Tractrix design for 5MR450-NDY
I am making some progress on the design and layout for the tractrix horn using Volvotreter's spreadsheet. This horn has a design frequency of 175Hz for a 7.1cm square throat. The predicted response was shown in post #39. Approximate dimensions are: 0.67m wide x 0.45 high x 0.54 m long. The design appears to provide about 109 dB sensitivity at 2.83v and 1m, and a 130 dB SPL at 1m and 37 volts when driven to xmax. Physically, the design looks like it could be a good candidate for some bass-injection ports a la Synergy. Maybe mount a pair of 12 in drivers top and bottom with slot ports along the corners and maybe get bass extension down to about 80Hz before handing off to a sub.
Predicted response modeled in Akabak with 16-segments:
I am making some progress on the design and layout for the tractrix horn using Volvotreter's spreadsheet. This horn has a design frequency of 175Hz for a 7.1cm square throat. The predicted response was shown in post #39. Approximate dimensions are: 0.67m wide x 0.45 high x 0.54 m long. The design appears to provide about 109 dB sensitivity at 2.83v and 1m, and a 130 dB SPL at 1m and 37 volts when driven to xmax. Physically, the design looks like it could be a good candidate for some bass-injection ports a la Synergy. Maybe mount a pair of 12 in drivers top and bottom with slot ports along the corners and maybe get bass extension down to about 80Hz before handing off to a sub.
Predicted response modeled in Akabak with 16-segments:
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I'd be curious about the response in a horn with fabrication as proposed a few times no here by Tom Danley.
You know, extending the shape woofer cone with stretch fabric and then impregnate it with epoxy to shape it a bit like his coax synergy horns...
You know, extending the shape woofer cone with stretch fabric and then impregnate it with epoxy to shape it a bit like his coax synergy horns...
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![DanleyMonfront[1].jpg](/community/data/attachments/390/390388-3911f320476b6f27df646786d51c49bd.jpg)
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I'd be curious about the response in a horn with fabrication as proposed a few times no here by Tom Danley.
You know, extending the shape woofer cone with stretch fabric and then impregnate it with epoxy to shape it a bit like his coax synergy horns...
This is a neat technique but this is more of a waveguide to help improve directivity than it is a horn. I have modeled this (SM100) and it works quite well with a 10in coax and a CD. Does not get the same 109dB sensitivity as the tractrix though even though both drivers are nominal 95dB to start. Also using a single fullrange for the critical 500Hz to 5khz and in the case of the PRV gets you to 15khz. I like the stretched fabric idea though. I think Danley uses molded plastic.
Tractrix 2-way Synergy
I added a pair of Kappalite 12's driving some injection ports in the tractrix at a few strategically placed points to get this nice 2-way system that reaches down to 80Hz for a good hand-over to a subwoofer.
Freq Response at xmax of both drivers (with some relative gain adjustment):
Cone Displacement for 5MR450-NDY and Kappalite 12:
Pretty cool huh?
I added a pair of Kappalite 12's driving some injection ports in the tractrix at a few strategically placed points to get this nice 2-way system that reaches down to 80Hz for a good hand-over to a subwoofer.
Freq Response at xmax of both drivers (with some relative gain adjustment):
Cone Displacement for 5MR450-NDY and Kappalite 12:
Pretty cool huh?
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I'm a little sceptic about the response in that horn. While the naked driver does very well off axis I think it is a result of the cone shape. Putting it behind that horn might screw that up. A prototype will tell us that though.
I think the waveguide I proposed would have more of a chance to keep that nice off axis response intact.
I think the waveguide I proposed would have more of a chance to keep that nice off axis response intact.
We will have to see how the prototype works. However, it is based on a type of design similar to the Bruce Edgar horn which I believe were well regarded for their uniform directivity. Some things that may be required include a thin layer of open cell reticulated foam around the throat to smooth out some of the early off axis reflections from the driver onto the walls of the horn.
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I was trying to match a TH sub to this system and just realized that 127dB SPL takes a lot of power to achieve down to 40Hz in a typical TH. I was a bit surprised to find that it takes a pair of TH-18's with LMS2400-8 running at 3kW for the pair to match this top. Am I doing something wrong or need to use a higher efficiency subwoofer?
This tractrix synergy is running at 225 watts on the 5incher and 700 watts for the dual 12 in drivers. Then add 3kw for the subs. That is a lot of power.
This tractrix synergy is running at 225 watts on the 5incher and 700 watts for the dual 12 in drivers. Then add 3kw for the subs. That is a lot of power.
In professional sound reinforcement (SR) 4 or more subs to 1 or 2 tops is common given the disparity in output. In situations where maximum gain (stadiums/concert halls/etc.) isn't required the tops are just run at a lower volume (which might be sub-optimal given the different headroom/transient reproduction of cabinets that are not matched in sensitivity due to the non-linear scale of each cabs repro).. Does this make sense? I'm just stating it intuitively, haven't run the numbers...
