Basic basshorn design questions

[jwc]

I have some questions about bass horns. I will start with simple questions and I will make sure Im on the right track before I ask moreotherwise I will lead down the wrong path and make myself look really stupid (not hard to do).

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I am trying to figure out how to figure/calculate an exponential bass horn (or Tractrix, maybe). Lets say it is one that the horn is split like the La Scala for instance. Take a look at my simple diagram there. It is the back side of a scala motorboard. The throat is 3 x 13. Therefore its area is 39 in² or 251.61 cm².

1: Now the chamber is split at the Splitter (not shown). To make calculations for an exponential or tractrix horn or whatever, the throat area is needed. So if one were to make calculations for a horn, do you start with ½ the throat area or the whole throat area when the chamber is split?

2: If say you want a 70Hz cutoff bass horn and the horn you are building is split like a scala, is both sides flared as a 70Hz horn or is there some sort of additive thing here? Hard to ask?

jc

[Guest " "]

most discussions on this forum refer to the area of the opening of both sides as being 78 total square inchs. rather than the area of motorboard opening.

can I ask you to clarify your objective

[DrWho]

hey jc, I think I get what you're asking...

The calculations for the waveguide involve a 'straight' distance from

the mouth by which the area of the horn at that length is calculated.

It is my understanding that when you split the horn, that you still

look at the total area of the horn for that distance from the driver.

Let's say that at 12 inches your exponential calculator says you need

an area of 144 square inches and at 24 inches you need an area of 300

square inches. If you have a split at 18inches, then the mouth on each

side should be 150 square inches so when added together it's a grand

total of 300.

Basically, you should calculate the straight horn of what you're trying

to accomplish and then fold it / split it however you want (keeping in

mind of course the compromises being made with any kind of fold or

split).

At least that's my take on it - I'm not for certain, but hopefully this

will get some discussion going - At least I think I'm answering your

question? I suppose you could always try to sit down and backwards

calculate the lascala bass bin.

[jwc]

Guys, both of your comments are helping. I am gonna think of a DIY project but I need to get a few points cleared-up.

Spkrf......I may have some terminology screwed up here. What you are calling "opening", I was calling throat. As you can see, the area of the "opening" is 39 sq in. So I must have the terminology wrong or something. If you want to call the throat at the end of the "wings" or "waveguides" or "deflectors", it is 66.75 sq in (or 133.5 by what DrWho just said). I was assuming the throat area was 39 sq in.

Who.....I followed everything you just said. Yes that answers my question partly. I am assuming then the throat in the above diagram is 39 sq in. From you logic, there is no "spitting" of the throat area for calculation purposes. Just split the throat after the calculations.

Also, Mike, I was afraid to reverse calculate a La Scala because I don't know if PWK went straight exponential or not. He may have had some modifications to the horn to correct any flaws in real testing. Don't know.

You guys are helping...thanks. I assure you, there will be more questions as the responses here keep coming.

jc

[jwc]

By the way. Anyone got a horn calculator for exponential and tractrix that is in inches?

[Guest " "]

Guys, both of your comments are helping.  I am gonna think of a DIY project but I need to get a few points cleared-up.

Spkrf......I may have some terminology screwed up here.  What you are calling "opening", I was calling throat.  As you can see, the area of the "opening" is 39 sq in.  So I must have the terminology wrong or something.  If you want to call the throat at the end of the "wings" or "waveguides" or "deflectors", it is 66.75 sq in (or 133.5 by what DrWho just said).  I was assuming the throat area was 39 sq in.

Who.....I followed everything you just said.  Yes that answers my question partly.  I am assuming then the throat in the above diagram is 39 sq in.  From you logic, there is no "spitting" of the throat area for calculation purposes.  Just split the throat after the calculations.

Also, Mike, I was afraid to reverse calculate a La Scala because I don't know if PWK went straight exponential or not.  He may have had some modifications to the horn to correct any flaws in real testing.  Don't know.

You guys are helping...thanks.  I assure you, there will be more questions as the responses here keep coming.

jc

 

I have seen a lot of forum discussions that focus on the two individual openings once you enter the compression area.

Do you compute horn values using the motorboard opening (3X13) or do you compute horn values using the openings of the indiviudal wings (which are each approx 3X13) .

My understanding is that math does not work out either way.

My personal take is that the LaScala size was a foot print issue and a construction goal to maximize raw materials. One pair of LaScala's can be constructed from 3 sheets of 4X8 plywood which just 4 spuare feet remaining from 2 of the 3 pieces.

