Originally Posted by
DaveSSS
If you linear you mean approximately the same percentage of change as sprockets go from small to large, then you won't find any made for modern drivetrains. It's also undesirable except where road gradients don't change much.
There's also the mathematical fact that as sprockets get larger 1T changes become smaller percentages. A 10-11 is an 11% reduction. A 16-17 is only a 6% reduction, but a 16-18 is back to an 11% reduction. I have a 13-15 jump that's almost a 13% jump. It feels too large compared to the same percentage with much larger sprockets. In my experience riding many thousands of miles in the mountains, larger percentage changes are not as troublesome in the larger sprockets. My 10-36 has 21-24-28-32-36 sprockets. The 21-24 is 14%, while the 32-36 is down to 11%. I wouldn't want any smaller percentage changes.
SRAM makes a 10-33 cassette to get a 1/1 ratio with a 33T little ring. The 28-33 jump is 15%.
Linear would be straight upwards line. In this case logarithmic would be more appropriate. Have read a lot of discussions about cassettes but never stumbled upon exactly this kind of aspect. Seems like loaded touring bikes are still compelled to use MTB cassettes mostly.