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Simple Tapped Horn Tutorial using Hornresp

191K views 136 replies 36 participants last post by  GPM 
#1 · (Edited)
Tapped Horn Design

We're up to v34 now, and there is a new download link.

Get it here:

http://www.hornresp.net/

After reading maxmercy's excellent post on front loaded horn design, I thought I'd share what I know with respect to tapped horns.
As I've said all along, I am an amateur, I do this as a hobby. I am not selling anything, just sharing what I have figured out.
I apologize in advance for my lack of sketchup skills. I hope that I can get the idea across.

What is a tapped Horn? I don't want to go into that here, as others far smarter than I have explained that already.

http://www.google.com/search?rlz=1C1...&q=tapped+horn

Google is your friend, I recommend links 1 and 3 first. Danley's white paper is excellent too, but may go over your head at first.

Do they work?
Absolutely.

Why bother with a tapped horn?

Cabinet size. While a tapped horn may not equal a front-loaded horn in output, it can produce considerable output from a cabinet that is ~1/4 the size of a 1/4 wavelength horn.

Are they hard to build?

No, not at all. In the simplest form, it is a box with a driver near one end of a sloped baffle inside, 7 boards.



Some Caveats:
Not all drivers will work in a tapped horn
Improper designs will kill a driver quickly
Overexcursion explodes out of the pass-band (use high-pass filters)

As with any horn, boundary loading is your friend, but unlike a front-loaded horn, you don't need it to flatten the response.

Number one rule - there is no free lunch.

There is no magic here, just physics and math.

Here is an annotated diagram so you know what I am talking about. S = area, L = length. Hornresp works in metric units, like the rest of the world...



One of the primary concerns in designing a tapped horn is if a given driver will work with a reasonable compression ratio, which is the area of the driver (Sd) divided by the area of the horn at the driver entry (S2).

Small drivers can work with a higher ratio, as can drivers with a more rigid cone. Personal experience suggests that 4:1 or less is fine for small, high-excursion 6 to 8 inch diameter drivers.

Larger drivers require lower ratios, for example jbell's PA tapped horns use Eminence 3015lf 15" drivers, and have a compression ratio of 1.26:1. These are an extreme example, SPL @ 40 Hz was the primary concern.



Yes, that is a 15. These are HUGE. More details here:

http://www.diyaudio.com/forums/subwo...ped-horns.html

So - how do we design one?

Select a driver. Lots will work, I'm choosing one that I have, and one that is cheap enough for anyone to experiment with this should you choose to play along at home. For this example, I'm using the MCM 55-2421 High-excursion 8" woofer. While perhaps it is not an ideal driver, it is cheap and I already have some (that makes it even better in my book).

http://www.mcmelectronics.com/product/55-2421

These drivers are often on sale, but you have to enter the correct code to get the sale price. I paid ~$25 each shipped for the last ones I bought.

Here is a link to how to enter your own driver parameters.

This cabinet will use two drivers wired in series. I've measured several of these drivers in the past, the thiele-small parameters I have are entered into hornresp.

Select a target low frequency response cutoff. Realistically, a low corner of 66% of the drivers Fs in free-air can be reached without losing too much efficiency or sending excursion through the roof. Higher frequencies = smaller boxes and higher efficiencies. It is all about the compromises.

In our case, since I have realistic expectations for these 8 inch drivers, I'll choose 30 Hz.

Next, I determine the minimum throat dimension.

Sd * 2 (number of drivers) / 4 (max safe compression ratio)

In this case, S2 should be approximately 105, so S1 can be smaller than 105. I'll start with 100.

Then I determine the mouth area. I typically use total Sd * 2 as a starting point, some drivers want more or less.

In this case, S4 should be around 836, I'll use 800.

Now, we have to determine the lengths of the various parts of the tapped horn. We know that the drivers have to fit inside this thing, so L12 and L34 have to be at least 21 cm (one driver diameter).

Experience has taught me that an additional few centimeters is a good thing, it makes driver installation and construction much easier.
I'd suggest 32 cm as a good starting point.

What about the L23 value? Lets use 250 cm for now.

OK, we have what we need to get started. I've attached a hornresp import file to this post so we all start at the same place. 
example.txt 0.3798828125k . file
 

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#28 ·
Yeah, the impedance is a little funny. I wouldn't worry about anything outside of the pass band.