The current size of the LaScala is the largest that can be constructed from 3 sheets of plywood. I don't think the size was the result of an exact formula that specified the particular foot print.

But can you explain what you would like to do? Perhaps others have done it and we can help point you to their work.

There is a version of the LaScala in diagram form that is based on a smaller foot print and a 10 inch driver.

A LaScala with a 70hz bottom end, would be a smaller LaScala. Is that what your after?

[jwc]

I see your point. I already pretty much know how to build a La Scala.

I am going to look into building a bass horn myself just for giggles. I want it to be like the jubilee in principle with one driver. There is a guy in Canada at FIRST OCTAVE AUDIO that build a cabinet like the jubilee with an 18" driver.

So it is a work in progress. I was wanting to get a few basics down first before I move on. It would be nice the first time I build one to use an "opening" of 3 x 13" and use a K33 or one of bob's woofers.

Now initial thoughts was to have a sealed chamber sealed that is about double the height of the La Scala. The wings would flare out about 60 degrees instead of 30 degrees. Then the rest would be a "w" like horn like the jubilee with a lower cutoff compared to the la scala.

Now I can put this on a poster board w/in a few weeks drawn out and bring it back here for proofread. However, I need a few things straight before I kick in gear. The above mentioned has already helped me start.

I was using the La Scala as demonstation to ask questions. I too believe that there probably is incorporated changes w/in the scala plan for production purposes. I however, am not interested in that.

So for where I understand at this point, the throat of the scala is 39 sq inches? If it ain't and its 78 sq in, then please point out on my diagram where the 78 sq in comes from. That motorboard IS the scala motorboard.

If I get this straightened out, I can move forward. would be nice to have a horn down between 35-40Hz. Of course lower is better but I don't want to build a monster.

jc

[jwc]

Now look at the image posted. Now I'm not trying to copy a Jubilee here. That "w" configuration isn't unique for just the Jubilee as I understand it.

The inner height to be somewhere between 38-42" and depth 24-28". If I use one K33, I will use the same motorboard opening. I want the back chamber wings to be 3" deep like the la scala. I should be able to go from there.

jc

[LarryC]

Spkrf......I may have some terminology screwed up here. What you are calling "opening", I was calling throat.

Where's D-Man? He e-mailed me a couple of years ago that the 13" X 3" was not the throat, but rather something he called the "cavity" IIRC. He said the throat was the beginning of the horn itself lay between the cavity opening and the splitter, and that, because the bass horn is split into two parts, the total area of the throat at the splitter was approximately 78 sq. in., not 39. Something like that.

I'm not trying to speak for Dana, but thought I'd enter that into the conversation until he appears.

Larry

[jwc]

Thanks Larry. If I get that part straight...I will press on.

jc

[Guest " "]

I see your point.  I already pretty much know how to build a La Scala.

I am going to look into building a bass horn myself just for giggles.  I want it to be like the jubilee in principle with one driver.  There is a guy in Canada at FIRST OCTAVE AUDIO that build a cabinet like the jubilee with an 18" driver.

So it is a work in progress.  I was wanting to get a few basics down first before I move on.  It would be nice the first time I build one to use an "opening" of 3 x 13" and use a K33 or one of bob's woofers.

Now initial thoughts was to have a sealed chamber sealed that is about double the height of the La Scala.  The wings would flare out about 60 degrees instead of 30 degrees.  Then the rest would be a "w" like horn like the jubilee with a lower cutoff compared to the la scala.  

Now I can put this on a poster board w/in a few weeks drawn out and bring it back here for proofread.  However, I need a few things straight before I kick in gear.  The above mentioned has already helped me start.

I was using the La Scala as demonstation to ask questions.  I too believe that there probably is incorporated changes w/in the scala plan for production purposes.  I however, am not interested in that.

So for where I understand at this point, the throat of the scala is 39 sq inches?  If it ain't and its 78 sq in, then please point out on my diagram where the 78 sq in comes from.  That motorboard IS the scala motorboard.

If I get this straightened out, I can move forward.  would be nice to have a horn down between 35-40Hz.  Of course lower is better but I don't want to build a monster.

jc

your drawing is 2 D, so you will not see the two 3X13 openings.

if you think in terms of 3 D, once you enter the compression chamber thru your illustrated opening, to the immediate left and right will be 2 openings each of which are approximately 3 X 13, the sum of the square of these two openings, is approximately 78 sq inches.

[ajsons]

jc,

I've been reading most of Dana's posts, he doesn't post in the weekends, I think he's busy teaching the choir.

