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One further point:
When deciding which chainset to use, you need to consider wear on the chainring teeth. There's no sense in fitting some prestigious brand if the only ring you've got is clapped out - you're building the bike to ride it, not just to look at.
It's a bit hard to tell from your pics, but the 5 pin ring seems pretty good while the Williams looks past its best. All 5 pin rings seem to be interchangeable ( although TA and other metric rings will need a little 'easing' with a half round file to get them onto an english crank).
Bear in mind that the teeth do not wear evenly - those in contact with the chain at top dead centre and BDC have no pressure on them and therefore no wear. It's usually possible to move the ring through 90 degrees so that the worn teeth are relieved of pressure.
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I hope this will be my final comment on cotter pins.
I regret having to say this, but cottered cranks are not really ideal for use with fixed.
Why? Because the cotter nearly always makes the chainset slightly oval, since it inevitably pushes the crank away from the spindle. Although the crank may seem to be a good fit on the spindle there is nearly always a bit of slack which is noticeable as a tight spot in the chain.
This doesn't matter with a freewheel since chain slack is more acceptable, but with fixed you really want to get the chain as tight as possible (allowing for free running of course).As we all know, millions of miles have been done on fixed with cottered cranks, but there must have been many occasions when chains came off because there was too much slack at the slack spot. It has happened to me!
Here is a tip: When adjusting the back wheel for chain tension, set the right hand crank at about
2 o'clock, which will probably be just before the tight spot. If you get the chain right at that point you should be able to get it as near as possible to perfect at the tight spot itself.Always keep a close eye on the chain and re-adjust when any slack develops - this will happen very quickly with a brand new chain.
It should also be mentioned that not all rear sprockets are as round as they should be. The late TDC sprockets were pretty bad in this respect and there are plenty of those still in circulation.
Should you not be considering the length of the cranks? Some people find this is critical, others less so. Personally I can't get on with anything other than 6 and 3/4" (170mm), but others seem to be able to adapt. I have a good anecdote on this but it can wait till we meet.
BB spindle length: there's quite a bit of variety - ideally you want the shortest spindle that will allow the chainring to clear the frame. I can't remember how the BW numbering system works, but you should probably avoid a spindle stamped 'GCC' (gear case clearance) . 'NGCC' would probably be OK.
I think there are three different types of RH crank so far as clearance is concerned:
Each of these will have a different spindle. Of course you may get away with excessive clearance, but it can affect the chain line badly, and I find it has an adverse effect on my right knee.
You may well know this, but the 5 pin chain ring in your photo appears to have the fixing bolts screwed in from the front side of the ring - they actually go in from the back (as with the Williams).
Personally, I like the Williams C34 (that's what you have there). They are a good, down to earth set, and there are plenty of spare rings knocking about - I may even have the one you need!