 Poster: A snowHead
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Didn't want to write off-topic in the thread about "Daft piste to be taken down on your first week" so here it goes.
A well known physics law stands that any phisical body stationed on the slope will start sliding down as soon as the angle of the slope reaches certain critical value.
This angle does't depend on anything but coefficient of friction.
Here is the formula
Where a - is a critical angle, and c - is coefficient of friction.
Tan(a) is a tangent of the angle i.e. Tan(a) * 100% will give the slope gradient in % as seen on the road signs
For an angle of 45 degrees the formula above will yield
Which means that for anything to be stationed on such a slope traction coefficient must be 1, i.e. it must be secured there.
It also means that such a slope will have no snow on it (except for a very thin layer stuck in terrain unevenness), as it will all slide down.
Thanks for reading 
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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Frozen water does tend to secure itself to rock at sub zero temps quite well.
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Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
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oleksii, I don't think you are working with real world conditions...
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You need to Login to know who's really who.
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oleksii, Thus demonstrating why a little knowledge can be a dangerous thing. The co-efficient of friction can go above one and Mosha Marc has alluded to how the structure of snow as a material might affect that.
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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| Quote: |
Frozen water does tend to secure itself to rock at sub zero temps quite well.
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It will create a thin layer of snow/ice but everything else will slide down.
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oleksii, I don't think you are working with real world conditions...
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No, it just that some people don't understand how steep 45 degrees angle really is.
The steepest road in the world is "only" 19 degress (http://en.wikipedia.org/wiki/Baldwin_Street,_Dunedin)
Last edited by Anyway, snowHeads is much more fun if you do. on Wed 12-09-12 12:21; edited 1 time in total
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You'll need to Register first of course.
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the coefficient of friction only works with perfectly smooth bodies in full contact with each other on a flat surface. It can't be applied to a whole mountain.
Nor does it take into account 'adhesive' properties of ice.
But you're right that people overestimate steepness. I wonder how much of that perception is down to the height of the individual. That would increase the perceived angle.
Last edited by You'll need to Register first of course. on Wed 12-09-12 12:22; edited 1 time in total
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Actually snow generally adheres up to about 60º.
Beyond that I'm sure you have seen pictures of snow securely stuck by the wind to vertical elements such as poles. The point is that it STICKS on rather than just resting on the surface (the kinetic energy of the blown flake will briefly melt the snow surface on impact), and then snow flakes themselves have complex shapes which latch onto each other. When adhesion between layers of snow is poor (for example with wind-blown snow, the flakes which form which tend to have lost their outer branches and behaves differently from other snow) then you get avalanches at considerably less than 45º, often right down to the ground. There is nothing magic about the figure 45º when dealing with real slopes.
However you are right that people considerably overestimate the steepness of slopes. Slopes of a bit over 30º regularly get called "near vertical".
Last edited by Then you can post your own questions or snow reports... on Wed 12-09-12 12:30; edited 2 times in total
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oleksii, have you seen a cornice before? That's entirely made from snow and not only does it go past vertical the snow slope below is often very steep, here is some reality for you:
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You'll get to see more forums and be part of the best ski club on the net.
You'll get to see more forums and be part of the best ski club on the net.
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oleksii, also here is some information about the range of the static co-efficient of friction for snow as measured experimentally:
http://arc.lib.montana.edu/snow-science/objects/issw-2002-523-527.pdf
Rearranging your formula and substituting the values you can see that snow will slide in a range anywhere between approximately 25 degrees and 65 degrees depending on the composition. As we can see from that it's possible for snow to remain static on a slope much greater than 45 degrees.
Last edited by You'll get to see more forums and be part of the best ski club on the net. on Wed 12-09-12 12:29; edited 1 time in total
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meh, nice photo. Looks like some places I know in Scotland. Is it Iceland?
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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snowball, nope, Lochnagar! Just a random picture I grabbed of the interwebs. 
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And love to help out and answer questions and of course, read each other's snow reports.
And love to help out and answer questions and of course, read each other's snow reports.
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here is some reality for you:
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That's right, snow is stuck in terrain as I said. You do realise that the rock half covered with snow on your picture is just about 45 degrees? Would you ski there?
Only very experienced pilots and astronauts can control themselves when aircraft tilts more than 30 degrees. Everyone else panics and screams errorneusly thinking that they will overturn next moment.
It's just the way human perception works.
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| Quote: |
Rearranging your formula and substituting the values you can see that snow will slide in a range anywhere between approximately 25 degrees and 65 degrees depending on the composition. As we can see from that it's possible for snow to remain static on a slope much greater than 45 degrees.
