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The classic transmission line
bass enclosure has never been completely and successfully modeled such that it can
be built from a pat set of equations. Some claim to have done this, but it doesn't
seem to allow a first time build without adjustments, so the models have enough wrong
to require a fudge factor at least.
I can give you the basics, and explain the first principles, and this might allow
you to forge ahead on your own. My data is taken from Bailey, and years of experience
of my own, culminating in several pairs of successfull T-lines, one of which I use
to this day.
- The line area should equal
or exceed slighty the cone area of the driver used. Normally, it is difficult to
make the line area exactly equal to the cone area, as the frame and mounting immediately
force an area larger than the cone area. The area can be gradually tapered down to
the actual area to save space, but it can remain the same as when it started, as
long as it is not more than than about 20-25% more area. This means a very tight
sizing for the woofer mount and the begining of the line.
- The line length should be 1/4
wavelength tuned to the resonant frequency of the chosen speaker IN THE BOX VOLUME
CREATED BY THE TOTAL T-LINE CROSS SECTIONAL AREA TIMES LENGTH, and as if the box
were a closed box. This is the hard part, as the line stuffing affects both the total
apparent line length AND the total apparent box volume simultaneously. I will discuss
this later.
- The line should be stuffed
with an average of about 0.5 lbs to 0.7 lbs of acoustical stuffing material per cubic
foot of line volume. The material chosen affects both the apparent speed of sound
in the line AND the apparent increase in box volume. Fiberglass or polyfill can be
used, but these are not the best. Acoustastuff and long hair wool are the prefered
materials (the new Miraflex by Owens-Corning may be OK), these both have convoluted
surfaces along the length of the fibers, which aid in the function of the material.
Some argue that the density should be greater just behind the driver, and gradually
taper off, while others argue that it should be uniform through out the line. I placed
a little extra right behind the driver, and then made the rest of the line uniform.
- Contrary to popular belief,
almost any driver can be used in a T-line, however, the driver resonant frequency
IN THE APPARENT VOLUME OF THE T-LINE should be as low as you want the bass to extend,
so if the driver in the apparent box volume of the T-Line has a resonant frequency
of 60 Hz, and you wanted to get down to 40 Hz or 30 Hz, obviously, this one wouldn't
be what you want. I wouldn't recommend trying to get super low, as the T-line will
have a very shallow roll-off at the line tuning, and useful bass response will extend
for an octave to an octave and a half below this point. My T-Line has a 40 Hz tuning,
and what with room gain and all, it is -3 dB down at 20 hz.
- If the line stuffing and the
tuning and the sizing and the spacing have all been done correctly, the T-line will
be down approximately 6 dB at the tuning frequency in an anechoic envirionment. In
most rooms, the bass lift due to walls and floor reinforcement will have the system
near flat at this point, depending on the actual frequency. The effective slope of
the roll off will be close to 6 dB/octave, and the low bass will not fall off a cliff
like a classic vented box does.
- The walls of the line MUST
be extremely rigid in order for the T-line to function as intended. Think in terms
of making the walls TWICE as solid as a conventional enclosure, or better. Fortunately,
the relatively small cross-sectional area, and traditional T-line construction techniques
make this possible to achieve. My last enclosure used 3/4 ultra high density particle
board laminated with 1/2 inch birch plywood.
- If the line is folded, place
reflector plates in the corners. Pretend you are trying to smoothly direct a flow
of liquid, make the fold or bend as smooth as you can. I placed a series of four
reflector plates in my bends, two for each half of the line. If mounting the woofer
facing forward, and having the exit port facing out to the side, these need reflectors
also, especially the area behind the woofer.
Now, about #2. This is THE hard part, juggling the length, volume, and stuffing
density to get the desired results. The speed of sound varies within the stuffing
material, changing with frequency, and is approximately 1/2 of the normal speed of
sound at the lower frequncy's, which makes the stuffing make the line seem twice
as long as it is when empty. Fully stuffed, the amount of apparent volume increase
is approximately 1.35 times the nominal volume, and depends on the material and stuffing
density.
The key to the whole mess is to design the line using the above information, and
adjust the stuffing density to fine tune the line. The stuffing density is best adjusted
in the last half of the line toward the exit. Taking an impedance measurement to
check the shape and nature of the LF impedance curve will tell you when you have
the tuning right. The flattest and smoothest impedance curve is the goal, with a
properly designed T-Line, the impedance has just the hint of a gentle broad bump
at the speakers closed volume resonant frequency. If the curve has a bass reflex
or vented box shape, with a dip inbetween two humps, not enough stuffing was used,
if the impedance variations are not very much, and there is a slight dip at the broad
hump, this may be the best you can do within the stuffing density constraints.
For those of you with speaker enclosure modeling programs, there is a technique to
fudge the modeling of a T-line. Programs such as SPEAK, which model the air volumes
associated with the enclosure can start with a vented box. make the vent the entire
T-line, and the rear enclosure volume near zero, say 0.1 ft3 The fudge
is adjusting the effective impedance of the air in the vent to simulate the stuffing,
or you will be modeling an open unstuffed pipe. The value of acoustic impedance is
around 100-140 for regular air, change that to half of that for a stuffed line (IIRC).
This comes very close to modeling the T-line, but is still only a first approximation.
Ultimately, you will have to build one to see how close you came. If you end up with
a line that is mis-tuned or doesn't work right, and just doesn't seem to want to
tune up with stuffing density adjustments, you can band-aid it by placing a lot of
acoustic resistance at the exit of the line, such as several layers of polyester
batting stretched and stapled over it. This will usually make it work half way well,
and is at least equal to a closed or vented box in output and capability.
I had to build a test line, then make adjustments, and build the final line.
Don't forget, the good types of stuffing require netting or dowel rods to support
it inside the enclosure, so it doesn't settle over time. If you don't do this, the
stuffing will settle into a lump at the bend, and cause acoustic refelcetions and
foul the line operation, causing lumpy uneven bass.
Below are links to relavent
posts I have made on T-lines"
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