It is my understanding that because the distance you might fall with slack in your tether when one stick climbing or other, that dynamic rope will not make much difference vs. static rope. You would need to be on a longer length of dynamic rope to gain the benefit of its stretch. It also could be too bouncy if you were to use it for SRT. Opinions vary.
Any amount of stretch is much preferable to none.
The fall factor calculation takes length of rope into account, and this length of rope in our case also includes the part wrapped around the tree (it stretches also if dynamic....but probably not as much since it is experiencing bark friction....but breaking free and sliding on bark could also have a cushioning effect....I think that part is all untested however).
It goes like this:
1. if you fall 20 feet on 20 feet of rope (a fall factor of 1), then you are going much faster than if you'd only fallen 2 feet. But, handily, dynamic elongation is is a percentage of rope length, so your rope might stretch 5 feet.....but you need it
2. let's assume you are using a tether and include the wrap around the tree, you'll be falling a shorter distance than your rope, but let's assume for sake of argument that you fall 4 feet on 4 feet of rope, you do not need as much cushioning (since gravity has acted on you a shorter period) and you get less also.....around 1 foot if we keep things similar here
But let's say it is only 2 inches of stretch. For some weird reason, maybe because it isn't intuitive, people besmirch 2 inches of give, when the alternative is 0.0 or close there in (zero stretch
When you have an impact the rope or surface that catches you does work on your body to decelerate it. Quick decelerations are worse than slower.
The basic Newtonian equation to describe this is:
Work = Mass X Acceleration X Distance
Which is rearranged to
Acceleration = Work/(Mass X Distance)
The Distance is the stretch of the rope in this case. For the same height fall, the Work required stays the same as it is a function of gravity and distance/time and Mass stays the same. You can see that varying distances from 0.5 inches to 2 inches will decrease Acceleration (deceleration here) forces by a factor of 4 (since it is linear and you can do all the math but the difference cancels to 2/0.5 = 4). By way of analogy, if you've seen a force draw curve for a bow....you are spreading out that peak and thereby lowering it....you do the same work but over more time so less work in any one period of time (and it is the peak that gets you).
Increasing stopping distance upon impact from extremely small amounts to simply a small amount is used in many safety applications and undergirds some basic concepts.
Consider somewhat compacted sand (silicon dioxide) versus much harder sandstone (same stuff packed more). If you fall and strike your head on compact sand the sand only gives an inch or so, but it is much preferable to the close to zero give of the sandstone. This is in part why we'd call one surface "softer" than another. Same thing with the hard foam in a bicycle helmet. It only gives an inch or so but that is enough to save your skull.
If you sit in a saddle with a dynamic rope tether and gently bounce, you'll notice the small amount of stretch even with gentle body weight and it becomes somewhat obvious it would help you.
I've had folks quibble with me over using the Work equation as being too simplistic. Yes, it is the first back of the envelope way I'd expect a physicist to approach this, but it is not a full simulation. I give you that, but it is a close enough for now approach....such as neglecting pipe friction when determining approximate pressure in a pipe given the amount of water above the location (hydraulic head).
You can easily find a good test that informs this. Drop tests with short nylon vs. dyneema loop slings. The nylon sling is often rated significantly lower than the dyneema sling, yet when both have a sufficient dynamic force (dropping a few hundred pounds with a fall factor of 2), then routinely the nylon sling survives and the dyneema one does not. This indicates that the peak force is below the lower rated nylon sling for its drop but higher than the higher rated dyneema sling for its drop.
This is not intuitive in part because it happens so quickly that we can't see it. In comparison, when someone falls a long distance on a dynamic rope and they spring around like a trampoline, then we can see that with our naked eye.
