Say I'm leading on a single-pitch climb, or the first pitch of a multi-pitch. The maximum fall factor I could theoretically have without hitting the deck is 1, but that's with a static rope, which of course I wouldn't use in this situation. This raises the question of what is the maximum fall factor I could have without contacting the ground at my belayer's feet. (If the rope stretches, then it's helping me by decelerating me at least somewhat, but I'd really prefer not to touch bottom at all.)
By UIAA standards, static rope stretch for an 80 kg climber is supposed to be no more than 10%. Dynamic rope stretch is going to be greater than this static value.
The UIAA standard fall is a fall factor of 1.77, and rope stretch for that fall is supposed to be no more than 40%. In the first-pitch scenario, you can't actually have a fall that puts this much stress on the rope, since you can't fall past the belayer, but we can be sure than the rope stretch in a first-pitch scenario will be no greater than this. (Again, this is for an 80 kg climber.)
What I can tell from this is that the rope stretch a is in the range 0.1<a<0.4, which is a pretty broad range. Therefore the fall factor f that just barely has me kissing sand is in the range 0.6<f<0.9. What is the actual critical value of the fall factor?