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Array/Room Modeling & Control, Part 2

David Kennedy • June 2019Tech Feature • June 17, 2019

Modeling & Set-up of Directional Sub Arrays…

In last month’s FRONT of HOUSE (May 2019, page 36) we discussed and compared five types of cardioid/directional sub arrays that have been in use for several years. By building and implementing increasingly directional sub arrays, sound energy can be reduced on the stage, ceiling and walls and focused on the audience, where it works better, sounding more direct/intimate and full of impact.

MAPP model of a classic/generic omnidirectional sub array

‡‡         Five VLF Arrays, Compared

Let’s examine direct-field coverage of four alternatives to the classic configuration seen above. The five coverage graphics (pressure maps) were provided by Bob McCarthy of Meyer Sound. The sample sub-arrays shown have a similar number of sub boxes/drivers, modeled in Meyer Sound MAPP and are shown with approximately the same 30 dB default scale and frequency.

Fig. 1 – MAPP model of a broadside array at 63 Hz

Broadside Arrays have woofers arranged in a row with the primary radiation at a right angle to the array/row. This has been a typical sub-array configuration, seen many times, in a horizontal row/line across the front of a stage (see Fig. 1). Note that with such a long sub-array, the coverage is too narrow — not omnidirectional at 63 Hz (as a typical small sub array would be); also note that there is far too much sub energy on the stage.

Fig. 2 – MAPP model of a beamforming array at 63 Hz

Beamforming delays can be applied to an in-line sub array to change the pattern width (or tilt the pattern of a vertical array down into the seating area). Beamforming delays in a horizontal sub line are applied with gradual tapering, equally to each end of the array (see Fig. 2). Note that even with the same long sub array, the coverage is a much better fit for the venue, when subs are delayed at each end of the array.

Fig. 3 – MAPP model of gradient array at 63 Hz

Fig. 4 – A gradient sub array comprised of three Meyer Sound 1100LFCs. Note the center box is reversed

Cardioid/gradient arrays are great for moderately sized venues, but as they are less efficient (see last month’s article for more details/options), they have a reduced maximum sound level — as needed for very large and outdoor venues. The coverage comparison, in the sample venue, shows the cardioid/gradient array has maximum cancelation upstage; more ideal coverage if all of the audience is in front of the stage — sounding more direct/intimate — but may not be the best sub array in this sample venue (see Fig. 3 & 4).

Fig. 5 – MAPP model of end-fire array at 63Hz

Fig. 6 – Bose MB24 WR mini end-fire bass-array

End-fire sub arrays have been less common, but they are very useful in long-throw applications such as very large and outdoor venues. Beamwidth can be varied to suit the seating area and can now be visualized in several modeling/mapping programs. An end-fire sub-array in the sample venue shows less cancelation onstage, but has higher maximum SPL, and better impact than a gradient array with the same number and type of subwoofers (see Fig. 5 & 6).

Polar plots of three different subwoofer arrays. Note that directionality increases at higher frequencies

Programs did not offer coverage modeling at very-low frequencies until more recently. Many years ago, E-V offered ArrayShow, a full-range array polar-plot simulation program, so that array engineers could estimate array effects on 3D polar plots; examples are shown in the Case Study section below (and in graphic above) with the interaction and polar summation of multiple-measured LF drivers in an array. It is now also possible to model the direct sound for cardioid sub arrays in many programs. But, due to lack of acoustical data at very-low frequencies, room modeling is not typically possible with subs.

While not an exhaustive tutorial, I will touch on some of the important issues associated with modeling sub arrays. I usually spend most of the modeling time near the center of the sub bandpass, about 63 Hz. Based on that center frequency (and the long/associated wavelength), the subwoofer drivers in an end-fire array should be spaced three to four feet apart, times at least three to four woofers and amplifier channels, aligned like train cars (as seen in the “Case Study” sidebar, and the Bose MB24 WR mini end-fire bass-array pictured above).

‡‡         Advice on Setting Up Cardioid/Gradient and End-Fire Sub Arrays

“If a cardioid sub setup is working correctly, it will cancel (have a notch) directly behind the rear subwoofer,” explains James Rush, primary systems engineer, JBL Professional. “Think about it in terms of transfer functions to a location behind the rear sub: The front sub has some transfer function due to its acoustic response EQ and the diffracted air path to the rear of the rear sub. The rear sub (with its position and delay) has a different transfer function. So, the trick is to just adjust the delay and level until you have an excellent notch — behind the rear sub at some frequency, say 50 Hz. This is usually what you want to do — attempting to cancel the rear bass output so the poor players on stage are not getting overwhelmed. In order to do this properly, you must be able to measure the outputs from each sub (amplitude and phase), and find the delay and level settings that put the two subs 180-degrees out of phase [out of polarity] and equal amplitude. This will create the notch. What is not so clear is that you will not be able to maintain that condition over a large frequency range.”

