I was wondering if anyone knew the equation to figure out what factor those big whippers are?

length of fall / length of rope out. 2 is the highest you can get ( falling twice as far as you have rope out) and that only happens on a multipitch route where you fall past your belayer without protection.

Kevin is correct with the basic formula for a fall factor, but there are many variables that affect the forces on a rope, a belayer and the climber not to mention the anchor that is taking the most force--usually the top anchor.

One of the best discussions of forces during falls is in Craig Connally's excellent book, "The Mountaineering Handbook". He has a whole chapter on climbing forces that is a must read.

There are certain situations where a fall factor can be more than 2. Top rope self belay is one of them. When the TR anchor is approached, the rope out can be mere inches. Carry on past the anchor (slings on a bolt for example) and a fall of several feet can load a few inches of rope. Very bad!

Slings are not dynamic and do NOT factor into rope length.

Here is the scenario:

Top rope solo. You have some device that slides up the rope but locks if you fall. The rope is tied off to the upper anchor. The anchor is 2 shoulder length slings on 2 bolt anchors in the typical way. As you approach the bottom of the slings, your rope clamp comes very close (say 3 inches) to the knot at the bottom of the slings. If you fall you have only this dynamic rope, no more. You can keep climbing as far as you can extend the slings (@ 18 inches). Now if you fall you can go 3 feet on a 3 inches of dynamic rope. That is a fall factor of 12. Granted, the total force generated would be on the low side in this fall, but it is still a bad scenario since you would static load the anchor and a very small length of dynamic rope.

I have top rope solo'ed for years and often encountered this very scenario. At some point in time someone showed me the error of my ways, and I now avoid this by either 1) not climbing above the anchor sling's lowest point or 2) leaving slack between the anchor and my rope grab device.

It is also a very good idea to back up a TR solo.

I see that situation (fall factor relating to top rope soloing) as more of a whiplash to the climber than impacting 2 equalized bolts or 2 equalized active trad placements to the point of destructive failure. Granted there is very very little dynamic absorption provided by the rope, but the only way I see anchor failure is using two crappy button heads slung using the ADT as the anchor.

(assume my equalization proposed uses a good angle between pieces; typically, I use either a limited extension sliding X or a cordalette/webalette -- I back up sometimes with static line, but never have failed the cord or a sliding X).

For a practical example, look at an aid climb lead where the climber neglects to clip the rope into the preceding placement and only has a daisy or other sling into the lower placement. The climber progresses to a higher placement which blows out and the climber loads the preceding piece with more than an 18" x2 fall, usually it's about 2'-3' x2, this equates to enough to force to snap the climber, but not really enough impact to blow apart a bomber piece rated about 10kN, I've seen 8kN hold a static impact about 4' fall distance overall, no problem.

While the fall factor may be mathematically increasing by formula in the top rope soloing, the impact force & duration is just not enough to fail an equalized anchor with 2 good placements. Certainly not 2 equalized 3/8" bolts in highly cemented rock.

One thing that is beneficial to the anchor in the top rope solo fall that generates moderate impact force & low duration is not introducing the pulley effect to the anchor. With this also, I don't see spring force playing a role, nor do I see the pendulum problem.

So is this "bad"? - yea, to the climber, their day is pretty much finished & might need to see a doc and get scanned to see if anything other than soft tissue was damaged.

But, my .02 is that the equalized anchor using good angles between pieces is not going anywhere.

You guys are soo funny....Has no one taken an aid fall onto their daisy before? I have and guess what I am still here...no snapped spine or anything. Also...nylon does stretch, so do static ropes.

BTW Lee, the trick for increasing safety when Top rope soloing is to use the rope to make your anchor ( bunny ears knot works wonders) Then nothing in your setup is static. I almost never use slings when soloing as the rope works better in most cases.

Kevin,

You are 100% right--we are soo funny. We're FUNNY but not FUN-AY if you know what I mean.

You're also right about using the rope as the anchor set-up when top rope soloing.

I still believe it is not good to take any length fall on static slings, daisies, whatever. It is also not good to load up a short piece of dynamic rope. Simple things to keep one alive.

I will cite Craig Connally's book again and in his expert opinion, you can have fall factors above 2, such as my scenario and in the via ferrata world.

thanks a lot for all your guys input

Thanks Brent. That is exactly what I was talking about.

How do you define the "rope paid out" in the via ferrata scenario? I personally don.t, seeing as to me, it's not climbing. That's akin to calling a boat ride swimming, or riding an airplane flying (to all those parachuters out there, you know what I'm saying. If you really consider this CLIMBING, power to ya mate, but by that definition, I took a nearly infinite fall factor when I fell out of bed this morning with no rope (limit as rope->0). See where that goes?


"I don't think FotH or the Beal site--the two I've checked from your list--provide unequivocal support to your claim. FotH refers to "length of rope fallen on," which is not necessarily the rope paid out. The video on the Beal site defines the fall factor as "hauteur de chute / longueur de corde utile."

except the part on the beal site that says very clearly that in "Its value, lying between 0 and 2 in climbing conditions, is ...." Pretty black and white. check here http://www.bealplanet.com/portail-2006/index.php?page=facteu>>>>>


"In normal roped climbing, fall factors do not exceed 2, but think of the following (admittedly unlikely) example. A climber takes a long fall, from 10 meters above the belay and with no intermediate pro. As he goes by his belayer, the rope gets snagged behind a flake so that only two meters are available to absorb energy. What is the fall factor? According to your definition, it's 1.2, but that definition makes the fall factor irrelevant in understanding the dynamics of that fall. If you measure the rope that stops the fall, the factor is 6, which tells you it's a very serious fall."

