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Old 3rd September 2003, 06:38 PM   #11
MarkMcK is offline MarkMcK  United States
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Greetings,

I have measured my old Acoustat panels, attempted to model the design, and calculated fill to void ratios for the plates. Still I am uncertain of the meaning of the results and I am uncertain of the validity of my models. Clearly this is a work in progress so please take what I say with a healthy dose of skepticism. Most of my work with ESL designs has been in the resonant structure of the diaphragms and not in the e field design of the plates.

The operation of an ESL is not complex and yet it is. We are concerned with plate fill to void ratios because of the interaction of two phenomena; e field strength and resistive loading of diaphragm movement due to constriction of air flow through the plate. Assuming non-chaotic operation and no surface (or boundary) effects, both phenomena should be fairly linear regarding efficiency. The relationship between the two phenomena is, however, inverse. The more plate fill to void the more even (and therefore stronger) the e field will be across the diaphragm. The more plate fill to void the more air resistance there will be to the movement of the diaphragm. The less plate fill to void, the less air resistance and the less average e field strength there will be. Combine the phenomena and you should have a graph with a distinctive bell shaped curve. In economics this might be called a “Laffer” curve.

A “Laffer” curve suggests the existence of an optimum point (or ratio) of operation. While the question asked in this thread was “Is a ratio of .27 too small?” that question seems to be a subset to another question, “What is the optimum ratio of operation?” To date (and I have been trying only for a couple of days) my models are inadequate to answer my own question. To further complicate my efforts, due to previous work on the resonant structure of ELS panels (and I do understand fairly well how these panels resonate), I know that their operation is both chaotic and impacted by surface or boundary effects.

To help in the modeling, I want to examine some real world models. Two basic plate designs have been produced; perforated metal sheets and wire grids. Forgetting the chaotic complexity I just talked about and trying to come back to the original question, calculation of fill to void ratio seems simplest using a sheet of metal perforated with a series of holes. Round wire plate designs are slightly more complex to calculate due to the cross sectional shape of the wire. Yet it is interesting that it was this wire design that both Hermeyer and Sanders chose for their featured ESL panels.

Just as a point of reference and because Acoustat sold a lot of panels, let me use it as a standard of an acceptable design. The Acoustat folk decided to make their panels even more complex than Hermeyer or Sanders. Each plate consists of a plastic square grid panel with plastic coated wires attached on the diaphragm side of the grid. Each square of the grid has outside dimensions of .627 inches by .627 inches. Each hole formed by this grid has inside dimensions of .509 inches by .509 inches. Each of the square voids is vertically bisected by three parallel plastic coated wires with a cross sectional diameter of .084 inches.

A simple calculation of each cell yields a fill to void ratio of .33. Because each cell void shares a side with the adjoining cells, the calculation across the entire panel will yield a larger ratio. In the case of the Acoustat, the ratio for the full panel is .41.

There is little diaphragm motion at the far edge of each panel, so the last row of outside cells are not wired and the diaphragm is not conductive. Do we include this last row of cell in our calculations? I did not. If you did, then the fill to void ratio will be slightly more than .41.

The calculation is also complicated by the diameter of the wire. The largest cross section diameter (or width) of the wire is below the plastic plate grid by a distance of one-half the diameter of the wire. For the two gaps formed between the three parallel strands, this is not important except at each end of the gap where the wires are bisected by the horizontal cross member of the grid. On the outside of the two most outside wires in each cell, there is a small gap between the parallel grid member and the wire. This gap is larger than modeled by the distance the greatest cross sectional diameter of the wire is below the grid member. Since, however, this gap is so small, the curvature of the wire will have little effect on the final fill to void ratio. For each cell it might increase from .33 to .35.

There is also much more diaphragm motion at the center of the panel than anywhere else. With any high frequency or high acceleration signal, pressure increase across the face of the diaphragm will not be even. To minimize short-term pressure build up, the ratio would have to be higher at the center of the panel than at the edge. Yet because the center of the panel is responsible for the bulk of the sound output, this is also where we want our highest e field strength. You cannot make the fill to void ratio too great even here. I have an instinctual feeling, however, that the optimum fill to void ratio is not going to be constant across a typically sized full-range ESL panel.

