calculating width of poly panel

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calculating width of poly panel

Postby Dirk Brouns » Mon Aug 15, 2005 8:25 pm

Hi all,

I'm about to build me some polycylindrical diffusors for the back of my drumroom and the way I want to do it is the following. I'm going to build a MDF frame with 120mm slat width that will be mounted against the wall. The frame will have 3 vertical and one horizonal section where triplex sheets will be jammed in between so they bend nicely like a poly...

Now, problem is, how do I calculate how much wider the sheets need to be so that they bend out around 100-110mm?
Say, I have a sheet of 1.2m lenght that will be bend into a 0.5m width and I want it to stick out in the middle 110mm, which formula do I need to use. My math classes are quite some years back, but I know this shouldn't be too difficult.

I'll see if I can attach a picture to make it more clear.

thanks,
Dirk
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Postby Dirk Brouns » Mon Aug 15, 2005 8:36 pm

OK, here is the image that should explain it.

Greetings,
Dirk
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Postby Bob » Mon Aug 15, 2005 10:20 pm

I don't know about a formula (although some variation of y = b + mx^z might work), but you could take a piece of string or a length of toilet paper, curve it the way you want, and then straighten it and measure it.
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Postby Paul Woodlock » Tue Aug 16, 2005 1:27 am

Bob wrote:I don't know about a formula (although some variation of y = b + mx^z might work), but you could take a piece of string or a length of toilet paper, curve it the way you want, and then straighten it and measure it.


bob ya beat me to it :)

I was just gonna say, draw it out on a big bit of cardboard and lay some string around the curve :)

OR, cut a thin strip of mdf a bit too long, and cut some of the length until it bends 11cm outwards.


Paul
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Postby Bob » Tue Aug 16, 2005 2:07 am

Paul:

Actually my first thought was to do what I did:
a) drive to home depot
b) bend a bunch of their thin plywood until you find one that you can bend without hydrolics
c) measure it's X and Y axis sizes for the standard 4' wide panel.

But, Dirk Brouns asked for a general purpose solution.
Regards
Bob Golds
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Postby photoresistor » Tue Aug 16, 2005 4:14 am

well if you can find a function that behaves like the poly panel you could integrate the square root of 1 + the derivative of the function, squared.   that'll give you the arc length of the function...  for that shape of the poly panel, itd be some transformed upside down parabola or something i think.
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Postby Dirk Brouns » Tue Aug 16, 2005 5:14 am

Yeah, the piece of string came to mind, but I want to have the sheets cut to length when I order them...

No math experts here?

Greetings,
Dirk
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Postby Bob » Tue Aug 16, 2005 6:28 am

Dirk

but I want to have the sheets cut to length when I order them

I don't think there is one formula/function to integrate.
How much it bends would depend on the material.
Here's two different bends, which have the same width and height, but different surface area.
Image

Perhaps you could bend your material, derive it's function ( y = b + mx^z for example), and use that.

Here's a circle (whose surface area is easy, but curve isn't recommended for diffusion), and a parabola.

I'd bet that any parabola function you use (y = x^2) would be close enough for you to estimate with.
Or you could guess that it's half way between a couple of triangles and a circle.

Image
Regards
Bob Golds
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"Be a rapturist -- the backward of a terrorist. Commit random acts of senseless kindness, whenever possible" - Jake Stonebender
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Postby Dan Nelson » Tue Aug 16, 2005 6:43 am

Look here
http://planetmath.org/encyclopedia/LengthOfACurve.html

and here
http://mathworld.wolfram.com/ArcLength.html

I'm thinking around 65-66 cm it really depends on the curve as Bob pointed out and you also have material thickness itself to worry about as well



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Postby Scott R. Foster » Tue Aug 16, 2005 11:09 am

...and the bevel of the edges [or lack thereof].
SRF
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Postby Dirk Brouns » Tue Aug 16, 2005 5:08 pm

Thanks all for the replies.

This is what I'm going to do. I'm going to build the MDF frames which will hold the band multiplex (3.6mm) sheets. I'll take some pictures during the build and then it'll explain itself what I'm doing.

When the frames are ready, I'll start with the widest sheet. I'll take a piece of say 10cm length multiplex and saw it about 10cm too long and start bending. I'll work my way, sawing incremental pieces off the width of the 10cm long sheet untill it sits perfectly within the widest frame. That will be the width for the widest sheet of 122cm long multiplex. After that I can use the same 10cm long piece of multiplex and move on (sawing of little pieces) with the next largest frame...

Makes sense? :mrgreen:

I'll come back to it in a week or so.

Greetings,
Dirk
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Postby Graham B » Tue Aug 16, 2005 7:43 pm

That makes sense to me, having made some myself.
BUT
You really must take Bob's advice "bend a bunch of thin plywood until you find one that you can bend without hydrolics"
Our first attempts were with a batch that was near impossible to bend!

