LINE ARRAYS CONCEPTS AND MODELING TOOLS Jeff Berryman May 29, 2010 / Rev. 1 A lne array s a stack of loudspeaker systems n a sngle lne. The lne s usually curved. Uncurved lnes do not have desrable drectonal patterns for most applcatons. Fgure 1. Lne array Most lne arrays are orented vertcally, although horzontal lne arrays are commonly used for subbass. For a vertcal lne array, the curvature and length of the array combne to determne the drectonal pattern of the array n the vertcal plane. In contrast, drectvty n the horzontal plane depends manly on the propertes of the ndvdual loudspeaker boxes and not on the geometry of the array. In a basc vertcal lne array applcaton, two curved vertcal lne arrays are hung from the celng -- one on each sde of the stage. In more ambtous applcatons, addtonal arrays ("sde arrays") may be deployed pontng offstage, to cover seats to the far left and rght. Ths technque s normally used for large arenas. Fgure 2. Lne array system n arena, showng vertcal front and sde arrays, stage, and horzontal subwoofer arrays stacked on floor
ACOUSTICS For a lne array loudspeaker system to work properly, the sound waves t emts must be formed n a partcular way so as to combne properly wth the emtted sound waves of the other loudspeaker systems n the array. Smply arrangng conventonal loudspeakers nto a lne would create a lne array, but one that would not work at all well over the whole frequency range. A key element of lne array desgn and use s the selecton of what s called the "array face curve". The face curve s the lne connectng the centers of the front faces of the boxes when they are confgured nto an array. The angle between boxes s adjustable; thus, a large varety of face curves may be constructed. The shape and scale of the array's face curve determne ts vertcal drectonal pattern. The goal s to choose a face curve that yelds a drectonal pattern whch provdes a unform sound level at all lstenng postons. For ths to occur, the array must compensate for dstance by drectng more sound to dstant postons, less sound to nearer postons. Selecton of the proper set of nterbox angles for a partcular stuaton s a relatvely complex task. The complexty arses manly because sound does not behave lke lght -- one cannot smply pont a loudspeaker lke a flashlght and have ts sound go only to the desred place. The drectonal pattern of an array s a complex functon of ts shape and sze, and of sgnal frequency. For ths reason, t has become standard practce n the sound renforcement ndustry to use computerzed acoustcal modelng tools to predct and optmze the drectonal propertes of lne arrays n stu. By usng these tools properly, the sound system desgner can determne the optmum array geometry specfcally for the venue of nterest. The resultng specfcaton s then used to erect the array. A bref ntroducton to array modelng physcs s n Appendx A, below. MECHANICS In typcal nstallatons, a lne array may wegh from 100 to 1500 kg or more, and be hung 15m or more above the venue floor. Usually, there are people underneath -- audence, performers, and/or crew. The arrays must be hung at precse heghts and tlted at precse angles. In tourng applcatons, array setup and teardown must be qute rapd - for average shows, 1.5 hours or less. For these reasons, mechancal rggng s a sgnfcant challenge, not only because of lfe safety, but also n the nterests of postonal accuracy, setup/teardown effcency, and general ease of use. In ths area, array desgn software must nclude functons to ensure that no array desgn exceeds workng load lmts or volates other mechancal constrants of the products nvolved. SOFTWARE Background Commercal lne array modelng software was frst felded n the late 1990's, and untl recently has evolved farly slowly. The software was typcally developed by the loudspeaker manufacturers and contrbuted to the communty at no cost. Most of t was Excel-based, usually wth addtonal VBA functonalty added. The models used were 2D (.e. planar) models that dsplayed smple XY graphs showng drectvty and coverage n the vertcal plane. They predcted only the drect sound feld due to the lne arrays, and dd not take reflectons, reverberaton, or absorpton nto account. 2