Now, after all this thinking, let me become practical. For each cell of the Acoustat, the fill to void ratio is .33 to .35. As you include more cells, this ratio will become larger, but not exceed .4 until all the cells of the panel are included. Since diaphragm deflection is not constant across the entire panel, which is the more important measurement? Right now my hypothesis is that the full panel average is not the more important ratio. Considering diaphragm motion, I believe the average operational fill to void ratio for an entire panel is going to be more than your .23 but less than the “ideal” minimum of .4.

Since the degree of diaphragm motion (or deflection) is not constant, but more concentrated in the center of the panel, you could bring the fill to void ratio closer to .4 here with less work than would be required to meet this ratio across the entire panel. Based upon my understanding of the complex deflection of ESL diaphragms, I would suggest an area of approximately one square foot (using the size of Sander’s panel as a reference). You don’t, however, have to make it square. Depending on the final shape of the panel, either an oval or a circle would be appropriate. Since your fill to void ratio is already .23, you will not even need to double the number of holes in the center “square” of the plates.

To make the modifications, choose the sides of the plates that will face the diaphragm. Place the two (or four or however many you plan to make) diaphragm sides of the plates face up. Either enlarge the existing holes or add new holes in the lands. With the small number of drillings needed, you should not require chemical etching to smooth the edges of the holes. Burnishing either by hand or by small machine tool should suffice to minimize the arcing danger. If you can securely clamp the plates together, try drilling more than one plate at a time. This will reduce the amount of burring on the drill out sides of the plates in the center of this metal plate sandwich.

In sum, I don’t believe you have much to fear going with the panels you found. Yes, the fill to void ratio is likely too small in stock condition, but little work will be required to increase this ratio at the most critical area of the plates.

Good luck,

Mark
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Old 4th September 2003, 05:03 AM   #12
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I got my perforated metal from a metal surplus place. It was $2 per square foot (aluminum).

McMaster Carr also has a selection of perf metal. You can pick exactly what you want.

I had mine powder coated for $100 and built up a great sounding set of cells. (I'm listening to them now).

WRT to the diaphragm moving more at the center, my experiments say that's not true. The diaphragm is uniformly driven, and if my optical tests are correct, the edge effect on a typical ESL diaphram seem extend about 1/4" in to the free diaphragm, beyond that the diaphragm is very pistonic.

In order to make the diaphram move more in the middle, the conditions at the middle would have to be quite different. Other than the edge constraints, the driving force is identical everywhere, as is the charge (assuming fairly high resistance coatings). An ESL diaphragm is quite pistonic, mapping a cell with close mic'ed SPL measurements will back this up.


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Old 4th September 2003, 05:05 AM   #13
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Also a big ESL panel is so directional; IE laser beams of sound, that it would have to be moving in a pure pistonic motion or the dispersion would be a lot better.

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Old 4th September 2003, 05:38 AM   #14
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Default Plastic or glass fiber mesh.

How about a plastic or glass fiber mesh as used in mosquito blocking nets. The material is very thin and the mesh is about 1.5mm square. It will be very open as compared to panels with holes in them. The mesh could be made conductive by painting them with conductive paint.
Does this make any sense ? It would also be very easy to get a very flat panel.

It just came to mind that in HT electric power lines the earth line at the top is arranged so that the power lines below it are within 30 degrees ( IIRC) to each side. Apparently its shielding effect from external fields is good in this area. So I guess the conducting wires or mesh will also follow the same principle. The Mylar film's surface will only get complete static coverage over the working range if this 30 degree limit is met. This would indicate that the 40% opening possibly has taken this into account.
What do you think ?
Ashok.
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Old 4th September 2003, 08:27 AM   #15
martinv is offline martinv  New Zealand
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Default Re: Plastic or glass fiber mesh.