To make the equation even more disparaging is that auditory perception of deep bass can require 20dB more gain to balance with the mids... So if you want your system to not only be equivalent in SPL but also in equal loudness given the ears decreasing sensitivity to bass, then you'll need maybe 4 subs to that single top
...
*I think* most reasonable people will just reduce their top horns output and probably not notice any difference in headroom or transient scale between LF/MF/HF...
To make the equation even more disparaging is that auditory perception of deep bass can require 20dB more gain to balance with the mids... So if you want your system to not only be equivalent in SPL but also in equal loudness given the ears decreasing sensitivity to bass, then you'll need maybe 4 subs to that single top
... *I think* most reasonable people will just reduce their top horns output and probably not notice any difference in headroom or transient scale between LF/MF/HF...
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Thanks Anthony Bisset for your observations of what is typically used in pro-sound installs. You are probably right, the easy thing to do is turn down the top to match the subs. Costs nothing to turn the volume down to 120dB but many thousands of dollars in subs and amps to bring the bass up to 127dB.
Several folks over in the Multiway forum have pointed out that they don't think the PRV in a tractrix will go past 5kHz. Even with a phase plug. I know F1 Axehead tops (R1 I think) go to 15kHz with 112dB sensitivity using a 5in driver. Although the F1 is not a tractrix, nonetheless shows that a 5in driver with proper phase plug can get up there. Is there any hope of a non phase plug horn going higher than 5kHz? I think there is as someone posted their recent experience with a Tang Band 2in full range in a large JBL horn designed for a 2in CD.
Several folks over in the Multiway forum have pointed out that they don't think the PRV in a tractrix will go past 5kHz. Even with a phase plug. I know F1 Axehead tops (R1 I think) go to 15kHz with 112dB sensitivity using a 5in driver. Although the F1 is not a tractrix, nonetheless shows that a 5in driver with proper phase plug can get up there. Is there any hope of a non phase plug horn going higher than 5kHz? I think there is as someone posted their recent experience with a Tang Band 2in full range in a large JBL horn designed for a 2in CD.
Martinssen I think was the one mating the 2in TB to the JBL horn no? Given the throat was 2inches - the combing is probably up towards 10k and small to moderate phase shift/combing above 9 or 10k is pretty easy to ignore for most people... There are details up there, but in a lot of music they're pretty indistinct.
Looking at the old Bruce Edgar midrange horn article, he says "With stiff diaphragm drivers a throat size equal to or slightly larger than the driver will give the most extended range". In a lot of measurements from this article we see output to 8khz (where his measurement window stops). No clues how the LE5 or others performed above that...
I think hf reach depends on the expansion rate, the driver diameter and the throat diameter before expansion crosses some threshold for cancellation.
If we look at the massive western electric 15a spiral horn, we see people using them up to 6khz and it has a really slow flare (although the we555 CD has a primitive phase plug which probably rolls off > 6khz).
Just guessing here, maybe if you use a 1:1 compression ration without compression chamber, you'll be able to push past 9khz... How articulate the treble will be though, seems hard to say... could be *a lot of combing/cancellation* at intervals related to the dimensions of driver and throat.
Radial horn to approximate tractrix in Akabak
There is an option to use a "Horn" radiator element which accounts for the non-planar nature of a horn's mouth output. It is actually very computationally intensive as the mouth is subdivided into many segments and each solved assuming propagation vector based on geometry of horn mouth flare. In Akabak Salmon T factors are used to describe the curvature with T=0 for catenoid and T=1 for exponential. As a guess, I am saying that the tractrix is somewhere in between a catenoid and an exponential, the degree of which is controlled via how big or small T factor is from [0,1]. It is interesting but the sensitivity at the lower frequencies is similar to the plane wave tractrix presented previously but there is falloff in the HF's, probably a lot closer to reality and it starts to drop above 5kHz and is down about -12dB by 15kHz. This is still very usable but some HF falloff is to be expected with this model. The nice thing about using a Horn radiator element is that a single element specified by the throat, mouth, length, and T factor, completely describes the horn. Putting in the same throat, mouth, length and T=0.5 factor, I get the following predicted frequency response:
What is neat is that the polar response now looks very nice for 500Hz, 2kHz, 4kHz (up to 2 kHz the directivity is uniform):
There is an option to use a "Horn" radiator element which accounts for the non-planar nature of a horn's mouth output. It is actually very computationally intensive as the mouth is subdivided into many segments and each solved assuming propagation vector based on geometry of horn mouth flare. In Akabak Salmon T factors are used to describe the curvature with T=0 for catenoid and T=1 for exponential. As a guess, I am saying that the tractrix is somewhere in between a catenoid and an exponential, the degree of which is controlled via how big or small T factor is from [0,1]. It is interesting but the sensitivity at the lower frequencies is similar to the plane wave tractrix presented previously but there is falloff in the HF's, probably a lot closer to reality and it starts to drop above 5kHz and is down about -12dB by 15kHz. This is still very usable but some HF falloff is to be expected with this model. The nice thing about using a Horn radiator element is that a single element specified by the throat, mouth, length, and T factor, completely describes the horn. Putting in the same throat, mouth, length and T=0.5 factor, I get the following predicted frequency response:
What is neat is that the polar response now looks very nice for 500Hz, 2kHz, 4kHz (up to 2 kHz the directivity is uniform):
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Seems to me you'd give up a lot of the good qualities of this driver for the gain in sensitivity. Most of that not needed in a home environment right?