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Yes, my formula was for ideal conditions. But anywhay, I just wanted to point out that most people don't understand how steep 45 degrees is. As said above 30 degrees is "almost vertical" as far as human brain concerned.
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You know it makes sense.
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oleksii, I've stood on and skied down slopes that I've measured at 50 degrees using a clinometer. There is so much empirical evidence of snow slopes steeper than 45 degrees I don't know how else to point out the error to you. If you want to pop over to Iceland at some point this winter I'll take you out and show you some!
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Otherwise you'll just go on seeing the one name:
Otherwise you'll just go on seeing the one name:
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I'm neither a physicist nor a mathematician - my humble understanding has always been that a 45 degree slope is equivalent to a 45 degree angle / side on an isosceles triangle. Am I wrong (the rock half covered in snow above looks almost vertical).
Thanks
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Poster: A snowHead
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oleksii, all you did was make the assumption that the coefficient of friction couldn't go over 1 when clearly and demonstrably this is wrong. Also yes, forty five degrees feels steep and is steep on skis! Only a little hop sideways drops you down equally as far.
Last edited by Poster: A snowHead on Wed 12-09-12 12:47; edited 1 time in total
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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Actually the little bit of snow slope in the foreground you are presumable referring to is more like 60º, reducing to 50+ briefly. However it might get less just below - perhaps 45º in which case I might well consider skiing it, depending on snow conditions etc. I don't disagree with your general point, though.
Last edited by Obviously A snowHead isn't a real person on Wed 12-09-12 12:52; edited 1 time in total
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Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
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maybe we're being a little harsh on oleksii, as it does make you think, no? i am wondering what the steepest I've skied is.
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You need to Login to know who's really who.
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under a new name, true, but he tried to make his point mathematically and slipped up.
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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 Easy Gully, Nevis Range, Scotland.
Perhaps I should mention it was named Easy Gully by climbers, not skiers (and, I assume, continued by skiers ironically).
Last edited by Anyway, snowHeads is much more fun if you do. on Wed 12-09-12 13:52; edited 1 time in total
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You'll need to Register first of course.
You'll need to Register first of course.
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| Quote: |
hat the coefficient of friction couldn't go over 1 when clearly and demonstrably this is wrong.
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No I wasn't wrong, CoF above 1 means that the gravitation alone is not enough to slip the object, i.e. someone (or something) should drag it and as soon as that something stops applying it's force the object will stop sliding.
Snow will of course freeze to much steeper slope (i.e. gain CoF > 1), but as soon as it collects the critial mass it will inevitably slide down, especially is someone decides to ski on it.
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Someone mentioned moguls not forming on slopes steeper than 40 degrees & Glencoe's Fly Paper is a good example to support that.
snowball, I'm glad you were thinking of the likes of Easy Gully which I think from memory was one of your favourite Scottish skis. It's steeper than 50 degrees levelling out to 40 after the buttresses underneath and about 30 by the time you get to the lochan far below. It sometimes has a big cornice at the top to make it look nastier. Pic below is just before I skied it in April (tiny cornice and fine weather) for the first time and it definitely had deep snow in it then too ...
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| Quote: |
maybe we're being a little harsh on oleksii
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Not at all  This is one of the most friendly forums I've ever seen, really.
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You'll get to see more forums and be part of the best ski club on the net.
You'll get to see more forums and be part of the best ski club on the net.
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| oleksii wrote: |
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here is some reality for you:
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That's right, snow is stuck in terrain as I said. You do realise that the rock half covered with snow on your picture is just about 45 degrees? Would you ski there? |
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moffatross, Interesting - I've never seen it without a cornice. I have always gone in from one edge in a descending traverse to avoid it (and keep my speed down). Your estimates of steepness are exactly what I would have guessed, though of course the lower slopes are progressively less than 30º. I skied it twice the last time I was there and would like to again. The first time I was there, though, it was icy and cut up by climbers' tracks where I would have gone in and i didn't try it.
Last edited by Ski the Net with snowHeads  on Wed 12-09-12 13:38; edited 1 time in total
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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| moffatross wrote: |
Someone mentioned moguls not forming on slopes steeper than 40 degrees & Glencoe's Fly Paper is a good example to support that.
snowball, I'm glad you were thinking of the likes of Easy Gully which I think from memory was one of your favourite Scottish skis. It's steeper than 50 degrees levelling out to 40 after the buttresses underneath and about 30 by the time you get to the lochan far below. It sometimes has a big cornice at the top to make it look nastier. Pic below is just before I skied it in April (tiny cornice and fine weather) for the first time and it definitely had deep snow in it then too ...
