## / Calculations for fall distance versus how high you clip bolts

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We all know that you should clip the first and second bolts at around waist height, to minimise the potential for a ground fall, but I thought I'd do some maths to figure out the effect of reaching too far to make a clip. This maths was surprisingly straightforward.

So assuming you fall off at the worst possible moment, with all the slack you need to make the clip:
1. If you reach a distance r above your belay loop to make the clip, the extra distance you fall below the last bolt is exactly r.
2. The total distance you fall is always 2*b (plus belayer slack and rope stretch), where b is the spacing between bolts.

Result (1) is (almost) independent of rope stretch and belayer slack, and means if you try to clip the second bolt at max arm stretch (about 1.2m above the belay loop for me), you'll end up 1.2m lower than if you tried to make the clip at waist level and fell off.

Result (2) means that after say the 3rd bolt, it makes no difference how far you reach to clip the next bolt -- you're only risking the same fall
distance.

The calculations are shown in http://www.ukclimbing.com/images/dbpage.html?id=206460 . I've also plotted the maximum reach above your belay loop you can make before risking a groundfall, for various values of the height of the first bolt and the gap between the first and second bolts. The calculation is:
height-you-fall-to = b1 - (b + r + slack + stretch)
where b1 is the height of the first bolt, and b is the bolt spacing after that. The location of the climber is where their belay loop is, so I've assumed a groundfall is falling to 0.9m (so their feet will just touch the ground), and slack + stretch together come to 0.5m. The 0.5m is probably optimistic, but early on the route the belayer should be being very attentive, and there shouldn't be much rope out hence not much stretch.

Apologies for over-analysing all this, hope some of you find it interesting, and the ones who are bored stiff have stopped reading before here ;)
In reply to beychae: why would you clip the first bolt at waist height? Doesn't matter if it's single pitch/big ledge and if it's multipitch it's gonna be ff2 but with more rope stretch

Good point! I should have said the second and (probably) third bolts.
> Result (2) means that after say the 3rd bolt, it makes no difference how far you reach to clip the next bolt -- you're only risking the same fall distance.

Of course, this assumes you fall off while attempting the clip, rather than while attempting to make upward progress.
In reply to beychae: Im not too sure I totaly understand your working out, but thats probably me, not your explanation. Not so long ago, at West View wall we worked out that if you were pulling through slack and clipping above your head, by the time the rope stretched, and the belayer got pulled into the wall, you could still potentially hit the floor whilst trying to clip the 5th bolt.
In reply to beychae: I may well be missing something but surely the extra distance you would fall would be 2r since to reach 1m above your belay loop you are pulling 2m of slack up since the rope needs to travel 1m up to the clip and then 1m back to the level of your knot. No?
In reply to 2PointO: Ok, no I was missing something, ignore me. Just realised that since you are comparing clipping above your head to clipping by your waist then it would be an extra fall of exactly r.

Assuming you're climbing and clipping in a straight line with only the minimum of required slack the fall distance is independent of how far beneath a bolt you clip from (ignoring rope stretch). This is because for every extra x metres you climb above a bolt you increase the potential fall by 2x metres, and for every y metres above your head you try to clip you need 2y metres of slack and therefore also have 2y metres more potential fall. Therefore whether you climb up to a bolt to clip it by your waist or pull slack up to clip it above your head the fall distance is effectively the same. The only substantive difference is that when clipping by your waist you start the fall from a little higher, which for the same fall length means you end the fall a little higher too, which if the ground is very close could be very significant.
> (In reply to beychae) Im not too sure I totaly understand your working out, but thats probably me, not your explanation. Not so long ago, at West View wall we worked out that if you were pulling through slack and clipping above your head, by the time the rope stretched, and the belayer got pulled into the wall, you could still potentially hit the floor whilst trying to clip the 5th bolt.

All-round hard-man Phil Thomas demonstration of the 'clipped fourth bolt-yarding up slack for the fifth bolt - cocking up it - fall'

Rather depends where the bolts are outdoors

use a clipstick!
I always feel that if I clip high there seems to be a bit more slack in the system as well, maybe this is the belayer over estimating. I think that clipping high means one ends up about 1.5m lower down the cliff at least. And 1.5m can be critical for the lower clips.

