# Angle of Repose Explained

The angle of repose or critical angle of repose of granular material is the steepest angle of descent relative to a horizontal plane in which the powder is poured to create an angle from 0 degrees to 90 degrees.

This will show us the properties of our powder, a cohesive powder will form an irregular heap, where a non-cohesive powder will form a regular conical heap.

For testing the Angle Of Repose we follow the US Pharmacopeia method described in General Chapter 1174. There is not a defined method or equipment for testing the Angle Of Repose in the USP. Because of this LFA has developed a method in which we feel fits the requirements outlined in the USP of being “practical, useful, reproducible, sensitive, and yield meaningful results.”

To test the Angle Of Repose, we use the "LFA ART 1" (Angle Of Repose Tester)

To perform this test, take your powder and gently pour it into the funnel, stir the sample if necessary.

Once the powder has formed a pile on the platform measure the height of the powder from the platform the highest point on its peak. (mm)

The tangent of the angle of repose in degrees can be determined by reading off the height of the powder cone in mm from the digital display. Here’s the calculation to calculate the angle of repose, however LFA does have a calculator on our website to do the math for you which can be found here: https://www.lfatabletpresses.com/angle-of-repose-calculator

tan-1(2h/d) - h is the height of the pile of powder and d is the Diameter.

Using a scientific calculator, multiply the height by 2 and divide this value by the diameter. Then, hit the inverse tan key or tan-1 and the answer just calculated. This will give you the angle of repose.

Below is a table of how the angle of repose might affect the ability of a powder to flow.

### Expected Flow

25-30 Excellent
31-35 Good
36-40 Fair - aid not needed
41-45 Passable - may hang up
46-55 Poor - must agitate or vibrate
56-65 Very Poor
>66 Very, Very Poor

An angle between 25-30 degrees will show excellent flow, meaning the formulation will move through your hopper, feed frame, die table and die bores smoothly.

However, from 41 to greater than 66 degrees you may experience issues such as rat holing or bridging within your hopper. Bridging is where an arch is formed of the hoppers funnel and rat holding is where a small hole or narrow channel forms to the outlet and therefore will lead to poor flow.

You may also get the same issues in the die bore where the formulation is incorrectly filling in the die bores, leading to varying tablet weights and sizes.

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