A few more advanced 2D modelers were offered; these were standalone programs (.e. they were not spreadsheet-based) and used more advanced graphcs -- typcally false-color plots of delvered sound level n the venue. For serous acoustc desgn, thrd-party 3D modelers were (and are) offered. These modelers are not wrtten by loudspeaker companes, are relatvely complex to use, and are expensve. They are engneerng software, not end-user tools. The man contenders n ths category are EASE and CATTacoustc. Today Today, manufacturer-suppled array desgn software s evolvng. Although many of the spreadsheetbased products (ncludng EV's LAPS II and EVADA) are stll avalable, many manufacturers are delverng or thnkng about newer optons, most of whch nvolve 3D or quas-3d modelng and user nterfaces. The leader n ths area s L-Acoustcs, the French company that felded lne arrays fst, n the md- 1990's. The new L-Acoustcs modeler, called "Soundvson", offers an attractve 3D nterface wth clever features for quck sketchng of typcal venue shapes, an evolvng database of pre-entered dmensons for well-known venues, and other features. We do not know f Soundvson contans a true 3D modeler (we suspect t may not), but t s nevertheless an appealng product. In a departure from prevous practce, Soundvson s not free. However, the prce s not hgh --125 one-tme. Another development s the emergence of OEM-frendly thrd-party modelers. Software Desgn Ahnert (SDA) now offers EASE Focus, a generc lne array modeler that can be customzed to accommodate dfferent product lnes. EASE Focus s a 2D modeler wth a relatvely attractve nterface that s stll evolvng. It offers convenent compatblty features wth EASE (another SDA product), the fullfuncton engneerng modeler mentoned above. An emergng queston for end-user array desgn software s that of platform. To date, array desgn software has been offered for Wndows and (sometmes) Macntosh platforms. However, wth the emergence of hgh-qualty PDA and tablet platforms, t wll not be long before users wll want handheld modelers -- partcularly n the tourng market. LAPS II and EVADA In the current market, EV's LAPS II and EVADA stand as relatvely well-evolved products, but are obvously agng. Acoustcally, ther 2D modelng s accurate, and they do a good job of supportng the acoustcal and mechancal propertes of all EV lne array product famles. However, ther user nterfaces are not partcularly attractve, and ther general level of nteractvty s prmtve by today's standards. Other than addng support for new products, t wll not be practcal to evolve the current LAPS II and EVADA products much more. 3
Appendx A: Array Acoustcs and Modelng We calculate the sound pressure produced by a lne array at a gven lstenng pont. Fgure 3. Sound pressure at lstenng pont The pressure s gven by the followng formula: p s e r kr where p = total complex sound pressure at gven lstenng pont e = base of natural logarthms = 2.71828... = -1 2π speed of sound k = ( λ = wavelength = ) λ frequency th s = complex ampltude of sound output of pont on face curve th r = dstance from pont on face curve to lstener Summaton s for all ponts on array face curve. Number of ponts on face curve s chosen so that adjacent ponts are less than λ/4 at the hghest frequency of nterest. For f = 20kHz, ths value s approxmately 0.35". 4
As long as the face curve ponts are correctly specfed, ths formula s accurate for all array szes and curvatures, and for all lstenng postons. In fact, t s accurate for any sound source that can be characterzed by a collecton of closely-spaced ponts. Ths s a relatvely smple formula. The man challenges for wrters of modelng software are: 1. Ensurng that the face curve array s correctly specfed. A major hurdle n ths respect s the ncluson of cabnet effects. Cabnet effects can be characterzed by addng addtonal ponts to the face curve array. These ponts need to have partcular ampltudes and phases that are not easy to compute. Most smple modelers gnore cabnet effects. The prmary effect of dong so s that the model results wll be naccurate for radaton angles that are far off axs (e.g. behnd the array). 2. Computng ths formula by brute force n 3D for all potental lstenng ponts n the venue s too compute-ntensve for ordnary hardware. In 2D, the problem s tractable, but n 3D, more sophstcated algorthms are requred to acheve acceptable compute tmes on normal personal computer hardware. EV LAPS II and EVADA are brute-force 2D modelers that gnore cabnet effects. We do not know how compettve programs operate, but we beleve that LAPS II's modelng s at least as accurate as any of the other programs of ts type. Another modelng approach s taken by such programs as Meyer MAPP. Ths approach uses measured drectonal pattern and frequency response data (aka "balloon" data because of the way t's often plotted usng 3D polar graphs) for the ndvdual boxes of the lne array. In use, the user descrbes to the modeler how the boxes are arranged n the array, and the modeler smply adds up the balloon data for all the boxes, takng care to account for phase and ampltude changes caused by the respectve poston of each box. Ths method can be qute accurate, but t s compute-ntensve. Meyer says they collect 1 ggabyte of balloon data per loudspeaker model, and the summaton s done on a small supercomputer of some knd, on the network. 5