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Postby Dirk Brouns » Tue Aug 16, 2005 8:46 pm

Ok, thanks for the tip.

But the multiplex I'm talking about is very easy bend, but I'll check it anyway.

greetings,
Dirk
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Postby Dirk Brouns » Fri Aug 19, 2005 8:29 pm

So I started buidling today 8O .

I started with the MDF frame and had worked out a clever way so I could trial and errod my way towards the right design without scrapping a lot of wood during the process.

I found this very flexible plywood in 120cmx60cm sheets that is very flexible in one direction and has a nice birch fineer finish (is that what you call it in english? :bang ). This matches my flooring and rest of the studio and means I don't have to paint them!

The MDF will be painted with a deep shiny blue color, same as I have used on my studiodesk (I'll get a picture of that when I'm finished).

SO, here come the piccies  :mrgreen: .

Greetings,
Dirk
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poly

Postby Dirk Brouns » Fri Aug 19, 2005 8:33 pm

this is how far I got tonight...

As you can see on the last picture is that it's kinda difficult to predict the correct length for a given space so the sheet bends nicely but stays within the frame. So the larger sheet that's sticking out will be shortened...

When all is done, I'll fill the space behind the sheets with rockwool.

Greetings,
Dirk
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Postby Bob » Fri Aug 19, 2005 8:37 pm

Dirk Brouns

There's pics, so I guess it happened. :)

Can you tell me
a) the weight per square foot of each of those membranes? (i.e. grab a couple and stand on a bathroom scale with them)
b) the depth of the arch
c) the cutting dimensions of the panels, and the length/width of each of the caveties you put them into (frames).

I ask (a) and (b) because I've been thinking about membrane absorbers in polys lately.
I ask (c) because you asked it at the beginning of this thread, so perhaps someone might want to know in the future.
Regards
Bob Golds
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"Be a rapturist -- the backward of a terrorist. Commit random acts of senseless kindness, whenever possible" - Jake Stonebender
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Postby Dirk Brouns » Fri Aug 19, 2005 8:45 pm

The depth of the arc is 10-11cm for all panels, but I will have different lenghts, all 60cm wide, varying from 40-60-100.

I just measured them like you suggested and they weigh about 1.1kg for a 120cmx60cm sheet, with a thickness of about 4mm.

Could you calculate the resonance frequency? Or why are you interested in those specs? Just curious.

Greetings,
Dirk
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Postby Dirk Brouns » Fri Aug 19, 2005 8:55 pm

Bob wrote:Dirk Brouns

There's pics, so I guess it happened. :)

Can you tell me
a) the weight per square foot of each of those membranes? (i.e. grab a couple and stand on a bathroom scale with them)
b) the depth of the arch
c) the cutting dimensions of the panels, and the length/width of each of the caveties you put them into (frames).

I ask (a) and (b) because I've been thinking about membrane absorbers in polys lately.
I ask (c) because you asked it at the beginning of this thread, so perhaps someone might want to know in the future.


c: the first one I did was 60cm wide (width of the sheefts so I only have to saw ones  :D ) and 60cm long. I made the box 55cm long and then it worked perfectly. For the larger one, the box is 95.6cm long so I calculated 102cm as a first guess but as you can see it's obviously to long.

Greetings,
Dirk
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Postby Bob » Fri Aug 19, 2005 9:21 pm

Dirk Brouns:

Resonance Frequency of Diaphragmatic Absorbers (pg 265 of "How to build a small budget recording studio from scratch 3rd edition with 12 tested designs")

f = 170 / sqrt (m * d)
f = resonance frequency in hz
m = surface density of the panel in pounds per square foot
d = depth of airspace in inches

Bad Assumptions:
1) Your panel is curved, so it will have more structural resistance, and more complicated wobbling, than normal.
2) It's also an arc instead of a flat surface, so I'll further assume that the area under the arc can be averaged into a depth for the above equasion.

I figure that the area under the curve is about 75% of the rectangular area, so I'll multiply the 10cm depth you mentioned by 0.75 to get an adjusted depth = 7.5cm.

7.5 centimeter = 2.9527559 inch

1.1kg for a 120cmx60cm sheet

1.1 kilogram = 2.4250849 pound
120cm * 60cm = 7200 cm^2
7200 square centimeter = 7.7500155 square foot
so the surface density is 2.4250849 pound / 7.7500155 square foot = 0.31291355481805165421927220661688 psf
I'll round that 0.313 psf.

f = 170 / sqrt (m * d)
f = 170 / sqrt (0.313  * 2.9527559 )
f = 176 hz.
Regards
Bob Golds
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"Be a rapturist -- the backward of a terrorist. Commit random acts of senseless kindness, whenever possible" - Jake Stonebender
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Postby Dirk Brouns » Sat Aug 20, 2005 11:54 am

Here's how far I got today. Tomorrow I'm going to finish the poly's and starting painting. Everything should be up on the wall next Wednesday...

Greetings,
Dirk
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