Compute D for dipole speaker

[DougL]

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

[DIY_newbie]

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

[AJinFLA]

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

[MBK]

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.

[Rudolf]

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/basepor...rt~=Excelsheet

This is as far as it gets to reality IMHO.

Rudolf

[MBK]

Hi Rudolf,

I don't think this addresses Doug's question - these tools help with proportions for smoothed diffraction, and room gain, but not with dipole rolloff due to "D"

[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".

[MBK]

Hi Rudolf,

maybe I just don't get it - the tools look like baffle step calculators of some sort to me, not dipole rolloff calculators...

[Rudolf]

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.

[MBK]

Hi Rudolf,

ok, I see - did not see this option...