Several manufacturers provide DSP presets for creating cardioid and end-fire arrays using their subs. There are also some single-driver active subs that have a cardioid preset in the built-in amplifier, which requires using at least one additional powered sub to create a simple cardioid sub array, without knowing everything about array theory (or measurement). For most users, the easiest option comes from brand-name one-box active cardioid subs with containing two or three woofers, and these are available in a variety of driver sizes and quantities.

By building more directional sub arrays, sound energy can be reduced on the stage, ceiling and walls; and focused on the audience, where it works better (sounding more intimate). This directional/focused approach has been well-known by leading P.A. system designers for decades; but more advanced tools are now available. These more directional VLF (very-low-frequency) arrays require more signal processing, amplifier channels and planning to implement, but the benefit can be about 20 dB less VLF energy where it isn’t wanted.

‡‡         Benefits of Directional Sub Arrays

Among these advantages are:

  • Improved low-frequency gain-before-feedback
  • Higher direct-to-reverberant ratio in venue seating areas
  • Less annoyance for onstage musicians and bystanders
  • Reduced loudspeaker array sound arriving at broadcast mics
  • Smaller cardioid arrays with more stable polar patterns
  • End-fire arrays with increased sound/transient impact over greater distances
  • Improved LF projection into large and reverberant spaces

Of course, the choice between the type of subwoofer arrays depends on the available space, desired SPL, directivity, amplifier channels and system budget, but whether using the DIY route or pre-manufactured solutions, directional LF arrays are an important tool in any modern sound system.

CASE STUDY: End-fire vs. Gradient Cardioid Sub Array Polar Plots

Fig. 8 – Custom-install tapered end-fire type main and sub arrays. Image: David Kennedy

FIG. 9: Polar plots of three different subwoofer arrays. Note that directionality increases at higher frequencies

Fig. 8 (above Fig. 9) shows the author’s custom-install tapered end-fire type main and sub arrays. Shown in Fig. 9 are three sets of three simulated polar plots, exported from ArrayShow. The top set of plots show a nearly uniform set of cardioid-shaped plots from a unique gradient-type sub array using four single-18 subwoofers (but polar plots don’t show SPL and transient limitations). The two stacked-pair sub array narrows coverage/dispersion slightly in the vertical plane at 80 Hz and adds 6 dB of headroom. The popular cardioid plots show only about 8 dB of attenuation 90° off-axis, but it does show a superior 30 dB of attenuation 180° off-axis (rear). The desired polar shape depends on the location of the subs and the microphones.

Shown farther below are polar plots, showing less-consistent sets of polar plots from two end-fire arrays (not showing higher SPLs and better and transients). The sub polar plot simulations below show how my unique, tapered-SPL 4-delay/pole end-fire subwoofer array design maintains off-axis polars/directivity all the way down to 50 Hz, showing a superior 15-20 dB attenuation at 90 Hz, as compared to the less consistent polar plots for a 3-pole sub array shown underneath (only -10 dB at 50 Hz). This special 4-pole end-fire sub array can be built from only two of my unique two-pole subs (with different sub drivers at each end). Four conventional dual-18 subs would be needed to provide this same sub array max SPL and performance. If less max SPL is enough, as few as four woofers (of adequate size and power) can be used with basically the same polar performance.

Thanks to Frank Ward (the project contractor) for input on this end-fire sub array design, and the client: New Hope SDA Church, Fulton, MD.

Q&A: Modeling Cardioid Subwoofer Arrays

We posed a number of questions (and elicited comments) regarding sub arrays to a number of industry experts. They included former EAW designer David Gunness, now of Fulcrum Audio; Sam Berkow, founder of SIA Acoustics; Bob McCarthy of Meyer Sound Labs; Rocky Giannetta, president, Layer 8; and Thomas Ryan, principal acoustic consultant of Technological Design Studios.

What modeling/simulation software programs can create very-low-frequency (VLF) 3D polars of CSAs?

David Gunness: EASE Focus, MAPP, EAW Resolution, COMSOL.

Does CSA modeling software consider the actual acoustic center? How is this provided for band-pass, bass/tapped horn or vented subs?

Rocky Giannetta: I would ask is why consideration is there for the actual acoustic center, and specifically how is this provided for vented enclosures. There has to be some consideration for the physical enclosures, which I’m not sure is available in the modeling programs. I’ve not deployed any directional subwoofer arrays I didn’t measure first, or that were designed by the manufacturer. I’ve found that the simple math of 1/4λ [Note: λ = wavelength — Ed.] spacing and 1/4λ delay + polarity inversion of rear racing or spaced subwoofer doesn’t necessarily yield the expected results.

Does modeling software consider the path length around the CSA enclosures or the extended baffling of additional sub boxes in large arrays?

