Belle/La Scala folded horn

[uams]

Hi all,

 

First post. 

 

This is perhaps a rather tricky question (i.e. one not that easily formulated), but nonetheless:

The Belle Klipsch and La Scala both use a 15" driver that is loaded via a folded horn. Being that the sound produced is a function of the driver + folded horn (incl. the throat), and the sound heard is that emanating from/through the mouth of the horn, how would one calculate/estimate the effective air radiation area here?

 

The 15" driver has a given cone radiation area, so far so good, but from what I understand that driver has its sound "squeezed" through a slot right in front of it (the throat), and from here the sound is then distributed through the folded horn to the mouth area.

 

So, what is the cone radiation area of the 15" driver "converted" into at the mouth of the horn? Is it simply, more or less, the mouth area?

EDIT: I'd assume the effective air radiation area heard and felt from the folded horn is larger, indeed considerably larger than that of the 15" driver, or not?

/M

Edited July 20, 2015 by uams

[Chris A]

I would instead recommend either Hornresp and/or AkabaK (assuming you have a 32 bit PC operating system available) to estimate power response of either design.  Here is a diyAudio thread on the subject of La Scala T/S parameters:

 

http://www.diyaudio.com/forums/multi-way/1344-lascala-plans.html

 

And Klipsch forum Hornresp information for the La Scala and Belle:

 

https://community.klipsch.com/index.php?/topic/103773-analysis-of-klipschorn-and-la-scala-cabinets-with-several-drivers/page-2#entry1144636

 

how would one calculate/estimate the effective air radiation area here?

 

Hornresp will help you convert parameters/data that you do have so that you can find the "Mms" (Thiele-Small parameter). I assume that is, after all, what you are trying to find: the output power vs. frequency...right?

 

Chris

[Chris A]

BTW: welcome to the forum!

[Chris A]

So, what is the cone radiation area of the 15" driver "converted" into at the mouth of the horn? Is it simply, more or less, the mouth area?

 

This is a bit obscure, but I believe the that answer is: the mouth area multiplied by some efficiency factor.  It will be a function of frequency and room loading.

Edited July 20, 2015 by Chris A

[uams]

 

So, what is the cone radiation area of the 15" driver "converted" into at the mouth of the horn? Is it simply, more or less, the mouth area?

 

This is a bit obscure, but I believe the that answer is: the mouth area multiplied by some efficiency factor.  It will be a function of frequency and room loading.

 

 

Chris --

 

Thank you for welcoming me, and for your informative replies.

 

I think I may have overstated the intend of my initial post a bit; I was merely interested in knowing, on more or less pure laymans level, if there was a way of estimating the effective radiation area from the folded horn with a 15" driver used. In your reply above this may have been approximated, though it's still not entirely clear to me  

I'm presuming the radiating area emitted from the folded horn is somewhat larger than the 15" driver used in front of it, so to speak, but a more precise estimate would be very welcome - if such is possible. I'm just curious to find out. 

 

Another question, if I may: what is the gain in efficiency created by the folded horn compared to the efficiency of the driver used - some 6-8 dB's? 

 

/Mikael

Edited July 20, 2015 by uams

[Chris A]

Generally speaking, the gain in radiating area is the proportional to the mouth-to-throat area ratio. 

 

The gain in SPL output is more like 15 dB over a direct-radiating open baffle configuration, i.e., no venting/reflex box gain.

 

For the La Scala and Belle vs. vented box  configuration (i.e., a Cornwall bass bin), it's about 4-6 dB gain.  The biggest deal,  of course, is the dramatic reduction in modulation distortion and reduced compression distortion of horn-loading over vented box.  That's what makes the Belle and La Scala bass sound so clean.

 

Chris

Edited July 20, 2015 by Chris A

[WMcD]

The answers are pretty much in Don Keele's article on optimum mouth size.  But the answers are a bit difficult to dig out.  I can help you with specific questions after you've read and if you care to know.

 

http://www.xlrtechs.com/dbkeele.com/papers.htm

 

The actual acoustic load at the mouth of the horn is just about always estimated as the acoustic load on a vibrating circular plate, either in free air or in half space (meaning a very large plane).  You'll see graphs of this in Don Keele's article.  The actual calculation involves Bessell functions.  We could undo the normalization of the graphs if necessary.  But generally, this gets up to a pure resistance at a frequency / wavelength where the circumference of the mouth is one wavelength. That is where kCaM = 1. You can see how important that number is for general discussion.

 

You will note that Keele is determining the proper mouth size for a horn of a given fc cut off frequency.

 

Your next issue is, what is the acoustic impedance of a horn at the throat of a horn.  Keele is using a classic set of data from Olson which shows how the throat impedance changes and actually reaches what it pretty much optimum without going to and "infinite" length horn.  Look very closely at where Olson stopped growing his horn.  That is what Keele found to be optimum.  So Olson must have known, I think.

