Quadratically constrained quadratic program

The American Death Triangle, also known as the "American Triangle", "Death Triangle" or "Triangle Anchor" is a type of rock and ice climbing anchor infamous for both magnifying load forces on fixed anchors and lack of redundancy in attachment to the anchor.

Description

A two-point climbing anchor requires three carabiners: one at each fixed point and one at the "focal point" where the load is transferred to the climbing rope. The aim is to distribute the force equally to each fixed point. A triangle anchor is formed by clipping a length of webbing or cord through all three carabiners, creating a shape which gives the dangerous anchor its descriptive name.

The force on each fixed point depends on the angle at the focal point. The following table lists the percentage of force transferred to the fixed point for various focal point angles, followed by figures for a standard "V" shaped anchor.

File:AmericanDeathTriangle.png

American death triangle showing the associated lines of force (in blue) acting on the anchors

Load per anchor based on a central, perpendicular application of 100 lbf of force

Bottom angle	Load per anchor (V arrangement)	Load per anchor (triangle arrangement)
0°	50 lbf	71 lbf (not physically possible)
5°	50 lbf	72 lbf
10°	50 lbf	74 lbf
30°	52 lbf	82 lbf
60°	58 lbf	100 lbf
90°	71 lbf	131 lbf
120°	100 lbf	193 lbf
150°	193 lbf	380 lbf

Table values are derived from vector analysis:

• For a V arrangement, $F_{\mathrm {Anchor} }={\frac {\mathrm {Weight} }{2\cos({\frac {1}{2}}{\theta _{\mathrm {Bottom} }})}}\approx \mathrm {Weight} \times 0.5+O({\theta _{\mathrm {Bottom} }}^{2})$

• For the Triangle, $F_{\mathrm {Anchor} }={\frac {\mathrm {Weight} }{2\cos(45^{\circ }+{\frac {1}{4}}{\theta _{\mathrm {Bottom} }})}}\approx \mathrm {Weight} \times 0.707+O(\theta _{\mathrm {Bottom} })$

The load on the sling is the same in each example. For the V arrangement, the anchor force is equal to the tension in the sling, but for the triangle the anchor force is greater than the sling tension.

Aside from the magnification of forces, the death triangle violates several rules for building climbing anchors, including

• Redundancy: if the webbing fails on one leg of the anchor, the entire anchor will fail.
• Extension: if one of the anchors fails, the webbing will extend its full length and shock load the remaining components of the system

An alternate V-shaped form of the death triangle involves clipping a single loop of webbing or cord to each anchor then clipping the third carabiner over the loop rather than through it, allowing the latter to slip off the loop if either anchor fails. The correct method puts a half twist in the cord and clips the free carabiner through it. If either anchor fails the free carabiner will remain attached to the cord.

Special circumstances, such as when an experienced climber employs opposing forces to keep passive chocks, simple cams, or spring loaded multiple camming devices in a crack, may call for a triangle. Even then, special provision must be made to provide redundancy and eliminate extension in the protection system.

See also

• Climbing

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

External links

• Climbing Anchor
• Climbing Anchors includes photo