Keeping Climbers Alive with Physics

Tommy Caldwell (second from left) and Kevin Jorgeson (fourth from left) celebrating
their climb of Dawn Wall yesterday afternoon. Credit: Peter Stevens via flickr

Yesterday afternoon in Yosemite National Park, rock climbers Tommy Caldwell and Kevin Jorgeson made history by completing the first free ascent of Dawn Wall, reputed to be the hardest climb in the world. Caldwell and Jorgeson owe their success to their remarkable perseverance, strength, technique, and also to three key bits of physics keeping them alive.

The Dawn Wall

The Dawn Wall is a 3000 foot route up Yosemite’s famous El Capitan feature.

El Capitan, Yosemite, California. Credit: cropped from wasim muklashy via flickr

Unlike the initial ascent of the Dawn Wall route in 1970, yesterday’s feat marked the first ‘free’ climb of the route. This means that Caldwell and Jorgeson only used their ropes and anchors for protection and not to move upwards. Instead they gripped small features in the wall and balanced on razor-thin ledges. Some sections of the route were nearly impossible and both climbers fell many times before completing the moves.

The Physics of Climbing

Like all climbers, Caldwell and Jorgeson put their lives on the line with every move and fall, trusting in each other, in the correct manufacture of their gear, and most of all, in physics.


Credit: adapted from Bob via flickr
More than anything, climbing is a tug of war between the forces of gravity and friction. A climber might be able to muscle up a few moves, but he or she will quickly wear out. 
Instead of pure strength, the best climbers are very technical about how they hold on to the rock, maximizing the friction of their hands and feet in order to take the load off their arms. 
Some high-friction gear also helps.
Climbing shoes have a thick rubber sole which molds around small features in the rock and provides a much higher coefficient of friction than normal shoes or bare feet.
A dusting of chalk helps dry sweaty fingers and palms, again increasing friction and giving climbers a better grip on the rock.
Belay device setup. Credit: adapted from via Flickr

Friction is also crucial to the belay process, which allows a falling climber to be safely caught by his or her partner, “the belayer”. The static friction between the rope and the device reduces the force on the belayer’s arm. This means a smaller climber to safely belay for a larger climber (within reason).
Finally, climbers place pieces of gear in the rock along the way in order to protect from a fall. This is called “lead climbing” and the gear can be as simple as a wedge of metal which fits into a rock crack, gripping the sides of the crack through friction.

Gear placed in a crack along the route protects the climber from a fall.
Credit: Adapted from McKay Savage via flickr

Force Balance

Anchors are key to a climber’s safety. They connect the climber to the wall via the rope and the harness, and catch the climber in a fall. Anchors come in all shapes and sizes, and the climber must carefully think about balancing forces in both magnitude and direction.

One of the first rules about anchor building is redundancy. Never use one anchor point when you can have two. Therefore the most common type of anchor is the V-shaped anchor with two separate connections to the wall, joined by a piece of webbing.

If the angle at the bottom of the V is too large (> 120 degrees), then the force on each of the anchors can actually be greater than the total weight of the climber and means either anchor is more likely to fail.

The figure below shows the force placed on each anchor, for a range of angles. (If you’re interested how the forces add, here’s the math). Climbers try to keep the angles as small as possible in order to reduce the force on their anchors.

Typical anchor setup, with one piece of webbing connecting two anchors in a V-shape.
Setup is shown for a variety of angles and the corresponding force applied to each anchor.
Credit: author, Tamela Maciel

The ‘American death triangle’.
This anchor adds more force to
each anchor because of the
horizontal connection.
Credit: author, Tamela Maciel

Without properly considering the physics of forces, it’s possible to add a dangerous amount of load to each anchor. The so-called American death triangle is a classic example of this. A single piece of webbing joins two anchors and the climber in a triangle shape. The tension in the horizontal section of webbing adds an additional force to each anchor, making it more likely to fail under a heavy load.

As shown in the left diagram, a triangle anchor with a 40 degree angle at the bottom and a 50 kg climber places a force of 427 newtons on each anchor, compared to only 261 newtons in the similar V-shape anchor above.

Absorption of Kinetic Energy

When a climber takes a big fall, their potential energy is quickly converted into kinetic energy. If the climber is suddenly brought to a halt at the end of the rope, a heavy shock load spreads through the climber’s body, the rope, and the anchor. This sharp force, or impulse, can injure the climber and cause a piece of gear or anchor to fail.

In order to slow down and cushion the halt, an elastic rope is used. By stretching the rope the climber falls a bit further but the impact is much more gentle on the whole system. Kinetic energy is also absorbed by friction of the rope and by careful belay partners who jump up slightly to soften their climber’s fall.

Cushioning can only do so much and for very large falls the anchors, ropes, and climbing gear can still fail. Climbing gear is rated by how much force it can withstand before it breaks, measured in kilonewtons. A basic piece of gear might withstand up to 10 kN before failing — a very large amount of force that would be reached only from the largest of falls.

A “PhD on El Capitan”

Caldwell and Jorgeson are intimately familiar with these rules of climbing physics. The pair prepared for the Dawn Wall climb over the course of seven years, working the moves on individual sections of the route.

“[Caldwell] says this is his thesis, his PhD on El Capitan, everything he’s worked for,” said Becca Caldwell, Tommy Caldwell’s wife, to the Telegraph.

For the final climb from bottom to top, Caldwell and Jorgeson spent 19 days on the route without ever touching the ground. They slept in portaledges, tent-like platforms suspended from anchors in the wall, and used extra ropes to haul gear. They finally reached the top of El Capitan yesterday mid-afternoon west coast time, welcomed by friends, family, and climbing fans.

By Tamela Maciel, also known as “pendulum”

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