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Ease address formulas
PostPosted: Thu Jun 30, 2011 12:37 pm Reply with quote
Predrag
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Joined: 26 May 2011
Posts: 11




Dear Sir,
I work as a design engineer for telecommunication installation in buildings, hotels etc.
For a long period of time I am trying to figure out how to mathematically determine ceiling speaker coverage area and number of speakers in distributed ceiling speaker design in a manner to be in correlation with the data produced by your software (Ease Address). For example:
• Room dimensions: 13m x 6m x 3m (WxDxH),
• Ceiling speaker:
BOSCH LBC 3086/41,
SPL 6W/1W (at 1kHz/4kHz) 98/90 dB,
Opening angle: (at 1kHz/4kHz, -6dB) 180o/50o,
Tap: 3W
• Software adjustment:
Overlap type: Minimum overlap,
Type: Direct SPL,
Frequency: 4000Hz,
Bandwidth: 1 octave.
Layout type: Square
Formula used for calculations (source book „Sound System Engineering“ by DON DAVIS):
Speaker distance:
S=sqrt(2)*(h-l)*tan(coverage angle/2)
Where:
h – room height in meters,
l – ear height (1,7m),
coverage angle – speaker coverage angle at 4kHz,
Number of speakers:
N= (X*Y)/(2*((h-l)*tan(coverage angle/2))2)
Where:
X – room width in m,
Y – room depth in m.
Here are the results:
Ease Address:
1) Speaker distance: 1.2m,
2) Number of speakers: 55.
My calculations:
1) Speaker distance: 0.85m,
2) Number of speakers: 106,13..

I don’t know where the problem is. Please help me?
But the most important thing to know is which formulas you use in Ease Address:
1) To determine speaker distance and
2) To determine level variation due the layout pattern,

Thank you
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PostPosted: Tue Jul 05, 2011 3:08 am Reply with quote
Bruce
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Joined: 19 Apr 2005
Posts: 430
Location: Minneapolis, MN, USA




It depends on the Rated Coverage Angle declared by the manufacturer in their GLL data. They may have entered a different value than that shown for the 4 kHz used by SSE. You should contact them as indicated in the Info dialog box for the GLL to find out what value they used. On my copy it looks like they refer you to your local distributer listed on their website at www.boschsecurity.com.

That is for the value used to determine the speaker density, and is represented by the circle around the speaker in EASE Address. The actual coverage is determined by using the balloon data included in the GLL file and is also frequency dependent. So, the first is used as an approximate layout tool dependent on what value was used for the Rated Angle. The actual data for the coverage gives you the real overlap with respect to frequency.

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Best Regards,
Bruce C. Olson
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PostPosted: Tue Jul 05, 2011 7:09 am Reply with quote
Predrag
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Joined: 26 May 2011
Posts: 11




Thank you for reply, but the same problem with coverage angle appear with speakers from other manufactures (Electro Voice, Tannoy etc.).

Also you didn't answer second part of my question about formulas. If I know the equation you use in the program Ease Address, maybe I can figure out by myself where the problem is.

Thanks again for replay,
Predrag
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PostPosted: Fri Jul 08, 2011 12:22 am Reply with quote
Greg L
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Joined: 01 Dec 2009
Posts: 7
Location: Minneapolis, MN




Predrag,

Good day.

1. Notice the sqrt(2) in the formula you listed.

2. Notice the (almost) factor of two difference in the two predictions as to the number of speakers. sqrt(2)^2 = 2.

3. In the below image, notice the overlap from the book's suggested spacing (left 4 circles.) On the diagonal between four speakers, the listener will hear four speakers, each 6 dB down.

4. The ceiling to listener height difference (1.2 vs 0.85) implies something is amiss beyond how one defines 'Minimum overlap.'

I don't use EASE Address, what terminoloy to use for circular speakers arranged in a square pattern is possibly part of the problem <bg>

Greg

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PostPosted: Fri Jul 08, 2011 7:13 am Reply with quote
Predrag
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Joined: 26 May 2011
Posts: 11




Hi Greg,
Thanks for reply,
Correct formula for the number of speakers is:

N=x*y/S^2 = x*y/((sqrt(2)*(h-l)*tan(coverage angle/2))^2

And finally:

N=x*y/(2((h-l)*tan(coverage angle/2))^2)

Mentioned difference (1.2 vs. 0.85) is not a ceiling height/listener height difference. It is difference in ceiling speaker spacing.