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Cool photo.
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And love to help out and answer questions and of course, read each other's snow reports.
And love to help out and answer questions and of course, read each other's snow reports.
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You can see where the line of the actual stone edge of the gully is, just behind the people. Snow has built up and the cornice has slumped onto the snow below. There is often a curved crack in the snow, several yards behind the cornice, indicating this line.
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| oleksii wrote: |
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hat the coefficient of friction couldn't go over 1 when clearly and demonstrably this is wrong.
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No I wasn't wrong, CoF above 1 means that the gravitation alone is not enough to slip the object, i.e. someone (or something) should drag it and as soon as that something stops applying it's force the object will stop sliding.
Snow will of course freeze to much steeper slope (i.e. gain CoF > 1), but as soon as it collects the critial mass it will inevitably slide down, especially is someone decides to ski on it. |
This is wrong as well as an object with CoF of 1.73 will slip under gravity on a slope over 60 degrees. On a slope of 45 degrees if the snow had a coefficient of 1 it wouldn't slip (and would be at limiting friction), if it had a coefficient of 1.1 it wouldn't slip but if it had a coefficient of 0.9 it would slip. As we can see from the experiment linked above snow can have a widely varying coefficient from ~0.5 - 1.75. In reality it varies much more than that and is a more complex problem as the snow gains strength and is supported in a complex manner. You can get to the point where a massively heavy load of snow is supported by it's connections around it, then some bumbling idiot skis the slope causing enough load to break the connections and release the whole lot to slide on a slippy layer underneath. Hey presto, slab avalanche.
You should grab a copy of this if you are interested in this sort of stuff from a snow science point of view:
http://www.amazon.com/The-Avalanche-Handbook-3rd-Ed/dp/B001LN22QU?tag=amz07b-21
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You know it makes sense.
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Yep, definitely a different ballsiness required with a significant cornice snowball & I just couldn't bring myself to 'jump' into Easy under those conditions although I'd love to spend a day with an instructor who could show me how to do it on a slope without consequences or the need to poo myself or break myself in the process. As a conservative skier, liking to keep my skis in contact with the snow as much as possible, not really into speed but loving empty, natural slopes, it's always corniced entrances (and concerns about what the snow stability's going to be like when I do get in) that intimidate me most. And of course the fear of ice as a 20-30 degree icy slope can be downright dangerous with any exposure underneath.
I suppose the real question relevant to the OP's point though is whether snow can stick in any significant amounts without wind and drift to get it there i.e. are there any significantly snowy slopes over 45 degrees on non-windy mountains. 
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Otherwise you'll just go on seeing the one name:
Otherwise you'll just go on seeing the one name:
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moffatross, whats a non-windy mountain when it's at home? 
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Poster: A snowHead
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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Idris,
love it, you have some nerve. 
| feef wrote: |
| the coefficient of friction only works with perfectly smooth bodies in full contact with each other on a flat surface. . |
Not really as any surface (in the real world) in contact will apply force to an incline. I do agree that it a "very" small level this could be seen as smooth, but hey this is a ski forum so I think we're talking about snow and skis and other stuff like em.
| snowball wrote: |
| The point is that it STICKS on rather than just resting on the surface (the kinetic energy of the blown flake will briefly melt the snow surface on impact), and then snow flakes themselves have complex shapes which latch onto each other. |
Yep that's about right.
Just a little point; snow will not stick to anything, ice will. It is (as you say) the "increase" in energy of the QLL (at the surface of the flake's constituent crystals) on impact, that liquidizes it slightly allowing the QLL to increase to a depth that will bond before the increase in energy dissipates and the flake freezes onto something - normally my hat
| oleksii wrote: |
Which means that for anything to be stationed on such a slope traction coefficient must be 1, i.e. it must be secured there.
It also means that such a slope will have no snow on it (except for a very thin layer stuck in terrain unevenness), as it will all slide down. |
Hmmmmmm.
1st and most important snow doesn’t stay on a slope due to friction but due to (as snowball points out) to polorised bonding and linking. And yes I do know there are a gazillions website (and “irritatingly” even some school books) that say differently.
As for the rest???
I think you may have misunderstood slightly.
Think about it this way.
