Hi Grant
Consider that 50% efficiency is a horn “benchmark”, where half the actual power is radiated as sound, the other half is heat.
From that it may not be clear that going from the very difficult to reach 50% mark to the impossible 100% mark only results in a 3 dB increase in sensitivity.
It is possible to make a horn that is somewhat greater than 50% efficient if it is large enough acoustically and the bandwidth is limited.
Also, it may not be clear that when you say a horn has a smaller mouth, that this mouth is part of a horn that is wrapped up in a cabinet too.
It strikes me that maybe the white paper doesn’t explain clearly enough what the advantage of the Tapped horn is.
Hoffman’s iron law (the wall of science) limits the maximum efficiency possible given the box volume and low cutoff.
Take a subwoofer like the popular JBL-728 for example that has real measurements, go to the web site and pull up the pdf which has a measured response curve.
http://www.jblpro.com/srx700/728S.htmTake a snapshot with your pdf viewer, up to 200Hz, save it and stretch it out so it is easier to read in the subwoofer range.
This box has 2X cool18’s in each and occupies 19.25 cubic feet.
On the other hand, take the TH-115, it has one 15” and occupies 14.6 Cubic feet, so its not exactly fair with the 115 being somewhat smaller and lighter.
Compare the sensitivity for one box in the subwoofer range at a few spot frequencies (eyeballing from the graphs).
TH-115 728
35Hz 96 93
40Hz 102 96
45Hz 105 97
50Hz 103 97.5
60Hz 104 97
80Hz 106 98
100Hz 111 99
So, given the TH-115 is both smaller in volume, lighter and only has one 15 inch driver, what is it that makes it about as sensitive as 4 close coupled 728’s would be (+6dB) ?
That difference (and the reduced phase shift near the low corner) is the Tapped horn advantage.
Below is a measured response for 4 TH-115’s, measured at 10 meters, each driven at 28VRMS which into an 8 Ohm nominal load (like these) is 100W each.
This is +6 dB over what would give our equivalent 1 W sensitivity, subtracting 6 dB, one finds that say at 50Hz, the 1W sensitivity is 108.9 dB, just about 50% = 109dB
Now, with 58 cu/ft to work with, can you find any other way to get that kind of sensitivity, with that cutoff?
Given the measured response of a 728 here looks like the mfr’s curve if you add 20dB (for 10M distance)
http://www.prosoundshootout.com/Measurements/2006/JBL_SRX728 S_response.gif
How do these horns look in comparison adding 20dB.
http://www.prosoundshootout.com/Measurements/2006/Tuba36_qua d.gif
http://www.prosoundshootout.com/Measurements/2006/12Pi_dual_ response.gif
http://www.prosoundshootout.com/Measurements/2006/BASSMAXX_T ripp_dual_response.gif
Anyway I am sorry for the long explanation, hope it isn’t too much of a commercial.
Best,
Tom Danley