Reactance Annuling question

[horatio2]

I am running calculations in a spreadsheet for many 15" drivers according to Keele's LF driver horn formulae for St and Vb.  I pick up his mass roll off frequency as well.  These pretty much seem to tell the story for bass horn suitability of a driver, at least to a decent first order.

 

I have been working two horn cases:

 

Case 1: University Classic, for which I am unable to locate a design Fc for the horn, nor am able to locate firm Vb values.  Best estimates I have seen are between 80 and 106 liters, and I am not clear on whether those account for driver volume or not.  Any help here would be appreciated.  St is taken as 78 in^2 (6x13 slot)

 

Case 2: Klipsch corner horn, for which I have found information that suggests Vb is 64 liters (with or without driver?), and early khorn St of 78 in^2 (6x13) and later model St of 39 in^2 (3x13).

 

My question is on the Vb calculation of Keele: this is the Vb that optimizes bass response according to the reactance annulling principle.  The question is this:  If the computed Vb is LESS than the actual Vb for a given horn, would you expect that the bass response would still be down a bit under the Fc of the horn, but not as strong as the annulling case, and 2) if the computed Vb is GREATER than the actual Vb for a given horn, would you expect the response to begin rolling off above the Fc value at a greater rate than the rolloff for the flare rate?

 

I am suspecting that I am guessing out the answer, as I stated above, but I am wondering if this is one of those opposite situations that are counterintuitive (e.g., that actually the opposite happens to what I have stated above).

 

Vb doesn't seem to be all THAT sensitive, based on reports I have read from others.  I wouldn't want to miss it by say, 2x up or down, but I suspect getting it to within 10-25% is probably not going to be all that audible.  But, the issue is, suppose one case is +25%, and the other case is -25%.  My question is, which one would be preferred?

 

Anyone know this well enough to give the answer?

 

 

[boom3]

Bruce Edgar analyzed and IIRC, rebuilt, the University Classic about 20 years ago in the pages of Speaker Builder. I don't have the ish number but it's easy to find. Bruce is also gracious about responding to e-mail.

 

I can't tell you which way your horn response will go depending on the sign of your Vb number, but it is always easier to make things smaller than larger. Many builders have introduced non-resonant masses into their Vb's in order to fine tune the annulling. High-density rigid foam, like is used for aircraft structural work, is a good choice. You could cut  1 liter, 2 liter, etc blocks and see what diff they make in a Vb that seems to be oversized.

 

Paul stated circa 1945 that he preferred to have the Vb frequency slightly above the Fc of the horn, so that the Vb would control the diaphragm when the horn loading falls off (I am paraphrasing). I'd see what others have said since then on this subject.

 

Keep us posted!

[wvu80]

Anyone know this well enough to give the answer?

 

I don't. 

 

But I assure you, there are those here that do, at least for the Khorn.  I think they quit making that University speaker back in the late 1970's or into the 80's and I've never seen any discussion about it.

 

May I ask what the practical application of your work will be?  Are you trying to find a decent woofer for your Khorn, that sort of thing?

[jwc]

You have asked a very complicated question. If DJK wouid come on here for this, trust what he says.

 

I have built some bass horns. I'm not an expert.

 

I've done eperiments with removing and adding airspace to the woofer chamber. All I can tell that it does is effect the low end....meaning below the Fc of the horn. I think of it kinda like a woofer in a sealed cabinet once the Hz gets less than the Fc of the horn. Model some sealed woofer enclosure of different volumes on WinISP.

 

However, Annull is different...but to me I consider the above example what to expect when i calculated the annul of a driver in a certain woofer chamber of a Box behind a horn. Reason being.....it "looked" like it effected the low end and not the efficiency or mid band output at all. I can't tell you "how it would sound" as that experiment would be very timely.

 

So in short....short changing the back volume to be less in volume than the annull calculation....may effect the low end.

 

The MWM by Klipsch actually short changes the K43 or K33 driver by annulling closer to 50Hz.

 

jc

HornPaper-leach.pdf

[Chris A]

My question is on the Vb calculation of Keele: this is the Vb that optimizes bass response according to the reactance annulling principle.

