Fall factors.....

A fall factor is defined as the height of a fall divided by the length of rope you fall on to.

However, a definition is not necessarily an explanation. Try this for size:

When you fall, you gain speed, i.e. you gain energy. If you fall onto a rope, the idea is that the rope will stop you, i.e. you lose that energy again. The energy must go somewhere and it goes into stretching the rope. The capacity for a piece of rope to absorb that energy is proportional to its length. This means that a small fall (small energy) onto a long rope (lots of capcity to absorb energy) is OK, but a big fall (lots of energy) onto a short rope (little capacity to absorb energy) is bad news.

It may not be entirely obvious why a long rope can absorb more energy than a short one. It has to do with the fact that a piece of rope will get X% longer when you subject it to a force (it doesn't matter what X is). That's known as Hooke's law. So the change in length of a long rope will be much more than a short rope for a given force. The energy absorbed by a system is equal to force x distance (that's easy to understand, pushing a car 10 meters is ok, but pushing it a kilometer would be absolutely knackering, as would be pushing a 44 ton truck 10m). So if the distance is much more, you can absorb a lot more energy.

This is all very simplified and before anybody complains I know that perfectly well. I could set it all down in equations but I don't think that would help much. Since rope doesn't even obey Hookes law exactly, "correct" equations would be extremely complicated and of no use to anybody.

Mark