Flat-Top (Truncated-Cone) Stockpile Volume and Tonnage

Volume (cy) and tonnage of a FLAT-TOPPED stockpile - the truncated cone a radial stacker or a bulldozer leaves when it cannot peak the pile. From the base diameter, the flat-top diameter, and the angle of repose: the side slope sets the height h = (base_radius - top_radius) tan(repose), and the volume is the frustum (pi h/3)(Rb^2 + Rb Rt + Rt^2). An 80 ft pile with a 20 ft flat top at 37 degrees stands 22.6 ft and holds 1,841 cy (2,486 tons at 100 pcf). Set the top diameter to 0 and it collapses to the sharp conical stockpile. The angle of repose depends on the material and its moisture and steepens as it gets damp; an irregular base or non-level top change it. A survey volume governs for payment.

Rb = base_diameter/2, Rt = top_diameter/2; height = (Rb - Rt) x tan(repose x pi/180); volume = (pi height/3)(Rb^2 + Rb Rt + Rt^2); volume_cy = volume/27; tons = volume x density/2000.

Truncated-cone (frustum) stockpile geometry by name (angle-of-repose flat-topped pile); first-principles geometry.

The frustum-volume and angle-of-repose relations are public geometry and soil-mechanics practice.

Estimate. AHJ and licensed professional govern.

Field names used by the API: base_diameter_ft, top_diameter_ft, repose_angle_deg, density_pcf, volume_cy, tons, height_ft

• Shape truncated cone (frustum); height from the repose slope; top diameter 0 gives the sharp conesolid geometry
• Angle of repose 37 degrees default (granular material runs ~30-40 degrees); moisture and angularity steepen itsoil-mechanics practice
• Bulk density 100 pcf default loose (the material governs); a survey governs for paymentmaterials practice