Theory question for the experts: Depth vs Surface of absorption.

[UnderTow]

Hi all,

I have a (at the moment) theoretical question for the experts here: If one wants to try and control frequencies as low as possible in a room, is it best to maximize the area of absorption or the depth? (I intend to use Homatherm FlexCL).

Here are some pictures to make things clearer:

Option 1, full back wall as an absorber (except where the diffusers are):





Or Option2, the depth is increased by creating a bend by adding a wall:




Option 3 would be half half: The wall would only go half way up the room height and the cavity would be closed off at the top. The top half would be an absorber over the full width like in Option 1.

Or maybe the openings in Option 2 should be in the centre rather than the sides? (I am wondering this because of the plans for Darius' studio in Amsterdam where it seems that the air flow is open in the middle and the corners have multi-layered trapping but I could be misinterpreting the plans).

Note that the SketchUp sketches are exactly that, sketches. If any changes should be made like filling the whole air-gap with absorbent material because that is a better idea, then that is what I will do.

The depth of the whole back section (starting at the front of the wall/absorbent) is 542mm. The extra "depth" created by adding the wall is another 850mm on each side. (Total width of the room is 2700mm).

Is this extra 850mm going to significantly lower the frequency at which room modes etc are being controlled? Or not?

Thanks in advance for any comments, ideas, suggestions.

Alistair

[Dange]

In option 1 the entire wall is covered so will act in a broadband way when compared to option 2 which I reckon will act more like a tuned absorber (if the walls forming the cavities are solid). However the resonant frequency could be too low to be useful. Therefore option 1 is probably most effective

Option 3 will probably be just like option 1 but less effective as less of the area is 'absorber' and the tuned element won't function because the cavity isn't enclosed.

[UnderTow]

Thanks for your response Dange!

Originally Posted by Dange

In option 1 the entire wall is covered so will act in a broadband way when compared to option 2 which I reckon will act more like a tuned absorber (if the walls forming the cavities are solid). However the resonant frequency could be too low to be useful. Therefore option 1 is probably most effective

I guess I need to calculate the resonant frequency of those wells. And yes, the walls would be solid. Either brick or heavy plaster. I have to investigate what the best or most practical material is.

Option 3 will probably be just like option 1 but less effective as less of the area is 'absorber' and the tuned element won't function because the cavity isn't enclosed.

I should have been clear: In option 3 I would close the top of the cavity (with rigid material). I'll update my first post.

Thanks again,

Alistair

[DanDan]

What a clever idea. A bit like the transmission line used in PMC speakers.
I would recommend the sure thing though.
A deep fibre trap is pretty predictable.
Light cheap fibre will perform better than expensive dense stuff at such depths. Attic insulation supported by mesh and so on.
You could consider introducing laths on the front.
Even the simple Newell 543 sequence will cause some return of scattered HF.
More complex sequences will get closer to proper diffusion.
You could even 'tune' this broadly to your lowest length mode and the second one. Details at johnlsayers.com
If you go for tuned, broad laths, small gaps, I suggest creating an angle. A protruding V. This would redirect reflections towards the side walls where they could be absorbed by side panels or bounced to you if there is enough of a time lag to make this desireable. e.g. 20mS or more.

DD

[UnderTow]

Originally Posted by DanDan

What a clever idea. A bit like the transmission line used in PMC speakers.

That is the general idea, yes. :-)

I would recommend the sure thing though.
A deep fibre trap is pretty predictable.
Light cheap fibre will perform better than expensive dense stuff at such depths. Attic insulation supported by mesh and so on.

Hmm... I have been playing with the Chris Whealy Porous Absobrer Calculator and based on what I see there and together with your comment I am indeed starting to doubt whether the FlexCl is the right material for this as it has such a high Flow Resistivity. Interesting.

You could consider introducing laths on the front.
Even the simple Newell 543 sequence will cause some return of scattered HF.
More complex sequences will get closer to proper diffusion.
You could even 'tune' this broadly to your lowest length mode and the second one. Details at johnlsayers.com
If you go for tuned, broad laths, small gaps, I suggest creating an angle. A protruding V. This would redirect reflections towards the side walls where they could be absorbed by side panels or bounced to you if there is enough of a time lag to make this desireable. e.g. 20mS or more.

