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DrBurrito

Maximum horn compression ratio?

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Hi, I’m planning to build a tapped horn subwoofer around the BC iPal 18, which models very well in hornresp due to its extremely low q (0.14!) and high motor strength. There’s something magical about this driver; nothing else I’ve modeled manage to get as low with as reasonable a response curve in a not-too-absurdly-huge box. VERY low: I’m planning on scraping 10 Hz if I can!

One problem I’ve run into, though, is that the horn compression ratio wants to be quite high, for both response curve smoothness and to keep the box size reasonable. Something in the range of 1:6 all the way up to 1:10 works best.

Now this is far outside what is typically quoted for subwoofers, which are supposedly recommended to be held around 1:2, with 1:4 a typically quoted maximum. I’ve read two reasons for this maximum: avoiding excessive horn air velocity and thus distortion, and avoiding simply overstressing and blowing the woofer cone itself. However, I haven’t heard a good *quantitative* reason why the recommended ratios are chosen.

If there are any. Since this is databass, I hoped I could get a data-driven discussion on the real limits of horn compression ratios for subwoofers. Is the old 1:2 ratio just based on wimpy older drivers, and is outmoded by the new generation of crazy motor force neodymium magnet woofers, or are there some very good reasons to avoid going too high? How high, exactly, could you go, before you run into problems? Is 1:6 ok? What about 1:10?

I’m thinking of something like Ricci’s dual opposed 21 iPal build, which clearly ignored the typical rules of sealed box design and overwhelmed the limits of the tiny air volume with the iPals’ high motor force. If this can be done for sealed boxes, maybe something similar can be done to create mini-horn subs.

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Depends on the driver and the horn design. Driver diaphragm will limit the load it can handle, shape of the horn close to the driver affects how large pressure and flow creates distortion.

Huge motor force is good in a horn, and - as you experience - you end up with larger ratios.

The problem is not so much the high velocity at the throat, because it is large pressure gradients - pressure changing rapidly - together with large velocity that creates problems first. This causes flow separation and then turbulence, which means distortion, noise and efficiency lost.

Too high pressure at the throat causes nonlinearities due to the nonlinear properties of air.

Model it, simulate, and look at the numbers.

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I have, and the numbers look good with high compression ratios for sure. That’s why I’m curious if I’m missing anything.

I’m more worried about what hornresp doesn’t model than what it does. For instance, it’s not going to model driver failure! It doesn’t know anything about the strength of the cone or the surround glue or whatever.

On the other hand, if it does model distortion, I’d be interested to know about it. I haven’t seen that, only frequency response, max SPL, etc. Nothing about distortion.

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Here's the hornresp parameters, the frequency response, and a 1/4 cutaway view of the box with the accordion-fold layout I intend to use to get enough path length to get down to 10Hz.

The frequency response isn't audiophile flat, but I only intend to run this up to 60 Hz, so I should avoid most of the really choppy stuff. Below that, it doesn't strike me as unreasonable, especially with some room gain and EQ shaping.

Feel free to critique! This is my first horn, so if there's any obvious blunders I'm making (besides maybe a too-small compression ratio?), I'd be glad to hear about it.

 

 

Horn_fold.JPG

Hornresp.JPG

Hornresp2.JPG

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I will look at this when I get a chance. Very busy at the moment getting some more tests ready to upload.

Off hand. Interesting fold. Have you considered weight of the cab and internal pressures at high output? Bracing of the panels etc?

Check the particle velocities, acceleration forces and pressures at the throat and exit. They will likely be extremely high with such a high compression ratio. Also absolutely model with the Le option checked which derates motor force some. 

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No worries! I have considered the thickness of the main panels but I haven't yet included the bracing. That will cut down the area further, of course (or expand the box). 

Thanks for the tip on particle velocity. Audio folklore is that velocities should be below 10 m/s, and this gives a good rationale for this horn, I think.

I had been struggling to justify all this extra carpentry versus my first design, a Stereo Integrity HST18 low-tuned vented box. Why do all the work and have a larger box if I can get the same SPL at low frequencies just by getting a bigger amp and using a conventional low-Fs, large-Xmax driver?

Well, if port velocity is the measure of distortion we care about, the horn wins. I modeled both at the same RMS voltage, and at the voltage where the horn throat is hitting 10 m/s at its peaks at the horn mouth, the vented box is hitting 20 m/s at port tune at the mouth and and is over 10 m/s over most of its range.

