green mt. boy said:
Lots of smart folks are years ahead of me on this but I ask the question is 160 or offset the only way to go? Thanks for the comments.
160 mm non offset works. 150mm or 165mm non offset will also work. 150 non offset will mean gearing compromises. Having looked at it extensively, clearly the 2 obvious choices are 135 offset and 160 symmetric.
If you use 135 non offset in the rear, you will have a 92-109+ mm wide tire. that means the chain hits the tire inboard of about 55mm off centerline.
The attached picture is a quick mod of a sketch I did to check chain clearances. I never checked 135 non offset but I spent 10 minutes modifying a sketch to make it accurate to scale to show the problem you are dealing with. The "tire" is mounted to a 100mm rim, so it is ~107mm wide. The stays are 17 inches eff, which is the shortest you can get to work with a front derailleur, and near enough the shortest you can do without curved seat tubes and plate wishbones and other complicated crap. I did some paint drawing on top of the measured, to scale drawing to make it easy to see what I mean (hopefully). the chain (red) diverges from the front sprocket at the center of the BB. The widest part of the tire has to be a minimum of about 6 inches behind the BB center, which means it doesn't take much angle inward on the chain before the chain starts to touch the tire. Note that the red chain in the sketch is not to scale, and a real chain is wider, closer to the tire, and further from the drive side dropout in the higher position rear, small ring front. The second, angled red line shows the chain (again, narrower than reality to save time) coming from the middle ring position of a 100 mm shell standard chainline (ie wide as heck).
The bottom line:
treat the rear of a snow bike like a 29er fork or road pedals for an MTB or something. There are bodge fixes of various degrees, but you aren't going to just swap parts around from other bikes and be completely happy with it.
Nothing 135 and non offset makes much sense to me. 50mm rims seem much narrower than ideal for snow use and 3.7 tires. The compromises get worse or the possibilities go away with wider rims. I think I remember that the difference between a large marge and a 100 mm rim was about 2 gears in the rear on a 17.25 inch chainstay, and less with longer stays.
with 135mm non offset and 50mm rims:
1.) you can not get an IGH to work with enough chain clearance to the tire and a reasonable chainline. IGH's generally do not let you run the sprocket as close to the dropout as a cassette.
2.) you could get an IGH to work if you ran a badly skewed chainline and chain guides (basically derailleurs) both front and rear. there is a 1/2" dished 22t available for 3 tab/spline compatible IGH's, so that might just about get you there too if the hub you choose can clear the shift cable with that sprocket (S-A is I think the only one).
3.) you can get a 3 speed by having a triple up front and one sprocket in the rear
4.) you can get a 4 speed or a couple other bastards by having two, or maybe three rear sprockets, and only using the low ones with the bigger rings up front, in other words your lowest gear would be small-small, and other ratios could come from middle and big rings cross chained onto the larger sprockets in the rear.
5.) you could rig up a wear surface or side load capable idler or something to protect the tire front the chain, and let it rub like hell in low gears if you don't plan to use them often.
notice how stupid these possibilities are sounding? I am sure there are other stupid possibilities, but I haven't found any that make sense. I bet you could make a workable S-A 8 speed using the chopper offset sprocket and 135mm spacing, but then it is so custom that why not do offset in the frame and a better, more ideal solution?