Any object has mass (don’t ask why – it’s complicated and hurts my head) and so it is attracted to other mass. The result of this is that they move towards each other (sometimes, again – don’t ask) this means that if a lump of stuff (a lump is an extremely exact measurement of thingies) is on a slope it will slide down the slope.
Why?
Well it is moving towards the center of the earth, but the ramp is stopping it from going in a straight line, so let’s just say it does its best to get there the best it can and off it slides (downwards).
To understand what’s going on you need of think about the forces acting on the object.
OK then first we have the force of gravity (I know, before some git says it – gravity is not actually a force but a blah blah blah, but it is for this, so there  ) which is pulling the stuff in a (almost) straight line downwards. As SH’s will not allow any “weird” text in their forum I will call this force Fg.
Next we need to look at the angle of the slope (how steep is it). This is important as the difference between the angle of the slope and that of the line going straight down defines the weight of the object (along the slope) and the force that makes the object slide (I’ll call this force F||). Imagine putting some scales at right angles to the slope and then weight your object – this is F||
You can think about it like this F|| = Fg sin0.
So F|| is going to make our stuff slip down the slope.
But don’t forget that if the slope is not as steep then F|| = Fg sin0 will still be true.
Yada yada yada as the angular force (F||) is less but so is Fg as the angle has reduced so more of the weight is pointing downwards and this means it will either just sit there or start to slide slower (don’t even bother asking inertia – I’m too old for stuff like that).
Of course this only applies between smooth stuff and let's face it not much really is. In fact the world is lumpy, so we have to think about WHY would the stuff not start to slide (or just sit there) if the angle was less (so F|| is less ya see).
Yippee – Friction.
Oh hang on a minute, friction needs a force as well (just as I want to I’ll call this force F| - note just a single | there)
You can think of F| as being a force that runs perpendicular to a plane (that’s about at right angles, or as near as makes no difference). Another way to think about it is the amount of the stuff’s weight that that is a right angles to the plane (slope) in the directions of the mass/momentum (eg, in this case, downwards)
So to write this down we could say that
F| = Fg sin0 - so you can see that Friction has altered it as it used to be F|| = Fg sin0 (when there was no friction).
You could say that F| is the force the object exerts on the slope (well I would anyway)
If you were a real geek then you’d know that the opposite would also be true – but let’s not go there today children.
So back to your tan(45) = 1, this may be true in some case but not most.
Newton’s 1st law say that stuff will not move if everything trying to make it move are the same or they add up to the same. (that’s near enough)
His next law (appropriately called his 2nd) says that stuff will move if one of thing trying to make it move is strong than the other stuff (the forces are unbalanced) and that the acceleration of your stuff only depends how much force is applied and how much mass your stuff has in it.
So to work out what the F| (the friction) is, all we really need to know is what is Fg (your stuff’s mass) and F|| (as don’t forget that the angle will affect the forces)
QED -= different stuff will stick to slopes and the amount of stickie just depends on the amount of friction, the angle of the slope and the mass and do the three add up enough to overcome your stuff’s strong desire to move towards the center of the earth.
Last edited by Obviously A snowHead isn't a real person on Wed 12-09-12 14:54; edited 2 times in total
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Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
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I think quite often snow gets propped up, above a less steep slope below, like an inverted arch. This is why concave slopes are safer than convex ones.
Last edited by Well, the person's real but it's just a made up name, see? on Wed 12-09-12 14:42; edited 1 time in total
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You need to Login to know who's really who.
You need to Login to know who's really who.
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Wayne, what's your view on inner tip lead? 
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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Arno,
LOL - I did read that, and I have no thoughts on the subject 
(but, wow, didn't people get cross with each other)
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You'll need to Register first of course.
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snowball, this is definitely true, a layer also gets support from the sides and the top as well which is why you get pretty well defined 'walls' to a slab avalanche. These are the points of failure for where the slab was held in place over the bed surface it slides down. If you look at video of an avalanche you can see the bottom failure line give way pretty much at the same time as the others. Obviously it's not usually left behind as the slab falling obliterates it.
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That exact book has been sat on my desk for about 2 years, I just cant bring myself to read it as every time I turn a page I forgot what was on the previous one.
Must try harder...
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You'll get to see more forums and be part of the best ski club on the net.
You'll get to see more forums and be part of the best ski club on the net.
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Idris, were you heading up in that photo?
Last edited by You'll get to see more forums and be part of the best ski club on the net. on Wed 12-09-12 15:49; edited 1 time in total
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Idris, Cool photo, was the guy with the camera belaying you!
Note to self, think twice about skiing with Idris
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FAQ
a bit more than 45 I think 