Introduction
I've been doing quite a bit (well, in fact a lot) of reading on the Internet recently about "tapped horns" and I thought I might give the concept a try by building a "proof of concept", to (1) see if actual output match the simulations and  (2) if the results were actually worth it. So, I downloaded a copy of HornResp (an application that seems to be the best utility available online for designing horns), and in trying out different alignments using a spare driver I had on hand, I came up with a related alignment that's typically referred to as a "tapped pipe".

First, a few definitions that may help to clear things up a bit...

A "tapped horn" is basically a horn that physically consists of the driver mounted part of the way up the horn, rather than at the throat as is commonly the case.  The advantages of this configuration are increased response at the low end (a lot less dependency on mouth size) and a smaller box, compared to a true horn with the same cutoff frequency.  The disadvantage of a tapped horn is lower sensitivity and power handling compared to a true horn with the same cutoff frequency due to increased driver displacement within the pass-band.

A "tapped pipe" is basically a tapped horn where the cross-section of the horn remains constant from the throat to the mouth.  An early example of a tapped pipe is the "Jensen Transflex", information about which can be found elsewhere on the Internet. Tapped pipes are a bit easier to build than tapped horns (because of the constant cross-section), but the ability to "tune" the response by adjusting the change in cross-section is lost.

Design Phase
As this is going to be a "proof of concept" and likely destined for the scrap-heap, I decided to use one of the drivers I had lying around, rather than purchase a particular driver for the project. The intent of the design process is to come up with a tapped pipe alignment that extends the lower cutoff frequency as much as possible, while keeping the upper cutoff frequency of the tapped pipe as high above 80 Hz as possible. Excursion and box size are also taken into consideration - we don't want to end up with a 12 cu.ft. box with 0.5 watts of power handling!

Test Driver
The spare driver that I used for this exercise is one of the Pyramid W61 drivers that I used to use in my "El Uglito" 4th order bandpass subwoofer. I measured the parameters with my WT3 and came up with the following:

After playing around in HornResp for awhile, I came up with a tapped pipe with the following specifications:

S1 = S2 = S3 = S4 = 290 cm^2 (cross section of tapped pipe)
L12 = 11 cm (driver's center distance from closed end)
L23 = 177 cm (horn length, less L12 and L34)
L34 = 12.9 cm (driver's center distance from open end)

The total length of the pipe works out to 177+11+12.9 =200.9 cm. To convert this into an actual box, I divided this by four, then decided on dimensions that would result in a cross-section of 290 cm^2 for each section (here's where I made my first error - this approach actually results in a pipe length that's shorter than the design target, as it does not take into consideration the effect of the 180 degree join at the end of each section!).

HornResp predicts that the frequency response of this tapped pipe would be as follows:

The graph suggests that the frequency response would be essentially flat between 43 Hz (the length of the pipe works out to 1/4 the wavelength of this frequency) to just above 100 Hz.  There's a minor peak at 135 Hz, followed by a huge dip, but all of this is happening well above 80 Hz, the usual upper cutoff frequency of a bass unit or subwoofer. The "hash" above 200 Hz can basically be ignored - I'm sure that the folds in the tapped-pipe are going to have a radical impact on the frequency response at that point.

Once folded up, box size works out to around 2.4 cu.ft., which is quite large for a single 6.5" driver. On the plus side, there should a lot of room in that box to mount the driver, without overly restricting the cross-section of the pipe.

Construction
The following images indicate the construction phase of my "proof of concept" project:

 

1. All of the panels cut out and ready to assemble.  It took about half of a 4x8 panel of 3/4 ply to produce these panels.

2. Putting the first two panels together.  I started with the front panel (facing downwards in the image above and one of the internal panels.

3. Attaching the third panel.  This is the one that will eventually host the driver.

4. Attaching the 4th panel (which identical to the 2nd panel). The path that the pipe is going to take inside the enclosure should be clear from this and the previous picture.

5. Attaching on side.

6. Attaching the back panel.

7. Attaching the other side panel and the bottom panel. Now the internal structure of the pipe should be pretty clear.

8. Closing up the box.  Instead of permanently sealing up the box, I opted to use screw the panel in and use a thin strip of weather sealing to ensure an airtight seal. This will allow me to take apart the box in the future if I want to add any stuffing or otherwise change the box's internals.

This picture above should give a good idea of the size of the finished box.  Here the tapped pipe box is located next to my ACI SV10 subwoofer.  This is a pretty large box for a 6.5" driver.  When compared to direct radiator alignments, size is definitely not one of the tapped pipe's advantages. In these days of large drivers and cheap amplification, it's probably easier and better to go with a director radiator alignment for home or home-theatre use, unless there's a specific reason why you want to attempt one of the high-efficiency alignments like a tapped pipe, and you've got the available space (and the approval of your spouse to use it!).

Results
Below are the measured results, with the pipe unstuffed.

