First of all, I really appreciate that you are willing to take the time to engage in a lively and very technical discussion! I love this stuff, so I will probably drink you under the table.
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And neither the bight (by which I assume you mean a choked attachment) nor the tree keep the core from pulling out,per se. That is,it is easy to achieve maximum splice efficiency without the presence of either, though they can provide backup security.
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No, I did not mean a choked attachment, but I probably could have been clearer. I was trying to point out that the loopie is not intended to be used as an open loop. If I wanted to really put a loopie to the test (as I have done a number of times in one form or another), I would hook it up as an open loop and make sure that the spliced part was straight, not part of a bight, and finally I would make sure I installed pulleys at the two load points, not a shackle of some kind. This is the worst possible case, and the loopie will slip. Introduce some friction by using shackles (not girth hitched) at the load points instead of pulleys, and maybe the loopie will hold. Introduce more friction by putting a bight in the spliced section and applying the load there, and it will almost certainly hold. Add a mountain of friction by bending the whole works around a tree and further bend the shackle-holding bight through the spliced-section bight, and God can't pull it apart. The point is all those curves are doing something useful, and without some help the loopie can slip.
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Oy. First, the absence of the eye at "T" changes how the load is applied so much as to make "T" meaningless. In a conventional splice or a whoopie, half the load is applied by what is more or less an appendix in a loopie. But in all cases, the splice works because of friction generated along the entire length of the splice. Stitching in a conventional splice has no bearing on ultimate splice efficiency; it is there to make sure that the splice doesn't slip before enough load comes on to clamp the outer part around the inner. It serves no other purpose.
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Caramba. I agree that in a normal eye splice the stitching is just there to keep your dog from pulling the splice apart. But we are talking about an eye splice (loopie) where half the eye has been cut away, leaving just the appendix you mention. Now there can be no tension on the appendix, the missing leg of the eye, and we have a whole different animal on our hands. As I remarked in an earlier post, the loopie is like an eye splice with the entire load on the buried part. Here the stitching does do something.
I have done the following experiment several times with consistent results: Take two pieces of Tenex or Amsteel Blue and bury one in the other as if to make a splice. Now measure the force it takes to pull the core out, making sure the spliced area is not disturbed in any way. Let's say it takes 8 lbs to cause slippage. Repeat the exact same experiment, this time with 3 stitches of 2-lb. test sewing thread applied to the throat of the "splice." Now it takes 100 lbs. to pull the core out! Repeat again, this time with the 3 stitches near the end of the buried tail. Now it takes maybe 15 to 20 lbs. to pull the core out.
This experiment is precisely the worst-case loopie test--a straight pull to extract the core and no friction within a mile to help out. Anyone can repeat this experiment with a couple of pieces of rope and a bathroom scale.
So, back to the case at hand, if we apply this result to the question of where we should put a bight in the loopie sleave for the purpose of applying the load, it would seem it should be near the throat end, where I placed the arrow, not near the other end with the "T." The assumption is that this loaded bight is a bit like stitching--it creates friction that tends to lock the core and cover together. It should also have the big multiplier effect seen in my simple little experiment.
Hooray for the loopie. Not only is it a cool working tool, but a cool experimental one as well. The normal eye splice is such a well-behaved and predictable structure the inner physics is somewhat concealed. With the loopie it is all out there in the open, ready for someone with time on their hands to try to figure out the puzzle.