Even if there is no extra slack, and therefore the fall distances are, as you point out, the same. My head seems to measure the distance I might fall as how far below a piece I would end up and discounts how far above the piece I am, even when I'm 200m up. I guess I'm thinking more about what I'm going to hit.
>
> Assuming you're climbing and clipping in a straight line with only the minimum of required slack the fall distance is independent of how far beneath a bolt you clip from

Yes, that's exactly what I was trying to explain in my original post, and I found it slightly surprising. Although as David Coley points out, your belayer is likely to give more slack than strictly necessary if you reach far above your head to clip. Plus you'll be wasting energy pulling up rope. So ideally you should still clip near waist level even for higher up bolts.

Well, the interesting thing is that these points
> 1. If you reach a distance r above your belay loop to make the clip, the extra distance you fall below the last bolt is exactly r.
> 2. The total distance you fall is always 2*b (plus belayer slack and rope stretch), where b is the spacing between bolts.

don't depend on where the bolts are. But of course the chances of a ground fall are very dependent on where the bolts are, and I agree that outdoors the bolts are often fewer and further between than you'd like.
> (In reply to Bulls Crack)
>
> Well, the interesting thing is that these points
> [...]
>
> don't depend on where the bolts are. But of course the chances of a ground fall are very dependent on where the bolts are, and I agree that outdoors the bolts are often fewer and further between than you'd like.

And that's another question: would people ideally like to see the same bolt spacings found at climbing walls outside?!
In reply to beychae: you have too much time on your hands!

You are missing the most important point. Most bolts are placed in a position where they can be clipped easily overhead from a good hold. If you ignore that and continue till the bolt is at waist level, the chances are that you could be in the middle of hard/crux moves and unable to let go with either hand. Moral - clip as soon as you feel capable of doing so and forget all your 'over-analysing'. Oh, and get out more.
>
> You are missing the most important point. Most bolts are placed in a position where they can be clipped easily overhead from a good hold. If you ignore that and continue till the bolt is at waist level, the chances are that you could be in the middle of hard/crux moves and unable to let go with either hand. Moral - clip as soon as you feel capable of doing so and forget all your 'over-analysing'. Oh, and get out more.

I'd disagree - clip from the most efficient position, not the first opportunity you see. Some bolts are clearly placed with that thought in mind but not most. Unless you're at a proper rest position, the time taken to pull slack and reach for a high clip will often outweigh any advantage of a slightly better hold. The only time I'll clip above my head on an onsight attempt is when I'm at a rest I plan to stay at for a while, or where I've got a good position to clip from and the next series of holds look very thin. On a redpoint, when I've had a chance to figure out the most efficient place for each clip, more often than not that'll be somewhere between shoulder and waist height.

> [...]
>
> And that's another question: would people ideally like to see the same bolt spacings found at climbing walls outside?!

Absolutely not. I like to see the bolts as run out as it's safe for them to be - climbing should be about doing the moves, not clipping the protection. Old school bolting like they have in Finale Ligure should be re-introduced.

We all know that you should clip the first and second bolts at around waist height, to minimise the potential for a ground fall

Why?

Until you clip the first bolt you will hit the ground if you fall off, so, other things being equal, why not clip it sooner rather than later?

Yup, as pointed out by alooker at the top of the thread, that was a mistake - I should have said the second and third bolts.

You're over thinking it. Forget fannying about with maths and theory. In real life the most important factor is likely to be how secure you are when you choose to clip. You have to judge it for each clip but you're better off clipping early/high off good holds rather than late/low off poor holds.

Wow, we agree on something, Tim!

Obvious innit!

Chris

> I'd disagree - clip from the most efficient position, not the first opportunity you see.

That's not what I said. I said << Most bolts are placed in a position where they can be clipped easily overhead from a good hold >>. Bolts don't occurr naturally on crags, they've been placed there and if the equipper knows what he/she is doing then that is how they'll be placed. The odd occasion where some numpty has just put them just anywhere should be very obvious and will will only represent a tiny percent of routes.