• I still wonder though why he added the 3mm to some but not all rims though.

    Maybe because in most cases ERD is the given figure (either from the manufacturer or obtained by measurement), but for some rims the manufacturer states their NSD, so ERD has to be calculated from it?

    As long as you are putting an ERD into the calculation, you should be getting spoke lengths out. To check that you are putting ERD in, compare the value used by edd with data from the manufacturer if you can find it - if they say it's an NSD, it should be 3mm (ish) smaller than the ERD. The 'ish' might depend slightly on how the nipple sits in the rim's eyes, and significantly on how far the nipple's thread extends towards the hub.

    The basic spoke length calculation just works out the straight-line distance from the edge of the hub hole to where the spoke should end. This doesn't allow for the extra length taken up weaving the last cross, or the length gained from spokes stretching as they are tensioned. The weaving effect should be negligible (less than 0.01mm) unless you are weaving some weird pattern, but i'd expect spokes to stretch 0.4 to 0.6mm when tensioned. i.e. just on the bounds of consideration, but not enough to explain what went wrong above.

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