DD

What a great suggestion! I was already considering making the wall in Option 2 convex but you have certainly given me more food for thought. Thanks!

Alistair

[DanDan]

You are welcome. I do hope some others chime in here also. It has been a while since we have seen a taxing question.
If you do the wall, there is a conundrum. Do you make it rigid to persuade the bass to follow that path? Or do you make it essentially a large panel trap? i.e. free to vibrate, not braced. In either case I would fill the space behind with light fibre.
DD

[Northward]

Careful with Homatherm FLEX CL If you pack it.

Its resistance to flow is quite high, and it does not behave like rockwool.

You must have it within a sequence of air gaps.

Just sayin'.

Also, because of how it works, you can achieve what you're aiming at in drawing Nr.2 with drawing Nr.1

You'll need to tweak it a fair bit though, but think in terms of resistance to flow of rather high density panels like the Flex CL and what that means in terms of behaviour at LF if you have, say, 20cm of it at once.

That should get you somewhere. Maybe interesting, maybe not so interesting. Depends on the case and the maths. But I'd have a look if I were you.

[avare]

How low do you want to/hope to absorb? How deep is the absorber portion?

Option 1 in general is better. I write in general because the type of material used will be dependent on if it is completely filling the space behind the face of the absorber or with a gap. If completely filled, light insulation is best. Thomas and Dan already mentioned that.

If with a gap, then a denser material ~60 kg/m³ is better. Galaxy Studios uses ~12" deep absorbers with ~8" gaps at back. This combination yields quite good absorption down to below 50 Hz.

Andre

[DanDan]

Seems like a good question will get good answers....
DD

[UnderTow]

Hi Thomas,

Originally Posted by Northward

Careful with Homatherm FLEX CL If you pack it.

By packing you mean filling the space? It doesn't necessarily have to be filled. All options are still open at this point. Whatever gives me the best results. :-)

Its resistance to flow is quite high, and it does not behave like rockwool.

Yes I noticed. 76 KPa.s/m for the FlexCL. CORRECTION: The numbers are from 43 to 76 KPa.s/m. I guess that is depending on which thickness of the panels.

(I'm having a hard time finding the exact figures for the Rockwool available in NL. The products are slightly different to their German branch).

You must have it within a sequence of air gaps.

Just sayin'.

Thanks for saying. :-)

Thanks to your suggestion I've been playing with Porous Absorber Calculator Some interesting results but also a fundamental question: Which model to use? (More on that below).

Also, because of how it works, you can achieve what you're aiming at in drawing Nr.2 with drawing Nr.1

You'll need to tweak it a fair bit though, but think in terms of resistance to flow of rather high density panels like the Flex CL and what that means in terms of behaviour at LF if you have, say, 20cm of it at once.

That should get you somewhere. Maybe interesting, maybe not so interesting. Depends on the case and the maths. But I'd have a look if I were you.

Thanks for the suggestion. :-) I shall read/investigate more while keeping what you wrote in mind.


Back to the fundamental question about the Porous Absorber Calculator:

Which model should one use? (especially for LF).

The Delany and Bazley model gives me similar (if not identical) results to the Chris Whealy's Calculator: Very low absorption at low frequencies with the high Flow Resistivity product. Things look very different with the Komatus model. Here are some pictures using the same numbers, only the model changes:

Picture 1 is the Delany & Bazley model:




Picture 2 is the Komatsu model:




If I can trust the Komatsu model I might be able to come up with a useful absorption plot by mixing and matching depths and materials but I am not sure if I can trust it. What does everyone think?

Thanks again Thomas and everyone else giving feedback/suggestions.

Alistair

[UnderTow]

Hi Andre,

Originally Posted by avare

How low do you want to/hope to absorb? How deep is the absorber portion?

I have 542mm of space to play with. (21.34 inches) I will try and utilise this space as best possible.

As for how low do I hope to absorb, well I realise that everything is a compromise within any given physical space. If I can somehow get down to 50 Hz or beyond I will be more than pleased. Of course that is only relevant if the amount of absorption is worth it. I also have to keep frequencies above that in mind. I don't see much point in absorbing plenty at 50 Hz to leave huge problems higher up in the frequency range. So to answer your question: I don't know yet. :-)

My original question was to give myself a direction to investigate in so I can figure out the right calculations to make. I am already realising that just choosing the direction is already a complex task. :-)

Option 1 in general is better. I write in general because the type of material used will be dependent on if it is completely filling the space behind the face of the absorber or with a gap. If completely filled, light insulation is best. Thomas and Dan already mentioned that.

