

Here's an image which helps portray the geometry:

Imagine this was a crank with detachable chainring, with the bolts at the three vertices of the triangle. What we now have, in geometric terms, is an equilateral triangle in a circumscribed circle - where the diameter of the circumscribed circle is the BCD. Furthermore, you can see by looking at the image that the three sides of the triangle represent the bolt separation distance.

So, what we're looking for now is the relation between the bolt separation distance and the BCD. Now compare the above photo with the drawing below:

and in fact what we're after is the relation between S and r. In fact we're after the relation between S - which is the bolt separation - and 2r - which is the BCD - since we're interested in the bolt circle diameter and not the radius. From basic trigonometry we can say that

cosine (30) = r / (1/2 S) , or

cosine (30) = 2r / S , ie

cosine (30) = BCD / bolt separation , or

BCD = bolt separation / cosine (30)

Now, cosine (30) is 0.86603 so the ratio between bolt separation and BCD is always this value, and so

BCD = bolt separation/0.86603 = bolt separation*1.1547

and 116 = 100.45 * 1.1547 which why a small measurement error and getting a bolt separation of 102mm might not be a dealbreaker.

Cheers,
Gareth.

ps You can apply the same basic principles to any arm pattern since the arms are always equally spaced. 4-arm is a square in a circumscribed circle, 5-arm is a pentagon, and 6-arm is a hexagon. You can then apply geometric principles to work out the relation between the diameter of the circumscribing circle, and the length of the lines joining neighbouring points around its circumference.