Do you mean joists? Rafters are the pieces of wood directly under the roof deck and run at an angle toward the peak. Your goal is to add some storage space but no living space, right?

Without looking at a table my gut reaction is that even sistered 2x6's aren't enough for a 20' span. Obviously better than nothing but they should be deeper.

i am thinking you need to sister up 2x10's or 2x12's and give up a few inches in the attic. my garage is 2x12's running 20' and there is NO deflection. even when 3 heavy HVAC guys were up there putting a new airhandler in the ceiling did not move.