Yes. It seems to be the general consensus. Great!

If with a gap, then a denser material ~60 kg/m³ is better. Galaxy Studios uses ~12" deep absorbers with ~8" gaps at back. This combination yields quite good absorption down to below 50 Hz.

Andre

My total available depth is 542mm (21.34 inches). So the Galaxy Studios approach is interesting. I'll see what I can find on their studio design. I don't think my budget will allow me putting my house on springs though. ;-)

Thanks for your response and suggestions Andre,

Alistair

[DanDan]

Alistair, panels of rigid material start to behave a little like a board. Thus one could tend towards a panel trap behaviour.
Whealy doesn't have this behaviour in it.
If this behaviour is understood and worked out carefully it can be used to advantage.
However, if I were attempting this I would ask (hire) someone with the chops to do this.
Unless you go there, I recommend the sure/predictable. Galaxy is a pretty serious studio....

DD

[avare]

Originally Posted by UnderTow

Hi Andre,



I have 542mm of space to play with. (21.34 inches) I will try and utilise this space as best possible.

As for how low do I hope to absorb, well I realise that everything is a compromise within any given physical space. If I can somehow get down to 50 Hz or beyond I will be more than pleased. Of course that is only relevant if the amount of absorption is worth it. I also have to keep frequencies above that in mind. I don't see much point in absorbing plenty at 50 Hz to leave huge problems higher up in the frequency range. So to answer your question: I don't know yet. :-)

My original question was to give myself a direction to investigate in so I can figure out the right calculations to make. I am already realising that just choosing the direction is already a complex task. :-)

Yes. It seems to be the general consensus. Great!

My total available depth is 542mm (21.34 inches). So the Galaxy Studios approach is interesting. I'll see what I can find on their studio design. I don't think my budget will allow me putting my house on springs though. ;-)

Thanks for your response and suggestions Andre,

You are welcome.

Pullng some numbers from my memory, Non-Envonment studios typically use modified porous absorbers 2-4' (~600-1,200 mm) deep for "full range" absorption. Hidley has called some of these rooms as being 10 Hz rooms. I will leave th interpretation of what that means exactly, to the marketing sales types here.

If I were you with that space available and chose to use it for absorption, I would go with the lightest fibre type absorbent material and use a thickness that would yield a ~1,600 Rayls (4 times the impedance of air) surface impedance with rest being air gap.

I can not get more unequivical then my above statement/paragraph/great example of a run on sentence.

Unequivicably running at the keyboard,
Andre

[ritelec]

Originally Posted by DanDan

In either case I would fill the space behind with light fibre.
DD

Would bails of hay or straw work???

[Dange]

Originally Posted by UnderTow

Picture 1 is the Delany & Bazley model:




Picture 2 is the Komatsu model:




If I can trust the Komatsu model I might be able to come up with a useful absorption plot by mixing and matching depths and materials but I am not sure if I can trust it. What does everyone think?

What thickness and air gap is this?

I'm not familiar with Komatsu to know the accuracy at LF. I know that Delany and Bazley can be inaccurate at very LF. (I don't know the LF limit off hand, their prediction method is based on loads of test results, not a physical model of very small holes or similar. Their testing would have a LF limit and hence the results).

The resonance predicted by Komatsu at 180Hz may or may not be expected depending on the structure

[UnderTow]

Hi Dange,

Originally Posted by Dange

What thickness and air gap is this?

These graphs are with a 30mm absorber thickness and 120mm air gap.

Here is a link to the same calculations with both models superimposed in one graph: Porous Absorber Calculator - Results (What an amazing tool! :-)

I'm not familiar with Komatsu to know the accuracy at LF. I know that Delany and Bazley can be inaccurate at very LF. (I don't know the LF limit off hand, their prediction method is based on loads of test results, not a physical model of very small holes or similar. Their testing would have a LF limit and hence the results).

