Wavelength. 200 hz vs 1000 hz. I can't go higher than 1 khz or the waves disappear. I'm not too familiar with this feature and I don't have time to play with it, I have to go to work.
I'm not sure what point you are trying to make. In all these subs the wavelengths are going to be larger than the mouth.
I'm not sure what point you are trying to make. In all these subs the wavelengths are going to be larger than the mouth.
An externally hosted image should be here but it was not working when we last tested it.
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So when Cir is 1 or less the plane model is accurate and the mouth bubble does not need to be considered at all.
I'm just guessing, but in this case with this horn we are studying I think Cir is less than 1, so I guess we can just completely disregard the bubble.
Using short wavelength high frequency depictions to discuss a "bubble", or "interesting zone extending beyond the mouth" in a subwoofer is incorrect. I've been saying that all along. Confusing width of waves with wavelength certainly muddied the discussion until I figured out the error. Pics do indeed help in providing consistency in terms.
Danley is apparently including part of the "interesting zone" in his horn length, if I read that correctly. That is consistent with the argument of multiple horns increasing lf extension. How it can be included in a sim, I've no answer for that.
The mix in understandings between diffraction of hf waveforms, and wraparound consistent with lf operation does not help the discussion, they have different characteristics.
Thanks for the last two drawings, I appreciate the time and effort you have taken in this discussion with me.
Edit: There appears to be an error in your upper lf depiction. The green area in the pipe enters it's expansion phase (the intermediate one) and appears to be at least twice the length it should be. If software is doing that, there is a bug in the software.
jn
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Hi Guys
It’s fun to watch the arguing but measurements of the real things would be more telling.
Look at the radiation resistance curve for a horn (similar to that of a piston radiator).
The object of the horn is to “connect” or couple the impedance of the big end to the small end and this raises the efficiency by presenting more acoustic load to the driver.
When the mouth is “large enough” for the low cutoff, about 1wl in circumference, one has reached the knee in the radiation resistance curve and a further increase in area produces no significant increase in loading. In that case (operation where the big end is on the flat portion of the resistance curve, a constant radiator velocity produces flat response.
Once it is that large, one can also be sure that above the low cutoff, the horn is still “large enough” to reach the flat portion of the curve. Above the low cutoff, the active portion moves into the interior of the horn. The same is true for the dimensions which govern the radiation angle, it also moves into the interior when the frequency is increased (and is why curved wall horns generally have a much narrower radiation angle at high frequencies, it is more like the throat angle instead of mouth angle is setting the pattern and inferred in Don Keele’s pattern loss frequency thumb rule ).
In the real world, bass horns are rarely large enough to reach the plateau of that curve and so they spend much of the time on the sloped part of the curve and while there is a gain from even that impedance transformation, it is not as large as it would be with a full sized horn mouth.
If one were to plot the expansion of a duct on a flat baffle, one sees that the area is constant out to the end of the duct and then the area expands rapidly in a hemisphere bounded by the flat baffle and then expands spherically once past the baffle into free space.
Conceptually this is the same thing as a horn, acoustically it is different.
The impedance transformation or ability to reflect the big end impedance to the small end is in part set by the rate of expansion, if one compares the conical expansion to an exponential expansion rate, one can see the conical expansion has less low frequency loading while the exponential expansion has a constant rate of expansion, the conical expands very rapidly at the throat and expands more slowly as one moves towards the mouth.
For the simple exponential horn, the “high pass” corner for that impedance transformation is as mentioned related to the expansion rate, for a 30Hz horn, the area can expand no faster than doubling every two feet or so while at 300Hz, it’s more like 2.4 inches.
It was an offhand comment by Don Davis at a Synaudcon meeting in the late 80’s which lead to the Unity and Synergy horns over the last 18 years. He commented that conical horns have a more constant directivity but had inferior low frequency loading. Many years later after, it dawned on me why they had poor lf loading, it was because the rate of expansion at the throat was very rapid and wouldn’t couple the low end to the mouth. I thought “what if I coupled mid and low drivers into the conical horn through it’s sides where the expansion rate was more suited to mid range and low frequencies, into to the single horn body and at a dimension less than ¼ wavelength so that they coherently added into one new source”.
Doing that would eliminate the lobes and nulls in the polar pattern that separate sources produce and conceptually could act as if they only had one full range driver with no crossover. Sounded easy but has taken some time to work out.
