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Old 29th October 2010, 08:42 AM   #21
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Hi soho54,

Would appreciate clarification of the following points regarding your Version 5b spreadsheet :-).

1. How is the expression F3 / 1.4 used to calculate the "Flb" horn cutoff frequency value arrived at? Is it just an empirical formula - possibly an approximation to F3 / SQRT(2)?

2. What is the "1-3H Null" frequency, and how is the expression SQRT(((F3 / 0.85) * 2.25) * (F3 / 0.85)) arrived at?

3. Why is the horn mouth unflanged end correction 2 * (0.6 * Mouth_Radius) and not simply 0.6 * Mouth_Radius?

Thanks in anticipation.

Kind regards,

David
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Old 29th October 2010, 09:21 AM   #22
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Quote:
Originally Posted by soho54 View Post
I can't duplicate the error by starting from default, and changing Qes to 1.
Hi soho54,

Qes needed to be changed to 0.1 not 1, to generate the error :-). Now works fine in Version 5b.

Kind regards,

David
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Old 29th October 2010, 05:10 PM   #23
soho54 is offline soho54  United States
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David McBean,

I had a long post going answering your questions as I went along, until I got to the third one. At some point when moving my equations over from my personal scrap sheets diameter was input instead of radius.

Let me sort it out, and I'll answer the rest.
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Old 29th October 2010, 08:22 PM   #24
soho54 is offline soho54  United States
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Quote:
Originally Posted by David McBean View Post
1. How is the expression F3 / 1.4 used to calculate the "Flb" horn cutoff frequency value arrived at? Is it just an empirical formula - possibly an approximation to F3 / SQRT(2)?
That is exactly all it is. I was attempting to make the math look a simple as possible.

I added it, so that people who didn't understand what Fo was wouldn't have to worry with it. You just input a -3dB point under the FR low corner for a TH, and the output is close to what they expected. With the other setups it is closer to the actual FR low corner, but this is a TH centric sheet.

Quote:
Originally Posted by David McBean View Post
2. What is the "1-3H Null" frequency, and how is the expression SQRT(((F3 / 0.85) * 2.25) * (F3 / 0.85)) arrived at?
OK, this is a simple way to set the rear tap that is based on my original manual process. The ".85" was a crutch to get it to work when the end correction was off. It was less correct as you went up in frequency as well. It is back to SQRT(((F3/0.9)*2.25)*(F3/0.9)) now.

I'll explain how I do it manually first:
Quote:
OK, here is a pic, please use a four chambered horn for demonstrative purposes.

Click the image to open in full size.

The way I see it is hard to explain, so bear with me here. The arrow points to the 3rd harmonic. This is the key position. First set you last section way to long, and then slowly shorten it. It will start as a steep slope into a deep dip, but as you shorten it you will see a peak appear. It will slowly move down a few Hz at the same amplitude, and then start to rise in amplitude. What you want to do is to stop right at the point before it begins to rise in amplitude. While you are doing this the 1st peak is lowering, and the dip between the 1st&3rd should be filling in.

Now depending on the compromises you are making in your horn you may sometimes need to be in a slightly different spot. You need to visualize the top line hitting the 1st and 3rd harmonics, and extend it through the bandwidth of the horn. At the dip between the two harmonics imagine another line parallel to the first. You want all of the dips to fall inbetween these two lines if possible. (Just eyeball it, no need to get crazy)

In my example, the mouth(S5) is more compromised(undersized) than the middle section(S3.) This tends to make the dip between the 3rd&5th a little lower than a more ideal horn would. If the middle section(S3) is more compromised(undersized) the dips on either side of the 5th will be a few dB below the average range imagined above, but they will be at the proper angles.

The reason I said to use a four chambered horn, is because a three chambered horn can have problems at the middle and mouth at the same time. Normally, this manifests as a small mouth (lowered 5th dips,) and to large a mid section (peaky/raised 1st harmonic peak.) When this happens you still set the 3rd H the same way, it can just look odd sometimes. When this happens, you can leave it (as the peaks and dips are normally in the right places relatively,) redo the horn, or just set it to your preference.

I will add that you can check the rear tap by:
X=SQRT(H1 Hz * H3 Hz)
(c/X)/2= Distance from tap to the start of the horn in meters
What this is doing is setting the rear tap to throat distance to get the rear wave at 180deg out of phase exactly(ish) between the two resonances. This will allow the maximum usable bandwidth, while filling in the dip as much as possible.

To get the H1=(F3/.9) I ran different horns from 15Hz to 40Hz with six different drivers ranging from 6" to 21". I divided the F3 by the horns simed FR low corner peak for each one, and used the average. The spread was pretty small so it works out fine. H3 was done the same way. There was more variance here, but the median works out pretty well.


