I've had the view for many years that tapped horns are more like TLs than horns and noticed
that many showed SPL curves up around or well over 100dB suggesting that they were very
efficient. When you look closer it can be seen that they are being simulated at high power, 50,
100W or more, something to watch out for. Also, many simulations are into less than 2pi space,
1pi or even less. When I think of a horn I think of acoustic gain, 6 or 10 dB yet many tapped
horns only have 2 or 3 dB of gain. These structures are built and then we try to make them
more like a simple vented system by tapering them or adding damping. I don't like the
numerous peaks typically above about 100 Hz and indeed this is where we see gain on the
order of 10 dB but it is highly resonant gain and not really where we want it in a woofer.
The order matters when you cascade transfer functions in non-linear systems and those peaks
above 100 Hz amplify driver distortion in a way that cannot be removed with EQ.
I believe that tapped horns, like old TLs, give builders an excuse to use a very large box and
if they did the same thing with a traditional vented or passive radiator (PR) design they would
get similar results.
Here are some examples:

LittleMike's Anarchy Tapped Horn
See post number 2 for measured vs. Hornresp prediction:

Here is the image:
Note that the Hornresp prediction is about 3-4 dB optimistic at the bottom of the passband, and 1-2 dB optimistic over most of the rest of the passband.

LittleMike gives a reasonable rating of 86 dB at 1W 1m 2pi for the actual as built system here:

That tapped horn is about 1.75 cu ft internal volume, here is my simulation of the same driver in 1 cu ft,
vented not including the port volume, this sim has losses included:

Here is that curve raised by 20 dB by increasing the power X100 for about 126 W (28.3V) input just to better
center the curve on the chart. It is interesting to note that this is still within Xmax above 26 Hz:

The tapped horn does not have significant gain, perhaps 1-2 dB over the usual and smaller
vented design. My simulation was for an actual 1W into the driver I hope that LittleMike used the
same and not 2.83V. The driver is not optimal for that vented alignment since there is droop
above resonance but in any case I don't see a major advantage to this particular tapped horn.

VolvoTreter - The Tangband 30Hz Tapped Horn
Here's a small 30 Hz tapped horn at the VolvoTreter site, scroll down to the 30 Hz entry it uses
the Tangband 1139 in 65 liters (2.3 cu ft):

The Hornresp entries can be seen there, and this is as stated on the site "This is the theoretical SPL in quarter space
at 20V where Xmax (11.5mm !) will be reached:

Here is a lumped, vented analogy to the 30 Hz TH with the same TB driver. It requires a 25 liter box tuned to 30 Hz, here's the sim.
I used 112W which is 20.0 V input so that it can be compared to the 30 Hz TH at the Volvotreter site, this is half space - add 6 dB for ideal quarter space loading (1pi) to compare to the TH. This shows that the LF response of that TH can be roughly duplicated with a normal vented system, and it is in a significantly smaller box. It reaches max excursion at 27 Hz with 20V drive and is well below that above.

Here is a "small" tapped horn design by Mark with two CSS TRIO 8" woofers where I showed
that a vented box of the same size provided better performance:

My simulation results for a vented system as a sanity check:

My comment on the sensitivity being about 90dB/W - Mark responds in the next post explaining the simulation conditions:

I compare the two here, the vented design has 5 dB more output at 20 Hz and 4 dB more output at 30 Hz to
the equal sized horn1 the much larger horn2 showed some passband gain:

Mark was very open to my points and even planned to compare built vented to the horn, but it
looks like he dropped it since the thread is now dead.

Another popular small tapped horn is "The Tangband 30Hz Tapped Horn" at VOLVOTRETER's Site:

I made these comparisons for a few more tapped horns and I think only one had consistently more
output in the passband of 2 to 3 dB with equal power.

I'll have to search for the threads since they were just quick simulations and I didn't spend much
time on them.
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