I don't think the depths and/or gaps are inordinately small but the page comes with this comment about the dotted line in the Delany and Bazley model:

"Dotted lines indicate that the empirical relationship used to estimate absorber properties has been used outside of its applicable range. Results may therefore be less accurate than where a solid line is displayed."

And this info about the Komatsu model: "T. Komatsu. 2008. Improvement of the Delany-Bazley and Miki models for fibrous sound-absorbing materials. Acoust. Sci. & Tech., 29(2), 121-129."

Here is a link to the Komatsu paper: AST : Vol. 29 (2008) , No. 2 pp.121-129

EDIT I now see that the graphs diverge most when the Flow Resistance is very high or very low.

The resonance predicted by Komatsu at 180Hz may or may not be expected depending on the structure

The only variables given for the absorber are the depth and air flow resistance so that is all the calculator can work with...

Thanks!

Alistair

[DanDan]

The angle of incidence is also variable in Whealy.
0 degrees seems a bit extreme, there are many waves coming at the back wall at very different angles. However, the lowest modes' wavefronts should be pretty flat fronted, so it may be no harm to consider the worst case scenario. It's worth having a look at the other angles. Gives a clue as to why SuperChunks perform pretty well.
Here's an alternative Porous Calculator which includes some other algorithms, and random incidence.
Porous Absorber Calculator

DD

[UnderTow]

Hi again Andre,

Originally Posted by avare

You are welcome.

Pullng some numbers from my memory, Non-Envonment studios typically use modified porous absorbers 2-4' (~600-1,200 mm) deep for "full range" absorption. Hidley has called some of these rooms as being 10 Hz rooms. I will leave th interpretation of what that means exactly, to the marketing sales types here.

I could live with control down to 10 Hz. ;-) Unfortunately I don't have that depth available in this room.

If I were you with that space available and chose to use it for absorption, I would go with the lightest fibre type absorbent material and use a thickness that would yield a ~1,600 Rayls (4 times the impedance of air) surface impedance with rest being air gap.

Let me make perfectly sure I understand you. You are talking about the total airflow resistance of whatever depth material I am using right? So if I have material with let's say 32 KPa.s/m I would need 50 mm of total depth to achieve 1600 Rayls, right?

The smallest depth available for FlexCL is 30mm and the Rayls/m is between 43000 and 76000. In other words a panel 30mm thick would give between 1290 and 2280 Rayls total.

This leaves space for a 490 mm air gap behind the panel.

I can not get more unequivical then my above statement/paragraph/great example of a run on sentence.

Unequivicably running at the keyboard,
Andre

:-)

If I use the numbers calculated above (30mm panel, 490mm air gap) and fill them in the Calculator I get the following graphs:

Graph 1 based on Komatsu model: Blue line 76000 Pa.s/m2 ; Green line 43000 Pa.s/m2

Graph 2 based on Delany and Bazley: Blue line 76000 Pa.s/m2 ; Green line 43000 Pa.s/m2




These don't look particularly good. I'm not sure how much that has to do with the models, the materials, a combination of both... More things to investigate.

Thanks for your comments!

Alistair

[UnderTow]

Originally Posted by DanDan

The angle of incidence is also variable in Whealy.
0 degrees seems a bit extreme, there are many waves coming at the back wall at very different angles. However, the lowest modes' wavefronts should be pretty flat fronted, so it may be no harm to consider the worst case scenario. It's worth having a look at the other angles. Gives a clue as to why SuperChunks perform pretty well.
Here's an alternative Porous Calculator which includes some other algorithms, and random incidence.
Porous Absorber Calculator

DD

That is the one I am using but ticking the random incidence checkbox does indeed yield different results. Thanks for the suggestion!

Alistair

[Dange]

How does the Komatsu prediction look when it's 150mm absorber compared to 120mm air gap and 30mm absorber?

[DanDan]

Dange, that Calculator I linked is an online tool. Turns out Alistair is using it. It does Komatsu and Miki and others.
No Microsoft issues!

DD

[UnderTow]

Hi Dange,

Originally Posted by Dange

How does the Komatsu prediction look when it's 150mm absorber compared to 120mm air gap and 30mm absorber?