Again, checking the beal site, and many others, you'll find that the fall factor has nothing to really do with anything. It's a notion of something. It tells us a little about a particular instance, but it leaves out way too much info to be used in any meaningful way. Check the link above. Or google it, you'll find over 50 sites that all confirm the same thing.

Mind you, wikipedia does mention that fallfactors can be higher than 2 in via ferreta, but not climbing. Is this what you are getting at? If so, that's fine. How about a 1" fall above your anchors, that's a factor 2 fall mate, and you'd be pretty hard pressed to hurt yourself with that (if your harness and the "boys" are situated properly). How about if I'm 2" above, and as I fall, my partner sucks in the rope, meaning nearly an infinitely high fall factor based on your notion. Still equates to a 2" fall to me. If you really want, we could crunch out the whole m=Fa, and all that for your forces. Lord knows I can get more forces by taking a 5 footer at a fall factor of 1.

That's why I thought the horse could lay down. If you really want, there's plenty of sites out there that you can use to account for ALL forces affecting you in a fall, and not a one will resort to fall factor in any meaningful way, if even using it in a passing mention.

Sorry to come across like this, kinda my personality, kinda a long day of work, and kinda already been answered. No ill will intended, and if we ever cross paths we could try to measure the pull of gravity/atmospheric pressure of beer entering our gullet/belly.

and lastly sorry about the quotes, not used to the forums mechanics yet.

Charles, I disagree. Not on the beer part towards the end, but on three main counts.

1. Many reputable sources give a definition of fall factor that has the length of rope involved in stopping the fall at the denominator. Even more sources are ambiguous. The Beal site is one of the ambiguous one, or contradictory if you prefer.

2. The fall factor is a useful concept. Climbers should be familiar with it. Obviously, it refers to an idealized situation, does not help much in the analysis of short falls, and so on, but, as you and I and many others know, it reminds us that dw = F(x)dx.

3. Definitions are to some extent arbitrary. However, in practice, there are better definitions and worse definitions. A better definition for fall factor is one that allows one to apply the concept to a wider range of situations.

Oh, and if you take that limit for rope->0, you get the fall factor for a rope of zero length, not for no rope. Ask yourself "How long is my non-rope?" After that, maybe, it's time for a beer...

2-FF cannot be greater than 2. By it's very definition.

Ok, I'm a climbing nobody and I'm sure most people here have tons of experience more than I do... but here's how a guide explained fall factors higher than 2 to me:

Fall factor can theoretically be infinite. It gets higher than 2 if the belayer recovers some slack as the leader falls directly on the belay. If you manage to do this (I don't know why you would do it...) then the rope you fall on can be significantly less than half the fall, thus generating a fall factor higher than 2, and theoretically infinite (if you just recover ALL the rope as the leader falls).

Does this make any sense?

Reading through the posts above, it seems to me that it may be helpful if the fall factor is derived here, with some of its idealizations spelled out. There are several, but I believe that in the vast majority of typical falls, it captures very important dynamics. On the scale of physics problems, it is quite easy, but I apologize in advance to those who don't think in this way. Just skip to the next post.

A systematic way to approach this is through conservation of energy. The kinetic energy acquired by a falling climber is w*d, where w is the weight of the climber, and d is the distance fallen until the rope starts to catch (idealization number 1). The rope has a maximum ability to absorb energy proportional to the length made available to absorb energy (i.e. stretch), mathematically, E(absorbed by rope)=A*l, where A is a constant dependant on the rope, and l is the amount of rope out (idealization number 2, there is, for example, some energy absorption potential in the anchors, and belayer, etc.). To absorb all of the kinetic energy, we have the identity w*d-A*l=0 (for now, because of a desire for simplicity, I am ignoring the fact that A is not always going to be at its maximum value. I introduce this variation below). If the equation is not equal to 0, then that is energy absorbed by the climber.

Rearranging, we have, for safe climbing, w*d (less than) A*l, with the less than arising from the fact that A is for maximum absorption of energy, and ropes are designed to not, in general, need all of that, or to use all of that capacity to absorb energy. Since w and A are fixed by the climber and the rope, we want to rearrange the equation above to see how things change for different falls for a given team. Simple rearrangement gives w/A (less than) d/l. The right hand side of this equation is what we are getting at with the fall factor. The idea is that this inequality, which is a necessary (but not sufficient, for those who care) condition for safe climbing is hardest to satisfy when d/l is large. d/l is the fall factor. As seen from above, it measures how much we are flirting with reversing the inequality above and therefor having to absorb the excess energy by breaking bones, or anchors and then bones. Remember that there is a lot of uncertainty in the values on the left hand side of the equation.

The fall factor does not mean much when falls are extremely short (inches as noted above, for example), because the energy (w*d) that must be absorbed by other systems like the belayer, climber and anchor is so small. Also, energy absorption is in most cases a separate issue from the stress loading on the anchor. An anchor can take an enormous stress and not absorb a meaningful amount of energy. The rope snag example can be well captured by the fall factor as derived above, and does, in fact give a large fall factor.

I hope this helps more people than it confuses!

For those interested in a thorough treatment of this, click here
and open the attached pdf.