The idea for the Boundary coupled woofers like the 415 is that the hemispheric mouth “bubble” is actually bounded by the 60 by 60 inch flat baffle but in order for that to couple to the interior horn, the interior horn has to have an end area large enough to provide something close to the needed expansion rate to mate up to the exterior expansion. At the low end, the exit hole is a minor effect compared to the radiation resistances. The up side is whatever the acoustic gain is by that coupling AND the acoustic energy because of forward directivity which reduces the spl going to the rear. Keep in mind your talking about a subwoofer where 4 or 6 would be used in a large football stadium and ones and two’s per side for loud EDM events, not a home speaker unless one wants to dry their hair with it;
https://www.youtube.com/watch?v=Mz6qQIfIx6s
(yes she had ear plugs in)
Remember that a horn does not have to be a continuous expansion, a set of stepped diameter pipes will also work as a bass horn and here, the smaller “exit hole” is a way to couple the interior horn to the geometry of the exterior expansion. This way, the exterior hemispheric expansion, the pressure still coupled to the interior horn bounded by the cabinet wall, is arguably around 60 inches dia.
I guess a better way to illustrate this is to look at corner loading.
If one starts in a room corner and plots the area of expansion, say every ½ inch as one moves out of the corner, one see’s the area increasing rapidly AND that the rate of expansion so far as an exponential horn goes is also changing.
In order to benefit from fractional space loading, all one needs to be is in the corner. To actually couple into that corner expansion and get horn loading as if the walls were part of the same horn, one has to figure out how far from the corner you need to be for the rate of expansion (the high pass corner effect to horn loading) to be compatible with your desired low cutoff AND then build your horn so that it’s big end area is where it needs to be in that expansion AND is an area that is “as if” it were a single horn.
Horns are (my personal belief) an axial mode acoustic resonator which acts much like LCL series tank circuit (s) and like them, can match one impedance to another. If you consider the exponential horn, one finds that progression follows the LCL tank proportions. The difference being the horn is also a frequency variable device so it can cover a broader band and when the source and terminating resistances are near ideal, the evidence of the resonances are gone being dominated by resistances, leaving what appears to be an acoustic transformer.
Best,
Tom
It’s fun to watch the arguing but measurements of the real things would be more telling.
Look at the radiation resistance curve for a horn (similar to that of a piston radiator).
The object of the horn is to “connect” or couple the impedance of the big end to the small end and this raises the efficiency by presenting more acoustic load to the driver.
When the mouth is “large enough” for the low cutoff, about 1wl in circumference, one has reached the knee in the radiation resistance curve and a further increase in area produces no significant increase in loading. In that case (operation where the big end is on the flat portion of the resistance curve, a constant radiator velocity produces flat response.
Once it is that large, one can also be sure that above the low cutoff, the horn is still “large enough” to reach the flat portion of the curve. Above the low cutoff, the active portion moves into the interior of the horn. The same is true for the dimensions which govern the radiation angle, it also moves into the interior when the frequency is increased (and is why curved wall horns generally have a much narrower radiation angle at high frequencies, it is more like the throat angle instead of mouth angle is setting the pattern and inferred in Don Keele’s pattern loss frequency thumb rule ).
In the real world, bass horns are rarely large enough to reach the plateau of that curve and so they spend much of the time on the sloped part of the curve and while there is a gain from even that impedance transformation, it is not as large as it would be with a full sized horn mouth.
If one were to plot the expansion of a duct on a flat baffle, one sees that the area is constant out to the end of the duct and then the area expands rapidly in a hemisphere bounded by the flat baffle and then expands spherically once past the baffle into free space.
Conceptually this is the same thing as a horn, acoustically it is different.
The impedance transformation or ability to reflect the big end impedance to the small end is in part set by the rate of expansion, if one compares the conical expansion to an exponential expansion rate, one can see the conical expansion has less low frequency loading while the exponential expansion has a constant rate of expansion, the conical expands very rapidly at the throat and expands more slowly as one moves towards the mouth.
For the simple exponential horn, the “high pass” corner for that impedance transformation is as mentioned related to the expansion rate, for a 30Hz horn, the area can expand no faster than doubling every two feet or so while at 300Hz, it’s more like 2.4 inches.
It was an offhand comment by Don Davis at a Synaudcon meeting in the late 80’s which lead to the Unity and Synergy horns over the last 18 years. He commented that conical horns have a more constant directivity but had inferior low frequency loading. Many years later after, it dawned on me why they had poor lf loading, it was because the rate of expansion at the throat was very rapid and wouldn’t couple the low end to the mouth. I thought “what if I coupled mid and low drivers into the conical horn through it’s sides where the expansion rate was more suited to mid range and low frequencies, into to the single horn body and at a dimension less than ¼ wavelength so that they coherently added into one new source”.
