Why line arrays curve: splay angles and the shape of an audience
Abstract. A straight column throws a beam; an audience is not shaped like a beam. This note explains how cylindrical spreading changes the level-versus-distance law, why arrays are curved at all, and how splay angles distribute energy from the front row to the back wall.
Cylindrical against spherical spreading
A point source loses six decibels per doubling of distance: its energy spreads over a sphere whose area grows with the square of range. A tall coherent line radiates, in its near field, a wavefront that spreads over a cylinder instead, and the loss falls toward three decibels per doubling. This slower decay is the property that lets a line source hold level to the back of a large audience, and it holds only while the array is long compared with the wavelength and behaves as one source, which is what coherent coupling between elements protects.
Why the array is curved
A perfectly straight array concentrates its energy into a narrow beam at the horizon, which suits an audience of zero depth. Real audiences extend from a front row steeply below the hang to a distant back row near its axis. Curving the array, tight splays at the top, progressively wider below, points successive sections of the line at successive depths of the audience: the top of the hang throws far, the bottom fills near, and the level stays consistent along the floor rather than along the beam.
Splay as a design variable
Each splay angle sets how much of the array's length, and therefore how much of its energy, addresses each part of the room. Prediction software solves this distribution against the venue geometry, and the rigging reproduces it. This is also why splay resolution matters: coverage of the audience is being apportioned in those increments, and why the far-throw sections at the top of a hang benefit most from added elements, since throwing further means spending more of the line on the same angular slice.