DESIGNING YOUR T-LINE
This will be a quick and simple primer on how to design a consistent dimension ¼ wave t-line. There are a variety of different ways to build t-lines but this will be an explanation of what has been, for me, the easiest method. For the example, we'll use a single, hypothetical 15' driver.
First thing we need from our sub is Sd or, usable piston area. To find that we need the diameter of the driver, which is measured from the apex (center) of the surround on one side of the driver to the same point on the opposite side. For most car audio 15s, that measurement is 12.75".
Then we take that measurement and half it: 12.75 ÷ 2 = 6.375
Now apply the formula πR² to that number: 3.14 * 6.375 - 6.375 = 127.6
For our purpose, that number can simply be rounded to 127in².
Sd will be out line area. Line area is what would be called port area in a conventional vented enclosure but since our box is nothing but one long port or, line... it's called line area. This number can be modified for a couple of different reasons. First off, if your design is strictly for sound quality, I'd leave the line area equal to Sd but if you need to save space or you want a bit more of an SPL oriented box you can reduce that number by up to 40% with no serious affects on sound quality. What you will lose, in my experience, is performance on the top end of the sub bass region (60-100Hz). But, that loss is minimal, especially in a vehicle cabin. Aside from the aforementioned benefits, reducing line area also seems to increase cone control, which is really important for us bassheads since we tend to abuse our subs on a daily basis. smile emoticon
Next we have to calculate the tuning frequency of the line. For that you need to know the speed of sound in feet. That varies with elevation and other factors but for my area and conditions it's usually 1130 feet per second so, that's what we'll use. You can find it for your area if you like but for the purposes of what we're doing there is no need of that much accuracy. We'll tune our line at 30Hz, which is the most common tuning I use for daily builds. The formula is speed of sound ÷ tuning ÷ 4. This formula tells us the length of a sound wave at the tuning frequency we chose and then we take ¼ of that length for out box... hence ¼ wave transmission line.
For our box: 1130 ÷ 30 ÷ 4 = 9.41'
To convert that to inches: 9.41 * 12 = 112.92 or, round it to 113".
Now that the easy part is over we have to figure out a way to contort our 9' long square tube around and into the trunk or back seat of a vehicle. That's where line area reductions become pretty handy because even though the line won't get any shorter, its bulk will be lessened. If you have a large footprint but not a lot of height, I would recommend a snail shell styled box with the sub(s) in the center facing upward and the line terminus (port) facing out the side or rear, as in a trunk. If you have a wide but narrow space for the box, like the back seat of a truck or behind the back seat of a truck, a folded design with sub and terminus up works pretty good. Either way you're going to have some 90° and/or 180° turns to make and below I'll explain how I calculate the length of those turns.
The formula for circumference is πD or 3.14 * diameter.
For our box we'll assume the line dimension is 14" wide by 9" tall. I arrive at that measurement by dividing our needed line area (127in²) by the mounting diameter of our typical 15" driver (14") for a height of 9". Knowing that the line is 9" tall is important because that's the number we'll use to measure the length of our bends. Next we'll ad the thickness of our construction material to that number, which is normally 3/4" so... 9.75 is the diameter of our radius bends.
Now apply the formula to find the length of any 90° or 180° bends....
9.75 * 3.14 = 30.615 or rounded to 30.6. That's the circumference of our radius.
For 180° bends, divide that by 2 for: 15.3".
For 90° bends divide by 4 for: 7.65"
So now all you have to do is draw the line out and enter those numbers into any bends you have and then add them all up (along with the straight lines) to get the total length of your line. For a simple box I normally take my two most critical measurements and then start arranging my lines and bends through the center point of the line height until I find an arrangement that'll work.
Lastly, when figuring wave guides (45°s) for the bends, just measure from the pivot point of the radius at a 45° angle out to the desired line height and then measure across the line 90° perpendicular to get the width of your wave guide.