David Gunness: Audio industry software does not. FEA programs like COMSOL do.

How low in frequency does modeling/simulation software perform calculations of CSAs?

David Gunness: EASE currently only goes to 100 Hz. EASE Focus goes lower. Most 3-D modeling packages will model whatever frequency you want. [But not VLF room calculations.]

Thomas Ryan: Whether beam, ray, cone or hybrid tracing methods are used, predictions below 125 Hz are inaccurate. Below this transition region (the Schroder frequency) wave behavior dominates in a room. In medium to large rooms, this transition frequency can be anywhere from below 50 Hz to over 100 Hz. This of course is where sub-bass room modeling is needed. Another limiting factor is, per ASTM C423, construction and acoustic treatment materials are tested for absorption characteristics from 100 — 5,000 Hz using random incidence, diffuse noise. In a real room, sound is anything but random or diffuse and, depending on the room geometry, can strike room surfaces at shallow angles. This can literally turn absorptive materials into reflectors.

How is CSA modeling affected by room boundaries? How close can CSAs be to the stage/walls?

Rocky Giannetta: One benefit of these (CSA) directional arrays is to avoid boundaries behind the array, but what about boundaries spaced above the array?

David Gunness: Most people use modeling software to assess direct field coverage, without considering reflections off of boundaries. Nearby walls definitely affect the directional response of arrays, but there is no blanket statement to be made about how close is OK. It depends on the type of array, its size, the frequency range, and the objectives of the design. In some cases, the contribution of a wall might be helpful.

Sam Berkow: This is a killer point! Much as how EASE and other modeling programs do not truly consider reflections in sound system dispersion mapping, models and reflections are generally NOT considered in CSA maps.

Do any modeling/prediction programs have advanced features to improve accuracy at VLFs?

David Gunness: I’m not aware of any.

Is VLF (very-low-frequency) wave modeling much more accurate (and computationally heavy) than modeling with geometric acoustics?

David Gunness: Assuming you’re referring to finite element analysis (FEA) and boundary element analysis (BEA), they’re more accurate and the calculations are thousands of times more expensive; but in many cases it doesn’t matter. What is more important is that it may take days to create a good FEA model, while a model for geometric acoustical analysis may only take minutes.

Are there any studies of modeling/sim. software showing correlation between predicted and measured CSA room coverage of VLF?

David Gunness: Many practitioners have tried to close the loop by verifying their predictions with field measurements. Some have published their results. Generally, this is only viable outdoors, due to room acoustics that weren’t considered in the model.

Sam Berkow: We did a serious measurement study of the system at Pier 17 NYC as it is a very complex and large EAW Adaptive system intended to control LF dispersion away from nearby residences. It was very accurate — to about 63 Hz.

Gradient CSAs have reduced output as frequency lowers (compared to end-fire or VLF line- arrays w/same number of boxes) — so where does this reduced output go?

David Gunness: It doesn’t go anywhere — it just doesn’t happen. When two sources cancel, it looks to each of the sources like the acoustical radiation impedance is lower.

Modeling of sub arrays does not take into account all of the actual sound-wave path-lengths and boundary conditions in the field…

Bob McCarthy: There is a particular cardioid array configuration that requires special attention, due to fact that the prediction program does not include multiple enclosure baffle effects in its calculus: the gradient inverted stack. The delay value that achieves maximum rearward cancellation is affected by the added distance the sound must travel around the array. Therefore, the actual field values are slightly longer than those that show the best cancellation in MAPP, which does not account for the wraparound path. So, either use proven factory DSP ‘presets’ or confirm the delay values with field measurements!

Thomas Ryan: While the audio system designer is primarily concerned with loudspeaker interaction and pattern control, acousticians must make the complete audio system work within the confines of the physical room. This includes all the challenges of the reverberant field, background noise and sound transfer in and out of the room. Therefore, close collaboration between the system designer and acoustic engineer is crucial for a successful project.

System design tools available to the audio designer allow modeling of the broadband and sub-bass loudspeaker dispersion patterns, but only look at the direct field without any room interaction. These are very helpful to the design process, but must be used carefully when the project is indoors. Common room modeling tools such as Odeon, EASE/AURA, CATT and OTL share one thing in common, inaccuracy at low frequencies and no low frequency estimations below 100-125 Hz.

David Kennedy operates David Kennedy Associates, specializing in the design of architectural acoustics, AV systems and custom loudspeaker arrays. Since 1980, he has designed more than 300 auditorium sound systems. Visit him at


Step-By-Step: Phase-Aligning Cardioid Arrays*

By Bob McCarthy

*This is adapted from Sound Systems: Design and Optimization: Modern Techniques and Tools for Sound System Design and Alignment (used with permission).

