Dear Group 

   I got some very surprising result that you may find interesting! 

   I took the data Fred send for the Daiton speaker and the K15 cabinet and expanded my
   model a little. I assumed that the K-coupler was end-loaded, and side-loaded, respectively,
   and looked at the coupler input impedance, and SPL for the two systems. Finally, I also
   looked at the input impedance and SPL for at exponential horn suitable for the Daiton
   speaker using the same flare rate as the K15 cabinet. 

   I had to assume as a first principle that the K15 was a closed box (not reflex) and that the
   K-coupler was formed as a tube, but with same vol. and flare area as the original K15
   cabinet (see construction section on this site). However, this will not be significant for the
   main conclusions. 

   The Daiton driver is an effective 15" driver with a high Bl value (19.1 tesla*m) and an ESP
   value 87 Hz which is suitable for reflex, but too low for usual horn application 

   The flare rate of the K15 tapered opening, 5.12 1/m, corresponds to a cut-off frequency 142
   Hz. For max efficiency a suitable horn will have a throat area 300 cm^2, and a mouth area
   1160 cm^2, and length of 25 cm. This is basically a mid-range horn, and nobody would ever
   build such a horn. What is important is the strong varying throat mechanical impedance
   between 10-20 N*S/m (real part) and a ditto SPL +/- 3-4 dB around 105 dB with a steep
   fall-off from about 300 Hz. The estimated back-chamber volume was 18 liter. Just for your
   reference. 

   The end-loaded K-coupler (the speaker mounted at the end of the K-coupler with throat area
   equal the Sd value [speaker area] like Alan's "patio speaker"), and using the flare rate above
   and a back-chamber volume of 100 liter, which is the actual value for the K15, resulted in a
   real mechanical impedance S-shaped curve raising from near zero below 70 Hz, 10 N*s/m at
   1250 Hz, 20 at 2750 Hz, 30 at 5500 Hz and going up to about 40 N*s/m at high frequencies.
   The imaginary impedance was bell shaped with a maximum about 15 N*s/m between
   2000-3000 Hz. SPL was linear increasing from 80 dB at 20 Hz to 100 dB at 200 Hz, and
   more slowly up to 105 dB at 500 Hz, 107 dB at 1000 Hz up to a max value at about 108 db. 

   That result was expected. The K-coupler can be viewed as a horn with a cut or a hole in one
   side, which shift the acoustical or mechanical impedance frequency characteristic upward.
   This is well known from musical instruments (brass). The more smooth response curve
   compared to the horn above is due to the much longer K15 k-coupler (25 cm horn vs. 80 cm
   k-coupler). A 25 cm horn is a very short horn creating a lot of irregularities in the response
   function due to reflections. This is also very well known. 

   Then I moved the speaker 50 cm down from the "throat" (the exact distance is not important
   here in order to discuss the principles). The load on the speaker increased significantly up to
   about 2000 N*s/m (real part) and 1000 N*s/m (imaginary part), and the pressure curve totally
   changed form from roughly S-shaped to a kind of bell shape with a maximum between
   200-300 Hz. And further the SPL took on a maximum between 100-200 Hz, somewhat like a
   higher order bandpass system, but still showing the max SPL value up at above 108 dB. This
   is a function of the load impedance on the front and back side of the speaker, the resistance
   of the speaker driver motor and the driver suspension losses. 

   Fred, that may be your mid-bass reinforcement of 6-9 dB relative to reflex! 

   It also may explain the high efficiency of the K15 cabinet that people write about and praise
   so much. 

   I have to re-check this. But it seems like the original K15 cabinet can be viewed (and
   modelled) as a side-loaded lossy esponential horn. This turns it into a hybrid between a horn
   and a higher order band-pass cabinet. 

   Quite interesting. 

   I believe that John Karlson worked on the end-loaded k-coupler for some time but got very
   disappointing results in terms of low bass performance. Somehow he got the idea of side
   loading, and the bass (and a compact cabinet) came back as shown above. Adding reflex
   reinforced the low bass. The shelf in the K15 may balance out the port and the speaker
   output into the k-coupler. 

   It must have taken Mr. Karlson a lot of work and many experiences to get that far by try and
   error. I'm impressed! 

   And thanks to this group for your questions and steady interests in this rather strange
   speaker design (I actually build a K12 more that 30 years ago!). Without this Karlson family
   on the net I would never have got this far trying to understanding it. 

   From now on only hard work is ahead. I don't know. Somebody should write down the exact
   history and others could describe more systematically their application experiences. I think I
   now can do the theory. Others can do specific testing and measurements, and finally we may
   be able to pull a full paper together we can get published in the accepted speaker literature in
   order to prove that John's idea was something out of the extraordinary. Are you people
   interested? 

   regards, 
   Lars