I thought I understood what D meant from the Likkwitz site.
Link to basic explanation here and Graphic .
However, while discussing drivers, I encountered several definitions. For numbers, lets use a 1.2 meter high by 500 mm wide baffle radiating in half space, For a driver, use 270 mm where applicable)
A. D= 1/2 (Width - Driver Diameter), or (500 - 270) /2 = 115 mm
B. D = 1/2 Width, or 250 mm
C. D= square root (Width Squared / pi) Basically 10% larger than B" or 280 mm
D. D = Square root (( Width * Height) /pi) Basically taking the area of the baffle, and converting it to a circle, solve for D or 430 mm
My working assumption has been C. A poster that I respect suggested A. My experiences with a prototype speaker hinted that D was closer than C.
Your input is welcome.
Doug
Link to basic explanation here and Graphic .
However, while discussing drivers, I encountered several definitions. For numbers, lets use a 1.2 meter high by 500 mm wide baffle radiating in half space, For a driver, use 270 mm where applicable)
A. D= 1/2 (Width - Driver Diameter), or (500 - 270) /2 = 115 mm
B. D = 1/2 Width, or 250 mm
C. D= square root (Width Squared / pi) Basically 10% larger than B" or 280 mm
D. D = Square root (( Width * Height) /pi) Basically taking the area of the baffle, and converting it to a circle, solve for D or 430 mm
My working assumption has been C. A poster that I respect suggested A. My experiences with a prototype speaker hinted that D was closer than C.
Your input is welcome.
Doug
I assuming that this is a flat/non folded baffle?
If so I would calculate D as follows.
Center to Center horizontal = 500 mm = D1
Center to Center Vertical = 1200 mm = D2
initial roll off will being when the wavelenth is equal to D1 when the "sides" of the soundwave touch, the sharpness of the roll-off at ~3db/octave. The roll-off will increase until wavelength = D2, at this point it will reach its maximum of 6db/octave and continue for all frequencies below this point.
Think of it this way, you're launching a spherical wave from the baffle. Draw a circle over the square baffle with the diameter of the circle equal to 1 wavelength. The area of the circle overlapping the baffle is the amount of energy radiated forward, the part that sits outside the baffle is canceled by the back wave.. You'll start loosinga little on the sides as soon as D = D1, when D = D2 you will loose in all directions...
--Chris
If so I would calculate D as follows.
Center to Center horizontal = 500 mm = D1
Center to Center Vertical = 1200 mm = D2
initial roll off will being when the wavelenth is equal to D1 when the "sides" of the soundwave touch, the sharpness of the roll-off at ~3db/octave. The roll-off will increase until wavelength = D2, at this point it will reach its maximum of 6db/octave and continue for all frequencies below this point.
Think of it this way, you're launching a spherical wave from the baffle. Draw a circle over the square baffle with the diameter of the circle equal to 1 wavelength. The area of the circle overlapping the baffle is the amount of energy radiated forward, the part that sits outside the baffle is canceled by the back wave.. You'll start loosinga little on the sides as soon as D = D1, when D = D2 you will loose in all directions...
--Chris
See what happens when you post during lunch 
I was too used to thinking about H-frames where D is the distance between the front and rear waveguide openings. I believe you are correct, after re-reading SL's site about flat baffles, D is the avg. radius of your baffle referenced to the center of your driver.
Ok, now I'm just tired
cheers,
AJ
I was too used to thinking about H-frames where D is the distance between the front and rear waveguide openings. I believe you are correct, after re-reading SL's site about flat baffles, D is the avg. radius of your baffle referenced to the center of your driver.Ok, now I'm just tired
cheers,
AJ
I've thought about this quite a bit as well.
I concluded that in essence it depends on the listening position: D should be the path length difference on-axis at listening position between rear and front wave.
Case A: At nearfield, say at the front of the baffle close to the driver, D comes closer to 2x the average radius of the baffle centered at driver: the back wave has to make it around the baffle from the rear center plus in front from edge to center. Of course you'd still have to assume that the driver radius is small vs the baffle radius.
