Minimum bend radius for termination of rigging set-up?

[Phil]

Phil, what is source for the bend radius table please?
>>is it by chance an eye radius and not bit/bollard/pulley radius table?

I was told this info came from Yale many years ago and is only for Polyester and Nylon ropes. I cannot however provide anything that looks like an official Yale publication to support this claim. I do trust my source though as a person with a daunting amount of first hand knowledge on this subject.

In an attempt to expand my own knowledge, and because you mentioned the 4:1 50% strength loss was from Samson, I reached out directly to Samson to see what they had to say. I did not mention the 50% loss number. I just sent them my chart and asked if they had any published research or charts that could validate the numbers I had for polyester and nylon cordage. One of the application engineers responded back with the following:

"There are no standard set of recommendations across various rope types / constructions. Phil is correct that rope design will have an effect, but this is not typically investigated for every type of rope. Samson has a proprietary model for our AmSteel Blue product design (Dyneema HMPE 12-strand w/ specific twist / braid structure) that is utilized to confirm strength for specific use configurations (i.e., lifting slings w/specific bends). We do not have this same model across all types of products.

Not sure where the listed estimates come from, but they appear to be less restrictive than our AmSteel Blue model or similar high performance rope or wire bend loss factors published in IMCA / DNV / ISO standards. At the listed boundary cases for example, the 1:1 ratio would be closer to 50% strength loss and the 8:1 per our model for AmSteel Blue would be closer to 15%. These losses are generally expected to be less severe for traditional fiber types, due to the higher elongation of the material providing increased load sharing around tight bends, but we do not have a similar empirical model developed."

That statement is copied straight from my email.

Based on the last statement, I trust my chart to be close to accurate in a generalized sort of way.

 

[TheTreeSpyder]

i think they are being more conservative than before to newer age materials, experiences and litigation exposures (a covered hiney is a happy hiney).

Olds-Cool quotes:
"Where a rope bends more than 10 degrees around bitts or chocks, or is bending across any surface, the diameter of that surface should not be less than 3 times the diameter of the rope. Stated another way, the diameter of the surface should be at least 3 times the rope diameter. A 4-to-1 ratio (or larger) would be better yet because the durability of the rope increases substantially as the diameter of the surface over which it is worked increases. "
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"To assure maximum efficiency and safety, the boom-sheave diameter should be no less than 8 times the rope's diameter. The sheave's groove diameter should be no less than 10% greater than the rope diameter, and the groove should be round in shape, not "V" shaped. "
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And for me shows memorable pic i think they used a lot in previous guides. Found these on wayback machine. Arbormaster presenting Samson guide But anyway, 4x for 50% efficiency, and 8x for 100% dream efficiency are the numbers i 'grew up' in tree work with for synthetic lines of the time; and suspect many others too that sought documentation, of which there was very little. This here to me was 'new' when it came out, with the tree rigging drop science in it; like we and our perils were finally noticed ! And that is where i think Arbormaster came into picture here..
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4x diameter sheave for 50% efficiency fairly accepted as matching efficiency of lesser knots. No sense in paying more in cash, handling and space for a heavier 8x pulley, then put a 50% efficiency knot in system; that would then dictate the total system strength; per this chain link of weakest strength. When a 4x diameter pulley's discreeter size/weight/co$t would do as well !
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But anyway, we know there are ratios, larger is better/softer/less radical deformation bend, and applies to rope arcs on pulleys, bitts, capstans, tree branches... And efficiency floor falls sharply out for sure below 4x diameter, perhaps before in some materials (like maybe 8x in dyneema, stiffer braids etc.).
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The CoF of some newer materials is also MUCH lower, Dyneema CoF about like teflon's ! Handling has changed for these materials in this department too! Radial Friction CoF spreadcheat. Have added a dropdown in spreadcheat to change flat CoF and show radial CoF calc then and how applies to numbers of 180 arcs counted. Also notes on other materials and how they compare to those more familiar with, to see what matches experience and what is higher or lower etc.; in a more overall connected fabric overview of understanding rather than individual points.
Not also in the Samson doc the different elasticities of materials to take impact best/softest, and how that also plays out by the amount of 'rubber band'/length of elastic rope in scenario. Also, a fine point is a 2/1 support gives LESS elasticity as gives more strength, just like a stronger rope would. Elastic dampening response is by how much the hit encroaches on the tensile strength ceiling, stronger or doubled rope giving up less elastic dampening response.