Angle of repose

Talus cones on north shore of Isfjord, 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, or 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 correctly calculating stability in vessels.

It is also commonly used by mountaineers as a factor in analysing avalanche danger in mountainous areas.

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 are not always comparable. One method is the triaxial shear test, another is the direct shear test.

If the coefficient of static friction is known of a material, then a good approximation of the angle of repose can be made with the following function. This function is somewhat accurate for piles where individual objects in the pile are minuscule and piled in random order.[2]

$${\displaystyle \tan {(\theta )}\approx \mu _{\mathrm {s} }\,}$$

where, μ_s is the coefficient of static friction, and θ is the angle of repose.

This pile of corn has a low angle of repose

Here is a list of various materials and their angle of repose.[3] All measurements are approximated.

Different supports will modify the shape of the pile, in the illustrations below sand piles, though angles of repose remain the same.[6][7]

Support format	Support	Angle of repose
Rectangle
Circle
Square
Triangle
Double fork
Oval
One pit
Double pit
Multiple pit
Random format

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.[8] 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 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.

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