Flatliners Southeast Climbing FAQ's - Climbing Forces

Real world fall forces are mitigated by rope slippage at the belay end, movement of the belayer, and friciton at intermediate protection pieces. The calculations are based more on "laboratory" situations, so the actual forces experienced would be reduced to some extent.

Using the online impact force calculator , we can look at some hypothetical climbing situations. For these examples, I'll use my newest rope, a 60 meter 10.2 mm PMI Spire. The literature gives the impact force with this rope for a fall factor of 1.78 as 8.3 kN. Entering this into the calculator, we find my ropes modulus (shock absorbing characteristics) is equal to 19.99 kn. I weigh just a bit under 80 kg, but usually carry a light pack that brings me close enough to it.

Unlike our examples, a carabiner is not a perfect pulley. There is friction of the rope against the metal as well as a comparatively small radius over which it turns. According to Petzl , the coefficient of friction increasing the load on the climber's side of the rope is about 66% or 1.66.

By determining the load on the falling climber and the load on the anchor carabiner, we can deduce the load on the belayer, since we know the sum of the load on both ropes is equal to the load on the top anchor. (See pulley effect)

Starting small, lets look at a short top rope fall first. We've set up a top rope 82 feet (25 meters) high. Our climber climbs up 20 feet (6 meters) when he takes a fall. Thanks to our attentive belayer, there is 1 foot (0.3 meters) of slack in the system. There is 82 feet (belayer side of anchor) + 62 feet (climber side of anchor) + 1 foot of slack or 145 feet (44 meters) of rope out. Using the impact force calculator, we find the shock load the 80 kg climber with this fall factor 0.007 fall is 1.7 kN or 382 lbs. The force on the top anchor is 1.66 x 1.7 kN or 2.82 kN (634 lbs.). The force the belayer experiences is 2.82 - 1.7 or 1.12 kN (252 lbs.). While the climber barely notices the impact of this short fall, the load on the top anchor is 2.82 kN (634 lbs.).

Now lets see what happens with more slack. At 70 feet, the climber asks for slack to allow him to work out from under a 6 foot (1.8 meter) deep roof. Our belayer is distracted when his dog meets another along the trail and a scuffle ensues. The climber works his way out from under the roof and makes it another 6 feet (1.8 meters) up the face when he gives out and falls. 12 feet (3.6 meters) of slack are in the rope when the climber peels off. There is 82 feet (belayer side of anchor) + 18 feet ( climber side of anchor + 6 feet under the roof) + (6 feet of additional slack gained by the climbing above the roof) or 106 feet (32.3 meters) of rope in play when the climber falls 12 feet (3.6 meters). The impact force calculator shows us the falling climber experiences an impact force of 2.81 kN or 632 lbs. The fall factor is still low at 0.11. The force on the top anchor in this case is 1.66 x 2.81 or 4.66 kN (1048 lbs.). The belayer experiences a shock load force of 1.85 kN or 416 lbs. A fall of this magnitude is going to wake you up, but the forces are still quite manageable.

Moving on to a lead climbing situation, our climber leaves the ground. He progresses steadily upward, placing solid gear every 10 feet or so. At 130 feet, the belay anchors are in sight 20 feet above, but a difficult section lies ahead. He sinks a solid piece of gear deep in a constriction, and climbs another 10 feet before his strength gives out and he falls. He falls 20 feet (6 meters) before the rope comes tight. There is 140 feet (42.7 meters) of rope out. This produces a fall with a fall factor of 0.14. The impact force calculator shows us the falling climber experiences an impact force of 3.03 kN or 681 lbs. The last piece of gear, it's sling, and carabiner experience a shock load of 5.03 kN (1.66 x 3.03) or 1,131 lbs. The belayer catches a fall force of nearly 450 lbs. (2 kN). This situation would not be unusual in lead climbing, the forces are still relatively common for the climber and belayer. But in this case, instead of a burly top rope anchor, a single piece of gear took a load of over 1,100 lbs. Had this last piece been Metolius TCU Cam #0 with a strength rating of 1,000 lbf. (4.4 kN), it probably would have failed. Remember this when you are placing small gear, always double it up when possible, or place a lot more of it.

Our lead climber eventually makes the anchors, and his partner follows him up to it. Now his partner takes over the lead and starts up the wall. This next section looks difficult so they take the appropriate precautions. They build a second anchor and run the lead rope through it. If the leader falls, the force won't come directly onto the belay anchor. The belayer adjusts his slings to move out of the fall line of the leader, and the leader starts up. He sinks a good piece of gear 3 feet above the belay, and another at 10 feet. He sets the next piece at 20 feet. Looking ahead, he spies a small crack which may take gear about 13 feet above him, but it's at a sketchy stance. He reaches the crack at 33 feet, but while he struggles to get a piece of gear to fit, he falls. There is 33 feet (10 meters) of rope in use, our climber falls 26 feet (8 meters) before the rope comes tight. This results in a fall with a fall factor of 0.8. The impact force calculator reveals the falling climber experiences an impact force of 5.86 kN or 1327 lbs. At the belayers end of the rope, 3.87 kN (870 lbs.) is placed on the anchors. The piece of gear, sling, and carabiners which caught the fall 20 feet above the belayer were loaded with 9.73 kN (2187 lbs.) of force. Wow! Small gear is not going to hold a force like that. Cams with a range of ½ inch or less may fail. Small nuts may experience wire breakage. This is a lot of stress to put on your gear!

