End-Fire & Gradient Subwoofer Delay/Polarity Calculator

Reference: SUB-CARDIOID-01. Distinct from the existing Cardioid Subwoofer Array Configurator, which covers a simple front-back pair. These two forward-facing configurations trade hardware for real estate: sync by delay, cancel by polarity (gradient) or by matched phase in front and scrambled phase behind (end-fire). Not covered here: the gradient inverted stack, where the actual delay depends on the physical wraparound path between drivers and has to be field-verified rather than calculated.

End-Fire Array

A forward line of matched-polarity elements at fixed spacing, each delayed so all of them arrive in phase at the front. The rearmost element gets 0 ms; each element toward the front gets progressively more delay, matching the extra acoustic path the rear elements get for free. Needs at least 3 elements to actually randomize (not cancel) the rear — with only 2, use the gradient in-line pair below instead.

Quantity of elements Spacing between adjacent elements (m) Calculate

Gradient In-Line Pair (2 elements only)

Two forward-facing elements spaced close together (typically 1 m or less). The front element runs normal polarity with 0 ms delay. The rear element is delayed by the propagation time between them and polarity-reversed. This is a minimum-real-estate cardioid — more front/back rejection than an end-fire per meter of depth, at the cost of being fixed at exactly 2 elements (it doesn't scale up the way end-fire does).

Spacing between the two elements (m) Calculate

Source: McCarthy, Bob. Sound Systems: Design and Optimization, 3rd ed., §10.1 "Subwoofer Arrays" and §10.2 "Cardioid Subwoofer Arrays" (End-Fire and Gradient In-Line configurations). Rewritten in Ryan's own words from the source material. Speed of sound taken as 343 m/s (20°C), consistent with the other calculators on this site — treat delay values as a field-verified starting point, not a final setting.