The angle of repose, or critical angle of repose, of a granular material is the steepest angle of descent or dip relative to the horizontal plane to which a material can be piled without slumping. At this angle, the material on the slope face is on the verge of sliding. The angle of repose can range from 0° to 90°. The morphology of the material affects the angle of repose; smooth, rounded sand grains cannot be piled as steeply as can rough, interlocking sands. The angle of repose can also be affected by additions of solvents. If a small amount of water is able to bridge the gaps between particles, electrostatic attraction of the water to mineral surfaces will increase the angle of repose, and related quantities such as the soil strength.
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.
The term has a related usage in mechanics, where it refers to the maximum angle at which an object can rest on an inclined plane without sliding down. This angle is equal to the arctangent of the coefficient of static friction μs between the surfaces.
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.
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.
where, μs is the coefficient of static friction, and θ is the angle of repose.
The measured angle of repose may vary with the method used.
This method is appropriate for fine-grained, non-cohesive materials with individual particle size less than 10 mm. The material is placed within a box with a transparent side to observe the granular test material. It should initially be level and parallel to the base of the box. The box is slowly tilted until the material begins to slide in bulk, and the angle of the tilt is measured.
The material is poured through a funnel to form a cone. The tip of the funnel should be held close to the growing cone and slowly raised as the pile grows, to minimize the impact of falling particles. Stop pouring the material when the pile reaches a predetermined height or the base a predetermined width. Rather than attempt to measure the angle of the resulting cone directly, divide the height by half the width of the base of the cone. The inverse tangent of this ratio is the angle of repose.
The material is placed within a cylinder with at least one transparent end. The cylinder is rotated at a fixed speed and the observer watches the material moving within the rotating cylinder. The effect is similar to watching clothes tumble over one another in a slowly rotating clothes dryer. The granular material will assume a certain angle as it flows within the rotating cylinder. This method is recommended for obtaining the dynamic angle of repose, and may vary from the static angle of repose measured by other methods.
Here is a list of various materials and their angle of repose. All measurements are approximated.
|Material (condition)||Angle of Repose (degrees)|
|Bark (wood refuse)||45°|
|Clay (dry lump)||25–40°|
|Clay (wet excavated)||15°|
|Coffee bean (fresh)||35–45°|
|Gravel (crushed stone)||45°|
|Gravel (natural w/ sand)||25–30°|
|Sand (water filled)||15–30°|
|Urea (Granular)||27° |
|Support format||Support||Angle of repose|
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. 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:
Arthur De Wint Foote (1849–1933) was an American civil engineer and mining engineer who impacted the development of the American West with his innovative engineering works and entrepreneurial ventures. In northern California in the late 1890s, he designed and built the North Star Mine Powerhouse, the highest capacity impulse-turbine power-plant of the time, and now a California historic landmark; within that plant he designed and installed the then-largest Pelton wheel turbine. Later, he designed and built Foote's Crossing, a high bridge, and Foote's Crossing Road, both now memorialized as California and U.S. landmarks.Barchan
A barchan or barkhan dune (from Kazakh бархан [bɑɾˈχɑn]) is a crescent-shaped dune. The term was introduced in 1881 by Russian naturalist Alexander von Middendorf, for crescent-shaped sand dunes in Turkestan and other inland desert regions. Barchans face the wind, appearing convex and are produced by wind action predominantly from one direction. They are a very common landform in sandy deserts all over the world and are arc-shaped, markedly asymmetrical in cross section, with a gentle slope facing toward the wind sand ridge, comprising well-sorted sand.
This type of dune possesses two "horns" that face downwind, with the steeper slope known as the slip face, facing away from the wind, downwind, at the angle of repose of the sand in question, approximately 30–35 degrees for medium-fine dry sand. The upwind side is packed by the wind, and stands at about 15 degrees. Barchans may be 9–30 m (30–98 ft) high and 370 m (1,210 ft) wide at the base measured perpendicular to the wind.
