Valley Flashing Takeoff (Metal, Pieces, Ice Barrier)

A valley is the longest run on the roof for its plan dimension because it goes diagonally AND uphill: the multiplier carries 288 under the radical where a common rafter carries 144, so a 12-ft plan run at 6:12 is exactly 18 ft of valley against 13.4 ft of common. Ordering off the plan comes up badly short.

valley multiplier = sqrt(pitch^2 + 288)/12 (the framing-square 17-inch rule) against a common rafter's sqrt(pitch^2 + 144)/12; valley length = plan run x multiplier; pieces = ceil(LF x (1 + waste)/(stock - lap/12)); metal area = LF x width/12.

Valley geometry by the framing-square 17-inch rule - public geometry, no table reproduced.

The 17-inch rule is in every framing reference and on the framing square itself.

Estimate. AHJ and licensed professional govern.

Field names used by the API: valley_run_ft, valley_count, pitch_rise_per_12, metal_width_in, stock_length_ft, lap_in, waste_pct, valley_multiplier, valley_length_ft, total_valley_lf, effective_piece_ft, pieces, metal_area_sf

• 17-inch rule valley multiplier sqrt(pitch^2 + 288)/12; the fuzzer pins agreement with the hip-valley-rafter tileframing-square geometry
• Open valley exposed metal; closed-cut and woven valleys use shingles and are out of scopestated scope limit
• Valley ice barrier reported as an allowance at the metal width; the eave ice-barrier tile does not include valleysstated gap in the sibling tile