Tapered Roof Insulation Average Thickness and Quantity
Average thickness, board-feet, and average R for a slope-to-drain tapered layout: avg = start + slope x run / 2; board-feet = area x avg; avg R = avg x R-per-inch. A 40 ft run at 1/4 in per foot off a 1/2 in start averages 5.5 in, so a 2,000 sf field is 11,000 board-feet at ~R-31; a shallower 1/8 in/ft taper averages 3.0 in - 6,000 bf and only R-17. The slope has to serve both drainage (>= 1/4 in/ft) and the code R. Distinct from flat assembly-r-value.
Formula and source
avg_thk_in = start_thk_in + slope_in_per_ft x run_ft / 2; board_feet = area_sf x avg_thk_in; avg_r = avg_thk_in x r_per_in.
Tapered-insulation identity by name (average of a linear taper; board-feet and average R from the average thickness); first-principles arithmetic.
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