Case B: At "infinity" listening distance, the rear wave has to go the radius to reach the baffle edge, plus the (infinite) distance from baffle to listener. The front wave only has to go the (infinite) distance from baffle to listener. So, in this case, D approaches baffle radius asymptotically.
The effect depends on wavelength too: after all, your cancellation effect depends mainly on the phase difference between front and rear. Below 200 Hz, I calculated that the wavelength is so long that the differences between case A and case B become negligible in terms of phase difference starting at a listening distance of approximately 1.5 to 2 m for usual (largish) baffle sizes.
Conclusion: D corresponds to average baffle radius below 200 Hz if listening / measurement distance > 2 m.
I concluded that in essence it depends on the listening position: D should be the path length difference on-axis at listening position between rear and front wave.
Case A: At nearfield, say at the front of the baffle close to the driver, D comes closer to 2x the average radius of the baffle centered at driver: the back wave has to make it around the baffle from the rear center plus in front from edge to center. Of course you'd still have to assume that the driver radius is small vs the baffle radius.
Case B: At "infinity" listening distance, the rear wave has to go the radius to reach the baffle edge, plus the (infinite) distance from baffle to listener. The front wave only has to go the (infinite) distance from baffle to listener. So, in this case, D approaches baffle radius asymptotically.
The effect depends on wavelength too: after all, your cancellation effect depends mainly on the phase difference between front and rear. Below 200 Hz, I calculated that the wavelength is so long that the differences between case A and case B become negligible in terms of phase difference starting at a listening distance of approximately 1.5 to 2 m for usual (largish) baffle sizes.
Conclusion: D corresponds to average baffle radius below 200 Hz if listening / measurement distance > 2 m.
Doug,
why don`t you get beyond guesswork right from the start?
For everything above 200 Hz, the best OB proportion and the best driver position on the baffle I look at "The Edge":
http://www.tolvan.com/edge/help.htm
To find out, how the OB response is boosted by the floor and how the driver height on the baffle is interfering with the floor, I simulate with Thorsten Loesch´s xlbaffle.xls:
http://baseportal.de/cgi-bin/baseportal.pl?htx=/Data/exdreamaudio/download_ex&Art~=Excelsheet
This is as far as it gets to reality IMHO.
Rudolf
why don`t you get beyond guesswork right from the start?
For everything above 200 Hz, the best OB proportion and the best driver position on the baffle I look at "The Edge":
http://www.tolvan.com/edge/help.htm
To find out, how the OB response is boosted by the floor and how the driver height on the baffle is interfering with the floor, I simulate with Thorsten Loesch´s xlbaffle.xls:
http://baseportal.de/cgi-bin/baseportal.pl?htx=/Data/exdreamaudio/download_ex&Art~=Excelsheet
This is as far as it gets to reality IMHO.
Rudolf
Hi MBK,
AFAIK Doug is not looking for the "D" definition in the first place, but for a handsome formula to calculate dipole rolloff. But as he already found out, baffle height is as much a contributing factor to the rolloff as baffle width.
Both tools presented account for that. Thorsten Loesch even accounts for floor gain and driver T/S-parameters. Looking for smoothed diffraction, like Edge does, is just a nice extra IMHO.
That way you end at much smaller (and realistic) dimensions than by simply calculating with "D".
AFAIK Doug is not looking for the "D" definition in the first place, but for a handsome formula to calculate dipole rolloff. But as he already found out, baffle height is as much a contributing factor to the rolloff as baffle width.
Both tools presented account for that. Thorsten Loesch even accounts for floor gain and driver T/S-parameters. Looking for smoothed diffraction, like Edge does, is just a nice extra IMHO.
That way you end at much smaller (and realistic) dimensions than by simply calculating with "D".
MBK,
I just simulated a 150x500cm baffle with a 200 dia driver on it. The 6 dB dipole rolloff beyond ~200 Hz is clearly visible to me.
Keep in mind that this is a full space simulation (no floor gain). And note the checked "Open baffle" box in the right window.
EDGE even provides an "Open baffle bass drop compensation" calculator for active filtering.
I just simulated a 150x500cm baffle with a 200 dia driver on it. The 6 dB dipole rolloff beyond ~200 Hz is clearly visible to me.
Keep in mind that this is a full space simulation (no floor gain). And note the checked "Open baffle" box in the right window.