Ease Address calculated that the distance between speakers (for minimum overlap pattern) is 1,2m, and I calculated, from stated equations, spacing of 0,85m.

I still can't figure out how they do it in Ease Address?

Greg I appreciate your comment and thanks again.

Predrag
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PostPosted: Fri Jul 08, 2011 2:13 pm Reply with quote
Greg L
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Joined: 01 Dec 2009
Posts: 7
Location: Minneapolis, MN




Predrag,

Okay, maybe I should have been clearer. I assumed the ^2 at the end of the equation. Misread what you said about spacing vs distance.

0.6 = tan(25) * (3 - 1.7) this is the radius of the 'coverage' circle in the listener plane.

1.2 = 0.6 * 2 EASE Address spacing

0.86 = 0.6 * sqrt(2) Book spacing

Or, another way, 1.2 = 0.86 * sqrt(2)

This is shown in the diagram, left four circles are book, right four are Address.

Greg
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PostPosted: Mon Jul 11, 2011 7:17 am Reply with quote
Predrag
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Joined: 26 May 2011
Posts: 11




Hi Greg,
The picture from Ease Address (with input data the same as in my post: Bosch speaker, room: 13x6x3m, layout pattern: minimum overlap) show that layout pattern of the coverage circle in the listener plane, is indeed the minimum overlap. For the layout edge-to-edge (right four circles from your drawing) EASE calculated distance between speakers: 1,7m.
So I still think that the equations I use are different than the one they use. But it seems that equations are top secret.

No one from AFMG support team is willing to share them with us ordinary people.
Predrag
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PostPosted: Mon Jul 11, 2011 10:39 pm Reply with quote
Greg L
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Joined: 01 Dec 2009
Posts: 7
Location: Minneapolis, MN




Predrag,

>So I still think that the equations I use are different than the one they use.

Are you referring to the ‘book’ equations? I believe I showed what those were calculating. They will result in a rather large peak in the center of the four speakers.

I suspect AFMG’s formulas are rather complicated, as their frequency directional data is much more involved than the data on a manufacturers’ data sheet. There is also the issue of how to mathematically define what is optimal response in an area, given a frequency bandwidth.

For instance, what if one response is perfectly even, except a small area where it is +9dB, and another response is also perfectly even, except a larger area that is +6dB? Which is better? The same issue exists in the frequency domain. Also, as I assume you know, optimizing spacing for ‘X’ frequency, may result in overlapped coverage in a lower frequency.

With so many variables / dimensions, software cannot ‘automate’ all of your design decisions. Hence, you have to decide, with measurements, listening, or experience, what works best for your requirements.


> But it seems that equations are top secret.
> No one from AFMG support team is willing to share them with us ordinary people.

If you’re looking for a simple equation to define a magical spacing distance, maybe this is the wrong place. BTW, bashing AFMG in an AMFG forum is probably unproductive.

Greg
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PostPosted: Wed Jul 13, 2011 11:15 am Reply with quote
Predrag
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Joined: 26 May 2011
Posts: 11




Greg,

>Are you referring to the ‘book’ equations? I believe I showed what those were calculating. They will result in a rather large peak in the center of the four speakers.

I will repeat: You show on the right side of your drawing four 6dB circles in edge to edge configuration, and for that configuration EASE calculated as you said "magical spacing distance" of 1,7m (you calculated 1,2m).
Sorry that I can't post picture form software where you can clearly see this.

From the information I received from AFMG, they use speaker coverage area at 1000Hz, and circles shown on room layout window (in EASE) are - 6dB coverage cones (independently on the frequency or bandwidth you use).
So layout of coverage cones (6dB) is matching the ones from book but the results don't?

Anyway you said once that you don't use EASE Address, so have you any advice how to determine speaker distance, level variation due to speaker layout pattern and required number of speakers in the design phase, when object is in the architectural design phase?
It would be very helpful if you could provide some mathematical calculation too!

Thanks,
Predrag

P.S. It is a little bit annoying when you try to mathematically confirm results given by many programs(TOA Speaker placement Viewer, JBL Distributed System Design, EV Ceiling Speaker Placement Calculator etc.) and always fail in those attempts.
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PostPosted: Wed Jul 13, 2011 4:09 pm Reply with quote
Greg L
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Joined: 01 Dec 2009
Posts: 7
Location: Minneapolis, MN




Predrag,

> So layout of coverage cones (6dB) is matching the ones from book but the results don't?