Quote:
Originally posted by MarkMcK
Greetings,

I have measured my old Acoustat panels, attempted to model the design, and calculated fill to void ratios for the plates. Still I am uncertain of


Mark, thank you for your reply. You certainly have looked at and thought about this at some length!

When you mention 'fill to void ratio', I believe you actually mean the hole area divided by the total area (what is the correct term for this? Open area ratio I believe - I'll try and use this in future). At least going by your numbers (interesting!) it appears you mean open area ratio.

Quote:
strength there will be. Combine the phenomena and you should have a graph with a distinctive bell shaped curve. In economics this might be called a “Laffer” curve.

A “Laffer” curve suggests the existence of an optimum point (or ratio) of operation. While the question asked in this thread was “Is a ratio of .27 too small?” that question seems to be a subset to another question, “What is the optimum ratio of operation?”
That's a nice way of thinking about it, as a bell curve (or at least some curve with a central maxima). It would be nice to be able to objectivly measure the width and peakiness of the curve. I'm not sure what parameter would go on the Y axis though. Maybe distortion?

Quote:

There is also much more diaphragm motion at the center of the panel than anywhere else. With any high frequency or high acceleration signal, pressure increase across the face of the diaphragm will not be even. To minimize short-term pressure build up, the ratio would have to be higher at the center of the panel than at the edge. Yet because the center of the panel is responsible for the bulk of the sound output, this is also where we want our highest e field strength.
Have you measured the increased diaphragm motion at the centre? In Sanders book he states the motion is almost entirely postonic (is that a word? ) except for very near (0.25 inch) the edge of the cell. This is superimposed on the 'at rest' position of the diaphragm which he says is slightly bowed towards one stator.

Quote:
Either enlarge the existing holes or add new holes in the lands. With the small number of drillings needed, you

<snip!>

Good luck,

Mark
I thought about this too - enlarging the holes. I worked out for the stator panels I was looking at (1 or 4 panels, I forget) that there are around 40000 holes! I don't think I'd want to tackle even a small portion (5%?) of that number!

Quote:
Originally posted by ashok
How about a plastic or glass fiber mesh as used in mosquito blocking nets. The material is very thin and the mesh is about 1.5mm square. It will be very open as compared to panels with holes in them. The mesh could be made conductive by painting them with conductive paint.
Does this make any sense ? It would also be very easy to get a very flat panel.


Any idea how conductive conductive paint really is? I have no idea. I think for the stators it would have to conduct quite well though.

Sounds like an idea worth trying though. Any idea if there are problems applying paint to such a beast? I can imagine if I took to it with paint I'd end up half filling in the holes since they're so small.

Quote:
It just came to mind that in HT electric power lines the earth line at the top is arranged so that the power lines below it are within 30 degrees ( IIRC) to each side. Apparently its shielding effect from external fields is good in this area. So I guess the conducting wires or mesh will also follow the same principle. The Mylar film's surface will only get complete static coverage over the working range if this 30 degree limit is met. This would indicate that the 40% opening possibly has taken this into account.
What do you think ?
Ashok.
I have no idea about HT electric power lines - do they run an 'earth' line??? I though they didn't.

Your conclusion I think is correct though - if the holes are too large there will be areas of the diaphragm a long way from the stator, which is a 'bad thing'.
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Old 4th September 2003, 12:09 PM   #16
SY is offline SY  United States
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Quote:
How about a plastic or glass fiber mesh as used in mosquito blocking nets. The material is very thin and the mesh is about 1.5mm square. It will be very open as compared to panels with holes in them. The mesh could be made conductive by painting them with conductive paint.
You really don't want to do that. Getting the paint to adhere permanently will be a challenge. As will preventing it from blocking the holes. And to get it to coat evenly with no bumps or lumps (corona effect). Aluminized mesh is a possibility, but I don't see any advantage over using metal window screen- or for that matter, metal mesh made for silk-screen use.
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Old 6th September 2003, 06:46 PM   #17
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Default pic of acoustat panel...

Click the image to open in full size.

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