Branch Union TIP Rope Sawing During Climb - SRT
This popped up in another post so I thought I'd take a crack at it here. A lot of the data and analysis comes from the SRT Base Tied Tp Forces thread linked below.
The branch TIP union is a 180 degree wrap bollard with a tension ratio of 1.4 for a typical climb rope on average roughness bark. That means that the rope will slide over the union as you settle your weight onto the up rope leg until the tension rises in the down rope leg, maybe I'll rename that basal leg, to 1/1.4 x the up leg tension. So a 100 lb guy settles out : (1.0+1.4)x? = 100lbs, ? = 41.6 lbs giving 41.6 lbs in the basal leg and 58.4 lbs in the up leg. Oops. that's the DRT calculation! SRT: basal leg = 1/1.4 x 100 lbs = 71.4 lbs and climber up leg = 100 lbs.
If the climber's "weight" is incremented upwards both tensions rise maintaining the 1.4 ratio. The 1.4 value comes directly from at the point of bollard slippage so an initial climber weight increase will cause a small slippage or rope saw. Such an increase can come from initiating climber movement like pulling/stepping on an ascender. IIRC in my test data such an increase was 10% or 20% of the climber's weight or expressed in a ratio 1.1 or 1.2 G's. This is the source of bounce while ascending. Numbers can be 78.6 lbs, 110 lbs or maybe 85.7 lbs 120 lbs. After the slippage the basal rope side will stay at the higher tension value until the climber side drops to 1.4x less or 78.6/1.4= 56.1 lbs or 85.7/1.4 = 61.2 lbs as above example numbers. A principle of the tension ratio is that it matches the direction of motion of your rope through a device, pulley or other. There's a high side, loss and then lower tension side. This creates a hysteresis window that often confounds practical experiment measurements.
Now this is where it gets interesting. Descent. At first you apply hand pressure to your hitch/device which in itself doesn't change the up rope tension by the amount of hand force because while doing so you equally decreased the load on your bridge. But, it causes some reduction of grip of your hitch/device and it no longer supplies 1 climber G of support, so perhaps 90% or .9 G is still grabbing and the other 10% or .1G starts accelerating you toward mother earth. Now the up leg is at 90% of it's previous 100 lb load or 90 lbs so does the rope reverse the saw direction? In the case of descending after gentle settling to 71.4 lbs basal the bollard (union) won't slip until the climber side is below 71.4 lbs/1.4 = 51 lbs and 90 lbs is higher, so no slip. If you bounced/ascended and kicked the basal side up the 90 lbs doesn't make it down to/lower than 56.1 lbs or 61.2 lbs. so no slip. I could see that if you completely unweighted your SRT climb line and resettled onto it you could reasonably create a full reverse saw stroke. For completeness, at the stopping point of your descent you G spike the rope but my data was typical 10 or 20% only so that's the same calculation as for ascent.
So it seems that on initial settle onto the rope you get one forward saw stroke, any incremental climber G spikes create a little bit extra forward stroke, but in normal climbing negative G spikes are never large enough to reverse the bollard skid direction ie do the reverse rope sawing stroke. Maybe spring sap lubricated cambium has a tension ratio of 1.1 or 1.2 but then you've defeated all purpose of reasonableness if you're in that situation. The interested student could work the numbers.
The G spike values were from RW and ascender development I did that hasn't been published. Yeah aggressive climbing can increase the G spikes to some degree but I think you have to be pretty wild to create a significant effect from them.
link to related data and analysis thread: Seems like the right place to reference it - nerd content
Well, I finally decided to get off my duff, confined in the house in the evenings and set up a jig to measure the climber side rope tension and the base tie rope tension. This is a revisit of a hot topic back in 2013. I remembered P(r)etzl (Chicanery!!) publishing a study where they said the tip force was less than double the climber's weight. Well, I dug and found Kevin's post of the conclusions page by Pretzl where they stated the force in two stages. First they said that in SRT or DRT (they meant cinch tied SRT) the tip force was 50% more than the climber's weight. This is a...
I found during my testing a real non-linear initial settling of the rope length vs tension or "linear" %elasticity modulus, as the rope "cabled up" so it remains for the interested student to enlighten the details of this zero to low hundreds of lbs rope behaviour. I think it's severe enough to not even bother to try to calculate sawing motion size via use of a linear rope elasticity model.