The 2-Element Array

The 2-Element Array


  • Speaker Elements: FRONT (+) and REAR (-)
  • Processing: 2 channels (+ and -) for polarity and phase (+ and -) adjustment
  • Mic #1 (REAR): On-axis to the front/back line of the array. (1m to 2m behind rear speaker is typical but distance is not critical.) Ground plane OK.
  • Mic #2 (FRONT): This is optional for verification. Tuning is done at rear. 1m to 2m ahead of front speaker is typical, on same axis as the speaker.


  1. @REAR: Store phase response of Front (solo)
  2. @REAR: Mute Front and measure phase response of Rear (solo)
  3. @REAR: Adjust delay on Rear until its phase response matches Front solo
  4. @REAR: Reverse polarity of Rear channel (phase is 180° from Front solo)
  5. @REAR: Combine Front + Rear and verify cancellation
  6. @FRONT: Store both solo responses (with delay settings)
  7. @FRONT: Combine Front + Rear and observe

Outcomes and Actions

  • PASS @ REAR: Alignment is optimized when rejection in rear is maximized.
  • PASS/FAIL: Combined level @ Front should be about 20 dB above REAR, but may show less if mics are close-in. If unsure, move mics farther away and compare.
  • FAIL @ FRONT: If the phase response @ FX reach 360° then spacing is too high. Consider spacing reduction and restart procedure.

The Standard 4-Element End-Fire Array

The Standard 4-Element End-Fire Array


  • Speaker Elements: A (at rear); B, C, D (front)
  • Processing: 4 channels (A,B,C,D) for phase adjustment
  • Mic #1 (FRONT): On-axis to the front/back line of the array. (1m to 2m behind rear speaker is typical but distance is not critical.) Ground plane OK.
  • Mic #2 (REAR): This is optional for verification. Tuning is done in front. 1m to 2m behind rear speaker is typical, on same axis as the speakers.


  1. @FRONT: Store phase response of A (rear speaker), (solo)
  2. @FRONT: Mute A and measure phase response of B (solo)
  3. @FRONT: Adjust delay on B until its phase response matches A solo
  4. @FRONT: Repeat steps 2 and 3 for C and D solo and set delays
  5. @FRONT: Combine A+B+C+D. Verify unchanged phase and added level
  6. @REAR: Store A,B,C,D solo responses (with delay settings)
  7. @REAR: Combine A,B,C,D and observe

Outcomes and Actions

  • PASS @ FRONT: Alignment is optimized when coupling is maximized.
  • PASS/FAIL: Combined level @ FRONT should be about 20 dB above REAR, but may show less if mics are close-in. If unsure, move mics farther away and compare.
  • FAIL: If incremental delays between ABCD are >3 ms, then reduce spacing and restart
  • PASS: Delay is optimized when the arrivals match and coupling extends full range


Cardioid Subwoofer Array Theory

By Phil Graham

To recap cardioid subwoofer array theory, here are some guiding principles from a previous FRONT of HOUSE article by Phil Graham.

• Subwoofers aren’t very directional, so whether you’re standing in front of one or behind one, their response is similar. Turning a sub around backwards is simply a way to produce physical separation in space between the drivers.

• To produce directional response from a subwoofer array, you must physically space the boxes in some fashion. Only then can you delay certain boxes, change levels, and sometimes switch polarity. The core of directional control is physical spacing of the cabinets followed by signal processing; this processing will be delay at a minimum, and sometimes also changes in level and polarity.

• The larger an array is physically in any given direction, the more inherent directivity it has in that direction. A long line of subwoofers (e.g. stacked along the entire stage front), with no further processing, will have a more narrow and concentrated response in the direction where the line is long (i.e., perpendicular to the stage). Sometimes this is a desirable effect, like when two stages are adjacent and you are trying to minimize the spill between them. It can also be a disadvantage in a situation where the coverage area is much wider than the stage width.

• While directional subwoofer arrays are normally designed to have narrow directivity, one can use processing to broaden the coverage of an array that is large in one particular direction.

• Control of the array can be influenced in each of the three dimensions by different array sizes and placements in each dimension. For instance, if an array is large horizontally, but small vertically, it will have narrower coverage in the horizontal and broader coverage in the vertical.

• Design of these arrays necessitates the availability of additional DSP, and amplifier channels, as each component of the array requires specific processing for the directional control to work properly.

• Directional control is most effective in the “far field,” which means at a distance far enough where the loudspeakers are similar in level to each other. If you stand very near the array, so the volume is dominated by a specific loudspeaker, then the array’s directivity control will be found less effective.

• Simple arrays, like cardioid and end-fire, can be set up (and visualized) without array modeling software, but more complicated arrays, with directivity in multiple directions, are best predicted in software before implementing them in the field.

• Arrays need some space surrounding them to allow for the sound from each speaker to interact. One rule of thumb is to keep cardioid subs at least one meter away from any solid boundary.




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