You have to wait till Monday for his reply.

Most of the answer to your questions are on Gil's thread,

http://forums.klipsch.com/forums/thread/545202.aspx

The throat is 78 sq inches.

The motoboard opening is 39 sq inches, the K33 woofer works well with that opening. If you want to use another woofer, most likely you have to use a 78 opening, pretty much "standard" for a 15" woofer.

[WMcD]

I don't have all the references here. But let me answer some of your questions.

The PWK patents on the "Valerie" and the MCM 1900 are good primers on bass horn design. Go to www.uspto.gov. Do download the TIFF viewer plug in. Find the area of the site for patent search. Set up a basic search and look in "assignee" and set it to Klipsch. Youll find a bunch.

There is also the AES preprint on the LaScala which I posted a long time ago. Maybe someone can point you to it. The same is true of the AES article on the Jubilee.

The LS is the easiest bass horn to understand. The complicated exponential equation for expansion means that the area (note AREA) doubles every x distance down the horn. For the LS the x is 12 inches.

The small end of a horn is called the throat (up against the driver). The big end is called the mouth (the end open to the air).

You can split the path. That is done in the K-Horn, Jubilee, MCM1900, Belle, and LaScala. You use the combined area of the ducts.

Bass horns typically are a sequence of expansions which are made of plywood which is not curved to an exact exponential.

My reverse engineering of the LS is that it is a cube 2 feet on a side.

The throat is 1/2 square foot (almost). The first path is 1 foot long where the two sections take off toward the corners in the back. At the corners, the total area is 1 square foot. (see, it doubled).

Coming forward (after the bend), after another x of 1 foot, the area is 2 square feet. There is a bit were there is no expansion, but we're talking approximation. (Note, that area doubled again.)

Coming forward again to the mouth from that intermediate point, we have a mouth area of 4 square feet. (Note the area doubled again.)

There is much confusion over the 3 x 13 slot. Thaqt does not set throat size, in my view.

I had posted on this in the first incarnation of the website. I think it crashed, and is lost.

In my view, the restriction slot is there to form a chamber in front of the diaphragm. Classic theory is that it is possible to bump up the response at, here, 400 Hz, if you have a chamber in front of the diaphragm. The front chamber volume "spring" forms a resonance with the mass of the diaphragm.

I'm quite certain that this is what PWK was up to. You can find it in books he must have read. But he never explained it in print. (I should put this together again, but I'm working on "The Caves.")

The problem with forming a front chamber (with spring) is that the throat size of 1/2 square foot is just about half the diaphragm area. Consider the problem. You want a "pretty much closed" cylindrical volume in front of the diaphragm so air can be compressed. But the other end has a big hole (throat of the horn).

What to do? I think PWK put in the restriction slot. Now there is a better chamber formed. Maybe the little prism shaped splitter helps a bit to clog up the hole, additionally. The combination may causes lose overall, but you get the resonance.

None the less, the throat and exponential expansion only makes sense if you use the combined area of the two ducts, each of which are 3 x 13.

Best,

Gil

[ajsons]

JC,

The Jubilee paper shows how to calculate what the area should be at any point along the horn's path (Area analysis of points B, C and D).

Dana has a quick and easy way of calculating these. I don't want to deal with the math (my weakness), so I let the pc do it.

Here's a sample readout, the expansion for a 70hz corner horn. Pure exponental (M=1). "A" and "B" sides are distances between parallel sidewalls of the horn's duct, i.e under the 6" A side column are the distances between the non-parallel or expanding walls. If you're sure of your final height, let me know I'll rerun the figures with a different fc, dimension for A or B or both.

(These are based on Edgar's Show Horn article).

70HZ CORNER HORN

Throat = 78 sq inches
M = 1

Length Horn One-half 6 inches 38 inches
fm throat area area A sides B sides
--------- --------- --------- --------- ---------

1 83.25147 41.62574 6.937623 1.095414
2 88.85651 44.42825 7.404709 1.169165
3 94.83891 47.41946 7.903243 1.24788
4 101.2241 50.61205 8.435341 1.331896
5 108.0392 54.01958 9.003263 1.421568
6 115.3131 57.65654 9.609423 1.517277
7 123.0767 61.53835 10.25639 1.61943
8 131.363 65.68152 10.94692 1.728461
9 140.2073 70.10363 11.68394 1.844832
10 149.6469 74.82346 12.47058 1.969038
11 159.7222 79.86108 13.31018 2.101607
12 170.4757 85.23785 14.20631 2.243101
13 181.9532 90.97662 15.16277 2.394121
14 194.2035 97.10176 16.18363 2.55531
15 207.2786 103.6393 17.27322 2.72735
16 221.2339 110.617 18.43616 2.910973
17 236.1289 118.0644 19.67741 3.106959
18 252.0266 126.0133 21.00222 3.31614
19 268.9947 134.4973 22.41622 3.539404
20 287.1052 143.5526 23.92543 3.777699
21 306.435 153.2175 25.53625 4.03204
22 327.0662 163.5331 27.25552 4.303503
23 349.0865 174.5432 29.09054 4.593243
24 372.5893 186.2946 31.0491 4.90249

