LarryChannin wrote:from http://www.avsforum.com/avs-vb/showthre ... ost6138925
I tried applying the Perforated Panel calculator to takeaim's question regarding his soffit construction in the Broadband bass soffit construction thread and seemed to get useful results.
However, I haven't had any luck in getting useful results when applying the Slotted Panel calculator to predict what would happen if we cut slots into his existing seating riser.
ChrisW wrote:Hi Bob
Thanks for the info. I've had a quick look at the thread, and it does appear that the riser construction being modelled is not what my spreadsheet was designed to work on.
My porous absorber spreadsheet contains the calculations to predict the absoption of a two or three layer construction against a backing of infinite impedence. If other words, the quations in the spreadsheet allow for the following combinations:
1) Backing layer of infinite impedence + air gap + porous absorber + slotted/perforated panel
2) Backing layer of infinite impedence + porous absorber + air gap + slotted/perforated panel
3) Backing layer of infinite impedence + porous absorber + slotted/perforated panel
Larry Chanin's thread in the AVS forum describes a riser in which two 8" porous layers are separated by a layer of plywood. Unfortunately, my spreadsheet cannot account for the presence of this middle layer of plywood. And to be honest, it would be very difficult to produce a predictive tool that would produce anything like useful results for this type of construction. The plywood panel would have to be treated as an edge mounted diaphragm, and the properties of the plywood would then have to be entered by the user, and... you get where I'm heading?
I don't think such a tool would ever produce results that could be described as "useful".
However, having looked at the "No air gap" plot my spreadsheet is producing on the Slotted Panel spreadsheet, I suspect that there could be a bug in the calculations here.
I'll have to investigate and get back to you.
Regards
Chris W
I'm pretty sure that Dennis uses slotted risers all the time, so I guess I'm probably doing something wrong in applying the spreadsheet.
The problem as I mentioned in this thread, and over in the Bass Trap made out of a Seating Platform thread, is that Mr. Everest's formulas don't show us the effect of using insulation of any kind, nor as you pointed out, do they calculate absorption. Chris Whealy's spreadsheets do provide this and he gives credit to four professional acousticians who have reviewed his work. That's good enough for me.
ChrisW wrote:Hi Larry
Ok, I didn't know you were only trying to model the top section of the riser, so in that case you are using my spreadsheet correctly. And thanks for the compliments. These spreadsheets represent a large investment of time and effort. All donations gratefully received! :D
Now down to business, why doesn't my spreadsheet give you useful/helpful results?
Well I've checked the calculations in the spreadsheet against the methods and equations listed in section 6.3 of Cox and D'Antonio, and I can't find any errors in the calculation. So I entered the values quoted in section 6.4.1 (page 178) and got pretty much exactly the same curve as shown in the book in figure 6.18.
Then I realised what was going on. What value were you using for the flow resistivity? If you're using a typical value for Rockwool or medium density fibreglass (e.g. 16,500), then you will not get the useful results you require.
Change the flow resistivity down to about 450, and then the "no air gap" curve jumps up to useful values. If you don't know what the flow resistivity value represents, then I would recommend you read the sheet of the same name in the spreadsheet. This is the most important value for predicting the absorption of a porous material.
The higher the number, the denser the porous absorber. The denser the porous material, the fewer air gaps it will contain and therefore it will offer greater resistance to the flow of air through its fibres. On the other hand, the lower the value, the more open the fibre structure is (or to put it in non-technical terms, its all light and fluffy), therefore, air can flow more easily through the porous material.
If you take a look at the attached screen shot, you will see that I have been able to jig the numbers so that you get your broad absorption peak centred at around 200Hz. Using the following values, you should get the performance you're after:
Panel thickness = 38.1mm (1.5")
Distance between slots = 50.8mm (2")
Slot width = 19.1mm (3/4")
Cavity depth = 203.2mm (8")
Absorber thickness = N/A
Absorber flow resistivity = 450 rayls/m
Your riser needs to be filled with a very low density porous absober such a loft insulation batts that you have ripped apart to increase the fluffiness. When you do this, you please wear protective gloves, goggles, a breathing mask and keep your arms and legs covered; glass fibre is evil stuff!
According to IR761, 65mm glassfibre batts at 11.7Kg/m3 have an average flow resistivity of about 3,600 rayls/m. Therefore, you're really going to need to break this stuff up to lower this value. Try changing the flow resistivity from 450 to 3,600 and see how (without an air gap) it just dumps the performance.
Alternatively, continue using your higher density absorbent material, and just leave an air gap of a known depth above the absorbent layer... (this does sound simpler than ripping up glass fibre!)
Hope that helps.
Regards
Chris W
z1 = -j*rho*c*cot(k*l); %Impedance, top of cavity;
%Impedance of covering sheet
kd = a*sqrt(rho*w/viscosity);
s = kd*sqrt(-j);
z2 = j*w*rho*t./(1 - 2*besselj(1,s)./(s.*besselj(0,s)));
f = [62.5,70,79,88,99,111,125,140,157,177,198,223,250,281,315,354,397,445,500,561,630,707,794,891,1000,1122,1260,1414,1587,1782,2000,2245,2520,2828,3175,3564,4000,4490,5040,5657,6350,7127,8000,8980,10079,11314,12699,14254,16000]
nf = length(f);
w = 2*pi*f;
c = 343.38;
k = w/c;
rho = 1.204;
viscosity = 1.85e-5;
eta = pi*a^2/(D^2); %Open area
impedence = rho * c;
zair = -j*rho*c*cot(k*l); %Impedance, top of cavity;
%Impedance of covering sheet
kprime = a*sqrt(rho*w/viscosity);
z1 = j*w*rho*t./(1 - 2*besselj(1,kprime*sqrt(-j))./(kprime*sqrt(-j).*besselj(0,k*sqrt(-j))));
z2 = z1/eta + zair + j*w*1.7*rho*a/eta + sqrt(2*w*rho*viscosity)/(2*eta);
R=(z2-rho*c)./(z2+rho*c); %reflection factor
anormal=1-abs(R).^2; %absorption coefficient
hold on
plot(f,anormal,'g')
xlabel('f (Hz)')
ylabel('abs. coeff')
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