That's why I proposed the more shallow waveguide a la Danley. This is already a very sensitive driver but also has very nice controlled HF response for it's size. It would be sad to loose that i.m.h.o.
That's why I proposed the more shallow waveguide a la Danley. This is already a very sensitive driver but also has very nice controlled HF response for it's size. It would be sad to loose that i.m.h.o.
I hear you Wesayso - for home use I am happy to have it open-faced in a Nautaloss or an OB - it really does sound spectacular that way. Sounds clean and smooth like a TC9DFD but way more sensitivity and impact in the 200Hz to 500Hz range, and gobs of headroom with ultra-low distortion. I have been using the PRV in the Nautaloss as my main listening system for past couple of weeks and am enjoying it very much.
I am working on this tractrix design as a possible PA top to go with a very sensitive bass horn that I have. The application will be for pro/studio use - not home use. Just wondering if I can preserve the single point source magic and wide bandwidth while gaining sensitivity and improving directionality over 60 deg beam width.
I agree that the shallow waveguide would probably work really well and I have always wanted to try the fabrication method of stretching fabric over a frame and suspending a weight to get the shape then adding resin and maybe fiberglass or even burlap bags to lock the shape.
Tractrix 2-way Synergy w/ 2x TH-18 subs
This is purely academic at this point but I wanted to show what the 2-way tractrix Synergy and a couple of TH-18 subs could look like and the power they take. More of an exercise to see how to show three simultaneous sims on one speaker system.
The following gain factors were used: 0.95 for 5MR450-NDY's, 2.0 for the dual Kappalite 12's, and 3.5 for the dual 18 Sound 18LW2400-8's. At 26v overall, this This gives 24.7v for the highs, 52v for the mids, and 91v for the subs.
Here is the predicted freq response at near xmax of the Kappalites and 5MR450's and the thermal AES limit of the 18LW2400 subs (1.2kW):
Here is the corresponding cone displacements:
Here is the electrical power input (note that value for sub needs to be x2):
Here is the impulse response:
This is purely academic at this point but I wanted to show what the 2-way tractrix Synergy and a couple of TH-18 subs could look like and the power they take. More of an exercise to see how to show three simultaneous sims on one speaker system.
The following gain factors were used: 0.95 for 5MR450-NDY's, 2.0 for the dual Kappalite 12's, and 3.5 for the dual 18 Sound 18LW2400-8's. At 26v overall, this This gives 24.7v for the highs, 52v for the mids, and 91v for the subs.
Here is the predicted freq response at near xmax of the Kappalites and 5MR450's and the thermal AES limit of the 18LW2400 subs (1.2kW):
Here is the corresponding cone displacements:
Here is the electrical power input (note that value for sub needs to be x2):
Here is the impulse response:
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Wasn't sure if you are saying that the results look good or bad from an audiophile standpoint? I would be less worried about the neighbors and more worried about what damage the SPL's will do to the walls/windows/structure of the house (not to mention one's hearing loss)
DCR with the 5MR450NDY (4 ohm version)
Here is a design for compact DCR that reaches 100Hz. Cabinet 6 in wide x 6.67 in tall x 5 in deep for upper chamber and a 6 in wide x 3.33 in tall x 5 in deep lower chamber (all internal dims), and a 2.0 in dia x 6.5 in long vents (all three). Note that the vents will require some clever elbows to get 6.5 in length into a 5 in deep cabinet. If used with a -12dB/oct high pass at 100Hz, the 2mm xmax won't be reached until 15 volts input. At which point max SPL is about 108dB.
Here is a design for compact DCR that reaches 100Hz. Cabinet 6 in wide x 6.67 in tall x 5 in deep for upper chamber and a 6 in wide x 3.33 in tall x 5 in deep lower chamber (all internal dims), and a 2.0 in dia x 6.5 in long vents (all three). Note that the vents will require some clever elbows to get 6.5 in length into a 5 in deep cabinet. If used with a -12dB/oct high pass at 100Hz, the 2mm xmax won't be reached until 15 volts input. At which point max SPL is about 108dB.