Windrow (Elongated) Stockpile Volume and Tonnage

a compost row, DOT salt/sand pile, or aggregate windrow. Modeled as a triangular prism (the straight ridge run) with the two tapered ends together making one full cone: height = (width/2) tan(repose), cross-section = 1/2 x width x height, volume = cross-section x ridge length + 1/3 pi (width/2)^2 height. A 20 ft-wide pile at 37 degrees stands 7.5 ft; a 50 ft ridge holds 169 cy (228 tons at 100 pcf). Set the ridge length to 0 and it collapses to the conical stockpile. The angle of repose depends on the material and its moisture and steepens as it gets damp; an irregular base, a bulldozed flat top, or a pile against a wall all change it. A survey volume governs for payment.

radius = width/2; height = radius x tan(repose x pi/180); cross_section = 1/2 x width x height; volume = cross_section x ridge_length + (1/3) pi radius^2 height; volume_cy = volume/27; tons = volume x density/2000.

Elongated-stockpile geometry by name - a triangular prism (the straight ridge run) plus one full cone across the two tapered ends; first-principles geometry with the angle-of-repose relation.

The prism, cone, 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_width_ft, ridge_length_ft, repose_angle_deg, density_pcf, volume_cy, tons, height_ft

• Shape triangular prism (ridge run) + one full cone at the ends; ridge length 0 gives the conical pilesolid 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