When toproping and the climber falls and you get lifted off the ground you are both hanging from the rope.

When belaying off the anchor only one person is hanging from the rope.

You do the math.

where does the 2/3 come from? is this an empirical value derived from research somewhere (in which case i'd like to read the link if you remember where to find it)? or is the 2/3 a value that can be determined by math and physics? in that case would you mind posting the math or PMing me?

also, why is the climber's force double the static weight? clearly the climber must realistically undergo some acceleration and therefore an increase in force, but why is it double? is this value research based or math based?

In his paper, Richard refers to it as a "convention" to account for the reduction in force on the belayer's side of the rope due to friction between the rope and the carabiner. I presume that it is based on empirical data.


The peak force of twice the climber's weight for a fall-factor-0 fall is a consequence of using Hooke's Law to describe rope stretch. As you'll see, Richard provides two separate derivations of this result.

Jay

Colatown, the 2/3 value for carabiner efficiency is an empirically derived value that has been stated over and over in various places, and now has the status of "folklore." I don't know the original reference. I have seen 1/2 stated, but much less often. The fact is that the number will be different for different rope-carabiner combinations and probably, like other friction coefficients, has a sliding and a static value.

The fact that the peak tension in a rope with applied weight W is 2W is a simple conservation of energy consequence of Hooke's Law, viewed as a reasonable approximation to the behavior of a climbing rope. (Yes, there is some acceleration involved, since a climber who weights a rope will drop as the rope stretches.) The result assumes that the climber's weight is instantaneously applied to the climbing rope with no slack in the rope. Using various strategies to ease the weight onto the rope could, in theory, keep the peak rope tension no greater than the climber's weight, but this would not apply to catching a top-rope fall.

Whether the real result is more or less than 2W would be a matter for experiment. I'd guess a little less than 2W because of the internal damping effects of rope construction, but given the manifold uncertainties and variations in real-life practice, 2W is a very reasonable working estimate.

Apparently, I derived this result in the .pdf jt512 refers to, though I'd have to check back to be sure.

If this fact about minimum peak top-rope loads doesn't appear in some of the "bibles," that reflects either an unsophisticated approach to bible-writing (perhaps because the author(s) do not have a science background) or a lack of faith on the part of the authors in bible-readers, or an estimation that knowing the real figures will not contribute in any meaningul way to practical behavior in the field.

If this fact about minimum peak top-rope loads doesn't appear in some of the "bibles," that reflects either an unsophisticated approach to bible-writing (perhaps because the author(s) do not have a science background) or a lack of faith on the part of the authors in bible-readers...

So what is the question?

Are we talking about tension? From a toprope VS belaying on top there is more rope out and since it's dynamic rope, it's harder to get it tight.

Or are we talking about the weight the anchor sees? Assuming nothing dynamic, the anchor see's your weight and the belayers weight. Kindof. Actually this brings up another question. Lets assume we have a junk anchor that will fail at 300lbs. The climber weighs 100lbs and the belayer lowering her off is 200. The way I'm looking at it, the anchor feels the belayers opposing weight up to the weight of the climber (actually a bit less due to friction). I might accept being wrong about this but that seems to make the most sense to me.

haha this post got so off topic i just had a simple question on tention and it went into all this stuff i can't really say it was simple because i can't word anything well but how can i put a diagram so i can show what im talking about more clearly.

I claim that a toprope anchor should be built to withstand a force of at least 3000 lb.

Stop it. You're kill me.

Jay

Damn Jay, that's right up there with "all your base are belong to us."

yea that's what i was thinking if it was moving like while letting him down to find the tenition it would be more like T=m(g-a) t is tention m is mass and g is accleration due to gravity and a is acceleration of the system

A fundamental fact of physics is that motion at a constant velocity and motion of zero velocity are indistinguishable.

Jay

A fundamental fact of physics is that motion at a constant velocity and motion of zero velocity are indistinguishable.

Jay

thats not what im saying in both situations there is no acceleration so T doesn't increase

A fundamental fact of physics is that motion at a constant velocity and motion of zero velocity are indistinguishable.

Jay

I must be mistaken, but I just saw two cars on the street. One was parked and one was moving at a constant velocity of 30 mi/hr. I was able to distinguish them based on the motion.

On the other hand, both cars were moving at approximately 66,600 mi/hr around the sun, as were you. Still think you can distinguish constant velocity from zero velocity?

Jay