Next, a worse scenario. Our climbers make it to the next belay ledge. It's just a tiny lip with a small flaring crack above. They build and anchor with two micro cams and a small nut. Nothing else will fit. The belayer attaches with a four foot sling. The wall above is blank for another 20 feet, but a hint of a crack is visible up there that may take gear. They discuss rappelling from here, but the cost of leaving the gear behind clouds their judgment. Besides, higher up the climbing looks easier and there is the start of a good crack system that should take some bomber gear. If we can just make that crack...

The leader takes off, slowly inching his way up to the towards the suspect thin crack. Arriving, the leader finds no hope of getting in anything solid. It's not even a very good hand hold. Trying to work past it, the leader falls. There is 20 feet (6 meters) of rope out. The leader falls 40 feet (12 meters) and the belayer braces for the load of a factor 2 fall. The impact force calculator calculates the falling climber experiences the impact force of 8.75 kN or 1967 lbs. all of which is experienced at the anchor as well since there are no carabiners in the system to act as pulleys. Thanks to good equalization of forces during construction, the anchor holds.

Switching places, the other climber starts up the wall. He soon realizes he is not going to make it any farther than his partner. It's also too difficult to downclimb back to the belay anchor. Scouring the rock, he finds the tiniest of cracks and wedges a small nut into it. He attaches a carabiner, clips the rope through it, and gently eases his weight onto it. His partner gingerly lowers him down the the belay anchor. They decide to retreat and rappel to the ground.

One of them starts pulling the rope to retrieve it from the anchor above. The other looks up to see there is still a knot in the end of the opposing rope. Knowing it will not pass through the carabiner above, he dives for it but misses. He alerts his friend who stops pulling. The knotted rope end dangles several feet above them.

Still attached to the anchor by his four foot sling, the second climber climbs a few feet up the wall to grab the loose end and untie the knot. The sling comes tight as he reaches it. Just as he unties the knot, his foot slips and he falls. Both climbers plummet to the ground. What happened?

We'd already seen the anchor was solid enough to hold a factor 2 fall which generated 8.75 kN However, this short fall was different as it was not on the dynamic climbing rope. The climber fell on a 4 ft. sling. With no shock absorbing qualities, it was like falling on a steel cable. The impact force calculator is designed to look at dynamic ropes, not static ropes or slings. To allow it to do some calculations for us, I generously allowed 1% stretch in the system (Maybe this could occur as the girth hitch knot in the sling tightened). This gives us an impact force on the climber and the anchor of 16.45 kN or 3,698 lbs. (According to Petzl, the force is closer to 18 kN).

The forces generated exceeded the strength of the components of the system and probably the strength of the rock leading to anchor failure. The maximum force a climber can withstand for an instant without serious injury is 12 kN Even if the anchor held, the falling climber would have sustained severe, if not deadly injuries. Since his harness is rated to hold a force of 15 kN, it most likely would have failed as well.

UIAA limits for Climbing Gear:
Anchors: 25 kN
Carabiners: 20 kN
Slings: 22 kN
Harnesses: 15 kN

9.8 mm rope - 1,825 lbs. (Short sections of rope used in an anchor)
10.5 mm rope - 2,025 lbs.
11 mm rope - 2,090 lbs.
Locking carabiner - 4,950 lbs.
Non-locking carabiner -4,500 lbs.
6 mm cord - 1,500 lbs.
7 mm cord - 2,090 lbs.
8 mm cord - 3,150 lbs.
5.5 mm spectra cord - 3,800 lbs.
19 mm climb spec webbing - 4,900 lbs.
9/16" climb spec runners - 2,250 lbs.
9/16" spectra runners - 6,075 lbs.
1" tubular webbing - 4,000 lbs.
Rawl 1/2" x 3" bolt - 7,300 lbs.
Rawl 3/8" x 3" bolt - 5,200 lbs.
Hilti 3/8" x 3" bolt - 4,500 lbs.
Petzl 10 mm x 61 mm bolt - 4,000 lbs.

Rope Systems Analysis (a 13 page DETAILED discussion, complete with physics):

http://www.amrg.org/Rope_system_analysis_Attaway.pdf

The Physics of Climbing (for the truly mathematically minded, A very technical explanation of how physics applies to rock climbing)

http://student.kuleuven.be/~m9916724/physics/physics.htm

Loads, Energy & Ropes (the discussion is about caving, but the principles are the same):

http://www.bstorage.com/speleo/Pubs/rlenergy/Default.htm

FAQ: Climbing Physics - Climbing Forces - Some Hypothetical Instances