You didn't ask about this next part, but I get a lot of questions about. That is, why I used the drivers frame width as L34. It was chosen to help make folding easier. Using the 4 Segment TH that the sheet outputs, you can use the S3 to S5 distance length of the first folded segment from the mouth. With smaller driver you will find you may need to push the S3 back towards the throat a little when accounting for the acoustic path length. With the horn setup this way, you can move S3 back a good bit to compensate before the FR is adversely altered. If you would like to just a different position to help in a different kind of fold, you just have to play with the Wizard a little bit. I have plans to add folding to it at some point, but I want this to be where I want it before I move on.

Oh yeah, adding a revers taper to the first segment is no big deal either. Just get the horn right, then with S2 Fixed set in the HR wizard increase S1. When it is where you want it, you will need to go back and tweak the L45 a little. Calculate it before you change anything, and Capture the results. Then you can compare your new versions to the old to make sure it is still holding up. That's it.


Another pass.
Attached Files
File Type: zip Easy Horn v5c Excel.zip (25.9 KB, 79 views)

Last edited by soho54; 29th October 2010 at 08:50 PM.
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Old 29th October 2010, 10:22 PM   #25
soho54 is offline soho54  United States
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Sorry, I'm writing this in pieces as I get time. Let me try to add some more here.

There are two other ways to get the rear tap position from HR. With a horn shaped profile you can set the voltage to 0, and get the two peaks that way. You can also use the Impedance minimas.

At a set Fo with a driver, all three methods are within ~3cm of each other. However these latter two methods will give vastly different rear tap positions at other horn cut off points.

When they are close the dip between the 3rd & 5th peaks will be ~1dB deeper, but the ones above it will be ~1dB shallower than the FR peak method from the last post. In the horns with a very large difference there will be a more pronounced shift in the dips in the peaks >3rd, and the low corner will have it's Q flattened out. The FR will still be pretty close though.

There is something to think about here. My suggested -3dB position will get you into the zone where they all match up.

Last edited by soho54; 29th October 2010 at 10:26 PM.
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Old 30th October 2010, 08:11 AM   #26
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Quote:
Originally Posted by soho54 View Post
Let me sort it out, and I'll answer the rest.
Hi soho54,

Many thanks for the detailed response - very interesting stuff.

Kind regards,

David
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Old 31st October 2010, 06:03 AM   #27
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Hi soho54,

Just a thought...

The Goal Seek tool is now being used to find the value of Fh given the values of F3 and m. Perhaps it might be better to find the value of m given the values of F3 and Fh, since the value of Fh is normally of more interest than the value of m?

Kind regards,

David
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Old 31st October 2010, 07:09 AM   #28
soho54 is offline soho54  United States
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Quote:
Originally Posted by David McBean View Post
Hi soho54,

Just a thought...

The Goal Seek tool is now being used to find the value of Fh given the values of F3 and m. Perhaps it might be better to find the value of m given the values of F3 and Fh, since the value of Fh is normally of more interest than the value of m?

Kind regards,

David
I had someone asking me about this earlier today.

It can be added.
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Old 31st October 2010, 01:22 PM   #29
thosuk is offline thosuk  United Kingdom
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Thanks Soho54, this is really useful software. Your rapid responses and the expert comments show the true spirit and values of the forum.
Reference has been made to the Marshall Leach paper on annulling reactance. I recall that Michael Zhang wrote a utility some time ago based on the ML work http://fullrangedriver.com/singledri...oad/MLutil.zip which covers the annulling of a front loaded hyperbolic horn. Iíve compared your results for the front loaded horn case with his, and there are differences, generally around 10%. The *ML UtilĒ software is a little quirky (fL, fH and fs have to be integers, and Qts needs to be input even though it can be derived from Qms and Qes). Michael Zhangís software Readme refers to the corrections to the ML paper that were covered in letters to the editor after initial publication. The corrections are detailed immediately after the main paper in this link http://users.ece.gatech.edu/mleach/p.../HornPaper.pdf Incidentally, the link to Marshall Leachís paper in post #1 doesnít work for me, so I donít know if this included the corrections, or whether you were aware of them.
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Old 31st October 2010, 05:05 PM   #30
soho54 is offline soho54  United States
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Quote:
Originally Posted by thosuk View Post
Thanks Soho54, this is really useful software. Your rapid responses and the expert comments show the true spirit and values of the forum.
Hey, thanks.

The paper you linked to is the same one I am using, and that I tried to link to. For some reason the the link in the first post tries to pull up in it's foreshortened version as it shows up on the forum page. I didn't catch it until it was too late to edit the post. My sheet does include the info in the letters to the editor.

I just downloaded ML, and the results match up with my default driver/horn in v5c. Some of the cells on my second sheet are rounded to the hundredth place on the display, but the sheet uses the full 15 digit number in it's calculations. The hyperbolic flares are a hair different, but I am sure rounding differences would account for that. 3sq cm at 4m is pretty close.

Can you post the numbers used that didn't match up. I would like to see where/how they misconverge, and try to figure out the why.
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