I'm not much of a cyclist, really, just sort of a dabbler. Or maybe a wannabe. Living three miles from most of local civilization apart from the local gas station and Subway (that killed off the ma&pa deli, but that is another story for another thread, right) it has been hard to motivate for rides longer than a couple miles here and there, and only braving the one pinch point under the railroad bridge at 46.169566,-122.914977 once to go hang out at a friend's house. That bridge is between me and the few places I'd want to go, so I'm like scared of it. Plus I got this degenerative disk thing going on in my back that bugs me if I ride for more than a couple three miles. Despite that and an atrocious writing style, I am a fan of bicycles, and I am certain they are the only way going forward we can get people around, but only if this weird fascination with living ten miles and more from where we work doesn't work itself out.
So we gonna compare medical issues here? Nah, I'd rather ride my bike, but I understand what you are saying about your back. You need the best riding position for you, and I can't tell you what that is. (It's your back.) I can tell you that larger diameter, larger cross-section tires will give you a considerably less jarring ride, and that has to be a good thing. Look for bikes with 26x2.125 tires. (I'd say look at bikes with 29" wheels, but they tend to be a bit pricey.) Also, it's easy to gear a bike down, even a single speed (especially a single speed) to make it easier to pedal. That's a must for me. I've got an old Schwinn Typhoon coaster brake bike that I geared way down, and it is an absolute joy to ride all day. It has a 22-tooth rear cog and a 44-tooth chainring. That one-to-two ratio seems to be a Very Good place to start when you're looking for the right gearing on a utility bicycle. I have sevral bikes geared like that, and they are all a joy to ride.
With your back, you need to look at how far over you want to lean. Every bike is different, and any bike can be changed around for more lean or less. Again, it's going to be a matter of you trying all different bikes and finding the one that makes you smile. But know that all bikes can be altered. (And it's fun to shop!)
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