UKH

related to another topic, I'm interested in what angle a nut in a parallel taper will hold a fall. In order to explain what I'm talking about, I've drawn the following diagram. 

http://static.timparkin.co.uk/angle-of-dangle.jpg

I'm interested in what angle of overhang people would be happy to use a nut in a tapering but parallel crack in something like granite or equivalent hard granular rock. 

What I'm trying to find out is what angle of pull outward is OK for a nut to still hold (presumable a diminishing strength as the angle gets more outward? It's an open question as it depends on a lot of factors but I'm interested in a rough idea of what people think.

Honestly, I'd put a cam in there.

It depends on whether I'm carrying my protractor or not.

Do you know that angle between horizontal and vertical - that's 45 degrees..  no problem!

Assuming no horizontal friction/ stopping force 45 degrees

And me. But let's imagine we're pre-Jardine.

thanks!

Awesome - you've created one of those optical illusion thingys. I see a nut placed in a slab.  couldn't fathom it out and then my perspective changed and I can see your overhang.

Is the crack tapering (narrowing towards the bottom) or parallel? It can't be both.

lines drawn perpendicular to the crack on each side of it are parallel. Lines drawn down the crack are tapering 

It will depend on the angle of the overhang and the taper. Slightly counter intuitively a slightwe angle of taper will get you a greater angle of overhang.

Overall it is easier to think of a vertical wall with a tapered crack and an outward pull.  The nut slides down the crack until a balance of compressional and frictional forces stop it moving.  It's easy to show the contribution of the frictional forces increases as the taper angle gets shallow.

The frictional forces resist the sideways pull so the answer is it depends on the angle of the taper (and the coefficient of friction for the rock/nut combo).

Is the crack or nut on a treadmill?

A quick calculation on the basis of my email above suggests that for a near parallel sided crack (where frictional force dominate) the outward pull that can be resisted is equal to the downward pull which gets you a max angle of 45 degrees regardless of the coefficient of friction.

The reason is the nut is stopped from sliding down the crack purely by friction and, assuming the frictional force that needs to be overcome is isotopic, then the force required to move it in any other direction is the same.

For tapering cracks this drops quickly to about 1/2 this by the time you get to the average nut tapering angle (~15 degrees) but depends on the heavily  on the coefficient of friction (slipperier falls out easier). and this gives about 25 degrees.

However, please don't try this! the frictional forces that can be resisted require the nut to be set with the forces exerted down the crack before you can resist the force outwards - there is no guarantee in the event of a fall this will occur and the outwards pull is could be as low as the tug applied to seat the nut.

[plus it use idealised physics where infinite forces can be invoked without damaging the rock or nut]

Still it goes to explain why nut can be quite such a bugger to recover from parallel sided cracks.

This is a perfectly smooth crack, with no irregularities.  And you're placing it at odds with the angle of pull as a result. In reality, you probably find the bit where it's wide enough that you can stuff the whole thing in, draw it along a bit, and then pull it down again where it's perfectly trapped in the direction of pull.

Placing nuts is about find irregularities; and nuts should always be placed to be good in the angle of pull. So it's all a bit of a moot, abstract debate, which no one is going to be able to answer without setting up an experiment. And that experiment would be almost irrelevant to rock climbing, because no-one has ever seen a crack like the one in your sketch.

This. In Cairngorm granite flared cracks it's all about the irregularities. The advantage of the offset shape is that it permits access behind them in shallow placements

As a physics problem the min angle of pullout is a function of the coefficient of friction between the nut and the rock as well as the taper angle of the placement.

In reality a bomber nut is seated in a small constriction such that an outwards pull is resisted by that constriction. This is why alu offsets in particular have the central channel giving more opportunities for a constriction or irregularity to catch on the nut.

Absolutely! This is the problem about any generalisation (bloody real world!!)

Presumably, there are some situations where you don't find an irregularity, just as you sometimes find a natural taper to place a Wallnut and it's the regular taper, not a particular constriction, holding it in. I'm not an experience climber so this may not happen much and I've just bumped into this situation a couple of times.

With no personal experience of how much outward pull a walnut can cope with I was interested in people's experiences to give me an idea.

Brilliant - thanks for this response. Just the sort of thing I was after!

I studied biology, but I reckon the more your theoretical crack overhangs, the less it becomes tapered in the direction of pull. When it becomes 90° overhanging, there is no taper at all in the direction of pull. What's more, given the initial downward taper, the more your crack overhangs, the more it becomes flared and the less contact area there is between the sides of the crack and the front/back of the nut. By the time you get to 90°, only one side of the nut is in contact with the rock (unless it's an offset). I reckon that with the reduction in downward taper and the increase in flaring your nut becomes pretty useless on anything that tilts much at all.

Btw I reached my conclusions by making my hands into the shape of a tapering crack and tilting them, so it may all be bollox.

Also, I second what CWitter said about irregularities and someone else said about using a cam!

Thanks for that - this makes absolute sense based on my guess at the limit bounds of friction/angle etc

No problem - as before caveats apply and treat with caution etc etc.

It was a interesting distraction from a boring job! - I'll take the graph down in a few days so as not to spam up the "people" category.  If you want the details let me know.

Rotating the nut 90 degrees so that the wider offset side of the nut is facing outwards is probably going to increase the chance of resisting side pull though. Totem cam every time in reality though.