As DanDan wrote, the Calculator is online. You don't need to download anything to test it. But for your convenience, here are the graphs with the following parameters:



Or a link to the Calculator with those parameters already fed in: http://www.stanleyhallstudios.co.uk/...&s42=1&d42=120


Alistair

[DanDan]

Dange will love this calculator.
This might be a good place to express our thanks to Demetris for constructing this great online tool.
Now, Demetris, can you replace the rest of Microsoft?
DD

[PaulRain]

every time I see a different calculator I get different results....:(
it's also amazing how different are the results of the different models..
very interesting calculator btw...and very much interesting the Komatsu research

[Dange]

This is what I was thinking of:

150mm no gap vs. 30mm, 120mm gap

The prediction makes the 30mm absorber look a lot better than 150mm at low frequency, this doesn't seem right You need to compare this to real world measurements of gaps and no gaps absorbers with the same overall depth... maybe someone knows of some....

[PaulRain]

I think you should get better results with 300mm of 6000 Pa.s/m2 material...like the cheap insulation rolls.
400mm is even better....more it's nonsense, the increase in the absorbtion doesn't, in my opinion, justify the space taken and the money.
then, if you really need the back wall to do something, even if not much, under 40/50Hz then maybe it's better to increase the Flor Resistivity but you will loose absorbtion between 100/300Hz

[avare]

Originally Posted by UnderTow

Hi again Andre,

Hello and you are welcome for your closing remarks.

I could live with control down to 10 Hz. ;-) Unfortunately I don't have that depth available in this room.

If one takes the effective frequency as being a function of depth and 1.2 m is 10 Hz, then your room would be someting like a 22 Hz room. The double 2 has a nice ring to it.

Let me make perfectly sure I understand you. You are talking about the total airflow resistance of whatever depth material I am using right? So if I have material with let's say 32 KPa.s/m I would need 50 mm of total depth to achieve 1600 Rayls, right?

Of what you wrote, yes.

The smallest depth available for FlexCL is 30mm and the Rayls/m is between 43000 and 76000. In other words a panel 30mm thick would give between 1290 and 2280 Rayls total.

I wrote "I would go with the lightest fibre type absorbent material". That would be like a ~10 kg/m³ with a gas flow resistivity around 4000 kPa.s/m. For a surface impedance of 1600 Rayls, that works out to thickness of around 400 mm.

This leaves space for a 490 mm air gap behind the panel.These don't look particularly good. I'm not sure how much that has to do with the models, the materials, a combination of both... More things to investigate.

Model 400 mm of 4000 kPa.s/m³ material with a gap for the rest of the space you have allocated.

Dan already mentioned it, that 0° incidence is the worst case. The severe comb filtering shows that.

Good luck!

Absorbently modelled,
Andre

[prairiedog]

Which model should one use? (especially for LF).

The Delany and Bazley model gives me similar (if not identical) results to the Chris Whealy's Calculator: Very low absorption at low frequencies with the high Flow Resistivity product. Things look very different with the Komatus model.

Unfortunately I haven't got a simple answer to this. I was actually quite surprised to see how different the results are from the two models so I had another look at the original papers to work out the reason.

Each author did a series of impedence tube tests to derive data from which they developed their respective models. Most of the difference you have observed is due to differences in the test results.

In other words, Delany and Bazley tested a large number of different materials at various frequencies and developed a simple (but reasonably accurate) model based on their test results. 38 years later, Komatsu did his own tests and developed a more sophisticated model based on his results. At low frequencies and high values of flow resistivity, the differences between the two sets of test results affect predictions more than differences in the sophistication of the models. The choice of model therefore depends on who you think did the more accurate tests!

Although the effect you have observed is outside of the applicable range of the Delany/Bazley model, there is some evidence to support the accuracy of this model. Firstly, Mechel and Grundmann did their own tests in 1982 and their models give results closer to Delany/Bazley than to Komatsu. Further, the Allard/Champoux model which was derived using a more theoretical approach is also closer to Delany/Bazley than to Komatsu.

Having said that, I wouldn't recommend using the Delany/Bazley model outside of its applicable range. The Miki model is based on the same set of test data but should be more accurate at low frequencies. The Allard/Champoux model is probably also a good choice. I've attached an image showing results from these models along with Delany/Bazley and Komatsu.



Hope that's useful,
Demetris

[UnderTow]

Originally Posted by prairiedog

Unfortunately I haven't got a simple answer to this. I was actually quite surprised to see how different the results are from the two models so I had another look at the original papers to work out the reason.

