Line Array Vertical Coverage and Splay

The vertical angle a line array has to cover, the average splay per cabinet that covers it, and the level taper the splay pattern is being asked to recover. An array hung at a trim height must cover the angle between the down-tilt to the first row and the down-tilt to the last, and that angle is set by geometry rather than by the boxes: it is atan(drop / near throw) minus atan(drop / far throw), where the drop is the trim height above the listeners' ears. Dividing it by the cabinet count gives the average splay, which is the design starting point a manufacturer's prediction software then refines. The taper line explains why the splays are never actually equal: the last row is far more distant than the first, so it is much quieter by inverse square, and the array makes that up by aiming more of its energy at the far seats -- tight splays at the top where the boxes throw long, opening toward the bottom where they cover the near rows. An array trimmed at 26 ft over a seated audience with 4 ft ears, first row 25 ft and last row 150 ft, covers 41.3 down to 8.3 degrees, so 33.0 degrees across twelve cabinets is 2.75 degrees of average splay, against 20 log(150/25) = 15.6 dB of taper. Nearly sixteen decibels across thirty-three degrees is a lot of asymmetry to build in, and the top boxes will sit near the array's minimum splay while the bottom ones open to five or six. A design starting point; the manufacturer's prediction software and the array's mechanical splay limits govern the rig.

dh = trim_height_ft - ear_height_ft; angle_near = atan(dh / near_throw_ft); angle_far = atan(dh / far_throw_ft); coverage = angle_near - angle_far; avg_splay = coverage / cabinets; level_taper_db = 20 log10(far_throw / near_throw).

Line-array vertical coverage from the trim geometry with the inverse-square (20 log) level taper between the near and far rows, by name; a design starting point, and the manufacturer's prediction software and the array's mechanical splay limits govern the rig.

The coverage angle is trigonometry on the trim height and the two throws, and the taper is the inverse-square law. All five inputs are the rig's own dimensions.

Estimate. AHJ and licensed professional govern.

Field names used by the API: trim_height_ft, ear_height_ft, near_throw_ft, far_throw_ft, cabinets, angle_near_deg, angle_far_deg, coverage_deg, avg_splay_deg, level_taper_db

• Coverage is geometric the angle to cover is set by trim height and the two throws, not by the loudspeakerline-array design practice
• Taper drives asymmetry 20 log(far/near) is the level the splay pattern must recover, so splays tighten at the top and open at the bottominverse-square law applied to array design
• Starting point only the manufacturer's prediction software and the array's mechanical splay limits govern the rigmanufacturer array-design software