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OB Design

It's possible to design an open baffle speaker or subwoofer without a computer.  Without even doing any math at all.  It's probably not a good idea considering the selection of great inexpensive modeling software available today but it's interesting to see how the little details play off against each other.  You can start to design with a specific speaker driver in mind or you can begin with a predetermined baffle size and work backwards into finding suitable drivers.  Either way, the fs and qts of the bass driver will determine whether it is suitable for use in any given baffle. 
 
 

 

Starting with the driver's contribution, we can learn a lot by examining the picture of the effect of varying qts in an infinite baffle as shown above.  I created this theoretical situation by entering a driver's parameters and then changing only qts while everything else - including fs - remained the same.  This is a very rough example but it's clear that very low q drivers exhibit a rising response and very high q drivers have a big peak near fs when used in an infinite baffle.  The numbers might be a bit too small to read but samples are taken at qts = .25, .5, 1 and 2.
 
 
 

 
 
Now that the bold lines have been added to denote multiples of fs this chart can be used to loosely approximate any driver's behavior in IB.  Most available drivers will have a qts that will fit in between the lines somewhere between .25 and 2, with .7 qts having quite flat response down to near fs and being often quoted as the ideal qts for infinite baffle.  The raw IB data is the first piece of the puzzle.  For example, let's say we had a driver with a measured qts of 1.3 and 113 hz fs.  We could safely assume that in an IB it would be fairly flat down to around fs x 3 (339 hz).  Below that a gentle, wide peak about 2 or 3 db high near fs.  And below fs response drops off at 12 db/oct.
 
 
 
 
The next step is compensating for a baffle of finite size.  Above is a picture generated in The Edge so you can see the effect a baffle alone has on response.  The baffle being simulated here is about 8 inches wide by 20 high and the driver is centered about 1/4 of the way down from the top.  Below the baffle step frequency - about 450 hz in this case - response drops off at 6 db/oct.  An octave or so above the baffle step frequency (depending on driver position on the baffle) there is a big diffraction peak and then above that response evens out into the upper registers.  There are things you can do to counter the spiky diffraction peaks but we'll get into that later.  For now all we need to know is that an 8 inch wide baffle will support frequencies down to around 450 hz.  18 inches width will get you 200 hz, and if you wanted baffle support down to 100 hz you would need to a 3 foot wide baffle. 
 
 
 
 
Now that we know how a driver reacts in an infinite baffle and we know how a finite baffle size supports a certain frequency range we can sum the two together.  Going back to the example, a driver with 1.3 qts and 113 fs on an 8 inch baffle is modeled in the picture above.  Disregard the green line, we're interested in the response marked "Pioneer OB".  The baffle step induced rolloff around 450 hz is perfectly augmented by the peak near driver fs caused by high qts.  The result is flat response a full octave below the baffle step frequency.  The big diffraction peak is also seen here (although it's not at exactly the same frequency as the graph above due to mismatched driver position in my hasty modeling).  This example is based on an actual small open baffle project documented hereWith this information we can also derive that midrange drivers can have a fairly low q and still maintain flat(ish) response on a large baffle.
 
And that's how you can get a pretty accurate estimation of what's going to happen with any given driver on a baffle and if you understand the concepts involved you can do it almost instantaneously in your head. 
 
That's a good start but it's just the beginning.  There are several different ways to proceed from here.  Take another look at the last chart above and check out the green line this time.  That's the OB friendly Eminence Alpha 15A on a 20 inch wide baffle.  That speaker driver is used in a lot of DIY and commercial open baffle creations.  Some designers use this driver only from fs up to 200 hz to avoid and work around the first big diffraction peak, and they apply a simple filter to get flat response in that range.  Others prefer to run it all the up well past 1khz and into the driver's breakup region with no filters to tame the rising response or diffraction at all.  Some people prefer to use it in a multi-way with each driver on a separate baffle, specially sized to preserve decent power response for each individual driver.  As always, everything is a compromise.
 
OB diffraction is a big issue.  The effects are 2x worse than monopole diffraction.  As mentioned above you can try to work around it by crossing the woofer over below the first big diffraction bump and crossing the mid over above the peak like MJK does in his famous Fullrange + Alpha 15A project.  Or you could use a passive notch filter (or active eq) to get rid of it.  But there are effective mechanical solutions as well.  Offsetting the driver both horizontally and vertically is one of the most powerful tools.  Rounding off the baffle edges helps as well but only a large radius helps appreciably.  Lining the baffle, and especially the edges with thick, heavy felt or similar material can help too.  Larger drivers on big baffles don't seem to be as harshly affected as small drivers on little baffles.
 
Open baffle design can get a whole lot more complicated than this but that's beyond the scope of this discussion.  For further information on the subject look into the works of Sigfried Linkwitz, John Kreskovsky and Martin J. King.  Both of the latter have created widely renowned open baffle specific simulation software at very attractive prices (MJK's is $25, John's is free).  And there's always XLBaffle if you want a super simple free simulator.
 
Practice makes perfect.  Good luck.