Posted tagged ‘speaker system optimization’

Uncoupled Array Design: Beginnings and Endings (Updated)

March 28, 2010

** Update:  A downloadable version of the calculator to do this work is available (courtesy of Daniel Lundberg). Go to the bottom of this post for preview and instructions. 


When a coupled array is assembled, its operating range is limited primarily by its power capability. Even very large arrays will congeal fairly quickly and once they have joined together let no phase tear them asunder. Wow! Not often that we can work hard-core religion language into speaker array theory (not to say there is not a lot of mysticism out there in line array theory land).  So coupled arrays, once joined, once fully formed will maintain there shape over distance, finally either running (literally) out of air, or into the wall.  

Uncoupled arrays are quite the opposite. They can’t wait to destroy themselves. The battle begins with each speaker owning  its piece or real estate close by, in front of it. As we continue forward we have a happy meeting with the neighboring speaker’s response. They greet with an in-phase handshake and we have a crossover, known as the unity line.  At this point the speakers are working together and the line that runs from speaker center to center (through the crossover) is approximately unity gain. This is exactly what we want to happen – an extended line of unity gain, wider than a single speaker. Ideal for frontfills, underbalconies, parade routes, racetracks and more. This is both a happy beginning AND a happy ending.  How so? The beginning part is obvious, but the ending part…………well what I mean here is that this beginning is the best response we will get. It is all downhill from here as the more distant areas directly in front of each speaker no longer have sole ownership of the coverage. The others speakers are spilling in and they are arriving late. VERY late in acoustic terms. The displacement between the speakers (a factor that is large in an uncoupled array) now creates a very rapidly changing variation of time offsets between the elements. The result is combing that moves rapidly down in frequency and becomes stronger with each step we go deeper into coverage.  

How far can we go before we throw up the white flag and surrender? One could evoke a variety of subjective answers such as: until it sucks, or until I can afford another set of speakers to take over etc., but these are not very satisfying to me. There is a verifiable milestone: three’s company. When we reach the point where the entire length of the coverage line is within the pattern of three sources we have reached full immersion into the combing. Three is a magic number. With three sources arrayed along a line, or an arc it is impossible to find a location that is equidistant to all three. This guarantees two or three arrival times from speakers operating within their coverage  angle. That is the fight I was talking about before. The only way to stop the fight is to drown it out with another much louder speaker – like a mains to take over for your frontfill, or stop it – like a back wall for your underbalconies.  

In my book I go through a set of design calculations for uncoupled line source and point source arrays. The variables are the coverage shape of the speaker (The Forward Aspect Ratio/FAR), the spacing, and the splay angle. From these we can determine where the coverage will start (D unity) and where the coverage should end (D limit). If you know the speaker and where your audience starts, you can determine the spacing, and where you will need to connect to the mains. If you have fixed positions you can get the right speaker model etc.  

An example reference chart using a 80 degree speaker in an uncoupled line source is in the book.  This shows nicely how to solve for this particular model and then one can refer back to the FAR chart to get the angle/FAR conversion for other speakers.  

Uncoupled line source design reference for an 80 degree speaker

Design procedure for the same speakers as above

Another example reference chart uses a 90 degree speaker in an uncoupled point source source in the book.  In this case the splay anglwe variable is added to the equation.  

Design reference for 90 degree speaker in an uncoupled point source array

Design Procedure example for a 90 degree speaker

It is not possible to put an XL file into the book and not practical to give a separate chart for each speaker angle/spacing etc.  but folks that bought the book don’t have a working calculator/spreadsheet that they can go to on their computer so I was in the process of making one for the blog and then Daniel Lundberg contacted me with his calculator based on this same concept. Whereas mine was derived from observing the trends and behiavior of many, many, array interactions, Daniel’s goes to the heart of the trigonometry involved.  

So over the past few days I ran through some different models of speakers athdifferent angles and spacing to check for consistency between a) my published values derived through observation of other speakers at other angles  

b) Daniel Lundberg’s values derived through trigonometry and geometry  

c) what we can see on the MAPP plots now  

The good news is they are all in very close agreement.  The largest discrepancy is in the limit values for the longest range, and even these are relatively close.  

Comparison of observed and mathematically derived values 45 deg speaker with 4m spacing and 0 deg splay 45 deg speaker with 4m spacing and 4.5 deg splay

45 deg speaker with 4m spacing and 9 deg splay 45 deg speaker with 4m spacing and 13.5 deg splay

45 deg speaker with 4m spacing and 18 deg splay

45 deg speaker with 4m spacing and 22.5 deg splay


Here is what the downloadable version of the calculator to do this work looks like (courtesy of Daniel Lundberg). You can have a copy of it. Free. 

HOWEVER, the security rules of this blog host prohibit me from posting an XL file. 

Therefore, if you want a working copy of this calculator, you will need to send me an email request to If you think this is just a trick to get you on my mailing list…………



Breaking the line

January 9, 2010

A friend of mine who is not an audio engineer went to a show and later told me it sounded too loud and was unintelligible. Sound plausible? Sure. Now try this: a friend of mine went to a show and said it sounded like the line of the speakers had been broken. Still sound plausible? No?  I figure everybody knows what this sounds like since it is such a big issue for discussion. Every time I tune a system or hold a seminar someone tells me all the things I can’t do because I will break the line. Whatever you do don’t break the line because it will sound like…………………. Help me out here… sound like what?

