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Angle of repose


The angle of repose, or more precisely the critical angle of repose [1], is the minimum angle made by the inclined plane with the horizontal surface such that the body lying on the inclined plane is just at the verge of sliding down along the inclined plane.

When bulk granular materials are poured onto a horizontal surface, a conical pile will form. The internal angle between the surface of the pile and the horizontal surface is known as the angle of repose and is related to the density, surface area and shapes of the particles, and the coefficient of friction of the material. Material with a low angle of repose forms flatter piles than material with a high angle of repose. In other words, the angle of repose is the angle between the surface of a pile and the ground.

Contents

Applications of theory

Talus cones on north shore of Isfjorden, Svalbard, Norway, showing angle of repose for coarse sediment.

The angle of repose is sometimes used in the design of equipment for the processing of particulate solids. For example, it may be used to design an appropriate hopper or silo to store the material. It can also be used to size a conveyor belt for transporting the material. It can also be used in determining whether or not a slope (of a stockpile, or uncompacted gravel bank, for example) will likely collapse; the talus slope is derived from angle of repose and represents the steepest slope a pile of granular material will take. This angle of repose is also crucial in determining the correct calculus of stability in vessels.

It is also commonly used by mountaineers as a factor in analyzing avalanche danger in alpine areas.

Measurement

There are numerous methods for measuring angle of repose and each produces slightly different results. Results are also sensitive to the exact methodology of the experimenter. As a result, data from different labs is not always comparable. One method is the triaxial shear test, another is the direct shear test.

Exploitation by antlion and wormlion (Vermileonidae) larvae

Sand pit trap of the antlion

The larvae of the antlions and the unrelated wormlions Vermileonidae trap small insects such as ants by digging conical pits in loose sand, such that the slope of the walls is effectively at the critical angle of repose for the sand.[2] They achieve this by flinging the loose sand out of the pit and permitting the sand to settle at its critical angle of repose as it falls back. Thus, when a small insect, commonly an ant, blunders into the pit, its weight causes the sand to collapse below it, drawing the the victim toward the center where the predator that dug the pit lies in wait under a thin layer of loose sand. The larva assists this process by vigorously flicking sand out from the center of the pit when it detects a disturbance. This undermines the pit walls and causes them to collapse toward the center. The sand that the larva flings also pelts the prey with so much loose, rolling material as to prevent it from getting any foothold on the easier slopes that the initial collapse of the slope has presented. The combined effect is to bring the prey down to within grasp of the larva, which then can inject venom and digestive fluids.

See also

The angle of repose plays a part in several topics of technology and science, including:

References

  1. ^ A Mehta and G C Barker 1994 Rep. Prog. Phys. 57 383 "The dynamics of sand"
  2. ^ Effects of slope and particle size on ant locomotion: Implications for choice of substrate by antlions, Botz, Jason T.; Loudon, Catherine; Barger, J. Bradley; Olafsen, Jeffrey S.; Steeples, Don W.; (J. Kans. Entomol. Soc.), ISSN 0022-8567, 2003, vol. 76, no3, pp. 426-435 abstract
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