Above is the measured frequency response of the raw system, without any damping material inserted. As I'm driving the tapped pipe subwoofer using the subwoofer channel on my amplifier, the response also includes the effects of an active 12dB low-pass filter @ 100 Hz. Included in green is the theoretical response as predicted by HornResp.  As I got the pipe length wrong, there is a bump at 53 Hz which is not present in the HornResp predictions. I also later found a minor leak around the driver, which could account for the strange dip and peak just under 20 Hz.  Apart from that, there's pretty good correlation above 100 Hz, particularly considering the effect of the 100 Hz low-pass filter. It's clear from the measured results that HornResp has done a pretty good job of predicting the system's frequency response, with good correlation up to ~300 Hz. Above that point I believe the folds of the box are having an impact (Hornresp would not know how the box is folded).

 
Above is the impedance response of the system.  In green is the response as predicted by HornResp.  Again, I suspect that it's a bit different because I may have gotten the pipe length wrong, and the small leak could have caused the lower frequency peak to be a bit lower in level than expected.  Interestingly enough, apart from the lowest minimum and below, the other peaks that occur for the rest of the impedance response seem to be close matches in frequency, though the amplitude seems to be off (probably because of losses).

Below are the measured results, this time with the first two sections of the pipe partly stuffed with polyester fiberfill.

Above is the measured frequency response of the system, stuffed as indicated above. While the low frequency response remains approximately the same, the upper frequency response has changed significantly.  The peak and notch between about 120 Hz and 200 Hz has basically disappeared.  Again, as I'm driving the tapped pipe subwoofer using the subwoofer channel on my amplifier, the response also includes the effects of an active 12dB low-pass filter @ 100 Hz. However, the response above 100 Hz is significantly smoother in character than the response of the unstuffed pipe.  It sounds better, a sign that dealing with the frequency response immediately above the designated x-over frequency (in this case 80 Hz) to make it as smooth as possible would be desirable.

Above is the frequency response of the stuffed system compared to the raw system. The smoothing of up the upper frequency response is readily apparent here.  And it looks like I got the driver seal right this time - the low end response has apparently improved.

Above is the impedance response of the stuffed system.  The peaks and dips are a bit lower than the HornResp predictions (the green line) now, and the magnitudes are significantly different - not unexpected, as the damping would cause that.

The graph above compares the impedance response of the stuffed system (red) to the unstuffed system (blue). The peaks and dips have clearly shifted down a bit. This suggests that the resonant frequencies of the system have been shifted down by the addition of the stuffing.

Conclusions

1. I may have to be a bit more careful when calculating the total pipe length of these things.  Looks like I might have been off by a few cm or so, based on the impedance response and the frequency response of the un-damped system, which shows a bump at around 50 Hz, rather than a smooth and flat pass-band down to 40 Hz.  The impedance response also seems to be shifted upwards a bit at the lowest frequencies.
    

2. Don't even consider doing something like this unless you intend to use it with a 24dB/octave low-pass filter within the pass-band, and/or you plan to deal with the out -of-band response by another means. The out-of-band "hash" really colours the sound of this subwoofer.
    

3. Stuffing should be considered a mandatory part of this type of project.  Stuffing makes a significant difference at the frequencies above 100 Hz, smoothing out the response. Stuffing only half of the pipe is enough to make a significant difference.
    

4. There appears to be an audible increase in output at lower frequencies when using this type of alignment.  The response from the mouth of this tapped pipe has a tactile feel that this little 6.5" driver could not do on its own. It's quite impressive. However, output is limited by the driver's excursion capability.
    

5. It looks like HornResp does a pretty good job of predicting the frequency response of a tapped pipe, particularly within the pass-band.  Out of the pass-band, the response starts to differ, but that's likely because of the effect of the folds on the system's response.
    

6. From some impromptu listening tests, the tapped-pipe, after being stuffed, has a effortless and unrestricted sound, up to the driver's limits.  It's also not that easy to tell the driver's limits.
    

7. While the box size is small compared to a horn with a similar cutoff frequency, it's still large compared to a simple sealed or vented alignment with the same driver.  The internal box volume of my "proof of concept" tapped horn works out at around 2.4 cu.ft - enough to fit a 10" driver in a decent vented alignment capable of higher output and lower cutoff.  That 10" driver is likely going to need a lot more power though, and the alignment is certainly not likely to be capable of 92dB/1W/1M @ 50 Hz.
    

8. From the design work and the results, it looks like the best driver for a tapped pipe may be one with the following characteristics:

   • Fs = 45-55 Hz :  For a tapped pipe or horn, Fc, which determines the length of the horn, tends to be somewhere around 0.7*Fs. If you start with a driver with low Fs, the length of the horn could turn out to be impractical.
      

   • Qts = 0.45~0.55 : The driver's Q sets the bandwidth, but it seems to be difficult to get a smooth pass-band when Q us much higher than 0.5.
      

   • Medium Vas : If Vas is too low, the cross-section of the pipe turns out to be pretty small, leaving not much space for mounting the driver in the pipe. Of course, if the Vas is too high, the box ends up being very large.

Other thoughts
The Dayton 8" Series II driver is actually a drop-in replacement for my test driver in terms of parameters that affect the tapped pipe's frequency response, but it is theoretically capable of much greater SPL due to its larger Sd and Xmax.