In reply to GridNorth:
Perhaps someone could post the correct formula for how far below the last bolt you clipped, to highlight the bigger distance when falling trying to clip next bolt from below it?
I tried but brain was melting ...
In words, for a trad scenario, with a climber who also has a bionic extending arm.
Not computing rope stretch...
Gear 1 is at 6m
Gear 2 is at 10m.
The gear is good, and gear one is clipped.
A... Climber has clipped gear 1, climbs 4m so waist is at gear 2, tries to clip it but falls, has 4m of slack, is 4m above gear, will fall 8m, but falls 4m below last gear, stops 2m above ground.
B.... Climber gets 3m above last gear, can reach gear 2 1m higher, is on 3m slack, has to pull 1m to reach gear above head, + 1m to feeds back to harness, means adding 2m slack to 3m = 5m slack, falls b4 clipping, will fall 8m from position, 3m from above gear 1 but with 5m slack, ends up 5m below last gear, stops only 1m above ground.
C... Climber gets half way between gear 1 and 2, = 2m above gear 1, (has 2m slack on), decides to uses telescopic arm to reach 2m above to clip gear2, needs 2m to get to it plus 2m back to harness = 4m, total = 6m slack, falls off trying this, total fall = 8m, from 2m above gear 1, but 6m of this fall goes below gear1, distance from ground = 0...!
Realistically, In B, with rope stretch, and surplus slack in system, fall 5m below last gear which was 6m above ground, will be almost ground = 0 too.
Post edited at 14:50