 

One thing which I'll have to look at but has been pointed out by Bruce Edgar.  I'll do that in the next frame.

 

WMcD

Edited July 21, 2015 by William F. Gil McDermott

[LarryC]

I'm presuming the radiating area emitted from the folded horn is somewhat larger than the 15" driver used in front of it, so to speak, but a more precise estimate would be very welcome - if such is possible. I'm just curious to find out. 

I can't produce the advanced math and concepts that the others can, but can say based on experience and what I've read that, subjectively at least, the entire mouth area becomes the effective speaker radiating area.  In combination with the horn mouth radiating areas from the mid horn and tweeter, the whole front area certainly seems to be the mouth of the system, a much larger area than that of a 15" driver.

 

PWK seems to have contended that placing the speaker on or at a reflecting surface multiplied that radiating area.  Placing a LaScala right on the floor seemingly would multiply things by two.  One Klipsch brochure had this interesting diagram:

 

1957g.jpg

 

This represents a K-horn, of course, and extends the above contention to eight times.  Indeed, the entire corner produces a very large sound that seems to come from the entire corner, and adds greatly to the large-scale heft of the bass.

 

That's a very subjective comment, but that's how I perceive it.

Edited July 21, 2015 by LarryC

[WMcD]

To get an efficient transfer of energy we would like to have a good resistive load and that happens at kCaM = 1 which is to say were the diaphragm or the mouth has a circumference of the wavelength (which translates to a frequency). Or we can say the diameter is about 1/3rd of a wavelength.

(I'm doing this in sort of imprecise terms with the thought that getting the general concept is much more important than total accuracy. Also, the use of "normalization" in the graphs of impedance is very good for engineering types but very bad for ordinary people. Maybe the below will help. When we say kCaM = 1, what does that really mean in terms of physical size and wavelengths and frequencies? The below may help.)

A 15-inch driver has an effective diameter of about 12 inches and so the important wavelength is about 36 inches. What frequency in air has a wavelength of 36 inches. We use 13500 inch per second divided by 36 inches and get 375 per seconds, or cycles per second.

This means that our relatively large bass driver without a horn does not get to nice resistive loading until 375 Hz and up. Below that, it is dropping like a stone.

This is not going to change with different material for the diaphragm or a stronger basket or even a stronger motor system. This is because it is set by the disk of air sitting in front of the diaphragm, the stuff it pushes and pulls. We cannot change that with pretty drivers or T-S parameters.

What if we wanted resistive loading at 50 Hz? 13500/50 is 270 inches. Our disk can be about 1/3rd of that or 90 inches in diameter or 7.5 feet, effective diameter of the diaphragm which moves the disk of air. And we should actually expect the basket diameter to be 8 feet or better. Can't be done, though we could set up multiple boxes to make the equivalent.

What to do for a single bass driver? Is there something we can put in front of it to get the resistive loading down in freq? (And let me add, in the old days, the WE-555 had a diameter of about 5 inches, so we're really screwed out of bass loaded response.)

We have to realize that we can use a horn which has a mouth diameter of 8 feet. Still pretty big. But if it is in a corner, that can be reduced.

The nice thing is that building a horn with a big mouth is do-able while making a driver with a big diaphragm is not. But the big mouth of the horn drives the air disk in front of it just as a diaphragm would.

Nelson Pass, someplace, described a bass horn for outdoor use he made in college which had a mouth diameter of about 10 feet (?), which he called, "The Claw." And he describes how the cops showed up when he'd crank up The Claw. You also see some old cinema horns like this too.

But I was mentioning Bruce Edgar. He pointed out: It is true that when we make a horn, the resistive loading will go down to fc, and we do need the big mouth. And as we go down from just above fc, the resistance at the throat drops like a stone.

Still, the 15-inch driver, looking into the throat of a horn is seeing a resistive load down to almost fc of the horn.

So. In both cases (loading with and without a horn), the resistive loading drops like a stone at some freq. 375 versus 50 Hz. But with the horn, that point is much lower in frequency. We get bass loading.

Sorry that the above is so pedantic but some people here have liked my long explanations. Unfortunately it is necessary to get a bit complicated. The Car Talk guys observed that in some situations you can give an understandable explanation which is inaccurate, or give an accurate explanation with is incomprehensible.

WMcD

Edited July 21, 2015 by William F. Gil McDermott

[uams]

Hi guys --

 

Sorry for my late follow-up, and thanks for all the replies with different approaches on how to address my inquiry. 

 

WMcD, I appreciate your effort in supplying links and insights, but had some difficulty in discerning the theoretics and how they might apply. I guess I suspected my question(s) had been brought up before, and that some practical approximation could be made on the effective air radiation area at the mouth of the folded horn (or whereever and how this radiation area would manifest) with the specific design and driver size used. It's humbling to witness my simplified question lead to the necessity of complication..

