Thanks Bart. I think I understand what you got there, but I can't see any pictures on that thread, and I'm a little unclear on the setup. Would it be accurate to say that a canopy tie puts 150% of the climber's weight on the limb during acceleration up the line? Maybe assume 200% climber weight to add a safety factor to estimation?
If I interpreted your setup right, you used short lengths of rope. Increasing the rope length would decrease the force on the anchor due to more length to dissipate energy?
Where this thread came from, was there's a long limb on a pin oak at work. It had a decent size dead branch on it, and it's over the area where kids play. Last time I was up the tree, there was a trampoline under the branch, and I didn't want to move the trampoline by myself. Otherwise, I could have limb walked/crawled out to it. I could canopy tie to the branch close to the dead fork and cut it off. I'm 95% certain it would hold me without breaking, and it would be the fastest way to get to it. So, that got me thinking how to quantify the forces to anticipate when making these decisions on trees that are less reliable than oak.
It is considered ideal when the height minus 100 is equal to the weight. For women, height minus 110 is equal to weight. My height is 176 cm, weight 76 kg. By the end of summer I can lose 1-1.5 kg, but in winter I will return to my normal weight again.
Things vary very much while still being healthy and capable.
I went for a normal checkup, recently. By default, I'm getting a followup informational email due to a high BMI.
I am leaner than I've been in years, which, aside from when Dahlia was tiny, and I was a bucket baby, I've always been pretty-to-very lean from lots of activity.
When I was flying a bucket, I was still leaner than average, having a very healthy body composition.
Look up the bollard effects each time your rope redirects or does a 180ish over a tip. Use all that friction to your advantage to reduce the load on the last, presumably most vulnerable, support point before you. Then stealthy like a Lynx, no bouncing. If you play your cards (rope) right you can hang off a spindly tip that's almost completely in axial compression. Normal bouncing or climb motions probably add 20 to 30% and I don't mean aggressive DRT air humping. Normal rappel and stop similar size.
Basal tie SRT tip load 1.5 to 1.6, normal climbing, average bark friction. As a climber you can bounce the hell out of the line (if you so choose) and create big force bumps and also skid the rope over the tip/redirects and undo your beneficial friction at those locations. Lynx!
edit - the buildup of friction reduces the tension in the rope so the basal end keeps getting reduced, not the "you" end, which stays at "you" weight, but the tips themselves get reduced loading, in particular at the classic first tip in no-redirect basal SRT. Sorry for the in articulation. But the principle still stands.
Just as arc bridge gives greater support than linear bridge;
arc frictions are greater than linear frictions, and for the same cos+sine all uniquely working the same direction in a 180, unlike any other geometric form reason.
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Linear frictions are simpler, scalar, sine of direction of movement X CoF frictions of mated materials X distance.
>>2x as much distance, 2x as much effort, easy math.
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Radial frictions are cos+sine powered. Sum is greater than 1 except at the ends !!!
AND arc frictions EXPONENTIALLY COMPOUND per DEGREE.
So smaller round, gives same effect, just harder on rope bend and more concentrated frictions.
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Sine only powering frictions in linears will always be a factor of less than 1.0 for sine.
Radials give cos+sine powering frictions is =1 at the ends, and cos+sine >1 thru the sweep.
Then the compounding... 2.7182818 raised to the power of the friction CoF of the mated materials X PI (for now a radial CoF) X 180 'strokes'.
Anyway, just leaves common linear frictions way behind in base production of frictions, then the exponential rather than scalar progression/compounding in arcs...
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See, 180 arc, as 1 swing of pendulum, as 1 stroke mechanically, a 2nd 180stroke completing a full cycle; just as like piston arm. The Mechanics of Friction in Rope Rescue Stephen W. Attaway, Ph.D. International Technical Rescue Symposium 1999 spreadcheat
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.
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May the powers that be remain happy.
