I have a '53 Spitfire (32.4mm ID head tube), will buy a new fork that will take a 26.4mm race. I can't find a complete headset that has the 32.4 cups...
The OD for the original headset cups on your bike is 32.7mm. That is the standard dimension for the Chicago built electro-forged frame Schwinns from ballooners to lightweights. For reference the head tube ID measurement should be about 32.6mm for an interference fit.
My original cups are fine, so I can just buy a crown race and bearings to match.
You can get a NOS Schwinn crown race (aka lower cone)
here, and a new set of retainers
here. You can also ditch your existing retainers and simply use
loose 3/16" ball bearings. Using loose balls is cheaper overall plus you use more than 15 balls per cup (normally you fill the track in the cup with balls and then remove 1), which will increase durability and smoothness of operation.
In most cases it is cheaper to buy a complete headset vs. a couple of individual parts. Schwinn headsets (
like this one) are plentiful on eBay. You can also buy a brand new "
old school bmx" headset with the same measurements however I haven't seen any that match the quality and durability of an original Schwinn-built unit.
For more information on headset measurements see
Sheldon Brown's Bicycle Headset Dimension Crib Sheet. Note the row in the chart for "BMX/O.P.C" bikes, which has the dimensions for Chicago Schwinns.
One minor note for Schwinn bikes relative to the dimensions on that chart is that the steerer ID was 7/8" (22.2mm) for 1965 and earlier models. This only affects the stem and the hole in the top of the locknut (which may need to be enlarged if using a '66 or later locknut on a '65 or earlier fork and stem). This won't affect you if you are using a new fork and stem.
