a couple of old notes from Carl Neuser
Calculating K15 and K12's wing radius -
(t=1/2 gap at start; w = 1/2 final width)
"Compute the radius r as follows:
r = ( h^2 + w^2 - w*t + t^2 )/2*( w - t )
For Karlson 15, h = 30.19, w = 10.17, t = .23, r = 51
For Karlson 12, h = 23.5, w = 7.38, t = .25, r = 42.5
Once you have the radius you can make a saw guide to nicely cut the tapers.
If you want to compute values the above dimensions and the radius is used as follows:
h(x) = (-B -(B^2-4*A*C)^.5)/2*A
Where A = 1
B = 2*(r+t)
C = 2*r*t + t^2 + x^2
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Carl's old note from Ulfman's Karlson forum
Fred,
The Fh behaves different for the UF compared to a horn.
Fhm = factor * EBP
For a horn the factor is 2. This is why you can't get a horn to have an extended high end.
The UF 's advantage is that it is essentially "open" at MF and has extended band width compared to a horn.
If you make the UF less "open" the upper MF reduces. If you tighten it enough, the Fh is severely restricted, much like a bandpass.
Wayne, says the design of the box is a 4 deg of freedom system. The tapered slot requires complex mathematics to represent. To understand the UF remember the horn of the Altec (604) is essentially "open" to the enviornment with some box reverb.BTW:without reverb, electronic or mechanically induced to a critical minimum level, the reproduced sound will not sound real. Now the low end. The port output is driving the Karlson coupler. You don't want high frequency tube resonances coloring the sound. Therefor no tubes. Starting with the backwave, a low pass filter, and padding to kill a lot of MF/HF going to the port. The port mass is set to provide LF drive to the coupler. The mass loading of the coupler lowers the f3 while the coupler provides the gain. The front shelf blocks significant MF/HF from the top chamber. The rear volume is made small because a sealed coupler at LF loads similar to a horn. Likewise the ported volume can be lower like ported horns.
Remember, you can't be an expert on the UF without building and testing them.
Same goes for horns, sealed and ported boxes etc.
A formula for rear chamber volume -
vbr ~(vas*qts*fs)/fc;
vbf ~0.5 vbr;
slp ~0.2-0.4 sd