AngleOf

Repose

Angle of ReposeAngle of Repose is the maximum slope angle of non-cohesive (i.e. free-flowing) granular material.It is the angle between a horizontal plane and the cone slope of such material.Bulk cargoes can be categorized for trimming purposes as “cohesive” or “non-cohesive”.

Cohesive bulk cargoes, all damp materials and some dry ones possess cohesion. For cohesive cargoes, the cargoes should be trimmed reasonably level to the boundaries of the cargo space. Cargo space should be filled as full as practicable without resulting in any excessive mass of the material on the bottom structure or tween-deck.

The angle of repose is a characteristic of non-cohesive bulk cargoes, which is indicative of cargo stability, and the purpose of which is to minimize the risk of bulk material shifting; the cargo should be trimmed reasonably level to the boundaries of the cargo space.

ApplicationThe 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.

Measurement1 Pour the dry sand into a pile on a level

surface allowing it to build a pile from the top. This will result in a pile with a relatively circular base, making measurement easier.

2 Using the ruler and a tape measure, measure the height (h) of the pile of sand from the peak to the ground. Stand the ruler next to the pile so it can be read easily.

Extend the tape measure carefully to the top of the pile without disturbing the pile and allow the other end of the tape measure to intersect the ruler. While keeping the tape measure level, observe the intersection of the tape measure with the ruler. Write the value on the paper. (Example: h = 12 inches.)

3 Using the tape measure, measure the horizontal distance (d) from the middle of the pile to the edge. Place the tape measure on the ground beside the pile. Line up one end with one side of the pile and extend the tape measure to the other end of the pile.

Write the value on the paper and divide by 2. This will give you the distance from the center of the pile to the edge. (Example: Total distance on tape measure from one end of the pile to the other = 30 inches. Divide by 2 to get 15 inches. d = 15 inches)

4 The equation for calculating the angle of repose is: tan-1(2h/d). Using your scientific calculator, multiply height (“h” calculated in Step 2) by 2 and divide this value by the distance (“d” calculated in Step 3). Then, hit the inverse tan key (or tan-1) and the answer just calculated. This will give you the angle of repose, α.

Factors Affecting Angle of Repose

The individual material will affect the angle of repose, a reflection of the different coefficients of friction between different substances. The size of the particles is a factor. Other factors being equal, fine grained material will form a shallower pile, with a smaller angle of repose than coarser grains.

Moisture affects the angle of repose, as anyone who has ever built a sand castle can confirm. Moist sand has a much higher angle of repose than dry sand. And the method by which the angle of repose is measured can also affect the measurement.

Angle of Repose

Methods in determining the

Tilting Box Method

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 at a rate of approximately 3 degrees/second. Tilting is stopped when the material begins to slide in bulk, and the angle of the tilt is measured.

Fixed Funnel Method

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.

Revolving Cylinder MethodThe material is placed within a cylinder with at least one transparent face. 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. When describing the angle of repose for a substance, always specify the method used.

Shipboard Test Method

In the absence of tilting box apparatus, an alternative procedure in determining the approximate angle of repose is that the quantity of the material to be tested is poured very carefully out of a flask onto a sheet of rough textured paper, in such a way that a symmetrical cone is formed.

Full details can be found on BC Code( Code of Safe Practice for Solid Bulk Cargoes).

Angle of Repose of various materials

Material (condition)

Angle of Repose

Ashes 40

Asphalt( Crushed)

30 - 45

Bark (wood refuse)

45

Bran 30-45

Chalk 45

Clay (dry lump) 25-40

Clay (wet excavated)

15

Clover seed 28

Coffee bean (fresh)

35 - 45

Flour (wheat) 45

Granite 30-45

Malt 30-45

Wheat 28

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