 

Chris, wdecho and Larry - interesting notions on the qualities of folded horn bass (to lower mids) reproduction, as the more practical estimations on the air radiation area. They "resemble," or would somehow support my impressions of a pair of Belle-inspired speakers I heard last Spring, having never heard anything quite like it. 

 

/Mikael

Edited July 25, 2015 by uams

[WMcD]

I'm having a little bit of a problem with the question.

Let's just talk about the impedance "seen" by the horn (folded or not) at the mouth (the big end). We are "looking" out of the horn.

It is an acoustic impedance. We generally model the mouth as a disk of the same area. It does not matter what the horn is like (other than mouth size) or what the driver is like. This is because we are looking out of the horn and not into the horn (where they would come into play).

This has been tabulated for two conditions.

1) A disk at the end of a long tube. That is considered to be equivalent to a horn mouth hanging in free air.

2) A disk in a wall or "infinite baffle. That is considered to be equivalent to a horn sitting on a floor in a big room. This is fairly realistic. The article by Don Keele on mouth size give the general graph for this acoustic impedance. But it is "normalized." With some math we can undo that normalization. I'll give that a try over the weekend.

3) There is a third condition and that is a horn sitting in a corner. We have to consider the corner as being equivalent to a long conical horn with a half angle up around 40 degrees, and then figure that we are looking into the throat of that conical horn. This is equivalent to saying we are in 1/8th space or pi/4 solid angle. We can do a lot of math (I suppose) or model it with PSpice to get the acoustic impedance at the throat (small end) of that conical horn formed by the corner of the room.

WMcD

Edited July 25, 2015 by William F. Gil McDermott

[WMcD]

This is my best answer.

WMcD

Mouth Impedance of LaScala (final).zip

Edited July 26, 2015 by William F. Gil McDermott

[WMcD]

I did a bit of looking around.

Colin, long ago, posted quotes from PWK's article on the K-Horn.

https://community.klipsch.com/index.php?/topic/130410-unfolded-length-of-khorn/?hl=%2Bklipschorn+%2B%26amp%3B+%2Blength

As you can see, the mouth of the K-Horn is listed as 570 square inches which is about 4 square feet. Therefore, the mouth impedance curves I posted in the .zip file hold for the K-Horn, with the caveats about not being exactly in a corner. So, now we have a reference point for noodling. The K-Horn, LS, and Belle all have the same mouth size. That can't be an accident.

I recall that elsewhere PWK had said that the K-Horn doubles in area every 16 inches. IIRC the initial flare was half that in the original article and then he didn't use that after the 15 inch driver was adopted. So we have doubling of area every 16 inches down the K-Horn bass horn.

We can do a little reverse engineering and approximate that the throat is about 1/2 square feet. We leave out the half area restrictor plate.

Looking to the LS for guidance. Given that is a 2 foot by 2 foot cube, basically, I'm sure we can say that the LS doubles every 12 inches of path length. So we go from 0.5 square feet (or close to it) at the throat, then 1 square foot after 12 inches, then 2 square feet after 24 inches, and 4 square feet at the mouth after 36 inches of path length. Yeah, it is an approximating given the straight side of the dog house.

Overall, we see that the mouth to throat area ratio is 8:1. Or 1:8 throat to mouth areas.

The path length of the K-Horn is tough to figure out even with drawings. But given the throat size and mouth size, which are the same as the LS, we get the same three doublings in area.

So we can deduce something about the path length design goal of the K-Horn. The design goal must have been three, 16-inch lengths. For a total path of 3 x 16 = 48 inches.

We can't know with certainty what PWK was thinking about when he designing in the 1940's and 1950's. Just where in the structure he considered to mouth area to be is also an issue. But the above makes a lot of sense.

WMcD

[djk]

From the splitter to the edge of the doghouse (the top and bottom of the horn), it's roughly 8" (going either way), and the area roughly doubles.

 

Next we have a section that has no taper, about 10 inches from the (inside) back of the cabinet. Then the area roughly doubles twice in the last 14-1/2". Considering the areas that are expanding, the area doubles (roughly) every 8", and has a non-expanding air-path length of about 9".

 

The 1/4WL of 100hz is 33.9", the total length of the air path in the LS is 31.5", and I'll spot you rest for the distance from the motor board to the cone.

 

 

But wait, figure 5.11C shows how the radiation resistance peak moves up to about 140hz as you go to a larger throat and shorten the 100hz (nominal) taper rate horn to 34.5".

Edited August 1, 2015 by djk

[WMcD]

Thanks for the graphs, djk.

 

I did a little analysis and concluded the Klipsch bass horns are closest to 5.11D.

 

I use the 1/6th resistance as a figure of merit because that is where a -3dB point should be, in theory.

