RACK/ARRAYS & PHASE

d_{border}

Line Array Transition

Near-to-far field border distance, coupling limit and splay geometry.

MOD-06•WST LINE SOURCE GEOMETRY & FRESNEL ZONE BENCH

Line Array Near-to-Far Field Transition & Splay Designer

Calculate total line length $L$ , cylindrical-to-spherical Fresnel transition distance $d_{\text{border}}(f)$ , low-frequency line coupling cutoff, and J-array vertical coverage.

Array Format Presets

NEAR-TO-FAR BORDER @ 1000 Hz

d_{\text{border}}(f)

6.7m

≤ 6.7m: −3 dB/dbl Cylindrical> 6.7m: −6 dB/dbl

TOTAL ACTIVE LINE LENGTH

L_{\text{array}}

4.32m

14.2 ft (12 Elements)Vertical Splay: 32.5°

LOW-FREQ COUPLING LIMIT

f_{\text{low}} = c / L

79Hz

Directivity control above 79 HzTrim: 10 m

LINE ARRAY PHYSICAL & SPLAY PARAMETERS

Number of Flown Cabinets

N_{\text{cab}}

boxes

3 boxes24 boxes

Single Cabinet Vertical Height

h_{\text{cab}}

0.2 m0.6 m

Average Inter-Cabinet Splay Angle

\theta_{\text{splay}}

deg

0 deg8 deg

Inspection Frequency

f

80 Hz12000 Hz

Bottom Cabinet Trim Height

H_{\text{trim}}

3 m20 m

FRESNEL TRANSITION DISTANCE VS. FREQUENCY & J-ARRAY PROFILE

HOW IT WORKS: ELECTRO-ACOUSTIC PHYSICS & MATHEMATICAL DERIVATION

Wavefront Sculpture Technology (WST) & Fresnel Transition Distance

Developed by Christian Heil and Marcel Urban, modern Wavefront Sculpture Technology (WST) line arrays couple discrete loudspeaker enclosures into a continuous vertical ribbon source of total length $L = N_{\text{cab}} \cdot h_{\text{cab}}$ . Within the Fresnel near-field region, individual spherical wavelets interfere constructively along the forward axis to form a cylindrical isophase wavefront.

Crucially, the boundary distance $d_{\text{border}}$ between the cylindrical near-field ( $-3\text{ dB}$ loss per distance doubling) and spherical far-field ( $-6\text{ dB}$ loss per doubling) increases with the square of array length ( $L^2$ ) and linearly with frequency ( $f$ ). Thus, doubling the number of flown cabinets quadruples the throw distance of the cylindrical region at mid-frequencies!

Fresnel Near-Field to Far-Field Border Distance (Straight Line Source)EQ-01

d_{\text{border}}(f) \approx \frac{L_{\text{array}}^2 \cdot f}{2 c} = \frac{(N_{\text{cab}} \cdot h_{\text{cab}})^2 \cdot f}{2 c}

Low-Frequency Line Coupling ThresholdEQ-02

f_{\text{low}} \approx \frac{c}{L_{\text{array}}} \quad [\text{Hz}]

Below

f_{\text{low}}

, the total array length is shorter than one acoustic wavelength (

\lambda

), so vertical directivity widens toward omnidirectional radiation.

Nomenclature & Physical Variables

$L_{\text{array}}$
Total vertical length of the flown line array
Unit: m
$d_{\text{border}}$
Transition distance from cylindrical ( $-3\text{ dB}$ ) to spherical ( $-6\text{ dB}$ ) spreading
Unit: m
$\theta_{\text{splay}}$
Inter-enclosure vertical splay angle
Unit: deg

FOH & System Tech Field Application Notes

Use tightly coupled $0^\circ$ to $1^\circ$ inter-box splays at the top of the hang to maximize effective line length $L$ for the back of the arena, and open up splay angles ( $4^\circ\text{–}8^\circ$ ) on the bottom 3–4 cabinets to cover the near audience evenly.
Because low-mid energy ( $150\text{ Hz–}400\text{ Hz}$ ) transitions to $-6\text{ dB}$ spherical decay much closer to the stage than high frequencies ( $4\text{ kHz}$ ), long-throw top boxes require low-mid shelving cuts or shading to maintain tonal balance front-to-back.