Does anyone have a good method for calculating the force that a leader will generate on their gear in the event of a lead fall?

Link to Petzl Fall Simulator

Requires Java.

Scott Edlin offered something in a discussion over anchors:

Bombproof Anchor?

After looking at the forum that Mark pointed to (thank you for the tip), and looking at the force calculators on the net I have come to the conclusion that no matter what you do you are going to generate at least 5 Kn on your highest piece of gear. The equation at the beal website (http://www.bealplanet.com/portail-2006/index.php?page=force_>>>>> leads to a calculation of 3.55 Kn on the climber in the case of a 10 foot lead fall (5 feet above closest pro) with 80 feet of rope in the system (a factor 0.125 fall) The real point i was after is how much force is experienced by the highest piece of gear. The beal site points out that due to the pulley effect the force is magnified to 1.6 times the force on the climber. Meaning that in the scenario i discussed earlier the highest piece of protection experiences closer to 5.5 Kn in a vertical fall.

To me the next logical step is to say that any piece of protection that is not rated to at least 5 Kn should not be used to protect a leader fall. Am I off base in going that direction with my thinking?

Ben, the equation you find on the Beal site is somewhat conservative. Specifically, it assumes that the rope is fixed to the belay anchor. In reality, the rope slips through the belay device, and that reduces peak forces a bit. On the other hand, friction between rope and rock and anchors tends to increases forces a bit, but in the end that equation still overestimates forces a bit.

Overall, 5 kN is a good guess anyway, and in fact, CE/UIAA certification of "frictional anchors" (e.g., cams) requires a minimum strength of 5 kN.

ben,
you bring up a good issue here. i personally use micronuts rated to 5kN, and the purple #0 tcu (old style) rated to just over 4 kN. i have whipped more than once on that little tcu, and it has held. this leads me to believe that there are more variables in play here. for example, the entire system, from climber to rope to belayer has an incredible amount of dynamic play in it. this means that when a climber falls, his body, harness, nylon sling, and rope all give a little, thus absorbing a small, but significant load nonetheless. so i wouldn't go out and not place my tcu, but i would make sure it's bomber, the fall is a low factor, and you have bomber gear below it. in terms of gear rated to 2 or 3kN...that's another story. i've never fallen on a nut rated that low. has anyone? seems to me that's the territory of aid only.

It is correct that due to the pulley effect, the highest piece of gear that is fallen on takes almost double (1.8) the falling force of the lead climber. And some lead falls can come close to or exceed the breaking strengths of protection and that carabiners can also break under these loads due to cross-loading or open-gate or worse, both at the same time. When the bolt hanger or wire is sitting in the carabiner opening, keeping the gate open and somewhat cross-loading it, I believe the BD engineers said the strength is at around 4kn and they break easily under normal falls in this non-ideal configuration.

A good example of how the rope and belay technique factor into the "strength" but more the "dynamic ability" of the belay system is from a climb that we were doing a few years back where the crux was protected by two equalized, #1 stoppers that are each rated well under 5kn.

I was taking numerous lead falls on these pieces and why they held was primarily:
1. My belayer was positioned lower down the hill relative to the climb so that there was substantially more rope in the system.(40' vs 20' at crux)
2. I was using a very fresh (new) 9.2mm rope that has a very low impact force rating.
3. My belayer was jumping up a little when I fell to reduce the pulley effect on the anchor (can be done on multi-pitch routes as well).

Another climber tried this route with an older, thicker rope (not as stretchy), a belayer closer to the cliff (less rope in the system) and a non-dynamic belay technique. They weigh substantially less than me and broke the cables on both stoppers on their first fall.

Moral of the story: Thin, new ropes make the biggest difference in a belay system for absorbing force and a dynamic belay technique also reduces the force on your pro significantly.

I've stopped carrying heavier "screamers" for absorbing forces on minimum protection routes and instead haven't climbed with a rope thicker than 9.4mm for the last decade and know that this is the primary force absorber in my climbing system. Most of these thin ropes have easily taken more than 300 days of hard leading use on rock and ice before being retired to top-roping where forces are minimal and it would be almost impossible to break any rope or decent anchor.

Maybe take a look at a recent article on my website: http://climbinglife.com/tech-tips/tech-tips/what-s-the-force>>>>>
for more information regarding how forces can be applied to the belay anchor on multi-pitch climbs.

Actually brenta, ropes of different diameters do have different impact forces which are outlined on the page of the sterling website listed below. Ropes designed for sport-climbing abuse where impact force is not so important due to the strength of the bolts will show higher impact forces as this is a non-issue in the sport setting but the ability to take many, many falls is important. Ropes designed for trad use do have lower impact forces and this is why many ice, mixed and trad climbers use thin single ropes or even thinner double ropes which should be only be clipped individually to each piece of pro to effectively reduce their impact force.

http://www.sterlingrope.com/supportingdocs/2007_climbing_cat>>>>>

Sterling also has some important information about how wet ropes lose up to 70% of their strength and their tech manual if very informative:
http://www.sterlingrope.com/supportingdocs/techmanual.pdf

A dynamic belay probably makes as much a difference as a fresh, thinner rope but that is a trickier subject to debate as many folks don't like the idea of jumping or letting rope slip through their brake hands (gloves help) to reduce the impact force. But if you've experienced this first hand as the belayer or climber, you know that it's true.

One key component in the previous example that I neglected to mention was that after each fall, I pulled the rope down and retied into the opposite end which had not been fallen on (recently)and climbed on the fresh end, thus significantly reducing the impact force of the subsequent fall and letting the other end of the rope "rest" before putting it back in use. Progression of the impact force with use is another potential issue in the trad setting.

In climbing, with successive falls, the dynamic capacity of the rope reduces and thus the impact force increases. The beal website has some great info on impact forces, etc.

It is true that not all thinner ropes have lower impact forces and vice versa as it is primarily the design function of the rope that determines it's impact force; in general this is true and there are differences in impact forces between ropes, which might be a strong consideration in the purchase of a trad rope vs. a sport rope.

http://www.bealplanet.com/portail-2006/index.php?page=force_>>>>>

From the Beal website: A little physics

IMPACT FORCE EQUATION

F = impact force in Newtons
M = falling mass in kg
g = gravitational acceleration = 9,81 ms-2
K = caracteristics of the rope
(Young’s Modulus X Section of the rope)
f = actual fall factor

(I couldn't duplicate the equation in this forum but it's on the site)

value of K as a function of the
maximum impact force of the rope

F = 7,0kN -> K = 13700
F = 7,5kN -> K = 16000
F = 8,0kN -> K = 18500
F = 8,5kN -> K = 21200
F = 9,0kN -> K = 24100
F = 9,5kN -> K = 27100
F = 10,0kN -> K = 30300

When in doubt- not falling is the best option!