If we look at SPL, the numbers are less benign. I'm not sure what a bad value threshold is here, but we do see high pressures over more of the range at the horn throat, while the vented box is bad at resonance but much lower overall. Any ideas what SPL limit the throat should be limited to? Maybe a throat adapter could mitigate this?

Yes, the fold was key to the design. I did a good bit of math to get the fold sorted. The idea was to use the expanding radius of the accordion fold to create the flare, rather than tilt the wood panels at precise angles and struggle to crumple the fold into the box. This allows a very long horn path to be crammed into a not-completely-insane box in a fairly simple-to-construct way, i.e., via a sort of matroyshka-doll structure.  I'm not sure if there's a penalty to pay for the fact that the fold only really flares as it rounds the corners; I was planning on a more detailed Akabak model to capture this if it works out in Hornresp.

If this thing goes anywhere, I think it needs to be called the Longhorn. No connection to Texas, but it seems pretty obvious given the length of the fold.

Longhorn_1.JPG

Longhorn_2.JPG

Longhorn_3.JPG

Longhorn_4.JPG

HST18_vented_box_2.JPG

HST18_vented_box.JPG

HST18_vented_box_3.JPG

HST18_vented_box_4.JPG

Capture.JPG

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EDIT: modelling with lossy Le like Ricci suggested makes a big difference.

The horn compression ration to achieve an OK response becomes more reasonable, down to about 1:4. The horn flare has to get wider, though, resulting in a shorter and fatter box.

I'm re-posting lossy Le results with the HST-18 vented box for comparison. These are presumably more realistic. On the bad side, the box is getting a bit wider than I'd hoped.

Longhorn_1.JPG

Longhorn_2.JPG

Longhorn_3.JPG

Longhorn_4.JPG

HST18_vented_box.JPG

HST18_vented_box_2.JPG

HST18_vented_box_3.JPG

HST18_vented_box_4.JPG

Capture.JPG

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I see that you also have a throat depth of just over 2". Have you seen how tall the surround is on an HST? Are you sure this enough to clearance the surround at full excursion? 

Im not sure how a surround like that will fare in a high pressure horn loaded app. It might be fine but I have never seen it tested.

Things to consider.

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In my 18” subs using the HST-18, I allow almost 4” above the mounting surface to allow for excursion before the grill.

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Sorry, I’m using the HST (in a vented box) only as a comparison. It’s my baseline. It’s just there so I can convince myself the horn is worth the extra effort over a conventional ported box.

The system I’m trying to work out is the horn, which uses a B&C iPal 18”. The HST wouldn’t work for the horn; Qts is too high and motor force is too low.

At least per the numbers, 2” is enough clearance for the B&C, since it has a 20mm Xmax and folded surround. It’s not much, but it shouldn’t be hitting the other side of the chamber!

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I understand the HST-18 might not work in your situation but I’m a little surprised by the comment of not enough motor force.  Are you referring to the mkII driver or the original as the mkII uses the same magnet-motor as the HS-24 mkII.  And the HST-18 mkII is an 80 lb driver, mostly magnet.  I’m not trying to be defensive or suggest that the HST-18 is the best driver ever but I want to know what drivers you’re looking at if you consider the HST-18 MK II to have low motor force. :)

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Compared to an 18Ipal almost everything has lower motor force / efficiency. Of course the HST 18 has like twice the displacement capability though. 

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How are we comparing motor force?  The Bl for the HST-18 is higher than the Ipal.  But you also mentioned efficiency, yep, different ball park and design goals.  Sorry to take this off topic as I was just wondering.  Definitely not trying to say one driver is better than another.

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Dave,

BL rating means nothing alone. That does not tell you the effective efficiency or "strength" of the motor /coil system. Resistance also has to be considered at minimum. 

BL^2/Re

Or just look at Qts

Technically the normalized inductance should also be considered as it effectively saps the efficiency and raises Qts.

You need to include 3 parameters at minimum. BL, Dcr and Le. Or like I said just use the easy button and compare Qts, though that doesn't consider Le effects.