Simple barchan dunes may appear as larger, compound barchan or megabarchan dunes, which can gradually migrate with the wind as a result of erosion on the windward side and deposition on the leeward side, at a rate of migration ranging from about one meter to 100 meters per year. Barchans usually occur as groups of isolated dunes and may form chains that extend across a plain in the direction of the prevailing wind. Barchans and mega-barchans may coalesce into ridges that extend for hundreds of kilometers. Dune collisions and changes in wind direction spawn new barchans from the horns of the old ones and govern the size distribution of a given field.As barchan dunes migrate, smaller dunes outpace larger dunes, catching-up the rear of the larger dune and eventually appear to punch through the large dune to appear on the other side. The process appears superficially similar to waves of light, sound, or water that pass directly through each other, but the detailed mechanism is very different. The dunes emulate soliton behavior, but unlike solitons, which flow through a medium leaving it undisturbed (think of waves through water), the sand particles themselves are moved. When the smaller dune catches up the larger dune, the winds begin to deposit sand on the rear dune while blowing sand off the front dune without replenishing it. Eventually, the rear dune has assumed dimensions similar to the former front dune which has now become a smaller, faster moving dune that pulls away with the wind.Barchan dunes have been observed on Mars, where the thin atmosphere produces winds strong enough to move sand and dust.Bulk material handling
Bulk material handling is an engineering field that is centered on the design of equipment used for the handling of dry materials. Bulk materials are those dry materials which are powdery, granular or lumpy in nature, and are stored in heaps. Examples of bulk materials are minerals, ores, coal, cereals, woodchips, sand, gravel, clay, cement, ash, salt, chemicals, grain, sugar, flour and stone in loose bulk form. It can also relate to the handling of mixed wastes. Bulk material handling is an essential part of all industries that process bulk ingredients, including: food, beverage, confectionery, pet food, animal feed, tobacco, chemical, agricultural, polymer, plastic, rubber, ceramic, electronics, metals, minerals, paint, paper, textiles and more.
Major characteristics of bulk materials, so far as their handling is concerned, are: lump size, bulk weight (density), moisture content, flowability (particle mobility), angle of repose, abrasiveness, material form (powder, flake, granule, pellet, fiber or other) and corrosivity, among others.Bulk material handling systems are typically composed of stationary machinery such as conveyor belts, screw conveyors, tubular drag conveyors, moving floors, toploaders, stackers, reclaimers, bucket elevators, truck dumpers, railcar dumpers or wagon tipplers, shiploaders, hoppers and diverters and various mobile equipment such as loaders, mobile hopper loaders / unloaders, various shuttles, combined with storage facilities such as stockyards, storage silos or stockpiles. Advanced bulk material handling systems feature integrated bulk storage (silos), conveying (mechanical or pneumatic), and discharge.
The purpose of a bulk material handling facility may be to transport material from one of several locations (i.e. a source) to an ultimate destination or to process material such as ore in concentrating and smelting or handling materials for manufacturing such as logs, wood chips and sawdust at sawmills and paper mills. Other industries using bulk materials handling include flour mills and coal-fired utility boilers.
Providing storage and inventory control and possibly material blending is usually part of a bulk material handling system.
In ports handling large quantities of bulk materials continuous ship unloaders are replacing gantry cranes.Cross-bedding
In geology, cross-bedding, also known as cross-stratification, is layering within a stratum and at an angle to the main bedding plane. The sedimentary structures which result are roughly horizontal units composed of inclined layers. The original depositional layering is tilted, such tilting not being the result of post-depositional deformation. Cross-beds or "sets" are the groups of inclined layers, which are known as cross-strata.
Cross-bedding forms during deposition on the inclined surfaces of bedforms such as ripples and dunes; it indicates that the depositional environment contained a flowing medium (typically water or wind). Examples of these bedforms are ripples, dunes, anti-dunes, sand waves, hummocks, bars, and delta slopes. Environments in which water movement is fast enough and deep enough to develop large-scale bed forms fall into three natural groupings: rivers, tide-dominated coastal and marine settings.Crossing to Safety
Crossing to Safety is a 1987 semi-autobiographical novel by "The Dean of Western Writers", Wallace Stegner. It gained broad literary acclaim and commercial popularity.
