2013 TDF came with Claris rear mech, prior to that I think it was the 2300 which was a max of 28t ?
pasted from a post by
@RecordAceFromNew
"If your chainset is the same as the current Allez 16 then it would be a 52/39. That combined with the 2300 rear mech's
spec you have an official wrap range available at the back of 35-(52-39), which is 22.
What that means, is assuming there is enough clearance between the mech's upper jockey wheel and the cassette, the widest range cassette you can theoretically have is 11T to (11+22) or 33T.
However the 2300 rear mech's official maximum sprocket size is 26T - but that figure is nearly always a pessimistic guide, while in reality it is dependent on frame/mech hanger geometry as well as the rear mech's parallelogram dimension - fortunately you can find out what the largest rear cog your existing set up can* handle by just a ruler - the number of teeth you can add to the 25 currently is the clearance between the 25 and the upper jocket wheel (when the chain is on the 25) in mm divided by 2. If e.g. the distance is 10mm then the largest rear cog your system can handle is 30T, but 29T will probably be best to allow for measurement error and a bit of wriggle room for the chain etc.
8 speed Shimano compatible cassettes are widely available - since you can pick any Shimano or Sram 8 speed cassette, whether "for" mtb or road. In fact since you are looking for low gears, Shimano or Sram mtb cassettes will offer a wider choice, e.g. all Shimano and Sram 8 speed cassettes on
this page within the right tooth range are eligible.
Unless close ratio is important to you, if I were you I would pick one that starts from 11T (since wrap capacity is not going to be the limiting factor for the rear mech, and it will help speeding you downhill), and go up to near the maximum sprocket size limit by measurement as described above - that will give you the biggest range for the biggest hill most economically.
Regarding chain, if the existing chain is optimal in length then for every 4T increase in max rear cog size you should increase the new chain's length by 2 links above the existing. But if I were you I would not assume the existing length is right and just work out the optimal new length using a
chain length calculator.
* if you wish the clearance can be maximised, allowing a bigger cog, by
adjusting the mech's B screw."