 

Best,

 

WMcD

[djk]

"I use the 1/6th resistance as a figure of merit because that is where a -3dB point should be, in theory."

 

Where do you come up with the 1/6 resistance idea?

 

5.10C shows the radiation resistance going from 1.0 to 0.5, that's more like 3dB.

 

Doubling the throat and mouth area of 5.11C gives a 25" square mouth and a 25 in^2 throat, 34.5" deep.

 

Increasing the throat to 40 in^2 and that's quite similar to the LaScala, and you have an impedance peak at 140hz and a dip at 200hz.

 

I used Olson for many years, until Hornresp became available.

[pzannucci]

Wouldn't the easiest way to view the effective cone area of a horn (most simple terms),

 

Effective cone area = the mouth size that can support the frequency with the best acoustic load, lowest acoustic reactance value.

 

As the horn unloads lower in frequency, the effective cone area drops to close to zero just below the electrical fs of the driver?

 

Basically frequency dependent based on the size and growth of the horn.

 

Probably dumb but  . 

 

Since the horn is an acoustic transformer, it actually lowers the pressure at the mouth so definitely doesn't correlate to the normal concept of effective radiating area of a standard driver.

[WMcD]

"I use the 1/6th resistance as a figure of merit because that is where a -3dB point should be, in theory."

 

Where do you come up with the 1/6 resistance idea?

 

5.10C shows the radiation resistance going from 1.0 to 0.5, that's more like 3dB.

 

Doubling the throat and mouth area of 5.11C gives a 25" square mouth and a 25 in^2 throat, 34.5" deep.

 

Increasing the throat to 40 in^2 and that's quite similar to the LaScala, and you have an impedance peak at 140hz and a dip at 200hz.

 

I used Olson for many years, until Hornresp became available.

 

 

 

djk,

 

Thank you for your comments. 

 

I did look at some of my documents and I can't find the document which I was quoting.  (I'll find it probably when I'm looking for something else.  Smile.)  Actually, I'd like to do a write up on the subject but that will take some time. 

 

The Wente and Thuras Bell Labs article (it is in the Klipsch Papers) points has an equation for determining the relation of the best driver parameters and for a throat size.  Later Don Keele translated this to T-S parameters and we see it mentioned very often on the forum.

 

But the W&T article points out how important the optimized driver can be.  Attached is the important page.  According to their calculations (which they don't describe) their bass horn has resistive impedance at the throat which has a high of 2.75 and a low of 0.36.  That is not too far off the Olson plot which I pulled from your post.

 

They conclude that these result in 1 dB loss from the optimum.

 

I'm very confident this results from the circuit analogy for a generator with an output impedance (which is the driver) and a load (which is the throat impedance).  Don Keele shows this simple circuit in his paper on use of T-S parameters to predict driver choice and results.  He uses it for the mid-band.

 

It is a recognized principle of electrical engineering that the maximum transfer of power occurs when the generator output impedance and the load impedance are the same.  (Am I pontificating?)  The max efficiency is 50% because half of the power is dissipated in the generator and half in the load.  It is a little more difficult to find info on how much of a mis-match we need to get down to 50% of what is max in the load, but it does work out to as great as 6 and a little as 1/6.  Well, those may give -3.05 dB or so, but very close.

/

Anyway, I've draw up the circuit and plugged in numbers. It agrees with W&T.  Again -1.05 dB or so to be totally accurate.

 

BTW the high for W&T is 2.75 and 1/2.75 =0.364.  So they seem to be working with reciprocal values, as I did.

 

PWK's patent on the MCM has a comment on how the mouth size can be reduced with the use of a proper driver.  He must be talking about what W&T are saying about selecting about a driver.

 

While we're here, W&T also talk about the proper driver reducing oscillations in the horn.  This is a bit more difficult to understand.  We started saying that the generator impedance should be matched to the load at the throat, to which it is attached, for outgoing power coupling. 

 

They are referring to another phenomenon which is related.  This matched situation also causes the optimum transfer of power into the driver from the throat or incoming power coupling,. 

 

You may say, "What?"  How are we transferring power from the throat into driver?

 

The situation is transmission line theory.  It is that there is a reflection of energy when the mouth is small and so there is sound energy reflected back into the horn which eventually ends up at the throat.  This is what causes the wiggles in throat impedance. 

 

If the driver is a good match, it absorbs all of the incoming sound energy.  If it did not, the pulse would reflect back into the throat of the horn, and then reflect from the mouth, and back and forth. This is the oscillation.  Horn musical instruments do this.

 

I'll scan my calculations and post in a day or so.

 

WMcD

Wente and Thuras on Throat impedance and losses.pdf

Edited August 8, 2015 by William F. Gil McDermott

[WMcD]

Okay, here are my calculations.

 

Calculations of Losses Due to Throat Impedance.pdf