 

The question is this:

 

1) If the computed Vb is LESS than the actual Vb for a given horn, would you expect that the bass response would still be down a bit under the Fc of the horn, but not as strong as the annulling case, and

 

2) if the computed Vb is GREATER than the actual Vb for a given horn, would you expect the response to begin rolling off above the Fc value at a greater rate than the rolloff for the flare rate?...

 

...Vb doesn't seem to be all THAT sensitive, based on reports I have read from others. I wouldn't want to miss it by say, 2x up or down, but I suspect getting it to within 10-25% is probably not going to be all that audible. But, the issue is, suppose one case is +25%, and the other case is -25%. My question is, which one would be preferred? Anyone know this well enough to give the answer?

 

Have you seen this article?  https://community.klipsch.com/index.php?app=core&module=attach&section=attach&attach_id=28266

 

I believe that answer to both of your questions is like "power factor" in AC power circuits: too much or too little acoustic capacitance in the enclosure will result in reduced transmission power.  In terms of sensitivity to the compliance volume of air in the box + the driver's suspension compliance: in general, you'd want to be about 25% of optimal compliance to offset the horn's mass-like (moving air inductance) value coupled to the horn/driver. 

 

If the box is too big, simply place something inside the volume to reduce its effective volume.  If the volume or air in the box is too small, then all you can do in stuff it with fiberfill but that is only effective to about perhaps 10-20%, at most.  I'd make a box that's a little too big and fill it with something rigid/incompressible, then test the output until you find the optimal volume with the horn and driver that you'll be using.  At that point you can decide whether to continue using the box, or cutting it down and reusing the material.

 

Or you can use Hornresp and avoid all this - it will tell you the correct box internal volume for the driver and horn that you model. 

 

Chris

Edited October 7, 2015 by Chris A

[horatio2]

boom3:  The comment you paraphrased from PWK has the answer I was seeking: annul a little higher so that Vb keeps control over the woofer.  In other words, always have enough compliance in the box volume to maintain control.

 

For those who've offered the papers by Plach and Williams (the classic reference) and the paper by Leach (another take on horn design with T/S driver parameters), thanks!  I am aware of these, having collected my copies some 25-30 years ago, now (and that includes the reading of them ;-).  While I write a lot of software for the work I do, I am not so much a fan of using design codes that I cannot inspect, so I don't use hornresp or any of the other codes.  I guess that makes me old school, but there it is.

 

The SpeakerBuilder article that boom3 mentioned I also have, got the original issue from when it came during the days when SB still published.  That is the 'show horn' as I recall, and it is loosely based on the University Classic, but last I looked at this article, while Edgar mentions the Classic, he does not do any reverse engineering of it, other than to use it to suggest how he approached his own design (primarily with regard to folding choice).  I want to recall that the Edgar design was a 50 Hz flare, though.  All from memory, so don't quote me.

 

The reason I am asking the question is, when working with an established design like the Classic or the Khorn, you can't do too much (esp. if you have the cabinets already, as I do) to enlarge the volume.  You can take it down some, though, but this means you must choose woofers for which you have a reasonable chance of reaching the Vb.  Most of the 15" drivers I am looking at require somewhat larger volumes, a few have smaller Vb's, and so it's a push.  I am just trying to figure out the likely audible effects of going too larger or too small, and choosing the lesser of the evils.  It looks like choosing a driver that has a predicted Vb that is equal to or a bit larger than the available Vb is the way to go, if I am thinking about the Klipsch quote correctly.

 

I suppose one answer lies in the analysis I've done on the EV 15WK (1950's khorn) and the variants of the K33E (square and round): the old EV15 WK models at 84 liters for Vb, whereas the K33E models 210 (square) and 128 liters, respectively, for a 38 Hz Fc horn.  These K33E numbers would suggest a sloppy cone down low, but it may be that the small throat is keeping it in line, I don't know.  There's a lot about that Khorn design that seems to defy attempts to model it in any rational way.  But beyond that, there've been quite a few woofers used in that horn, and within a certain range of parameters, they evidently all see to work.

