I've recently bought a sturmey-archer AW hub from ebay to install on my bike instead of derailleurs (I may yet go hybrid by retaining the triple crank or installing two sprockets, but that's another matter.) I have all the bits- hub, sprocket, shifter, cable, adjuster, but I'm unsure how to route the shift cable. Most of the 3 speed bikes I've seen have a clamp-on fitting on the chainstay to secure the end of the cable housing. Being a mountain bike, my bike doesn't have that.

Is it a bad idea to simply run the cable housing to the stop on the downtube, and route the cable along the downtube and under the bottom bracket?


Pete

You can get Sturmey Archer casing stops, otherwise known as fulcrum clips in 15.9,17.5, or 19.1mm sizes. You can mount them on the chainstay or the seatstay, and run the cable down the top tube rather than the downtube.
Another option is a fulcrum lever, part # HSJ 905 on page 15 of this catalogue. It alows for a full length housing from shifter to the hub.
https://www.sturmey-archer.com/userfi...A2-Low-Res.pdf
That part is used in conjunction with HSA650 on the same page.
A standard M6x1 barrel adjuster screws into the end of the fulcrum lever.
The problem with running the bare cable under the BB is the routing from there to the indicator on the hub. If you can route the cable without interference from the chain or chainstays, it might work, but I doubt it.

Cool, I learned something new.

Picked up a vintage, Puch, mixte frame for my youngest daughter, and was going to re-purpose the 3-speed, Shimano IGH kit from another, lesser ride. However, the Puch doesn't have an appropriate, chainstay mounted, cable stop, on the non-drive side. Was going to simply machine up a little stepped tube, and a cable clamp, essentially matching those SA fulcrum clips. Still might, but nice to know those parts are available. Just did a quick search, and it looks like they show up in the QBP catalog, so they should be available from almost any LBS.

A Shimano 3 speed is a whole other animal. If all the parts are there, including the external shifting mech, it should take a full length housing from shifter to hub. All you need to worry about is securing the housing to the frame.
Edit: If the Shimano hub is an older model with an open exposed bell crank, then you will need some sort of housing stop.

Yep, older model with the exposed bell crank, so some sort of stop is required. For me, not a real issue either way.

What I would really like to find for her rig is an inexpensive 5-speed SA. The new ones, I could find, are priced almost up there with what I can get an 8-speed Shimano for, so I don't see the point. On paper, the 5's look nice, with 100% being smack dab in the middle, and also the possibility of drum or coaster variations. Although, are those just SA vaporware?

Nope. In stock right now at UBS.

Yes, you can run bare wire from the old rear derailleur stop on the down tube front,
under the BB, and down the chain-stay to pull the little indicator chain,

back on classic 3 speeds they fitted a roller by the top of the seat tube, and the wire run was bare
from the front of the top tube.

you could put one of the cyclocross rollers made for top tube mounted FD cables and bottom pull mech.
put one at the bottom, if you don't like the plastic under the BB guide..