There are a few unique features that defines a Bailey transmission line.
- The stuffing is supposed to make the TL a half wave length tube at the woofer Fs. There should be a single impedance peak at around 27 Hz for the Focal.
- The stuffed tube is supposed to make a phase inverter at the Fs. The sound attuation should be decreasing as the frequency goes down.
- The sound pressure at the TL opening is supposed to be similar to the front sound and 180 degrees out of phase.
- Overall, the TL is designed to have a -3 dB poiont around the Fs.
So your items 1, 2, and 3 are all physically impossible. This pretty much undermines most of everything else you are saying. Just as an aside, if you look at the geometry of Bailey's TL and the wave equation solution used by Bradbury (which applies the boundary conditions I stated above to solve the equations of motion) you will find that they are not compatible. I will let you figure that out on your own.
Bottom line from my perspective, your understanding of the physics of how a TL works is extremely shallow. You have been sucked in my the rhetoric and mystique that surrounded TL design for decades. There were some very good TLs produced in this time period which were the result of the natural insight of the designer, luck, and trial and error building and not based on any sound engineering design methods or equations.
The "art" of TL design has moved forward significantly to more of a sound engineering approach with several different software packages available for simulating and designing the geometry and the placement of fiber materials. You have your mind so closed that you cannot question your own beliefs or probe to see what makes sense and what is pure technobabble. We really have no common gound to discuss TLs, the forum members can decide who to follow for themselves.
The Bailey/Radford and Bradbury papers are still my brass tacks. People are entitled to their opinion as long as they can ignore the scientific facts behind it.
I must admit that audio design, particularly speaker enclosure, are not 100% science yet. But trying the wrong science on a computer and blasting the correct science is not right.
When Bailey proposed a new enclosure for bass loading, he proved his design by experiment and listening results. Bradbury quantified the reduction of the speed of sound in fiber filled tube analytically and correlated them with test data.
All these are objective truth.
I built the original Bailey design more than 30 years ago following the recommendation by Jastak in the Audio Amateur (1973, 1:3). I used the Philips 10100 10" woofer. The HF section was two Janszen 2-panel electrostatic, crossover at 1K Hz. An execellent system for my small apartment room and very affordable for a graduate student. It replaced the Larger Advent's that I had before them. The cabinet went into storage when the Philips driver deteriorated due to age and I could not find a suitable replacement. (I have recently purchased a pair of Peerless CSX 850146 and may rebuild the TL sometime.)
"The Bailey designs were almost completely stuffed with wool and did not allow a free flow of air to line terminus". And the non-linear effect of flow resistance (frequency dependent) threw a lot of people off balance. The mathematic is only based on linear algebra which most upper class undergraduate students should have taken. (An "extremely shallow" understanding of the mathematics is sufficient, but required.) Prof. Bradbury at University of Surrey (UK) published an elegant paper on this topic and proved the foresight of Dr. Bailey. It is one of the most significant and elegant piece of work on the theory of transmission line enclosure.
It showed both qualitatively and quantitatively how the sound wave propagates in a long fiber wool filled line by test and analysis. It provided a sound guidance on what to look for if you want a substitue for the long fiber wool.
Bradbury showed excellent comparison between his test results and analytical calculations. I am talking about Figures 5 and 6 on page 166 of Journal of The Audio Engineering Society, Vol 24, #3, April 1976. Yes, the comparison were NOT perfect. The experimental data points did not lay on top of the line. But in engineering, these are execellent comparison in trend and in magnitude.
Mr. Martin King, you keep bad mouthing the work by Bradbury. What problem did you find with his test methodology? You stated (in another post) that you "rederived all of the equations and replicated the numerical results". Can you point out where the typo is in the Bradbury paper? Did you calculation showed same result as Bradbury's once you corrected the typo? You do not need a PC to do this. It can be done on a piece of paper. You do need to have some working knowledge of linear algebra and complex number. Did you ever try to duplicate his experiment with the proper dimensioned long fiber wool? (I suspect you never read the Bradbury paper. BTW. Bradbury showed how fiber glass would respond and why it is not a good TL stuffing material too.)
It is wrong for you to say the genius work by Bailey, Bradbury and Fried as "physically impossible" without showing any proof. The non-linear nature of the low frequency response of the TL design is not "rhetoric and mystique that surrounded TL design". They are based on sound science and engineering work. You can replace the linear algebra equations with your simple linear wave equations, but your equations do not describe how sound wave propagate in the Bailey TL.
Personally, I have done NO original work (experimental or analytical) on transmission line bass loading. But I have lots of respect for the work that the trailbrazer did because they had results that can be heard. I asked you the same questions on an earlier thread on "Transmission Line" and you never answer. I don't expect you to this time either.