Doing that would eliminate the lobes and nulls in the polar pattern that separate sources produce and conceptually could act as if they only had one full range driver with no crossover. Sounded easy but has taken some time to work out.
The idea for the Boundary coupled woofers like the 415 is that the hemispheric mouth “bubble” is actually bounded by the 60 by 60 inch flat baffle but in order for that to couple to the interior horn, the interior horn has to have an end area large enough to provide something close to the needed expansion rate to mate up to the exterior expansion. At the low end, the exit hole is a minor effect compared to the radiation resistances. The up side is whatever the acoustic gain is by that coupling AND the acoustic energy because of forward directivity which reduces the spl going to the rear. Keep in mind your talking about a subwoofer where 4 or 6 would be used in a large football stadium and ones and two’s per side for loud EDM events, not a home speaker unless one wants to dry their hair with it;
https://www.youtube.com/watch?v=Mz6qQIfIx6s
(yes she had ear plugs in)
Remember that a horn does not have to be a continuous expansion, a set of stepped diameter pipes will also work as a bass horn and here, the smaller “exit hole” is a way to couple the interior horn to the geometry of the exterior expansion. This way, the exterior hemispheric expansion, the pressure still coupled to the interior horn bounded by the cabinet wall, is arguably around 60 inches dia.
I guess a better way to illustrate this is to look at corner loading.
If one starts in a room corner and plots the area of expansion, say every ½ inch as one moves out of the corner, one see’s the area increasing rapidly AND that the rate of expansion so far as an exponential horn goes is also changing.
In order to benefit from fractional space loading, all one needs to be is in the corner. To actually couple into that corner expansion and get horn loading as if the walls were part of the same horn, one has to figure out how far from the corner you need to be for the rate of expansion (the high pass corner effect to horn loading) to be compatible with your desired low cutoff AND then build your horn so that it’s big end area is where it needs to be in that expansion AND is an area that is “as if” it were a single horn.
Horns are (my personal belief) an axial mode acoustic resonator which acts much like LCL series tank circuit (s) and like them, can match one impedance to another. If you consider the exponential horn, one finds that progression follows the LCL tank proportions. The difference being the horn is also a frequency variable device so it can cover a broader band and when the source and terminating resistances are near ideal, the evidence of the resonances are gone being dominated by resistances, leaving what appears to be an acoustic transformer.
Best,
Tom
Seeing that the discussion is about subwoofer waves, why doesn't the HR Wavefront Simulator go below 100hz???
Hey Tom, long time..
Who's arguing? We're discussing...I think there is a difference.
Measurements? Where's the fun in that?
You're supposed to bring cool looking false color images to the table..
Or a drink..
John
We have a measurement, it's on your site and we have been referring to it. What we need is accurate plans to sim from, or for someone to measure something else that already has accurate plans to sim from. Since neither of these are likely to happen soon your measurement and a guess at the plans are all we have to work with.
Clearly a lot of thought went into the design of this line of subs but my only interest is in how to accurately sim this design (and all other designs).
This design can be simulated to a fairly high degree of accuracy, like all other designs.
If we took this cab and buried it so the front face was flush with the ground, I don't think anyone would disagree that there would be no trouble simulating it in Hornresp or Akabak. In that case it would just be a regular horn in 2 pi space with a bit of mass loading at the mouth and an infinite size boundary surrounding it.
And I think realizing that is the key.
The only difference between burying it in the ground and having it stand up (with it's boundary extension surrounding the mouth) is the boundary around the mouth is now a finite size, much smaller than the ground it was buried in. And the finite size boundary is what diffraction accounts for.
As long as the diffraction model can accurately reflect the physical situation of a finite boundary it should provide a sim as accurate as the situation in the bolded paragraph.
I have been thinking about this bubble and whether or not it affects the length of the horn. Even if there is a bubble that has a horn like expansion beyond the baffle - the hard edge of the aperture or horn mouth serves as a hard acoustic boundary condition for the fundamental wave to "attach" to - thereby defining the 1/4-wave length. Any "soft" edge bubble "horn" will have a hard time competing with a hard edged boundary condition, and as a result, the low bass extension will be dominated by the physical hard edge. There may be a mild extension due to the bubble but it will be minor compared to the main one defined by the physical aperture or edge. A soft edge using a series of sawtooth patterns or a bunch of small Karlson slots may help to provide a smooth impedance transition from horn mouth boundary to free space.