 

I am looking closely at a Kappa C because it is so very close to the target numbers, close to the EV 15WK, and within a few percent of an EV 15L.  All these need the large slot throat of the 1950's khorn, and would seem to match well to the Classic, which has the 6x13 throat like the 1950's Khorn.  I was first looking at the CB15, because it has a higher BL motor, but CB15 numbers just don't dial in as nicely as those for the Kappa C.  I know another prominent member of this list uses a CB15 in his Khorn with a 6x13 throat and is very pleased, waxing rhapsodic about the thwack that it has.  That is what I am going for- the in your face punch that an A7 has.

 

Thanks for all your well reasoned and studied responses!  I knew I could rely on this site-

[horatio2]

The advice to look at Edgar's Show horn sparked me to re-read that article.  It is an excellent article as it covers most of the design issues one encounters with folded bass horns in real listening environments (rather than a recapitulation of the infinite horn cases).

 

He mentions that in actual testing, he had to double the Vb in his design (according to Leach's formulas) in order to get it to resonate at the desired design frequency.  This is interesting to me, because when I run the Keele calculations for St, Vb and mass rolloff, they match pretty well to the Leach counterparts EXCEPT for the Vb.  Leach gives about half of the Keele values.  I remember running into this when I did a LaScala-like design in the early 80's, and I never could resolve the reason, until, that is, I re-read that Edgar article.  Message: believe the Keele numbers, at least as regards Vb.  Another interesting part of that article is the very practical guidance on setting the Vb experimentally.  But you need to have a pretty good guess to begin with, because if you build it too small, you are out of luck, as it is really difficult, in most horn designs, to increase Vb.

 

As an example of this issue, run the driver case shown in the Leach article through Keele's equations, and you will see what I mean.  Edgar evidently thought the difference had to do with Leach's equations being set for infinite horns.

 

The Khorn, though, defies much of what we try to do, with the design equations, it seems.  We are constantly told, for bass horns, go with drivers that have low Qt and/or Qes and high Fs, to get that mass rolloff as high as possible.  And yet, the drivers that PWK chose seemed to go the other way on Fs, trying very hard in the 1950's to get the Fs numbers down by almost any means possible, and the Qes and Qt values, well, it is evident from the T/S parameter sets on the K33E that drivers ranging from 0.28 to 0.68 in Qes have been used by the factory. In the same design.  With only a throat size change.

 

So what's a good driver, then for these applications?  I guess it keeps coming down to high motor strength, principally.  But there are evidently other factors, because, as a practical example, I have tried an EV15L in a 3x13 slot Khorn, and it just did not do what I expected, nor was its performance remotely acceptable to me.  A K33E on the other hand, seemed to do very nicely by comparison.  But I am really interested in opening that slot to 6x13 like the early models, and running a driver with very high strength motor in there, and seeing what I get.

 

On the University Classics that I built, I am running a driver that by all estimates according to theory should provide excellent performance in this design, and I am not at all happy with the result.  This is a driver that has parameters not all that different from a K33.  But I think a high strength motor is needed here, too.  We shall see.  I am focusing first on the Khorn, hoping to take this design to its roots by going to a 6x13 slot and a strong driver, but with a lower Fs than typical of the 1950's.  The fallback is the venerable K33E.  Then I will move to the Classic and see what can be done there.

[boom3]

Horatio,

I found the exact citation for Paul's comment I mentioned.

 

"A Note on Acoustic Horns", proceedings of the IRE, Vol. 33, No. 7, July 1945

 

"Thus it is preferable to resonate the system somewhat above cutoff, or at least some frequency at which the resistive component of throat impedance is sufficient to load the diaphragm and limit its motion to within the range of amplitude over which the suspension reactance is nearly linear."

 

Boom

[horatio2]

Boom3:

 

Thanks for the precise rendering of this quote.  I will have to look in my literature collection on horns to see if I have this paper.  If you have a pdf, I would be grateful.

 

The Plach and Williams paper linked to earlier in this thread was not the one I thought it was- it references the original, classic work, though.  I found that linked to paper quite interesting and helpful.