 

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The BL^2/Re is the ticket.  The Qes or Qts are influenced by Kms (suspension stiffness) and Mms (effective moving mass) as well.  Higher values of either parameter increase Qes and Qts while affecting efficiency at either frequency extreme.  Higher Mms reduces efficiency at the high end.  Higher Kms reduces efficiency at the low end, although the K of the air spring in a small sealed box can overwhelm the effects of Kms in the final product.

Comparing the IPAL-18 to the HST-18mk2, the HST has approximately double Mms but only about half the Kms of the IPAL-18.  So the influence of these parameters on differences in Qes/Qts is kind of a wash.  The IPAL-18 will offer much more upper frequency efficiency overall.  The HST-18, while having quite a bit less BL^2/Re will still hold its own pretty well below the resonance frequency in an I.B. or large sealed box.  As the box size is reduced, the HST-18 loses the benefit of its more compliant suspension and the efficiency advantage of the IPAL-18 will widen.

However, note that the stronger motor of the IPAL-18 has a downside, at least in a sealed box.  The stronger motor will tend to increase the back EMF around the system resonance, requiring higher voltage (but not power) to drive it.  This problem is substantially mitigated by its very low resistance, provided that the amp is capable of operating stably under such conditions and capable of delivering the desired amount of power within the lower impedance parts of the response within the desired bandwidth.  And of course, the IPAL -18 may require some signal shaping (EQ) to achieve the desired in-room response, but this may be true for either driver depending on the room.  On the other hand, a ported box will tend to increase the sensitivity of a driver for frequencies near and a ways above the port tune, which can offset much of this effect.  A horn will tend to increase sensitivity (and efficiency) even further, and the higher back EMF may even be more desirable for a flatter native response.

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Thanks for the lesson guys.  The knowledge level here is amazing.  I know that's pretty basic for you guys but I'm just fine with having other people design drivers for me and with knowledgeable people like all of you, can you blame me. :) 

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SME,

Yes mass and suspension compliance affect Qts. Higher mass and stiffer suspension both squelch efficiency. No need to worry about those if strictly comparing the motor and coil systems with BL^2/Re, but in many cases what people compare is off the shelf drivers. There the Mms and compliance matter and those are factored into the final Qts value. Resultant Fs also shifts the efficiency maximum. As will the final enclosure design, etc.

We really can't just look at Qts though due to complex inductance effects on these types of drivers. 

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Hi @Ricci,

I think we basically agree here.  I just wanted to point out that the efficiency reducing effects of mass and stiffness act in different frequency areas.  That's important for a driver like the HST-18, which while having fairly high mass is primarily designed for good performance at lower frequencies where the extra mass is not as detrimental.

Inductance effects are interesting.  In the simplest, linear model of inductance, Le has zero effect on efficiency.  The existence of Le merely reduces sensitivity, which coincides with a rising impedance.  However I gather that in the real world, inductance effects can cause actual energy loss.  How substantial is this in practice?

Per my notes above, reduced sensitivity can be worked around by using low resistance coils and/or multiple coils in parallel with an amp that is stable and capable of delivering most of its rated power into much lower minimum impedances.  I imagine this along with EQ can help overcome reduced sensitivity due to inductance effects.  However, inductance effects will also likely increase distortion also, so there's that.

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Yes we are in agreement. We dove a bit deeper than expected. Again. But it happens. Yep extra mass or lowering of Fs shofts the max efficiency point down in freq. 

What were we supposed to be discussing? Horn compression in the throat? Ha.

  • Haha 1

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Thanks guys.  Appreciate the in depth response and sorry for the off topic.  Interesting to read and learn but I’m not as interested in being able to design drivers further than I know what I want something to do.  Cool stuff as always on Data-Bass. The guys on this forum are amazing.

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Yes, this is very educational. 

Without knowing the equations behind hornresp’s horn frequency response simulation, I can’t say for sure, but I did observe that the key thing in getting a response that wasn’t too peaky was low woofer Q.

The woofer needs motor force to drive the horn, but in my simulations I found that a more vented-box-oriented driver like the HST18, despite having fairly high motor force, tended to have sharp peaks in the response unless the box was way too large.

The BC 18 iPal has the lowest Q of any woofer I know of, and it seemed to do the best job of getting down to 10 Hz in a somewhat reasonable box without too peaky a low-frequency response.

Now I don’t know that Q is really the most important parameter in play, but it does make some intuitive sense that lower Q —> wider bandwidth around Fs —> easier to get less peaky response below Fs.

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