"Crossing the chain" defined?
 

Ok, so here's my drivetrain. The chainring is in parentheses and the cogs are not (duh). The cogs in bold and underlined are the ones I think I can use with that chainring. With the triple, assume that the middle ring and the middle cog are in perfect alignment. With the double, assume that the middle cog lines up perfectly with a point exactly between the two chainrings. Can I exceed these limits I've set for myself, or are they too restrictive?


Triple

(48) 12 13 14 15 17 19 21 23 25

(36) 12 13 14 15 17 19 21 23 25

(26) 12 13 14 15 17 19 21 23 25

Double

(48) 12 13 14 15 17 19 21 23 25

(36) 12 13 14 15 17 19 21 23 25

That's relatively accurate. The only thing that I would change is the middle ring of the triple with the smallest cog. Even that combo should not be a problem. The middle ring of a triple is positioned almost as far to the right as the big ring on a double, so I treat it the same - no use with the largest cog.

The 48/21 should also be useable, at least briefly. There is no exact match for this ratio with the 36. A 36/15 is a little bigger and the 36/17 is smaller.

Cross chaining is overly vilified here on the forums. I do it all the time for short periods in the big/big combo. Now I don't ride around constantly in that combo, but if I am climbing, I will use that combo rather than risk throwing the chain by going down to the small CR. Nothing will happen to your bike as long as the ders and chain legnth are properly set up.

As suggested by DaveSSS using all the rear sprockets with the middel ring of a triple isn't a big issue. I've run with a 1x8 setup on an older errand/commuter run bike for years with no sign of shortening the chain life or odd sounds of protesting comeing from the drivetrain. The single ring being aligned with the middle of cassete by mounting the ring to the inner side of a triple crank set.

I think that what you're showing is fine and it is how you should try to use the gearing the vast majority of the time. But with a double in particular there's no major foul in selecting the big to big for a short time here and there if it'll do the job or if it'll avoid the risk of dropping the chain off the inside during a loaded shift as San Rensho suggested.

Haven't seen any evidence of reduced chain life due to cross-chaining and my practice is to use any gear combination that feels smooth and doesn't make excess noise. On my bike with a double that includes every cog in combination with the large chainring and all but the smallest with the small one.

You may be restricted from running 36-12 by the chain rubbing the big ring. otherwise you should be able to use all the cogs with the middle ring.

+1 The evils of cross chaining are exaggerated.

Assuming the RD has the capacity and the chain is the right length, no great harm will come of cross-chaining. Certainly the middle ring should be usable with the entire cassette, otherwise 1xX setups wouldn't exist.

Though it isn't sudden death, riding crossed over is less efficient and causes extra drive train friction and wear. It's a matter of degree, with the most crossed being the worst. But riding crossed may make sense from time to time in certain situations, such as topping a grade and needing one more downshift, yet not enough to shift the front.

The other problem with cross chaining on certain bikes is that it might make FD trim issues, or the chain may rub the larger chainring on small/small combinations.

Other than doing it overly much, with the noted extra wear issue, I go simply by function. If it works w/out excessive noise or other problems there's nothing terrible about cross chaining a particular gear. I ride my large/large on some uphills on a particular short (one hour) ride I do because I can do the entire ride in the large chainwheel that way.

I just swapped out my 36t ring for a 40. Now I have a 48/40 double. I'm using old Sakae SX cranks, which are basically the same as the old Sakae Signature cranks on my fixed gear except with holes drilled for a granny gear.

Best I can tell, the chainline is identical to a road double.

Now, I know I can fit a granny gear on there and have it clear the chain and shift properly (because I did exactly that until I replaced my frame and couldn't find my 26t ring. Still can't find it.)

So what I'm thinking of running is a 48/40/26 with the chainline remaining inboard as if it were a double. Basically cyclocross gearing with a granny.

Here's my thinking. I seldom use the granny gear unless I'm desperate. When I do, I'm usually only on the three biggest cogs.

What the 48/40 gives me is a very nice range of gears where I crank 90 rpms in exactly the speed range that I ride on flat ground. Did I mention that the nearest hill to where I live is 30 miles away? I go months on end where my most serious climbs are overpasses and bridges. For those special occasions, I'll have my granny gear.