 

Spent much of this weekend cleaning up the bass horns, fabricating 'wings' to partially close up the sides of the horns (like the last production models of the OEM Klipschorn) and opening the throats, preparing new motor boards.  I hope to get some measurements with REW somewhere along the way- probably outdoors measurements, as these are in my garage at present.

 

Right now, I am deliberating on which woofer to choose: Kappa 15C or Legend CB158.  I like the lower Fs of the Kappa C (31 Hz), but I really like the strong output of the CB15.  Keele modeling shows the Kappa to require the smaller throat and Vb, and both bracket the model for an EV 15WK.  The CB15 seems closer to the K33E round magnet St and Vb, too, and shares a similar Fs (34, vs 34.5 or so).  I know many have found good results for the Kappa 15C in the LaScala and in vented box designs.  I have seen reference to exactly one lister who's used the CB15 in a bass horn with essentially the same parameters as the Khorn (throat is 6x13, but flare is 38 Hz, same corner design, slightly different folding), and really liked this.

 

I am using a biamped setup with a miniDSP (since 2011), and so I have no concerns regarding differences in sensitivity of the bass horn vs. the top end- I will dial it in as needed.

 

Anyone have any advice on the woofer choice?  I suppose I could buy one of each and try both, too.

[jlossint]

I am running calculations in a spreadsheet for many 15" drivers according to Keele's LF driver horn formulae for St and Vb.  I pick up his mass roll off frequency as well.  These pretty much seem to tell the story for bass horn suitability of a driver, at least to a decent first order.

 

I have been working two horn cases:

 

Case 1: University Classic, for which I am unable to locate a design Fc for the horn, nor am able to locate firm Vb values.  Best estimates I have seen are between 80 and 106 liters, and I am not clear on whether those account for driver volume or not.  Any help here would be appreciated.  St is taken as 78 in^2 (6x13 slot)

 

Case 2: Klipsch corner horn, for which I have found information that suggests Vb is 64 liters (with or without driver?), and early khorn St of 78 in^2 (6x13) and later model St of 39 in^2 (3x13).

 

Vb doesn't seem to be all THAT sensitive, based on reports I have read from others.  I wouldn't want to miss it by say, 2x up or down, but I suspect getting it to within 10-25% is probably not going to be all that audible.  But, the issue is, suppose one case is +25%, and the other case is -25%.  My question is, which one would be preferred?

 

Anyone know this well enough to give the answer?

 

My experience is that Vb is sensitive and actually detrimental to a good bass response. Try an arbitrary horn design in "Hornresp" simulation program and you can easily see what impact Vb has on the bass response and how. A Vb of 64 liters for a 50 Hz horn seems to me to be grossly over sized, 30-40 liters seems more correct. Actually, if I recall correctly, PWK stated that the khorn should have a Vb of about 37 liters. The throat area is of great importance in the upper end of the frequency response of the horn together with a rapid horn expansion in the beginning of the horns first 10-12 inches.

 

//Peter

[John Warren]

"Vb doesn't seem to be all THAT sensitive, based on reports I have read from others.  I wouldn't want to miss it by say, 2x up or down, but I suspect getting it to within 10-25% is probably not going to be all that audible.  But, the issue is, suppose one case is +25%, and the other case is -25%.  My question is, which one would be preferred?"

 

Klipsch questioned the rear chamber volume and revised it.

 

Link is to a model of the Klipschorn bass horn referencing Keele's paper which really is Beranek's model in the electrical domain.

 

http://northreadingeng.com/Klipschorn_model/basshorn_model.htm

 

The Klipschorn bass horn with three rear chamber volumes is shown in the plot below.  These are predictions from the model.  Vb is directly proportional to Lceb which is an inductor in the electrical domain.

 

Making Vb smaller (50% actual) improves low end at the expense of high end output.  Doubling does nothing of significance.

 

The model result seems to support Klipsch's statement that the smaller rear chamber causes a "bump" in the 60Hz response which the model does show.  The actual acoustic response would likely be a peak just above 50Hz.

Edited March 19, 2016 by John Warren