Add Nexus 3 Speed to Electra Jeremy

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Hey guys, I have an Electra Jeremy that I love to ride but want to upgrade to a 3 speed hub. I finally found a good deal on a Nexus 3 speed, so I've got the hub now.

The diameter of the 3 speed hub's flange is slightly higher than the original 1 speed, but am I correct in thinking that I can re-use the original spokes? I am thinking that I can get away with it since the spokes come out at a tangent from the hub flange and not straight out like a radially spoked wheel, so a small increase in hub diameter means a very small difference in spoke length.

Let me know what you think, thanks!
 
It may work or not. You may need to go from a 3 cross to a 4 cross lacing. No way to tell unless you measure and calculate or trial and error.
 
Thanks guys. Per the spoke calculators I tried online it looks like the recommended spoke length difference is just under 2 mm. I'm going to a larger hub flange, so I think it might work with the old spokes.
 
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