Top Rope Anchors - is a figure-8 on a bight stronger or just easier to untie than an overhand knot?
I've been learning to build basic TR anchors; a sling clipped to two bolts with a master point in the loop of a figure-eight on a bight. While learning this I struggled to get a tidy figure-eight knot in the sling–especially on a three-point anchor. I asked my friends who overseeing me if I could use an overhand instead of an eight--and that started a debate.
One friend is of the opinion that there isn't a relevant difference in terms of the strength of either knot, either in normal circumstances or in the event that one leg of the anchor were to blow out. His opinion was that I could tie an overhand for the master point and be just as safe–the only downside being that it would be more difficult to untie after being loaded.
The other friend is of the opinion that a figure-eight is stronger than an overhand, and that an overhand isn't suitable for the master point.
So, is it unsafe to use an overhand knot for tying the legs of an anchor together to make it into a master point?
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His opinion was that I could tie an overhand for the master point and be just as safe–the only downside being that it would be more difficult to untie after being loaded.
Yes, this is correct.
Many people seem to think that commonly used climbing knots can slip if there's not enough friction to make them hold, and that we should choose a knot based on whether it's "stronger" against this type of failure. Actually, slipping is not a mode of failure for any of the types of hard knots customarily used in climbing (as opposed to something like a Munter, which is designed to slip, or a granny, which is not used in climbing because it's not secure).
The only mode of failure for an overhand or a figure-eight is that you can put so much tension on it that the rope breaks. It simply doesn't happen in any realistic climbing situation that we put so much tension on a climbing rope or a cordelette that the cord breaks, and therefore this is not a realistic concern for these knots. (Tests do show that one type of knot may cause the rope to break under less tension than another. This is because the rope tends to break at a place where it's tightly curved. However, the amount of tension required is still just not something that happens in a climbing application.)
As Shem Seger pointed out in a comment, the application referred to in the question is also one in which we have multiple strands. For example, if the anchor being described in the question is being built with a cordelette made out of 6 mm nylon, then we have 6 strands coming down from the gear to the knot, and 3 independent loops forming the master point.
It's true that a figure 8 is easier to untie than an overhand, and that's why we use it to tie in on our harness. However, that's not a particularly realistic concern for the application described by the OP. The question describes a triply redundant anchor, which points down. The only direction of pull it is likely to experience is down, i.e., you're going to use it to support body weight and possibly catch a top-rope fall. Those aren't likely to produce enough tension to create any serious problems with untying the knot.
A lead fall (unless it's a factor-2 fall) is going to generate an upward force. It could be a much bigger force, but because it's upward it's actually not likely to stress this knot at all. The concern here is not that the cordelette will break, it's that the anchor probably isn't designed to hold against that direction of pull, so you may have pieces popping out. This is one of the reasons why it can be a good idea to supplement your anchor with a piece that is intended to hold against an upward pull.
In the case of a factor-2 fall, the big concern is that this can be an extremely violent fall that can actually destroy your pro or break the rock. The cordelette is not the weak point in this situation.
A more realistic consideration here is simply how much cord you have. A figure 8 uses up more of your cordelette. If you don't have enough length available in the cordelette to tie a figure 8, then that would be a good reason to use an overhand.
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This answer does not provide much new information to Ben Crowell's and Charlie Brumbaugh's, but I am not entirely in agreement with all their different conclusions.
TLDR:
In your use case and most use cases strength reduction by a knot is not an issue, so use whatever save knot you are comfortable with. In general consider the rule of 50% strength reduction by any knot. This is easy engough to remember and when you are building anchors for multi-pitch climbing and want to have some safety margin, this can become relevant.
Explanations:
My climbing reference just states that any knot reduces the breaking strength (force at which a rope/sling/cord breaks) by 50%. This is meant to be a safe rule of thumb, not an exact number.
I also learned that one important factor that reduces the breaking strength how sharply a rope is bent in a knot. From this and tests I learned that an overhand on a bight is worse than a figure-8 on a bight, which is again worse than a double bowline. On the other hand you are talking about a cordelette setup, so you have 4 or 6 (or rather unlikely even more) strands in your knot. For the reason above this should reduce the breaking strength less, as the radii of the cord within the knot are bigger.
So far about principles. In your use case of a top rope anchor I totally agree with Ben Crowell: This is completely insignificant. As long as you do not use a really feeble and thin cord for your anchor, you will have enough strength left after deducting the generous 50% mentioned above. Also if you use so many strands the knot gets big and is thus much easier to untie. So this advantage of a figure-8 is less important as well.
In general one cannot completely dismiss this mode of failure. A knot in a rope/sling/cord does reduce its breaking strength significantly. So if you use a rather thin cord (e.g. 5mm diameter: 5^2 * 20 = 500kN) for building an anchor (e.g. when you ran out of material on a longer route - should not, but can happen) and use a single strand between center point and a piece of protection, this strand has an effective strength of 250kN which can be easily reached in a factor-2 fall. Sure, one should not do such a thing (but you see many people who carry only such thin cords) and even then it is an unlikely scenario, but it is a scenario. And due to Murphy we know that what can go wrong will go wrong.
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Doesn't really matter for top roping, you've got so much rope out when you're top roping that when you take a fall pretty much all the force is absorbed by the rope, your anchor is holding only a little more than the body weight of you and your belayer most of the time.
Mountain guides will tie an overhand knot, figure eight, or figure nine depending on how how high they want their master point to be. When top belaying, you want the master point as high as possible, so figure nines are good at taking up any extra sling, especially if you're anchoring in an inline crack.
For top roping however, I wouldn't recommend tying a large master point, because as soon as you deviate from your line (which happens on a lot of top roping routes) then your anchor isn't going to be equalized. On a two bolt top roping anchor I would use a sliding-x with maybe a couple stopper knots tied into it if I was using a sling.
I favour equalettes when I'm setting up top anchors myself, they're the most SRENE anchor in my opinion.
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