In Crossing to Safety, Stegner explores the mysteries of friendship, and it extends Stegner's distinguished body of work that had already earned him a Pulitzer Prize (for 1971's Angle of Repose) and the National Book Award (for 1976's The Spectator Bird). Publishers Weekly described the novel as "an eloquent, wise and immensely moving narrative," and "a meditation on the idealism and spirit of youth, when the world is full of promise, and on the blows and compromises life inevitably inflicts." The story is told mostly in flashback; the narrator, Larry Morgan, and his wife, Sally, settle into their new home in Madison, Wisconsin, as Larry begins a term teaching creative writing at the university's English department. They soon befriend another couple, Sid and Charity Lang, and learn of Sid's ambition to succeed as a writer. As their careers mature, they take different paths, but they spend much of their time together on summer vacations in the small Vermont town where Charity's family has been coming for decades.Stegner's powerful but unassuming narrative traces the bond that develops between the Langs and the Morgans from their first meeting in 1937 through their eventual separation on the occasion of Charity's death from cancer.Inclined plane
An inclined plane, also known as a ramp, is a flat supporting surface tilted at an angle, with one end higher than the other, used as an aid for raising or lowering a load. The inclined plane is one of the six classical simple machines defined by Renaissance scientists. Inclined planes are widely used to move heavy loads over vertical obstacles; examples vary from a ramp used to load goods into a truck, to a person walking up a pedestrian ramp, to an automobile or railroad train climbing a grade.Moving an object up an inclined plane requires less force than lifting it straight up, at a cost of an increase in the distance moved. The mechanical advantage of an inclined plane, the factor by which the force is reduced, is equal to the ratio of the length of the sloped surface to the height it spans. Due to conservation of energy, the same amount of mechanical energy (work) is required to lift a given object by a given vertical distance, disregarding losses from friction, but the inclined plane allows the same work to be done with a smaller force exerted over a greater distance.The angle of friction, also sometimes called the angle of repose, is the maximum angle at which a load can rest motionless on an inclined plane due to friction, without sliding down. This angle is equal to the arctangent of the coefficient of static friction μs between the surfaces.Two other simple machines are often considered to be derived from the inclined plane. The wedge can be considered a moving inclined plane or two inclined planes connected at the base. The screw consists of a narrow inclined plane wrapped around a cylinder.The term may also refer to a specific implementation; a straight ramp cut into a steep hillside for transporting goods up and down the hill. It may include cars on rails or pulled up by a cable system; a funicular or cable railway, such as the Johnstown Inclined Plane.Mary Hallock Foote
Mary Hallock Foote (1847–1938) was an American author and illustrator. She is best known for her illustrated short stories and novels portraying life in the mining communities of the turn-of-the-century American West.Mass wasting
Mass wasting, also known as slope movement or mass movement, is the geomorphic process by which soil, sand, regolith, and rock move downslope typically as a solid, continuous or discontinuous mass, largely under the force of gravity, frequently with characteristics of a flow as in debris flows and mudflows. Types of mass wasting include creep, slides, flows, topples, and falls, each with its own characteristic features, and taking place over timescales from seconds to hundreds of years. Mass wasting occurs on both terrestrial and submarine slopes, and has been observed on Earth, Mars, Venus, and Jupiter's moon Io.
When the gravitational force acting on a slope exceeds its resisting force, slope failure (mass wasting) occurs. The slope material's strength and cohesion and the amount of internal friction within the material help maintain the slope's stability and are known collectively as the slope's shear strength. The steepest angle that a cohesionless slope can maintain without losing its stability is known as its angle of repose. When a slope made of loose material possesses this angle, its shear strength counterbalances the force of gravity acting upon it.
Mass wasting may occur at a very slow rate, particularly in areas that are very dry or those areas that receive sufficient rainfall such that vegetation has stabilized the surface. It may also occur at very high speed, such as in rockslides or landslides, with disastrous consequences, both immediate and delayed, e.g., resulting from the formation of landslide dams. Factors that change the potential of mass wasting include: change in slope angle, weakening of material by weathering, increased water content; changes in vegetation cover, and overloading.
Volcano flanks can become over-steep resulting in instability and mass wasting. This is now a recognised part of the growth of all active volcanoes. It is seen on submarine as well as surface volcanoes: Loihi in the Hawaiian volcanic chain and Kick 'em Jenny in the Caribbean volcanic arc are two submarine volcanoes that are known to undergo mass wasting. The failure of the northern flank of Mount St Helens in 1980 showed how rapidly volcanic flanks can deform and fail.Nancy Shade
Nancy Shade (born May 31, 1946, in Rockford, Illinois) is a spinto soprano, best known as a singing-actress. She made her formal debut as Leonora in Il trovatore, in Louisville, in 1967. In 1971, she made her first of many appearances at the New York City Opera, as Musetta in La bohème. She also sang there in Mefistofele (directed by Tito Capobianco), Madama Butterfly (opposite José Carreras), Pagliacci, Susannah, and Die tote Stadt (in Frank Corsaro's production).
