XKi - X's ab initio Karlson 6th Order Bandpass

X15 used around 23 degrees . If I were trying a "new" K15 size coopler without the front shelf, then would go with ~23 degrees for a more shallow front chamber and more height. The shape of the front chamber above the baffle sets a lot of the front chamber volume. Carl appeared to use an ellipse rotated where it looked like a bass clef symbol.

Here's how Karlson stated the effects of the angle in the 1951 "Acoustic Transducers" patent. His patent reads a lot better and direct than most I've seen.


An examination of Figs. 1, 2, 3, 4 will show that all of said tapered aperture coupling chambers have been designed with a diminishing interior cross section starting near the apex of each aperture and narrowing down to a minimum at each base of said aperture. The inclined planes thus presented to the energy being propagated toward the tapered aperture end of each coupling chamber deflects said energy upward through said tapered aperture. This action assures a more uniform release of said energy over the entire length of said aperture than would be normally experienced by a uniform cross sectional area. In addition to this feature a minimum discontinuity is also presented at the open ends of said coupling chambe'rs by this structural design.

A less obvious result of the inclined plane so created in the path of the enclosed sound waves is in its influence of the radiation pattern of said coupling chamber. Properly designed relative to the rate of taper in the aperture, a uniform distribution of energy can be realized over the entire length of said aperture, especially for the high frequencies. When this occurs a roughly semi-cylindrical wave front results. This constitutes an ideal manner of propagation of these sound waves since the high frequencies will not be sharply beamed in any one direction.

If the angle that said inclined plane makes with the plane of said tapered aperture is greatly increased, several effects may be observed. Among these are (1) lower frequency limit (2) increased reverberation time (3) poorer transient response and (4) less uniformity in the radiation pattern throughout the frequency range. Obviously, optimum results for any particular application would be subject to some trial and error tests.
 
- don't know if one has been built yet (?). XRK971 sketched details of a rather large version



my sim for a tiny version with 21 liter back chamber
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X's cabinet

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