As you noted the peaks here will not be as high in real life, but those are some crazy high numbers. I am more interested in the shape the dips take. The same with driver displacement bumps.
 
#29 ·
First, very interesting thread. The correlation between excursion bump and valley and SPL output gives us clue on how to modify the BL value or Qts to get smoother output. For instance, at excursion peak, if the SPL output is too high, increasing BL value can reduce the SPL output at that frequency. On the other hand, at excursion valley, if the SPL output is too high, reducing BL value can reduce the SPL output. Overall, it is a process of how we can pick a BL value to get the smoothest output. Of course other factors such as fs and Mmd affects the general shelving direction.
 
#30 ·

Quote:
Originally Posted by Rythmik /forum/post/17914722


First, very interesting thread. The correlation between excursion bump and valley and SPL output gives us clue on how to modify the BL value or Qts to get smoother output. For instance, at excursion peak, if the SPL output is too high, increasing BL value can reduce the SPL output at that frequency. On the other hand, at excursion valley, if the SPL output is too high, reducing BL value can reduce the SPL output. Overall, it is a process of how we can pick a BL value to get the smoothest output. Of course other factors such as fs and Mmd affects the general shelving direction.

Thanks, and thanks for your insight. I'm still trying to wrap my head around driver parameters and their influences on the response in a tapped horn. While Bl is key, I think Bl by itself only tells part of the story, it needs to be looked at along with Re at the same time.


Some manufacturers present the ratio of Bl/sqrt(Re), which seems to have a good correlation with a driver's performance in a tapped horn.


I have a reasonable approximation of the tutorial tapped horn already under construction, and I have several other sets of 8" drivers in addition to the MCM 55-2421s. My current plan is to swap out the pairs of drivers and compare specifications, predictions, and measured performance later in this thread.


Any other suggestions as to how I could explore this further?
 
#31 ·
You have to keep the cone and suspension compliance in mind as well.


Look at the real parameters BL, Re, Mmd, Sd, and Cms, not derived ones. Of course different parameters are needed for different horns (bandwidth, horn/driver size, compression,...)


Here is a link to the patent application with the supplemental images in a pdf link.

http://www.freepatentsonline.com/20090087008.pdf
 
#32 ·
I've got a question about these sims. Hornresp is assuming a conical expansion which means both the X and Y dimensions are growing as you go along the line. But it seems like people are folding these so only one dimension grows linearly along the line. The depth of the box stays constant and the internal baffles all expand about the same amount. Simple example measuring the area at equal 1/4 points along the line....

Code:
Code:
Conical Folded
S1      100     100
S2      194     475
S3      475     850
S4      944     1225
S5      1600    1600
Now you could adjust the angles of the individual folds so it follows the conical expansion more accurately but it doesn't really look like that's what Danley is doing. Help.
 
#33 ·
catapult,


Something is off there. You seem to be comparing an exponential profile conical horn to a straight conical one with a single taper.


In order for the second column to match the first you would need multiple conical sections. It is the surface area change that counts, not the shape as much. You could build an exponential "T" horn out of square boxes if you wanted too.


Here is a link to a paper that talks about it, but the site isn't working right for me today. http://www.scribd.com/Loudspeaker-Ho...rt-1/d/9778607


EDIT: The link is working again.
 
#34 ·
catapult,

I see you changed your numbers.



To add to that last post, remember a TH doesn't need the mouth area of a regular horn. As a result you can get away with a less exponential profile. Hornresp will only simulate the horn profile you input. You can see it in the Schematic Diagram section. In order to simulate your "conical" example you would have to use multiple conical sections, or input it as an exponential horn.


Hornresp thinks of conical as a straight wall from throat to mouth section. The shape doesn't really matter, only the area. At sub frequencies it doesn't really mess anything up. At higher frequencies it messes up the directivity graphs.


I will add that they seem to do a little better with non-ideal drivers with two conical sections after the throat, with varying expansion rates.
 
#35 ·
While we model a conic expansion (both x and y expand), we typically draw and build a parabolic expansion (either x or y expand), which is close enough for most, especially within the ranges of tapers we're usually dealing with. A sequence of varying prismatic sections can be used to approximate conic (or any other) flare rate, it just takes more math to fold things up.


There is a great series of posts explaining this here and I'd rather link to it than try and re-explain it.


A few posts later, here is the answer from Mr. McBean himself.
 
