Huh? The rope does not have an absolute maximum impact force. The maximum impact force for a particular rope is a function of the fall factor and the weight of the climber.

Jay

right, the rope doesn't have an absolute maximum impact force, which is why I said, "about at the maximum impact force." Regardless what I was trying to say is that once outside of the linear elastic region (region with a constant modulus which on a rope doesn't really exist to begin with) hookes law no longer applies.

Well, you need to provide some evidence that predictions using Hooke's Law with a constant modulus are poor approximation of the maximum impact force.

Jay

The evidence has already been provided. The fact that the ropes in that BD test were all breaking at around 10 kN shows that once you reach that value, the rope will just stretch without taking a higher load until it breaks. look up any typical stress strain curve, and you'll see what I mean.

I'm not trying to argue with you or anything, but just stating that ropes don't behave exactly like a typical linear elastic material, this approximation is fine for certain things, but once the loads are to high, it no longer works.

I didn't say that a piece with a 50% probability of failure is bomproof. That'd be stupid. If I did then it was a mistake in wording.

The 1% failure rate is about the same as a condom. I don't have any babies and I haven't died yet so 1 in 10,000 seems infintesimal to me. Maybe once I knock some girl up I'll make sure I place three pieces all the time. I guess that word is open to a lot more interpretation than I thought. Infintesimal is obviously a lot smaller number for you. You're prejoratively a sport climber. I am not. I have seen a lot of things that I thought wouldn't hold that did so my assessment of what constitutes bomber might also be different than yours.

I'm not that casual about risk. Like I said before, there are a lot more factors going into it. Will I fall? Will I get in gear before I might fall? Will the catch be very dynamic? Will I hit something before my full weight comes onto the anchor? Placing two pieces at an anchor is not the norm for me but I do so on numerous occasions. If the anchor is marginal I'm sure to say so and place more gear. 6.25% probability of failure if it gets fallen on is pretty damn low.

I'm not casual, I'm tolerant. You're not, that's why you stick to sport climbing and I like a little more variety in my repetoire.

Jmeizis, you can add one more factor into your little hypothetical equation that will radically improve its usefulness, without requiring a supercomputer to calculate the probabilities:

Equalization

Let's say you are capable of creating an anchor that equalizes somewhat (distributes would be a better term than equalizes).

The point of the anchor is to be capable of holding the worst possible fall - a FF2, which can easily generate forces up to 18kN on the anchor.

Now let's look at your pieces again, and say that you estimate that each placement is 90% likely to fail at 18kN, 20% likely to fail at ~10kN, 10% likely to fail at ~7kN, and 2% likely to fail at ~5kN.

A single piece anchor gives you around:
90% chance of failure.

Two pieces, equalizing at 40/60 give you around:
20% x 10% = 2% chance of failure.

Three pieces, equalizing at 30/30/40 gives you around:
2% x 2% x 10% = 0.004% (four in 100,000)

Add a fourth piece, equalizing at 25/25/30/20, and you might see something like:
2% x 2% x 2% x 1.5% = .00001%

So three looks like the magic number to me.

GO

Could you cite the specific literature you are referring to, because it seems to contradict what rgold, who seems very familiar with the literature, has said; namely, that Hooke's Law is a very reasonable model of the max. impact force of a dynamic rope, except when the fall is very short (and very long?). Note, that these exceptions are for extremes of fall length, not fall factor.

There's still a small chance that all the pieces will fail so why not place 4 or 27. If you have a 12 piece anchor and 11 of the pieces fail then you'll be on one. So by that trend of thinking we can't possibly be safe...ever. We're all gonna die!

The purpose of the anchor is to save the lives of the climbing party in the event of a fall, not reduce their chance of death to only 6%.

It's why, when I build anchors, I build ones that I think have essentially no chance of failing.

Did you read the thread? No-one is pulling numbers out of their ass. Almost all the replies advocate thinking things through.

You're creating a reality in your head again.

But a million to one? Not in your wildest dreams are you going to construct such a robust anchor on a trad climb in the real world.

Why? You don't think that there are placements that have a probability of failure of 1%?

Jay

These are the papers I was looking at both by Attaway:
http://web.mit.edu/...d_order_rope_fit.pdf

http://lamountaineers.org/xRopes.pdf

In the second paper he cites a work by Toomey (1988) in figure 13 which shows cartoon load vs extension curves for dynamic and static ropes. The dynamic rope line curves up and the static rope line is initially concave up then goes concave down.

"Dude, don't even THINK about falling...."

You have to think every anchor through and every situation is not the same.
I rarely use two. Though two pieces can be plenty strong I want every anchor to hold as though it's holding a train. Yeah a single tree is great. Two bolts are good but combinations are what I look for.
If I climb with someone and after seconding come to the anchor and only find two pieces in place as an anchor when more locations for gear is available I get offended. Your life as well as mine, if I'm climbing with your are paramount. This way you and I can climb again even if it is never together again.
Build it strong so there are no doubts in anyone's mind.

I don't feel like doing a literature search again. Prove to me that ropes obey Hooke's Law.

You already have the evidence. Draw the best-fit straight line that passes through origin to the data for the PMI 10.6 mm dynamic rope in Figure 1 of Attaway (2002). The departure from linearity is minor.

Jay

I did a linear fit forced through the origin and a 2nd order polynomial forced through the origin.