Short Cage on a Triple - Check My Derailleur Math
The details...
Cassette: 7 speed, 12-28
Chainring: 9 speed triple, 26,36,48
Desired derailleur: 10 speed 105 short cage, 33T capacity
Bike: 1992 Miyata 1000. 19 rides out of 20 I ride it as a double. That said, I'd like to preserve the granny gear option for when I tow the dog trailer and/or attempt to climb walls.
This short cage derailleur won't have enough capacity for me to run the full cassette on all three chainrings. However, my understanding is that, if I avoid cross chaining, I can still make it work. If I wanted to know how many of my cassette sprockets would be usable on the granny gear, would I look for the sprocket having no less than:
28 - (33 - (48 - 26)) = 17 Teeth.
Is that right? If it is, that means that I could still access the largest four cogs of my cassette from the granny gear (the fourth is 18T). And I don't see attempting to access anything smaller than the second largest cog.
As a secondary question, if I were to, say, lend the bike to my elderly father and he tried to use the small ring and small cog, what's the worst case scenario there? The chain would slip the granny gear chainring? Is there any chance the loose chain would hop the cassette and fly into the rear wheel spokes somehow?