In 1973, Shade sang the title role of Manon Lescaut (opposite Harry Theyard) at the Spoleto Festival, under the direction of Luchino Visconti conducted by Thomas Schippers. The following year, she sang in a Concert Version of Mefistofele at London's Royal Festival Hall, opposite Norman Treigle in the name part. In 1976 she created the role of Barbara in the world premiere of Gian Carlo Menotti's The Hero (conducted by Christopher Keene) with the Opera Company of Philadelphia. That same year she made her Covent Garden debut as Giorgetta in Il tabarro, and in 1979, performed the eponymous role of Lulu at the Santa Fe Opera, which was the American premiere of the completed, three-act version of the masterpiece. Also in Santa Fe, she appeared in La traviata (1976), Salome (1976), Erwartung (1980) and We Come to the River (1984).
For the New Orleans Opera Association, she sang in Manon Lescaut (1974), a double-bill of Il tabarro and Pagliacci (1976), as well as La bohème (as Mimì, 1978). At the San Francisco Opera, in 1976, the soprano appeared in the world premiere of Andrew Imbrie's Angle of Repose (with Chester Ludgin and Susanne Marsee), and returned the following year for Marguerite in Faust under the direction of Jean Périsson. She also was seen at the San Diego Opera, in Mefistofele (conducted by Werner Torkanowsky, 1973), La traviata (1977) and Falstaff (1978). The soprano was also heard in the United States premiere of Lowell Liebermann's The Picture of Dorian Gray, at the Florentine Opera, in 1999, which was broadcast over NPR.
In 1986, she sang Zoe in the world premiere of Hans Zender's Stephen Climax at the Oper Frankfurt.
One of Shade's greatest successes was as Marie in Zimmermann's fiercely difficult Die Soldaten, which was recorded (with Bernhard Kontarsky conducting, 1988–89) and filmed (in Harry Kupfer's production, 1989). She sang the work at the Vienna Staatsoper in 1990, which was preceded by Salome. In a different vein, she was in the first complete recording of the musical comedy The Most Happy Fella (as Marie), alongside Louis Quilico, which was published in 2000. In the same year, the soprano was also acclaimed for her performance as the Woman in Erwartung, at the Prague State Opera.Philip L. Fradkin
Philip L. Fradkin (February 28, 1935 – July 8, 2012) was an American environmentalist historian, journalist, and author. Fradkin authored books ranging from Alaska, California, and Nevada, with topics ranging from water conservation, earthquakes, and nuclear weapons.
Born in Manhattan, Fradkin grew up in Montclair, New Jersey and attended Montclair Kimberley Academy, graduating in the class of 1953.In 1964, Fradkin began working for the Los Angeles Times, and the following year was part of the metropolitan staff awarded a Pulitzer Prize for its work on the 1965 Watts riots. In 2005, Fradkin was given the California Award by the Commonwealth Club of California.
He commented on controversial issues such as plagiarism allegations towards Wallace Stegner's Pulitzer Prize-winning novel, Angle of Repose, based on the letters of the American Old West author Mary Hallock Foote.Powder
A powder is a dry, bulk solid composed of many very fine particles that may flow freely when shaken or tilted. Powders are a special sub-class of granular materials, although the terms powder and granular are sometimes used to distinguish separate classes of material. In particular, powders refer to those granular materials that have the finer grain sizes, and that therefore have a greater tendency to form clumps when flowing. Granulars refers to the coarser granular materials that do not tend to form clumps except when wet.Principle of original horizontality
The Principle of Original Horizontality states that layers of sediment are originally deposited horizontally under the action of gravity. It is a relative dating technique. The principle is important to the analysis of folded and tilted strata. It was first proposed by the Danish geological pioneer Nicholas Steno (1638–1686).
From these observations is derived the conclusion that the Earth has not been static and that great forces have been at work over long periods of time, further leading to the conclusions of the science of plate tectonics; that movement and collisions of large plates of the Earth's crust is the cause of folded strata.
As one of Steno's Laws, the Principle of Original Horizontality served well in the nascent days of geological science. However, it is now known that not all sedimentary layers are deposited purely horizontally. For instance, coarser grained sediments such as sand may be deposited at angles of up to 15 degrees, held up by the internal friction between grains which prevents them slumping to a lower angle without additional reworking or effort. This is known as the angle of repose, and a prime example is the surface of sand dunes.