[jwc]

This is great. The throat was my hang up. Let me chew on some of this tomorrow and go a little further. I have the AES Jubilee article..I'll skim it again. If someone has the La Scala one...I'll check that out to.

Why in the heck couldn't I think of that 39 sq in plus 39 sq in is 78 sq in.

jc

[ajsons]

JC,

A 70hz corner horn is a short horn. A 60hz will be like 34-36" long.

[Guest " "]

This is great.  The throat was my hang up.  Let me chew on some of this tomorrow and go a little further.  I have the AES Jubilee article..I'll skim it again.  If someone has the La Scala one...I'll check that out to.

Why in the heck couldn't I think of that 39 sq in plus 39 sq in is 78 sq in.

jc

You were getting close....did not want to lead the whitness.

[DrWho]

I wrote a spreadsheet to calculate tractrix expansion rates if you're interested...though it's not perty and probably hard to use - you really need to understand the math involved (it's pretty much just doing the plugging and chugging for me). I think I might still have the exponential version around somewhere too.

The reason I bring it up is because I've modelled a lot of expansions and noticed that you have to be careful near the throat. Depending on the shape you choose to go with, you might end up with wierd crap happening on the 'dependant side' - like the opening gradually getting bigger and then getting smaller and then getting bigger again.

Actually...I would be very much interested in research involving the shape of the sides of the horns. The horn types we have now are just area expansion rates and don't dictate anything about the shape. Maybe that's the bubble thing Roy is always talking about.

[Guest " "]

I wrote a spreadsheet to calculate tractrix expansion rates if you're interested...though it's not perty and probably hard to use - you really need to understand the math involved (it's pretty much just doing the plugging and chugging for me). I think I might still have the exponential version around somewhere too.

The reason I bring it up is because I've modelled a lot of expansions and noticed that you have to be careful near the throat. Depending on the shape you choose to go with, you might end up with wierd crap happening on the 'dependant side' - like the opening gradually getting bigger and then getting smaller and then getting bigger again.

Actually...I would be very much interested in research involving the shape of the sides of the horns. The horn types we have now are just area expansion rates and don't dictate anything about the shape. Maybe that's the bubble thing Roy is always talking about.

Thats kinda whats happening in the LaScala. It expands from the throat to the first turn. From the first turn to the begining of the dog house flare it remains the same, no expansion, just lenth. Then during the last section it flares out agressively.

The belle does not have this section of no expansion.

There would be no way of getting rid of this dead zone, with out making the LaScala wider. Seems like the only purpose it has is to add depth to the doghouse to ensure woofer magnet clearance.

[ajsons]

Mike,

Tractrix bass horn is not the way to go, per Edgar. He says "tractrix bass horn" is a contradiction of terms.

http://www.positive-feedback.com/Issue4/edgarinterview.htm

" ......so when I built a 70 Hertz Tractrix Bass Horn (Speaker Builder, 1983), I
was in for a surprise. The problem is that the Tractrix is a short horn. If you take the equivalent Tractrix and equivalent exponential horns (same mouths, same throats, same flare rates), the Tractrix horn is shorter. At the low end, the response on any horn is limited by the throat reactance, which peaks at the flare frequency. The exponential horn is long enough that if you can put on a back chamber and resonate it with your loudspeaker at the flare frequency, you can partially cancel out that throat reactance.
With a hyperbolic exponential horn, you can cancel it out exactly.

With a Tractrix horn, you don't cancel it out at all, so the 70-Hertz horn rolled off at 100 Hertz. It sounded very good, but the problem is that the Tractrix horn response just does not extend to the flare point. There is no way that you can do it, so you have to live with the consequences. Well, for a midrange horn that's not too bad. The 300-Hertz horn that I make turns on at around 400 Hertz, and since its size is not huge, I can build a full-size
300-Hertz horn. It sounds very nice, but it won't turn on until 400 Hertz."