EDGE even provides an "Open baffle bass drop compensation" calculator for active filtering.
Attachments
Alright, I'll explain:
The Edge page didn't open on the link you gave at first try. So I read a short summary somewhere else on that page and then wrote my first reply w/o actually trying the program, and w/o reading your original link where the author explains the capabilities in detail...
(now it makes sense does it?
)
Anyway: it worked eventually, so I tried and played with both the spreadsheet and the Edge, and compared to my actual measurements in half space outdoors and indoors. Not bad, hits the general looks of the real measurement, but major peaks and dips differ from reality. Then again I have a (shallow) U-frame (about 15 cm), and real life MLS resolution does not come close to the simulation's "exact" prediction.
I'd say all in all Linkwitz gives quite a good approximation with his formulas using "D", and real life from this short experiment still differs from both by enough a margin to warrant a lot of experimentation, guesswork, and tacit knowledge. 
The Edge page didn't open on the link you gave at first try. So I read a short summary somewhere else on that page and then wrote my first reply w/o actually trying the program, and w/o reading your original link where the author explains the capabilities in detail...
(now it makes sense does it?
)Anyway: it worked eventually, so I tried and played with both the spreadsheet and the Edge, and compared to my actual measurements in half space outdoors and indoors. Not bad, hits the general looks of the real measurement, but major peaks and dips differ from reality. Then again I have a (shallow) U-frame (about 15 cm), and real life MLS resolution does not come close to the simulation's "exact" prediction.
I'd say all in all Linkwitz gives quite a good approximation with his formulas using "D", and real life from this short experiment still differs from both by enough a margin to warrant a lot of experimentation, guesswork, and tacit knowledge.
Konnichiwa,
Just to add, the XLBaffle Spreadsheet was written using a first approximation of the dipole rolloff and based on an AES Preprin and simplifications of the math in that, the room effect is largely fudged, the end result remains REMARKABLY close.
I have previously criticised the math and detail given on Siegfried Linkwitz's site as being not useful insofar, as it does not predict what really happens.
I have noticed more or less recently that SL himself includes the issues that cause the diations in his analysis elsewhere on his site. When combining these with his basic math we arrive back at similar results to my own spreadsheet and experience in performance.
The key difference is that Mr. Linkwitz treats these effects as undesirable deviations from the ideal that must be equalised out in order to allow the equalisation to applied such as i we where to equalise an ideal dipole while I treat them as usefull resources to minimise (or eliminate) the need for equalisation on Dipoles.
Some of this "it's an error so let's remove it" philosophy can be noted here:
http://www.linkwitzlab.com/models.htm#D
This section also covers some of the desirable properties of dipole cone drivers (rear radiation rolloff at high frequencies, increased beaming at higher frequencies).
The differences overall acrue as follows:
1) Mr. Linkwitz's Math assumes more or less a round baffle with D(iameter) equal to the smalles baffle dimension, one might call this worst case condition. Using "The Edge" (yummy when from Pizza the Hut) gives a more accurate result.
2) HOWEVER both "The Edge" and Mr. Linkwitz's pages assume a dipole in completely open space, which is simply not present in a normal audio system. In reality we have two more effects.
3) First, for a wavelength with a length longer than than two times the distance to the floor (eg, 65cm floor distance, critical frequency around 260Hz) the floor reflection begins to be progressively in phase with the direct radiation, giving a boost of around 3db at the critical frequency and levels out at a total of 6db LF gain one octave below. The bottom line is that we have 6db more SPL at all frequencies more than one octave below the critical frequency and a 3db boost at the critical frequency not accounted for in traditional dipole theory.
Mr. Linkwitz covers this in some detail:
(see http://www.linkwitzlab.com/models.htm#F1 )
It should be noted that sidewall reflection invariably happen too and usually happen at a lower frequency and will add another up to 6db LF SPL
4) We have so far assumed that the rear wave of the dipole either wraps around forward arund the baffle or is "lost in space", but in reality we have a rear wall which will reflect back our rearwave towards the listener.There will be some attenuation and (obviously) some delay, if we take our exampe of 1m distance to the rear wall the sound will be delayed by 6mS.
