Hi Ian.
Diameter is what you measure.Here's an example http://www.mathopenref.com/diameter.html
Measured across the face of the wheel not the back.
Coach wheels are usually 14mm.Hornby & Bachmann make them.
You need to know the diameter AND axle length. Standard is 26mm however its not always adhered too. The thing is dont always replace like for like as manufacturers will often use a stock wheel for ease, in this case their 3 hole wagon wheel. AFAIK no coaches ever ran with this type of wheel so if you are going to the effort to replace them you may as well use something more accurate. Having said that I am not sure Annie and clarabel are based on real coaches anyway.
26mm is pretty much standard these days (it was the dimension used by Romford back in the day), but check it just in case, as a few manufacturers use (or used) 24.5mm - Lima is one that comes to mind.
The 12.5mm diameter wheels you need are those available in Hornby pack R8096.As Jim S-W points out 3-hole wheels are wagon wheels,so the plain discs would be more suitable.
Unfortunately the design of these models is a work of pure Hornby fiction,being based not on a real prototype,but to fit on the old Tri-ang era derived brake van underframe,complete with the overscale buffer height,so fitting 14mm diameter wheels [which would normally be more appropriate for a coach] would only raise the buffer height,adding to the inaccuracy...
Just beware too that sometimes this makes matter worse, ensure your new whizzo wheels work and run free, if not you have to file the ends down, add a drop of oil into the hole and hope for a better result, chinese accuracy is not always famed for its accuracy.
*** More to the point, the existing bearings may have worn and the older plastic in the existing bogie may also have shrunk. The axle lengths will be fine... The axles are made with high production rate gear and a repeat CNC lathe has the same sort of abilities to be accurate time after time anywhere in the world.
Pinpoint bearings are pinpoint bearings. You may need to deepen or clean up the bearing a little but please do NOT file them. This will guarantee faster wear and give less free running than a properly mated pinpoint axle and properly coned bearing. There is a proper tool available for this called the "truck tuner" thats available from Micro-mark in USA and probably from one or two UK specialists too.
I have found the Hornby wheel packs - which are made with lathe turned wheels and axles, to be of good value and quality all of the time - with Bachmanns a little less so if they happen to use the older style cast wheel centres with the short stub axles.
Very nice wheels will also come from Ultrascale, Branchlines or Markits for OO, but expect to pay "more than a little more" per axle.
On the subject of lubrication, I never use oil on my pinpoint bearings. I just spin the end of a pencil in the bearing and then, just to make sure, I rub the tip around the axle end.
Except that to cite one particular incidence, Oxford Rail are noted as 'wandering off', 28.3mm over pinpoints on their recent release of a (very fine) GER design van. It's of no concern, since they work as they should...
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