Cross pollination of climbing cultures
May the powers that be remain happy.
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 reflection of bouncing while you ascend. Then they said with an SRT base tie, you increase the tip force by 50% over DRT/cinch SRT. Why not 2x? Because of friction at the tip.
Enter the test jig. I put a load cell at the base tie, a load cell at the "climber" and ran the rope 180 degree Uturn over a rounded 4x4 so the rope is sliding across the grain like a tree branch. I hooked a string and pot to the rope on the climber's side about 6" from the tip to measure rope movement/sliding. I used my medium 11.5mm lanyard. This gave the following graph:
There's 15 seconds of data across the bottom, lbs force on the left scale and inches rope position on the right scale.
Follow, between 0 and 2 seconds I ramp up the climber load to about 250 lbs (the yellow line in the middle) and the lower white line, the base tie tension, ramps up to about 120 lbs. Holy Pretzl values Batman! So what gives? Enter the bollard equation. T2/T1 = exp(mu x angle in radians) i.e. e to that power. So 2 = exp(mu x 3.14 radians) i.e. 2pi radians is 360 degrees. Messing around, mu = ln(2)/3.14 = 0.22 which is about the right value for friction. Now look at the highest line and see the rope skidded about 2" during the tension rise, which I also visually watched. So takeaway? 250 lbs + 120 lbs not equal 500 lbs. It's less. So what happens next?
From about 2 seconds to 5 seconds the rope stays still but the climber side tension drops to about 100 lbs, goes back up to 200 lbs and back down to a little bump around 100 lbs. The base tie tension stays pretty much 100 lbs the whole time because it's strung tight with unchanged length between the bollard (tip) and the base tie. Close to 5 seconds the climber tension actually equals and the drops below the base tie tension - and the rope skids back again towards its pre-loading position. I slacked the system close to zero from the climber side and you'll notice the base tie side held a little residual tension - because the rope didn't want to skid around the bollard (tip).
From 7 seconds to the end is a re-try. Wash, rinse repeat. The only oddity is the ripple in the base tie tension which I chalked up to some flex in my "tree" which was a 2x10. The width of the 4x4 was perhaps enough to torque the board a bit. I did the same thing with a 2 1/2" diameter locust branch as the tip because it has rough bark. Mu started at 0.5 and quickly dropped through .44, .4, .35 etc down to between .25 and .3 as the rope smoothed the bark down. I moved the rope aside and verified the smoothing effect. It took about 6 heavy load cycles to grind the bark surface down. There was less base side ripple which suggested my torquing/bending idea might be right.
One neat thing from either the HSE report or one of its references was that bollard friction is dynamic because the rope changes its level of stretch between the bollard entry point and the exit point - because one is high-tension and the other is low tension. So the rope undergoes a stretch within the bollard wraps. Cool.
One conundrum I didn't find was that I thought I could get the climber side tension dropped to equal to base tie, then continue to reduce it and have the bollard friction hold the base tie constant at least for a while to achieve the "strung" base side that's higher than the climber side. I would achieve a small reversal and then the rope would slide. This happens at the 5 second mark. Maybe I did achieve it and it's just different than I thought it would be. This was consistent across data sets.
Here's the only piece of the Pretzl info I could dig up. I thought there was a pdf but I couldn't find anything in my archives.