Okay, the two examples you compared, 'book' and 'AFMG' vary in their center to center spacing. Given the criteria, 'AFMG' suggested a spacing of 2 * radius, which is the right four circles. The 'book' suggested a spacing of sqrt(2) * radius, which is the left four circles.

I have all of AFMG's software *except* EASE Address. I suppose I could dl it. If you'd like to PM me, I'm Greg @ (the domain of the image).

What is the correct spacing given that all normal 'overhead' speakers have directional characteristics that vary with frequency? Each program may define that differently, and hence, recommend different spacing.

Greg
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PostPosted: Mon Jul 18, 2011 11:35 pm Reply with quote
Bruce
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Joined: 19 Apr 2005
Posts: 430
Location: Minneapolis, MN, USA




Predrag wrote:
Thank you for reply, but the same problem with coverage angle appear with speakers from other manufactures (Electro Voice, Tannoy etc.).

Also you didn't answer second part of my question about formulas. If I know the equation you use in the program Ease Address, maybe I can figure out by myself where the problem is.


Let me restate the answer in a different way then. It appears by simple inspection that they use 65° for the rated angle. How do I know this? I just recalculated for the Rated Angle based on the values given by EASE Address.

The demo files provided with EASE Address show the rated coverage angles in the name. For example, take the one called "Ceiling Lspk A (30 W, 70x70)", if you try your calculations with 70° you will find that the values match.

_________________
Best Regards,
Bruce C. Olson
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PostPosted: Tue Jul 19, 2011 6:53 am Reply with quote
Predrag
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Joined: 26 May 2011
Posts: 11




Hi Bruce,
If I understood correctly I should do reverse calculation for every other speaker except, mentioned AFMG Ceiling LSPK, to see what coverage angle is used in calculations.
Then, I don't see any purpose of published datasheets provided by loudspeaker manufacturers.
Also, what about Number of speakers? Results don't match too!
And finally, what about level variation?

Best regards,
Predrag
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PostPosted: Tue Jul 19, 2011 7:00 pm Reply with quote
Stefan
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Joined: 19 Apr 2005
Posts: 164
Location: Berlin, Germany




Hi Predrag,

1. The speaker that you mentioned has an internally specified opening angle of 65 degrees. In general, please refer to the corresponding loudspeaker company if you have questions about their data files. With respect to our software, we will discuss better ways of displaying important calculation parameters such as this one.

2. At the given relative height of the loudspeaker above the listening plane, h = 1.3 m, the angle of alpha = 65 degrees corresponds to a projected coverage circle with the radius of r = 0.828 m, r = h x tan (alpha / 2), in the listening plane.

3. The three geometrical layouts, Edge-To-Edge, Minimum-Overlap and Center-To-Center, derive directly from this. For a square layout, Edge-To-Edge equates to a speaker spacing of 2 x r, Minimum-Overlap to 1.414 x r and Center-To-Center to 1 x r. The corresponding values of 1.7 m, 1.2 m and 0.8 m are clearly reproduced by the software.

4. When dividing the available room area by the squared spacing distance one obtains 26.99, 56.88 and 113.77 loudspeakers. In the software, depending on the placement of the grid inside the room and for the given dimensions of 13 m x 6 m, Edge-To-Edge obviously yields 21 to 32 loudspeakers, Minimum-Overlap 55 to 72 and Center-To-Center 105 to 128. This seems to be correct - in most cases the room area cannot be divided up ideally among (whole) loudspeakers.

5. Looking at the output numbers of the example that you cite, 0.85 m and 106 loudspeakers, it seems that these would relate to a Center-To-Center setup. In any case, with the given information you should be able to compare with other sources very easily.

6. The Level Variation is computed based on the currently selected loudspeaker type and the given mapping parameters. It is directly related to the Direct SPL plot shown in the mapping. But it does not account for boundary effects, meaning that for each loudspeaker it is assumed that it has all neighbors in place.

We hope that this answers your questions.
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PostPosted: Wed Jul 20, 2011 7:09 am Reply with quote
Predrag
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Joined: 26 May 2011
Posts: 11




Hi Stefan,
Thanks for this detailed information. That's all I've been asking for.
I think that other users of EASE Address, would appreciate if, as you said ''discuss better ways of displaying important calculation parameters such as this one'' (speaker opening angle).
Thanks again for the time you spend for such detailed reply.


Best regards,
Predrag
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