FAQ: Climbing Physics  Understanding Fall Factors
What is a fall factor?
The fall factor is a derived number used to evaluate the shock
loads generated on the climber, belayer and anchors that occur when
a climber falls. The higher the fall factor, the greater the forces
placed on the components of the system. The math is simple:
Fall factor = length of fall / length of rope
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Why is it confusing?
The maximum fall factor generated in climbing situations is 2.
A quick look at the math is just a little misleading. A climber
can't fall farther than the length of the rope, right? So the length
of the fall can't be more than the length of the rope, right? 1/1
= maximum fall factor of 1, right? Not, quite.
Actually,
it IS possible for a climber to fall farther than the length of
the rope. In a worst case situation, the climber can fall TWICE
the length of the rope out. The diagram gives the classic example.
Two climbers are hundreds of feet up a cliff face. The lead
climber leaves the belay and climbs 10 feet above his anchored
belayer. When he falls, he falls not only the 10 feet he climbed
above his belayer, but continues to fall another 10 feet until the
rope comes taught. Though he climbed only 10 feet, he falls 20 feet.
Fall factor = length of fall / length of rope
Fall factor = 20 feet of fall / 10 feet of rope
Fall factor = 2
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Reducing the fall factor
Big fall factors are bad! They indicate tremendous forces in the
system which may lead to failure of one of the components. Remember,
the climber and belayer are both components and will absorb some
of the forces. In the situation diagrammed above, if the anchor
fails, both climber and belayer plummet to the ground. Learn to
recognize situations with high fall forces especially if your anchors
or gear placements are less than ideal.
The
simplest way to reduce the fall factor is to reduce the distance
of the fall by placing gear. If the lead climber is able to place
a piece of gear once he has climbed 5 feet, then falls once he has
climbed 10 feet above the belayer, he will fall only 10 feet (hello
belayer) instead of 20 feet. The fall factor is now 1.
Fall factor = length of fall / length of rope
Fall factor = 10 feet of fall / 10 feet of rope
Fall factor = 1
By placing a single piece of gear, most of the forces are now removed
from the critical belay anchor securing the climbers to the cliff.
Placing
that single piece of gear has a surprisingly big effect on reducing
the forces in the system. Even if the lead climber continues 20
feet above the piece of gear placed 5 feet from the belayer, then
falls, the forces are reduced. Of course, the climber is going to
take a 40 foot fall. Let's hope he doesn't hit the belayer on the
way down!
Fall factor = length of fall / length of rope
Fall factor = 40 feet of fall / 25 feet of rope
Fall factor = 1.6
We're lucky enough in this instance that the climber was able to
place one bomber solid piece of gear to catch him. It took a tremendous
amount of force, enough to rip out many of your smaller pieces of
protection or even break the rock it was placed in.
Assuming
our climber was lucky enough to get a second solid piece of gear
in 25 feet above his belayer, we can look at how a 20 foot fall
now affects the system. Our lead climber continues above the second
piece of protection for another 10 feet, then has the misfortune
of peeling off the rock. He falls 20 feet  the 10 feet he was above
the last anchor plus the 10 feet of slack in the rope once he falls
to the level of the last piece of protection. In this instance the
fall factor is 0.57.
Fall factor = length of fall / length of rope
Fall factor = 20 feet of fall / 35 feet of rope
Fall factor = 0.57
The good news for the belayer is the climber is not going to fall
onto him. He is also going to experience less force from the fall.
The top piece of protection still takes a tremendous amount of force.
It is clear now that the amount of rope out has a great effect
on the fall factor (and the forces on the components of the system).
In our first example, the climber took a 20 foot fall resulting
in a factor 2. In this case our climber took a 20 foot fall resulting
in a factor of 0.57. Even when the climber took a 40 foot fall,
because he had placed gear, the fall factor was reduced to 1.6.
This is so because of the increased length of the rope in use. It
is the reason climbers use specifically designed dynamic climbing
ropes.
Rule: Place gear frequently in the early part of the climb
when there is only a short amount of rope out.
Another technique for reducing the forces in a fall is to incorporate
a dynamic belay. Rather than belaying directly off an anchor, incorporate
the belayers body weight in the system so there is some movement
when the forces come to bear. Allowing a small amount of rope slippage
through the belay device is a practiced art that also cushions the
shock.
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Dynamic Ropes and Fall Factors
The shock load resulting from a fall in a climbing system is the
result of three factors; the energy absorbing (stretch) characteristics
of the rope, the fall factor, and the weight of the falling climber.
The amount of stretch designed into in dynamic climbing ropes varies
from about 6  10 percent. The climbing industry (U.I.A.A.)
has set standards of the amount of force a climbing rope must absorb.
According to the International Mountaineering and Climbing Federation
(Union Internationale Des Associations Des
Alpinism) a dynamic climbing rope must be designed to absorb
enough energy so that the maximum force on an 80 kg. (180 lb.) climber
in a factor 2 fall is not more than 12 kn. (2698 lb.) (See What
is a Kilonewton). All of the other components in the climbing
system (climbing gear) are designed to function with these levels
of force. It is the design of dynamic climbing ropes which limit
the force the climber experiences.
Knowing this we can draw several conclusions:
Do not use static ropes for climbing. Static ropes stretch very
little at all (0.5 to 1.5 percent or less). Forces generated in
a climbing system can quickly exceed factor 2 if a static rope is
used, causing grave (deadly) injuries to the climber and generating
forces in the system which exceed the strength of the gear used.
(a fall of as little as 4 feet on a static rope can create enough
shock load to cause injury, death, or failure of climbing gear).
A static rope may be used (cautiously) in a top
rope system or a gym where falls are measured only in inches,
but not in the system used for lead climbing.
The more rope out in the system, the more gradually the energy
can be absorbed. For example, if a rope with 10 percent stretch
is 10 feet long, it will have 1 foot of stretch to absorb the energy
of a fall. However, if 100 feet of rope are in play, the shock will
be absorbed by stretching 10 feet. Surprisingly high forces can
be generated in our first example where the climber was just leaving
the belay with just a small amount of rope in use. We see in later
examples that the fall factor reduces dramatically as the amount
of rope in use increases.
Particularly burly climbers need to make allowances. The system
is designed for an 80 kg. (180 lb.) climber. If you weight considerably
more than this, or are carrying a heavy pack, you will need to take
the additional forces generated into account. Place more gear, and
place it closer together. Build your anchors stronger or double
them up whenever possible.
Additional Comments
Our first example of a factor 2 fall should raise some concerns.
Anchor failure in this situation is mostly likely fatal to both
the climber and belayer. It is good practice to set up a second
anchor in addition to the main anchor when belaying a leader who
is climbing above. At minimum, run the rope through one bomber piece
of protection separate from the main anchor before the lead climber
departs. The leader should also try to place a good piece of gear
as soon as possible above the belayer.
In our example, there was a good chance the lead climber would
fall onto the belayer. This situation should be avoided whenever
possible. You can build the main anchor to one side of the route
(good practice), or the climber can try to stay to one side of the
belayer until enough gear has been placed to protect him from a
fall. The climber must think not only of protecting himself, but
also protecting his belayer while he climbs above him.
Links
Fall Factor
and Climbing: Impact force calculator
Climbing
Forces in Leader Falls (.PDF file)
Forces
on the falling climber depending on different belaying techniques
Planet
Climbing Training  Advanced Belay Techniques
Climbing
Ropes
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