#36 ·
Soho, you're quick, yeah I changed the numbers when I goofed the math the first time.



Lilmike, thanks for the links. It sounds like adjusting the folds to more closely follow the conical flare works better although it's probably no big deal as they all say -- it just makes figuring the folds a little harder. Figure the length of each fold and what the area should be at that length. Doing that automatically does the slow-early, fast-later thing they are talking about if you look at a 2-D picture of the folds.
 
#37 ·

Quote:
Originally Posted by lilmike /forum/post/17916380


Some manufacturers present the ratio of Bl/sqrt(Re), which seems to have a good correlation with a driver's performance in a tapped horn.

Would you want Rv here instead?

Rv (virtual mechanical resistance)= Bl^2/Re
 
#38 ·
I'm going to go back, and highlight a few things in the Tom D. quote section.
 
#40 ·

Quote:
Originally Posted by Rythmik /forum/post/17914722


First, very interesting thread. The correlation between excursion bump and valley and SPL output gives us clue on how to modify the BL value or Qts to get smoother output. For instance, at excursion peak, if the SPL output is too high, increasing BL value can reduce the SPL output at that frequency. On the other hand, at excursion valley, if the SPL output is too high, reducing BL value can reduce the SPL output. Overall, it is a process of how we can pick a BL value to get the smoothest output. Of course other factors such as fs and Mmd affects the general shelving direction.

Want to work on a servo controlled horn sub ?



How clean would that be.
 
#41 ·

Quote:
Originally Posted by Ricci /forum/post/17923402


Want to work on a servo controlled horn sub ?



How clean would that be.

Wouldn't that take away some of the impedance peaks that are needed for a good horn? Just asking cause I don't know much about servo controlled stuff. I still believe a standard horn within its limits should be cleaner sounding but I am just guessing on that.
 
#42 ·
OK. After a little bit more refining of the model, I made some sawdust and took some measurements.


I'll cut right to it - how does 27-90 Hz. +/- 3 dB of 90 dB @ 2.83 volts sound?


After working out the impulse response and phase issues discussed earlier, the model was revised a bit more. Once I was happy with it, I made a sketchup diagram of a single-folded tapped horn that matched the model as closely as possible.




It's nothing special, it just allowed me to figure out the dimensions and cut-list. If anyone wants the actual file, PM me an email address.


Then - it was time to make some sawdust. Let's just say that it has been a little while since I built a sub - and it shows. It is certainly not a thing of beauty. Ultimately, in translating the model to MDF, I missed a few measurements slightly, and I also had to allow for an access hatch to install the drivers. I measured what I built, then revised the model to reflect the reality. I also broke in two new MCM 55-2421 drivers and measured the Thiele-Small parameters of the pair, as well as an older one that I had sitting around. All three measured very similarly. I averaged the parameters of the two I used and entered that into Hornresp.


Here is the final input screen:




Here is what I measured (2.83 V, 1 Meter, groundplane)




Here it is compared to the model:




Well, it appears that all the bumps are in all the right places, and are a little bit flatter than the model predicted, though the response is also down a few dB from the predicted SPL (which could be my meter or measurement technique, my mic and meter are not perfectly calibrated).


I also ran an impedance sweep with my Woofer Tester 2:




Looks like the resonances may have attenuated the high Q peaks. The slight shift in frequencies could be due to the straight line measurements I used when I calculated the path length.


Anyhow - in a nutshell, this little exercise completely met my expectations and nearly matched the predictions of the simulation. While the drivers may not be ideal for use in a tapped horn, they certainly perform as predicted.


I've not really had a chance for any sort of subjective listening yet, I barely got the basic measurements done and plotted up today.


Let the armchair quarterbacking begin.
 
#43 ·
It looks like you installed both drivers the same way. Drivers facing the throat, and sitting on the mouth side, correct?
 
#45 ·
Yep, that will do it.


You need to add in the throat chamber that mounting that way creates.




EDIT: and account for cone dish cc's.

EDIT: You need to add a Vtc of 636, and Atc of 532. This will shift the FR down a few Hz to match the measured response.
 
#47 ·
This is with no damping martial, correct?
 
#51 ·
I really like seeing the hornresp values vs the actual values. I wish we could get some more graphs like that. What I would really like to see are more tests. What did you use to do your tests? I have a bunch of different subs and would like to some tests on hornresp vs actual. Also check the sealed box vs horn box in measurements vs projected.
 
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