Each author did a series of impedence tube tests to derive data from which they developed their respective models. Most of the difference you have observed is due to differences in the test results.

In other words, Delany and Bazley tested a large number of different materials at various frequencies and developed a simple (but reasonably accurate) model based on their test results. 38 years later, Komatsu did his own tests and developed a more sophisticated model based on his results. At low frequencies and high values of flow resistivity, the differences between the two sets of test results affect predictions more than differences in the sophistication of the models. The choice of model therefore depends on who you think did the more accurate tests!

Although the effect you have observed is outside of the applicable range of the Delany/Bazley model, there is some evidence to support the accuracy of this model. Firstly, Mechel and Grundmann did their own tests in 1982 and their models give results closer to Delany/Bazley than to Komatsu. Further, the Allard/Champoux model which was derived using a more theoretical approach is also closer to Delany/Bazley than to Komatsu.

Having said that, I wouldn't recommend using the Delany/Bazley model outside of its applicable range. The Miki model is based on the same set of test data but should be more accurate at low frequencies. The Allard/Champoux model is probably also a good choice. I've attached an image showing results from these models along with Delany/Bazley and Komatsu.

Hope that's useful,
Demetris

Hi Demetris,

Thank you for commenting. And thanks for providing the calculator itself. :-)

More food for thought...

Alistair

[UnderTow]

Hi again Andre and everyone else,

I have some more questions for anyone willing to reply. I realise that asking the questions is a lot easier than answering them. :-)

Originally Posted by avare

If one takes the effective frequency as being a function of depth and 1.2 m is 10 Hz, then your room would be someting like a 22 Hz room. The double 2 has a nice ring to it.

22 Hz doesn't sound too shabby. :-)

I also realised I have room at the front of the studio to make an 80cm deep bass trap. 90 cm high minimum or even more if I increase the speakers height and angle them downwards to the listening position. I still have to think about that...

Something that would resemble the bottom half of this graphic from the SAE:

I wrote "I would go with the lightest fibre type absorbent material". That would be like a ~10 kg/m³ with a gas flow resistivity around 4000 kPa.s/m. For a surface impedance of 1600 Rayls, that works out to thickness of around 400 mm.

I hear what you are saying but I can't help noticing quite a few European rooms using high density / high Flow Resistivity materials. Northward designs or Newell designs. In the Loudness Studios in Portugal, Newell uses 80 Kg/m³ material.

And Thomas has made the following comments about FlexCL:
- Density / surface impedance are ideal,
- Excellent acoustic performances, superior to rockwool of equivalent density and thickness,

(Plus his comments above in this thread).

I am hoping that if I somehow figure how best to use this material and get the design right, I could achieve better results than with lower density material rockwool.

Model 400 mm of 4000 kPa.s/m³ material with a gap for the rest of the space you have allocated.

Looking purely at absorption the low-density material looks best but when I look at the impedance graphs things look very different.

Here are the three graphs with the following parameters:




How important is impedance? What is the effect of the Real and Imaginary components? (I realise they refer to the phase but how does this affect acoustic treatment?)

How do absorption and impedance respectively affect room modes? How do the Real and Imaginary components each affect room modes? Will they affect horizontal and vertical room modes differently? And oblique?

Dan already mentioned it, that 0° incidence is the worst case. The severe comb filtering shows that.

Are the room modes more affected by the 0 degrees incidence vs random incidence or less? (or differently?)

Based on reading and looking at various other studio designs I have added another option to my list of things to research:




In such a design, how do I calculate the ideal angles of the hanging boards? The distance between the boards? (Idem for the side walls and possibly the ceiling). How do I determine the best type of material for covering the planks and it's ideal thickness? Etc. ;-)

I have also looked at the MyRoom design white paper by Zorica Davidocic and Bogic Petrovic as a variation on the Non-Environment design. More food for thought. :-)

I've ordered Philip Newell's book and a measuring microphone. This will keep me busy for a while I guess. :-) I am in no hurry to to finalize the design. I prefer taking my time and getting it right. I also intend to hire an acoustician to look at my final design before building anything.

In the mean time, any comments, suggestions etc are more than welcome.

Good luck!

Thanks Andre! :-)

Alistair