Going back to Tom Danley's April 07, 2005 explanations might help you better understand the BDEAP and the later BC horns.
4 Labhorns vs 2 or 4 Bdeap32?
Then a few years later, Ivan Beaver had more comments:
http://forums.prosoundweb.com/index.php?topic=96010.5;wap2
Art
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Weltersys,
I finally got a chance to read Tom Danley's explanation of the BDEAP (Bounary Dependent External Air Path, patent pending). In a 2x2 configuration, he said that the cabinets provide a wall for enhanced directivity, like a 180 deg "horn" with very rapid expansion. This is exactly how I modeled the BC415's expansion from the aperture of the 60in x 60in box face. But as I noted above, having the expansion occur over a true flat wall vs a very shallow 4in deep horn makes a big difference. Which leads me to think maybe there is something to making the box wall slightly cupped (by say, 4 inches over the 60in square wall) to enhance the bass extension, directivity, and efficiency, without taking up hardly any bulk. This could be as easy as adding lightweight XPS foam panels to the outside with a slight slope.
I finally got a chance to read Tom Danley's explanation of the BDEAP (Bounary Dependent External Air Path, patent pending). In a 2x2 configuration, he said that the cabinets provide a wall for enhanced directivity, like a 180 deg "horn" with very rapid expansion. This is exactly how I modeled the BC415's expansion from the aperture of the 60in x 60in box face. But as I noted above, having the expansion occur over a true flat wall vs a very shallow 4in deep horn makes a big difference. Which leads me to think maybe there is something to making the box wall slightly cupped (by say, 4 inches over the 60in square wall) to enhance the bass extension, directivity, and efficiency, without taking up hardly any bulk. This could be as easy as adding lightweight XPS foam panels to the outside with a slight slope.
The vortical flow caused by a sudden expansion flow is well known and real. It will take at minimum a time dependent 2d axisymmetric computational fluid dynamics model to capture properly. Something like ABEC3 or Comsol Multiphysics to model properly. In my AkAbak model, I am simply using a "horn" element with a very shallow depth and this only captures the enhanced directionality and edge diffraction and boundary reflection effects. I don't think it will capture a virtual lengthening of the horn mouth due to the vortical structure.
Still chasing the vortex theory?
Try to remember this. I'm going to make it bold because it's important. If you built this sub flush into the ground (or even into a wall) it could be simulated just fine with Hornresp or Akabak because it's just a regular horn. No need to account for any vortexes or air flares.
Take it out of the ground flush mount (or wall flush mount) and the only difference is the finite boundary size. That's what a diffraction sim is for. I don't think a short horn element is the proper way to simulate diffraction, that's what people try to do with Hornresp and it doesn't work. A proper diffraction sim should take into account the boundary size, shape, and sound source location.
Try to remember this. I'm going to make it bold because it's important. If you built this sub flush into the ground (or even into a wall) it could be simulated just fine with Hornresp or Akabak because it's just a regular horn. No need to account for any vortexes or air flares.
Take it out of the ground flush mount (or wall flush mount) and the only difference is the finite boundary size. That's what a diffraction sim is for. I don't think a short horn element is the proper way to simulate diffraction, that's what people try to do with Hornresp and it doesn't work. A proper diffraction sim should take into account the boundary size, shape, and sound source location.
The BC415 is "just a regular horn" that expands to roughly 50% of it's boundary baffle area, then for .75 inch reduces to roughly 25% of it's boundary baffle area, then expands to a 60" x 60" 180° boundary encompassed by a 180"x26" perimeter at 90° perpendicular to the 180° boundary that has only one side flush to the ground.
Wall mounted, the BC415 has a 240"x26" perimeter at 90° perpendicular to the 180° boundary and 90° perpendicular to the wall. Ignoring the "baffle step" is equivalent to burying one's head in the sand, as a sub this large will seldom be buried "flush into the ground" or soffit mounted in a wall.
When you take a "regular horn" of the volume of the BC 415 and enter parameters as described above in Hornresp or Akabak, does it result in a response like the BC415?
If so, fine- reverse engineering "mission accomplished"
.In Hornresp (as far as I recall) it is not possible to go beyond a horn expansion equivalent to 180°, so the BC could not be simulated "as built".
Xrk971's Akabak sim based on my sketch is fairly close to the BC415 measured response, but may not have used the same expansion/reduction scheme the actual cabinet uses.
