Track Ballast Section Volume, Tonnage, and Surfacing Raise

The section is wider at the bottom than at the top because of the side slopes, and on a 1.5 to 1 slope with a foot of depth that is three extra feet of width -- a large fraction of the total. An 8 ft top width, 12 in deep, on 1.5 to 1 slopes is 11.0 ft at the bottom and 9.50 sq ft of section, which is 1,858 cu yd and about 2,601 tons per track mile at 1.40 tons per placed cubic yard. Take the same section off as a plain rectangle at the top width and you get 8.00 sq ft, roughly 16% low, which is 411 tons a mile of ballast that never gets ordered and shows up as a train that runs out two thousand feet short of the crossing. The distinction that decides a surfacing order is between the full section and the RAISE. Lifting existing track 2 in over 3,000 ft needs about 148 cu yd of lift volume plus what fills the crib and shoulder the lift opens up, against the 1,056 cu yd the full section over the same length would imply -- ordering the full section for a raise buys several times what is needed, and ordering the raise volume for new construction buys a fraction of it. Placed density is the other quiet term: ballast is bought by the ton and placed by the cubic yard, and the conversion runs roughly 1.35 to 1.45 tons per placed cubic yard for typical granite, so using loose density overstates the yards a ton will cover. A prismatic volume for a uniform trapezoidal section. It does not deduct the ballast displaced by ties, which is a real deduction, or the crib volume between ties on a raise; it does not handle transitions, turnouts, crossings, bridge approaches, or variable-depth sections, and it does not account for ballast lost into a soft subgrade, which on bad track can consume a large multiple of the calculated volume. It does not design the section, which is set by the railroad's standard plans for the class of track, axle load, and subgrade, and it does not evaluate ballast fouling, drainage, or the subgrade condition that usually decides whether more ballast will actually fix the track. The railroad's standard plans and engineering instructions govern.

bottom width = top + 2 x slope ratio x depth; area = (top + bottom) / 2 x depth; volume cu yd = area x length / 27; tons = volume x placed density; per mile = area x 5,280 / 27; raise volume = top width x raise depth x length / 27.

The trapezoidal prism and a placed-density conversion in tons per cubic yard, by name, as standard track surfacing practice; 27 cubic ft per cubic yard and 5,280 ft per mile are exact. The railroad's standard plans set the section and the supplier's material sets the density.

Prismatic volume arithmetic on the user's own section dimensions and an entered density; no standard plan is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: top_width_ft, depth_in, side_slope_ratio, length_ft, density_ton_per_cy, raise_in, bottom_width_ft, area_sqft, cy_per_mile, tons_per_mile, understated_pct

• Side slopes are most of the error taking the section off as a rectangle at the top width understates it, and the gap grows with depthtrack surfacing practice
• A raise is not a section a surfacing lift needs the lift volume plus crib and shoulder fill, not the full sectiontrack surfacing practice
• Placed density, not loose roughly 1.35 to 1.45 tons per placed cubic yard for typical granite; take it from the supplier's materialsupplier material data