Pioneered by Meyer Sound in the early 1980s, curved horizontal arrays formed with trapezoidal enclosures have been an industry standard for decades, and their behavior is widely understood. Recently, the sound reinforcement profession has exhibited considerable interest in new implementations of the venerable line array concept, and in these implementations the array is often curved (in some instances quite radically) to accommodate coverage requirements. But the behavior of curved "line arrays" is complex, varying with frequency, and must be understood in order to correctly implement curvilinear vertical arrays.
Practical contemporary line array systems generally employ direct-radiating cone drivers for low and mid frequencies, and high-frequency wave guides with a tightly controlled, narrow vertical coverage pattern. The narrow vertical pattern of the wave guide is required both to match the vertical directionality of the line array of woofers, and to minimize lobing and cancellations caused by multiple arrivals. (A detailed discussion of line array theory is available here.) Straight line arrays of such hybrid elements are very useful in long-throw applications because they can be designed to maintain consistently narrow vertical directivity across the audio spectrum, projecting most of their energy in a forward beam.
Figure 1 shows the directional radiation pattern of a straight array (0° splay between cabinets) of six Meyer Sound M2D Compact Curvilinear Array Loudspeakers at 500 Hz, and Figure 2 shows the same arrays directional pattern at 2 kHz. The M2D uses two 10-inch cone drivers to reproduce low and mid frequencies, and a compression driver with a high-frequency horn having narrow vertical directivity for high frequencies. This arrays low-frequency directivity is the result of constructive and destructive interference between the sound fields of the 10-inch cones, and its high-frequency directivity is controlled by the horns.
Fig. 1. Straight Array Sound Field at 500 Hz
Fig. 2. Straight Array Sound Field at 2 kHz
Figure 3 shows the far-field frequency response (with one-third octave resolution) of this array. Note that it is nominally flat across the audio spectrum.
Fig. 3. Straight Array Far-Field Frequency Response
As its name suggests, the M2D is designed specifically for implementing vertical curvilinear arrays of up to 12 cabinets having 0° to 7° splay between adjacent units. Figure 4 shows the directional radiation pattern of a curved array (5° splay between cabinets) of six M2Ds at 500 Hz, with three measurement microphone positions designated A, B and C. Figures 5, 6 and 7 show the far field frequency response (one-third octave resolution) at each of these positions.
Note that there is a pronounced high-frequency rolloff that is consistent at all three positions. This characteristic is attributable to the fact that, while points within the coverage area "see" all of the woofers, any particular place in the sound field is covered in large part by only a single high-frequency horn. The degree and shape of the rolloff varies with the amount of splay between the cabinets.
Fig. 4. Curved Array Sound Field at 500 Hz
Fig. 5. Far-Field Frequency Response at Mic Position A
Fig. 6. Far-Field Frequency Response at Mic Position B
Fig. 7. Far-Field Frequency Response at Mic Position C
The array will require equalization to restore a flat response, and the consistency of the rolloff across the sound field indicates that equalization can achieve uniformly flat response. Meyer Sounds MAPP Online incorporates a virtual VX-1 Program Equalizer that can be used, together with array predictions such as those shown here, to determine settings that may then be transferred to a physical VX-1 when the array is installed. This "pre-equalization" facility will assure that, upon installation, the array will afford nominally flat response across its coverage area.
Fig. 8. MAPP Virtual VX-1 Controls
Note: All frequency response examples shown in this paper include air absorption at 20° C, 50% relative humidity and 1013.25 mb barometric pressure. MAPP Online includes environmental controls that allow these settings to be adjusted.