Art
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Yes I know that. That's not the point. The point is that if you DID flush mount it in the ground it would be a simple 2 pi sim, and to address the next quote, Yes, if it was simmed in Hornresp or Akabak in 2 pi and measured while buried flush into the ground the sim and the measurement would match well. This is just to say that there's no wizardry going on with this horn (no vortexes or air flares changing the tuning), just a bit extra forward directivity and radiation resistance due to the finite boundary, and if you can simulate a finite boundary you can simulate this horn.
When you take a "regular horn" of the volume of the BC 415 and enter parameters as described above in Hornresp or Akabak, does it result in a response like the BC415?
If so, fine- reverse engineering "mission accomplished"
In Hornresp (as far as I recall) it is not possible to go beyond a horn expansion equivalent to 180°, so the BC could not be simulated "as built".
Xrk971's Akabak sim based on my sketch is fairly close to the BC415 measured response, but may not have used the same expansion/reduction scheme the actual cabinet uses.
Art
J.A.G.,
We seem to be in agreement, if you can simulate a FLH that ends with a finite boundary that starts with a horn that expands from roughly 50% of it's boundary baffle area, then for .75 inch reduces to roughly 25% of it's boundary baffle area, then expands to a 60" x 60" 180° boundary encompassed by a 180"x26" perimeter at 90° perpendicular to the 180° boundary with the mouth boundary perpendicular to the ground, you may be able to accurately simulate the BC415.
Easy as that, but anything not considering those details will be a model of something other than the BC type of horn.
Art
Hi, couldn't resist.
(After too many months way, I'm back in the AkAbak' crying game, hence my return to the forum. When I read this part of your post it got me thinking.)
I remember a few years ago I analyzed this. I even sent my findings to David McBean I think, but I should dig into my archives to find it.
From the back of my head, the way I did this was to take the formula for the surface of a sphere and divide it by 8.
- This gave me the mouth area of a corner horn at a given distance. Then using small increments (4 inches) and the second mouth area, the local flare rate was calculated with HornResp.
- Using the formula of the surface of a circle and then recalculating it for the circumferance, I found the wavelength at that same distance, till where the horn terminates/works (Cir=1)
Putting those 2 tables in a spreadsheet and plotting the curves, revealed that they intersected somewhere around 300Hz, where something interesting happened: If I remember correctly, the optimal point (=local flare rate) to load the corner at 30Hz, was somewhere around 2 meters, but the mouth circumference was 30Hz at 1,2 meters, so there was nothing to be gained anymore after that point! You cannot hornload a corner below give or take 300Hz.
I used the offset horn panel in HornResp to check this.
If someone would want to try this anyway, he would have to restrict the corner with a wedge shaped cabineth (and good luck making the calculations and the folding scheme on that one.)
cheers and hopefully this is of some help to persons wanting to create a corner horn.
Hi, couldn't resist.
(After too many months way, I'm back in the AkAbak' crying game, hence my return to the forum. When I read this part of your post it got me thinking.)
I remember a few years ago I analyzed this. I even sent my findings to David McBean I think, but I should dig into my archives to find it.
From the back of my head, the way I did this was to take the formula for the surface of a sphere and divide it by 8.
- This gave me the mouth area of a corner horn at a given distance. Then using small increments (4 inches) and the second mouth area, the local flare rate was calculated with HornResp.
- Using the formula of the surface of a circle and then recalculating it for the circumferance, I found the wavelength at that same distance, till where the horn terminates/works (Cir=1)
Putting those 2 tables in a spreadsheet and plotting the curves, revealed that they intersected somewhere around 300Hz, where something interesting happened: If I remember correctly, the optimal point (=local flare rate) to load the corner at 30Hz, was somewhere around 2 meters, but the mouth circumference was 30Hz at 1,2 meters, so there was nothing to be gained anymore after that point! You cannot hornload a corner below give or take 300Hz.
I used the offset horn panel in HornResp to check this.
If someone would want to try this anyway, he would have to restrict the corner with a wedge shaped cabineth (and good luck making the calculations and the folding scheme on that one.)
cheers and hopefully this is of some help to persons wanting to create a corner horn.
In AkAbak this is easy to do by turning on corner boundary conditions "Bottom-Corner" switch for reflection. Set distance from walls and floor. It makes a big difference in gain in low frequencies and your finding that it has no effect below 300Hz is incorrect. It is not the same as setting 1/8-pi space as it is frequency dependent gain.
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