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Let's say you went to your local car audio store and bought a new woofer driver and a box. You install the woofer in the box, get it wired to your amplifier, set the gains, and give it a listen.
It sounds better than the speakers that came with the car, but something is missing. You want more romp. You want some wind. You want your seats to shake like they do in the IMAX theater.
You get the spec sheet out of the folder you filed it away in and you see "enclosure specs". The box you picked up at the store matches the sealed box spec listed on the sheet. But below that, you see ported enclosure specs. The ported enclosure is larger than than the sealed enclosure. The ported spec also includes a parameter called a "tuning frequency". Your gut feeling says "this is going to be louder"
How does a ported enclosure work?
Let's start with how an enclosure works, regardless of "alignment".
If the woofer were to play without a box, the waves from the front and rear of the cone would cancel each other out. The lowest frequencies are effectively nullified.
A sealed enclosure will contain the rear wave. Containing the rear wave will allow the front wave to play music. The air in the box works as part of the woofer's suspension. We can use this air volume to change how the woofer behaves. In general, the larger the box, the lower it will play. A smaller box won't play as low, but it will produce a small ripple in the SPL curve.
A ported box will work to delay the rearward wave so it's in phase with the forward wave. The waves work together at the port resonance. We can change the behavior of the box through "tuning". Tuning is changing the frequency that resonates in the port. We can tune in more low-frequency extension. We can also tune in more sound pressure levels.
Like a sealed box, the ported box behavior changes with box volume. A larger ported box can play lower than a smaller ported box. A larger box also has more SPL potential. If you need a visualization, think about blowing across a bottle. A beer bottle will "whistle", while a gallon jug will "hum".
This extra performance comes with some trade-offs. You'll encounter some "group delay" in bass response around the tuning frequency. You may also experience a slight distortion in the music. Finally, you'll end up with a rapid roll-off in response below the F3 frequency. F3 is the frequency where the subwoofer response begins to fall off as frequency falls. A sealed box rolls off much shallower.
Let's go through a design exercise. We'll design a ported enclosure around a Rockford Fosgate Prime 10 inch R2 D4. We want the box to fit between the shock towers of a compact hatchback. Let's limit that box to 24 inches wide.
How do I know my woofer would work with a ported enclosure?
We need to know if the woofer can work in a ported enclosure. The woofer's spec sheet lists Thiele-Small Parameters. We can use two of those parameters to compute Efficiency Bandwidth Product or EBP. We need to know Qes and Fs. Qes is the "electrical q-factor" parameter for a given driver. Qes is a unitless number that determines how long the woofer's electrical section will ring at Fs. Fs is a measurement of the woofer's resonant frequency, measured in hertz (Hz).
The formula for determining Efficiency Bandwidth Product is as follows:
EBP = Fs/Qes
A woofer that is a good candidate for a ported box will have an EBP of 50 or above. In the case of a Rockford Fosgate Prime 10 inch R2 D4, the Fs is 34.9hz and the Qes is 0.58
EBP = 34.9/0.58
EBP = 60.17
Our Rockford Prime 10 inch R2 D4 subwoofer driver is a good candidate for a ported enclosure.
How do I design the custom ported box to fit my car?
We will need to know the following:
- The "net" volume of the subwoofer enclosure
- The desired tuning frequency of the subwoofer enclosure
- Material thickness
- The woofer cone's radiating surface area (given as Sd in the Thiele Small Parameters)
- The woofer's Xmax Thiele Small Parameter
- The woofer's physical displacement (sometimes listed as DD or Driver Displacement)
- Two dimensions of the box (we will compute the third dimension)
For our exercise, we know the following:
- Net volume: 1.35 cubic feet
- Enclosure tuning: 43hz
- We will use 3/4 inch material
- The cone's radiating area (Sd) is 339.8 square centimeters
- The woofer's throw (Xmax) is 6.5mm
- The woofer basket and magnet displacement (dd) is 0.039 cubic feet
- The enclosure will need to be 12" tall externally. Internally, the box will be 10.5 inches. We want it to be 24 inches wide so it fits between the shock towers of our hatchback.
From here we can compute the gross external dimensions. Let's assume we're making a circular port. We need to compute the port area and length.
Port length is dependent upon port area, enclosure volume, and port tuning. We already know the enclosure volume and port tuning frequency. So we need to compute the port area before we can compute port length.
How Big Does the Port Need to Be?
For our purposes, the Minimum Port Area is dependent upon the woofer volume flow rate. This flow rate is stroke volume multiplied by the tuning frequency. The goal of these computations is to make the port not "chuff" at full volume. We want the enclosure to sound clean. We need the port opening to be large enough where it will not chuff. We need to know how much air volume is going through the port in a given second. Then we can compute the needed area to prevent excess compression by taking the square root.
Other factors can alter the port area, but this calculation works for 80% of cases.
First, we need to compute the stroke volume in cubic meters.
