Question

Finding the radius based on height of my building and max angle of repose?

Answer 1

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.