Grain Bin Wall Height for a Target Capacity
The inverse of the grain-bin-capacity tile: the eave (wall) height a round bin needs to hold a target bushel capacity, eave = (target_ft3/packing - roof_cone_ft3) / floor_area (1 ft^3 = 0.8036 bu). Storing 12,875 bu in a 30 ft bin with an 8 ft peaked fill needs a 20 ft wall; widen to 42 ft and the wall drops to about 8.9 ft, since capacity grows with the square of the diameter but only linearly with the wall. Answers 'how tall a bin' instead of the capacity of one. A geometric fill volume; the manufacturer's rated capacity and the structure govern.
Formula and source
floor_area = pi x (d/2)^2; cone = (1/3) x floor_area x peak; eave = (target_bushels/0.8036/packing - cone) / floor_area. The inverse of bushels = (floor_area x eave + cone) x packing x 0.8036.
Bin geometry first-principles; USDA FGIS standard bushel conversion by name.
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