As our rear-wave is in opposite polarity to the frontal one at around 90Hz (for our 1m distance) we can conclude that it will re-inforce our front wave at 90Hz, BUT it will cancel it at 45Hz, of course in reality the rear wave is somewhat damped and will thus not lead to such extreme problems and more interesting, by tuning the rearwall distance carefully one should be able to "fill in" the combfilter response caused by the floor reflection to a good degree, usually a "golden ratio" placement of the speaker which accounts for the inverted polarity of the rear wave makes for a rather smooth response.
Anyway, the above items are intended to illustrate why a dipole that SHOULD roll off at 200Hz and SHOULD be down 12db at 50Hz may very well be flat at 50Hz, in room.
Sayonara
Rudolf said:
Just to add, the XLBaffle Spreadsheet was written using a first approximation of the dipole rolloff and based on an AES Preprin and simplifications of the math in that, the room effect is largely fudged, the end result remains REMARKABLY close.
I have previously criticised the math and detail given on Siegfried Linkwitz's site as being not useful insofar, as it does not predict what really happens.
I have noticed more or less recently that SL himself includes the issues that cause the diations in his analysis elsewhere on his site. When combining these with his basic math we arrive back at similar results to my own spreadsheet and experience in performance.
The key difference is that Mr. Linkwitz treats these effects as undesirable deviations from the ideal that must be equalised out in order to allow the equalisation to applied such as i we where to equalise an ideal dipole while I treat them as usefull resources to minimise (or eliminate) the need for equalisation on Dipoles.
Some of this "it's an error so let's remove it" philosophy can be noted here:
http://www.linkwitzlab.com/models.htm#D
This section also covers some of the desirable properties of dipole cone drivers (rear radiation rolloff at high frequencies, increased beaming at higher frequencies).
The differences overall acrue as follows:
1) Mr. Linkwitz's Math assumes more or less a round baffle with D(iameter) equal to the smalles baffle dimension, one might call this worst case condition. Using "The Edge" (yummy when from Pizza the Hut) gives a more accurate result.
2) HOWEVER both "The Edge" and Mr. Linkwitz's pages assume a dipole in completely open space, which is simply not present in a normal audio system. In reality we have two more effects.
3) First, for a wavelength with a length longer than than two times the distance to the floor (eg, 65cm floor distance, critical frequency around 260Hz) the floor reflection begins to be progressively in phase with the direct radiation, giving a boost of around 3db at the critical frequency and levels out at a total of 6db LF gain one octave below. The bottom line is that we have 6db more SPL at all frequencies more than one octave below the critical frequency and a 3db boost at the critical frequency not accounted for in traditional dipole theory.
Mr. Linkwitz covers this in some detail:
(see http://www.linkwitzlab.com/models.htm#F1 )
It should be noted that sidewall reflection invariably happen too and usually happen at a lower frequency and will add another up to 6db LF SPL
4) We have so far assumed that the rear wave of the dipole either wraps around forward arund the baffle or is "lost in space", but in reality we have a rear wall which will reflect back our rearwave towards the listener.There will be some attenuation and (obviously) some delay, if we take our exampe of 1m distance to the rear wall the sound will be delayed by 6mS.
As our rear-wave is in opposite polarity to the frontal one at around 90Hz (for our 1m distance) we can conclude that it will re-inforce our front wave at 90Hz, BUT it will cancel it at 45Hz, of course in reality the rear wave is somewhat damped and will thus not lead to such extreme problems and more interesting, by tuning the rearwall distance carefully one should be able to "fill in" the combfilter response caused by the floor reflection to a good degree, usually a "golden ratio" placement of the speaker which accounts for the inverted polarity of the rear wave makes for a rather smooth response.
Anyway, the above items are intended to illustrate why a dipole that SHOULD roll off at 200Hz and SHOULD be down 12db at 50Hz may very well be flat at 50Hz, in room.
Sayonara
AJinFLA said:Ok Doug,
posting at lunch again
Dipoles are definately fun to play with. Empirical results are often the most important. Enjoy.
cheers,
AJ
I have to agree, simulation could only give you a hint what will go on, but reallity will be different.
Stephan
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