There is a rule of thumb for minimum size to leave between eye-to-eye splices, 5 fids? Can't remember where I heard it. Spiced hitch cords get a bit shorter - a 28" 8mm hitch cord is ~ 4 fids between the eyes. The biggest issue pushing the lower bound is having enough space to complete the second splice.
For your ring and ring starting with 13 feet of rope, I'd guess it'll end up a bit over 10 feet long. Here's how I usually work the math for splices:
(Everything is in metric because I find it easier to deal with.)
I always start with a diagram of what I'm making, with key measurements, calculate the fid length. (21x the rope diameter), and work it out from there.
Next step is figuring out the eye size, the distance between 'R' and 'X'. I like getting the math done ahead of everything else. In the example I'm using 80mm (~ 3 1/8") for the eye circumference, would produce a loose eye.
For an eye-to-eye, the final length ("L") between the bearing surfaces is going to be the same as the rope, minus:
- 2x the fid length, one for each end.
- 1/2 of the eye circumference (E = R-X) on each end, because the rope is doubled up here. (This assumes the eye is flat, which it's not, but close enough.)
So, the generic formula for an eye-to-eye splice is:
Final Length = Rope Length - 2*fid - Eye size
There's some additional length loss from the braid expanding during the bury, 5% or so.
Edit: Triple-checked I guess. Wouldn't have expected so many nerds to work splice math over lunch...