Stroke volume = Sd * Xmax
Stroke volume = 0.0339m2 * 0.0065m
Stroke volume = 0.002145m3
Next, we need to know how much volume flow rate by multiplying by the tuning frequency.
Volume Flow Rate = Stroke volume * tuning frequency
Volume Flow Rate = 0.002145m3 * 43hz
Volume Flow Rate = 0.0092m3
Now we can determine the minimum port diameter by taking the square root of the volume flow rate.
Minimum Port Diameter = SquareRoot(Volume Flow Rate)
Minimum Port Diameter = SquareRoot(0.0092m3)
Minimum Port Diameter = 0.096m
Let's multiply that by 39.97 to come up with inches:
Minimum Port Diameter (inches) = 0.096m * 39.97 Minimum Port Diameter (inches) = 3.83 inches.
We'll go ahead and round that up to 4 inches since that's a common diameter port size. The outer diameter of a typical 4 inch PVC pipe is 4.625.
Calculating Port Length
We need to know the port length in inches. We can then determine how many cubic inches the port will occupy within our enclosure. We can determine port volume by multiplying the port's outer diameter by the port length. The math gets a bit complicated here. I'll show my work to help you out.
We need to know the enclosure volume in cubic inches, tuning frequency in hertz, and port radius in inches.
Radius = diameter / 2
Enclosure volume in cubic inches = enclosure volume in cubic feet*1728
Enclosure volume in cubic inches = 1.35 * 1728
Enclosure volume in cubic inches = 2332.8
Let's use "friendly" names for the variable names for the rest of the formulas to make the work easier to follow.
Constant = 14,630,000
R2C = Radius^2 * constant
Frequency2Volume = (Frequency ^ 2) * Volume
Port length = R2C / Frequency2Volume - (1.463*radius)
Okay, it's a bit to digest, so we'll go through it one step at a time.
R2C = 2^2 * 14,630,000
R2C = 4 * 14,630,000
R2C = 58,520,000
Frequency2Volume = 2332.8 * 43^2 Frequency2Volume = 2332.8 * 1849 Frequency2Volume = 4,313,347.2
Port Length = 58,420,000 / 4,313,347.2 - (1.463*2)
Port Length = 13.54 - 2.93 Port Length = 10.47 inches
Tuning our 1.35cf box to 43hz with enough port area, the port should be 4 inches in diameter and 10.47 inches in length.
Gross Volume Vs Net Volume
Gross Volume is Net Volume plus whatever else is going inside of the enclosure. In this case, we have a woofer basket, cone, and magnet, and also the volume of the port.
To keep the math easy moving forward, let's keep everything in cubic inches.
Net Volume = 2332.8 cubic inches.
Driver Displacement volume = 0.039 cubic feet = 67.39 cubic inches
Port Volume = 1/2 port outer diameter ^2 * Pi * port length
Port Volume = (1/2 * 4.625)^2 * Pi * 10.47
Port Volume = (2.313^2) * Pi *10.47
Port Volume = 5.35 * Pi * 10.47Port Volume =16.8 * 10.47
Port Volume = 175.9 cubic inches
Gross volume = Net + Driver Displacement + Port
Gross Volume = 2332.8 + 67.39 + 175.9
Gross Volume = 2576.09
Let's round it off to keep the math easy, our subwoofer's gross volume is 2576 cubic inches, internal.
Yes, internal. The external volume is dependent upon material thickness.
But we don't need to compute gross external volume. We can compute the three internal dimensions. Then we add double the material thickness to each to come up with the three external dimensions.
We know the box needs to be 12 inches tall and 24 inches wide. Let's get the internal measurements by removing the material thickness.
Internal dimension = external dimension - 2*material thickness
Internal height = 12 inches - 2*0.75 inches
Internal height = 12 inches - 1.5 inches
Internal height: 10.5 inches
Internal width = 24 inches - 2*0.75 inches
Internal width = 24 inches - 1.5 inches
Internal width: 22.5 inches
We'll compute the internal depth through some simple division.
Internal depth = gross volume / internal width / internal height
Internal depth = 2576 cubic inches / 22.5 inches / 10.5 inches
Internal depth = 114.5 square inches / 10.5 inches
Internal depth = 10.9 inches
We can round this up to 11 inches to keep the math easy with the saw.
Reversing the above formula, we can get external dimensions.
External dimension = internal volume + 2*material thickness
External depth = 11 + 2*0.75
External depth = 11+ 1.5External depth = 12.5
Our enclosure needs to be 12 inches tall, 24 inches wide, and 12.5 inches deep.
The port needs at least one diameter of open space behind it so it can breathe. Placing it on the front face would yield only 1.28 inches behind our 4-inch port. You should install the port on the side of the box.
I'm going to let you compute the individual dimensions. Hint: you need six panels.
You can use this site's box calculator to design a slot ported subwoofer with a Rockford Fosgate R2D4-10.
Further Reading: What is a subwoofer? Subwoofers Explained
