Wednesday, May 25, 2011

Pool House dimensions hit the sweet spot

I am now calling the fancy brick shed that is almost under construction (down payment made, waiting for engineering review of concrete slab) the "pool house".  Actually, there isn't any pool yet, but my long term backyard plan is to have a hot tub right next to it at the end of an extended patio.  Pool House sounds a lot fancier than Shed, and in fact the building currently being designed will be much more upscale than the usual shed.

One of the functions of the pool house will be to store the factory boxes I have for many of my most important hifi components...

This Pool House is not primarily intended as a "man cave" (my whole house is currently a man cave, and I intend to keep it mostly that way, perhaps conceding design authority over one bedroom, one bathroom, and some of the area in the kitchen to a friend who hopes to move over in about a year).

But just because I'm an audiophile, and I think it's the right way to do things, I've kept acoustics in mind from the very beginning, and tried to design around a set of well known dimensional ratios for room acoustics.

I originally intended to fit the 1 : 1.28 : 1.54 ratio.  Assuming the (originally planned to be unfinished) ceiling would be almost 10 feet high, it seemed to follow that the (exterior) dimensions should be about 12 and a half feet, and 15 feet.

Then it became clear that brick wall construction eats a lot of interior space because the walls are about 6 inches thicker (shortening each non-vertical dimension by one whole foot).  Well that changed the calculations entirely, so I started fudging, and with sloppy and probably incorrect math changed the 15 foot exterior dimension to 14 feet 10 inches.  I wanted to have it less than 15 feet anyway to avoid the need for an expansion joint in the foundation (given 6 inch slab, and normally you can have 2.5 linear feet for each inch of slab thickness, or so I have read on the web).  14 feet 10 inches seemed to be changing the non-vertical ratios as needed for a one foot loss to wall thickness, AND to be playing it extra safe wrt the slab design.

But then, after further pondering, I decided it would be even better for ensuring the longevity of my hifi boxes if I moderated temperature (and therefore humidity) swings somewhat by having fully insulated and finished walls and ceiling.  Now that's adding another 4 1/8 inches to each wall, assuming 5/8 interior sheetrock.  Once again blowing up my calculations, though this time the ceiling height was being reduced as well.

But then the contractor asked if I would rather have 8 foot or 9 foot walls.  This was important to the engineering.  Well I had been worried about enough loft space, and after a day of thinking about it decided to go for the 9 foot walls.  I was still uncertain about height of the finished ceiling (I figured about 8-8.5 feet) given 9 foot walls.  But then yesterday I found that with 9 foot walls, I can have 9 foot minimum ceiling height, and it can easily rise to 9.75 or more by attaching ceiling to the underside of the rafter braces, though the lower the braces the better.  The roof is intended to be either 5/12 or 6/12 slope.

So now I finally had all the details for evaluating the acoustics.  And bringing all the numbers together, I hit another sweet spot exactly with a 9 foot 5.5 inch ceiling height.

Here are the numbers.  The exact thickness of each side wall from exterior to inner finished wall is:

4 inches brick
1 inch air gap
tar paper (not expected to affect wall thickness significantly)
3/4 OSB sheathing
3.5 inch framing
5/8 interior sheet rock (hope to get Quiet Rock 528 if affordable)

That adds up to 9.875 (9 7/8) inch thickness.  Two walls reduce each dimension by 19.75 inches from the exterior.

This reduces the 14 foot 10 inch exterior length to 13 feet 2.25 inches on interior.

This reduces the 12 foot 6 inch exterior length to 10 feet 10.25 inches.

Those are fixed by specifications already given to the engineer.  I wouldn't want to change them much anyway.  There is some still some play in setting the ceiling height because the braces can either be raised or lowered a bit.  It turns out, the perfect spot is hit right at 9 feet 5.5 inches ceiling height.  This gives one of the most commonly used dimensional ratios:

1 : 1.14 : 1.39

This is the most cubelike of all the well known and accepted acoustically optimal dimensional ratio sets.  It is a sweet spot.

And I hit this mostly by luck...I had actually been aiming for a different ratio, but because of errors in calculation followed by a new optimization, I got there.

Here is a online great dimensional ratio calculator (the best I have seen, complete with loads of results and documentation):

This is much better than the RoomModes calculator provided by RealTraps because it runs on all computer systems (as a server-side script), includes oblique and tangential modes in the calculations, and provides vast documentation.  BTW the 1:1.14:1.39 ratio set was extensively analyzed by L.W. Sepmeyer in 1965.  This is discussed here:

One slight flaw in my reasoning is the slight rise in the celing from the 9 foot side walls to 9 feet 5.5 inches in the central region.  This is a very slight vaulting (correct word?), fortunately it in the desireable direction wrt the long "listening axis" of the room.  This may have effects mostly on the oblique and tangential modes assumed in the acoustical optimization.  I'm not sure what to do about that.  Would it be better acoustically if I just had a completely flat ceiling at 9 feet? The 5.5 inch rise only takes about 1 foot inwards from the side walls, then the ceiling will be flat (under the brace) from there on to the center.  I would like the extra height to increase loft storage height and volume (and wouldn't mind more actually, 5.5 inches increases loft volume by 10 cuft, and probably soon enough the extra 5.5 inches in height will prove to be essential for something).

Or maybe I should raise the ceiling height just a bit more to compensate for the vaulting.  It's well within structural considerations to raise ultimate ceiling height to about 10 feet in the central region, but then that starts getting too cubelike (2 almost identical dimensions) for good acoustics.  So 9 feet 5.5 inches is a good compromise given what I know now.  A flat ceiling at 9 feet also looks pretty good acoustically, it comes close to the 1 : 1.2 : 1.5 ratio set (actually 1 : 1.2 : 1.46) which might even be slightly better than 1:1.14:1.39.  The whole range from 9-9.5 feet is excellent, when you get down below 9 feet certain other acoustic problems occur.

Here is a blog in which Ethan Winer claims that vaulting is great (well, so long as you buy his Real Traps to run along the peak).

The real world is never as simple as some of these acoustical optimizations assume.  For example, the walls are not perfectly rigid, rather somewhat flexible and damped.  And then there is the framing and sheathing, etc., behind the walls.  All these are active to some degree.  And then there are the windows.  And then there is the stuff you put in the room.  Most of this doesn't have much effect, but all together it has a substantial effect that is way beyond the power of free simulators to estimate.

Often when people try to build to the correct ratios, or modify to them, they find it doesn't make as much difference as expected.  The correct ratios are not magic numbers that make all the room modes go away, they are simply magic numbers that prevent (to some degree) the room modes from adding up in especially undesireable ways, as often happens in the real world.  Perfect ratios or not, a fantastic amount of properly designed acoustic bass traps would be required to get to truly accurate sound reproduction; even to meet international standards for accurate musical evaluation (based on RT60 and the like) my 1:1.14:1.39 room would have to have about 360 effective sabins of broadband damping, according to the calculator above, and the damping itself can cause problems if not properly engineered and installed for the room at hand. Good luck.  A well designed $500 bass trap can give you about 16 sabins at 50 Hz. while an ineffective trap for $250 might give only 0.5 sabins at 50Hz (I have actual products in mind).   As the bass trap sellers say, you'll run out of room before you run out of the need for more bass traps.  (And money also, but they don't say that.)

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