The deaf and blind test

I invite you to blindfold me and roll me around the venue. We can listen to pink noise or any music besides Steely Dan. As we move I will use my trained ear to tell you when it gets louder/softer, more reverberant or less, brighter or duller. I can tell you specific peaks and comb filter areas, and even identify transitions between elements of the sound system or the timing and strength of echoes. This is not because I am special – any audio engineer with a trained pair of ears can do this.

Similarly you can stuff my ears and put me in a remote room in front of my FFT analyzer and I will be able to identify all of these same features as you move a measurement mic around the room. Admittedly this is not something everyone can do, but with sufficient training and experience you can. The reason is these are objective, verifiable, audible characteristics of the sound system in the space. A 6 dB level difference between two locations is not a theory – it is true or not true. It can be directly experienced and measured.

The sound of breaking line

Here is what I cannot tell you by either of the above methods: whether or not the line array theory has been violated and the line is broken. When the line breaks do we hear a snap? Does the frequency response show tear marks? These are absurd questions but please tell me: what are the tell-tale signs? Why is there such widespread fear of breaking the line? The best I can figure is that it is the fear of breaking the party line, as much or more than the acoustical line.

There are two principal manifestations of the “Don’t’ break the line” strategy. First is the prohibition of level tapering within a multi-element array. So if it’s 6 dB too loud in the front area (a verifiable fact I can hear and measure) we should not solve this with level tapering because we will break the line (a theoretical construct that I cannot characterize sonically or measure).

The second is the prohibition of spatial separation between sections of an array. So when a balcony depth is more than half the hall depth we should not split the array into upper and lower sections (which would have measurably superior uniformity) but rather keep it together to preserve the line.

Level Tapering

Let’s start with level tapering. Let’s consider a basic arena shape in the vertical plane: Longest throw to the top – shortest to the bottom.  Is the relationship of level taper to line breaking a digital phenomenon? i.e. one or zero? Broken or unbroken? If we have 16 identical boxes in a line and they are run at the same level it is assured that our line is unbroken. If one box is down 0.1 dB is the line broken or just slightly bent? If it is broken already I have bad news: You have never heard an unbroken line, because manufacturing tolerances aren’t that good. How about variations of 1 dB? Again, nobody can deliver you 16 boxes that are within a single dB.  

 Let’s step it up: Turn the bottom box down 6 dB. This makes it effectively half a box. The loss in the lowest frequency range (where directionality is so low and wavelengths so large that they sum well) that the combined response is reduced by less than 0.25 dB. This does not seem so scary for the big picture does it? Let’s go further and reduce 3 boxes by 6 dB. The lowest frequencies now lose 1 dB. The high frequencies meanwhile are substantially reduced in the area where the bottom three boxes are pointed – such as the early rows of seats. This is a tangible benefit (up to 6 dB of HF control) for a minimal cost (1 dB loss in overall LF power).  Is the line broken now? If so, how can I tell? Is it broken everywhere or just at one place. Is it broken at all frequencies?  It should be easy to find the break point at 10 kHz, since there is enough directional control to hear the isolated areas on either side of our fault line. You could find it blind-folded or measure it with an analyzer. Do you think you can identify a break point at 100 Hz? Good luck. These large wavelengths do not turn on a dime. When people talk fretfully of breaking the line is it the VHF range they are worried about? Not from what I hear. The concerns I hear are much more about the lows than the highs.

A practical taper is usually more gradual with 1-3 dB steps being more typical and which makes it difficult to locate the transitions in the space. If we tapered the bottom 5 boxes at 3-3-3-6-6 dB we would get an overall LF loss of 1 dB, and gain substantial HF steering. The same price would be paid for a taper of 1-1-1-1-2-2-4-4 dB on the bottom 8 boxes of our 16 element array. These are just two of a myriad of options that can be employed to help tailor the response of our bent/broken system to the shape of the audience.

To offset the un-characterizable, un-measurable theoretical problems this tapering will cause there are additional benefits: besides increasing front-back level uniformity in the HF range it also improves uniformity (to a lesser extent) as frequency falls – all the way down. The dB that we lose in the low end is offset by the fact that the beam center is steered upward off the floor and therefore spread more evenly front to back. (This is covered extensively in the book Sound Systems: Design & Optimization.)

Many experienced engineers have espoused to me the perils of breaking the line. Yet all strive for front/back level uniformity. There is a limit to how much we can squeeze these systems by splay angle asymmetry alone. Once that option has been exhausted and the cluster ain’t coming back down we need to look at how much level disparity is still left. If it’s too loud in front, I vote we break the line and turn down the lower boxes. If you have a better measurable, verifiable method, I would love to hear it.

Theory world

One funny historical aspect related to this subject: 25 years ago when we started bringing FFT analyzers in to tune sound systems, many engineers would deride us. They resisted our use of an analyzer to help make decisions, saying we lived in “theory-world” and that they lived in the “real-world”. Nowadays some engineers still want to limit the actions we perform based on the analyzer but now the problem is that I live in the “real world” and they are in the “theory world.”  Funny that one eh?

We will save the balcony battles for another day……………

Line Array Tuning

January 6, 2010

I’ve opened a new page on line array tuning entitled

“The ABC’s of Line Array Tuning”   you can find it in the tab at the upper right corner.

Comments welcome