The maximum angle of repose is the maximum angle at which a material can be piled without slumping. The material piled up will form a cone.
If we project the situation on a 2D plane, we get a triangle rectangle (see picture attached). We know one angle and the Opposite side (height) and we need to find the Adjacent side (radius).
Recalling trigonometry formulae:
tanα = O / A
Solving for A:
A = O / tanα
We can now substitute our data (O = 20):
1) Sand, Bank Damp
α = 45°
A = 20 / tan(45)
= 20
The radius is 20 feet.
2)Sand, Bank Dry
α = 35°
A = 20 / tan(35)
= 28.5629
The radius is 28.6 feet.
3) Sand, core
α = 41°
A = 20 / tan(41)
= 23.0074
The radius is 23 feet.
4) Sand, foundry prepared
α₁ = 30°
A₁ = 20 / tan(30)
= 34.6410
α₂ = 44°
A₂ = 20 / tan(44)
= 20.7106
The radius is between 20.7 and 34.6 feet.
5) Sand, Foundry shakeout
α = 39°
A = 20 / tan(39)
= 24.6979
The radius is 24.7 feet.