Similarly, sediments may drape over a pre-existing inclined surface: these sediments are usually deposited conformably to the pre-existing surface. Also sedimentary beds may pinch out along strike, implying that slight angles existed during their deposition. Thus the Principle of Original Horizontality is widely, but not universally, applicable in the study of sedimentology, stratigraphy and structural geology.Rotary feeder
Rotary feeders, also known as rotary airlocks or rotary valves, are commonly used in industrial and agricultural applications as a component in a bulk or specialty material handling system. Rotary feeders are primarily used for discharge of bulk solid material from hoppers/bins, receivers, and cyclones into a pressure or vacuum-driven pneumatic conveying system. Components of a rotary feeder include a rotor shaft, housing, head plates, and packing seals and bearings.
Rotors have large vanes cast or welded on and are typically driven by small internal combustion engines or electric motors.Sandfall
Sandfall (sand fall or grainfall) is a term applied to a variety of forms of sedimentary transport or sedimentary features belonging to the larger category of mass wasting, and are driven by wind, water currents and gravitational forces.
One, sometimes spectacular, form is superficially similar to waterfalls and may be found under dry, desert conditions or in submarine conditions. The sand either falls vertically over suitable drops or cascades down hard slopes. The process has been described as "dry sandflows cascading down the escarpment face, where the grain concentration decreases dramatically and the streaming component of stress greatly exceeds the collisional component" Sandfalls are found in sandstone canyons such as Antelope Canyon. A similar process occurs in submarine environments driven by water currents and gravity. Sandfalls on a large scale occur off the southern tip of the island of Mauritius, where strong ocean currents move sand from the high coastal shelf over the edge and into the abyssal depths. Sandfalls in the submarine San Lucas Canyon off Cabo San Lucas, Baja California were dived by Jacques Cousteau. Carter (1975) argues that the ubiquity of this process is evident from the examples from the sides of submarine canyons documented by Dill (1964) and from seamounts and deep-sea trenches documented by Heezen and Holhster (1971).Also sometimes referred to as sandfall, is the movement of sand on the "steeply sloping surface on the lee side of a dune standing at or near the angle of repose of loose sand and advancing downwind by a succession of slides wherever that angle is exceeded." The process of sand falling like rain has also been referred to as a sandfall.Sands Hall
Sands Hall (April 17, 1952) is an American writer, theatre director, actor, and musician. The daughter of novelist Oakley Hall, she was born in La Jolla, California, and graduated magna cum laude with a Bachelor of Arts in Drama from the University of California, Irvine. She earned two Master of Fine Arts degrees from the University of Iowa, one in Theatre Arts and the second in Fiction from the Iowa Writers' Workshop. She also studied at the American Conservatory Theatre Advanced Training Program.Hall's writing work includes the play Fair Use, which explores the long debated plagiarism in Wallace Stegner's Angle of Repose, and the novel Catching Heaven, a Random House Reader's Circle selection and a 2001 Willa Award Finalist for Best Contemporary Fiction. She has taught writing for the University of California at Davis Extension Programs, and the Iowa Summer Writing Festival. She is currently Visiting Assistant Professor of Creative Writing at Franklin & Marshall College in Lancaster, Pennsylvania, and on the staff of the Community of Writers at Squaw Valley, California.
Her work in the theatre includes seasons at the Oregon Shakespeare Festival, Colorado Shakespeare Festival, Lake Tahoe Shakespeare Festival, the Old Globe Theatre and internationally at the Maxim Gorky Theatre in Vladivostok, Russia. She is currently an Affiliate Artist with the Foothill Theatre Company in Nevada City, California.Scree
Scree is a collection of broken rock fragments at the base of crags, mountain cliffs, volcanoes or valley shoulders that has accumulated through periodic rockfall from adjacent cliff faces. Landforms associated with these materials are often called talus deposits. Talus deposits typically have a concave upwards form, while the maximum inclination corresponds to the angle of repose of the mean debris size.
The term scree comes from the Old Norse term for landslide, skriða, while the term talus is a French word meaning a slope or embankment.Wallace Stegner
Wallace Earle Stegner (February 18, 1909 – April 13, 1993) was an American novelist, short story writer, environmentalist, and historian, often called "The Dean of Western Writers". He won the Pulitzer Prize in 1972 and the U.S. National Book Award in 1977.William Lewis (tenor)
William L. Lewis (born November 23, 1931, Tulsa, Oklahoma) is an American operatic tenor and academic.