Subwoofer Ports

Subwoofer ports (a.k.a vents) are interesting things.  In a previous post I provided some background into how ports worked, in this post I am going to dig a little deeper into port design, a.k.a. port tuning.

Flared Ports with Wooden Connector Rings

The Port Formula

There is a formula that you can use to design a port, since formulas tend to scare people away and there plenty of tools available to do the calculations for you this blog post will focus on understanding the four main parameters that you need to think about when designing a port. 

• Tuning Frequency
• Enclosure Volume
• Port Cross Section
• Port Length

We can manipulate any three of these four items and the formula dictates the forth parameter.  For this post we are going to examine how the tuning frequency, enclosure volume, and port cross section influence the length of the port.  It is very important to understand the impact of these four parameters as they will determine the size, shape and sound of our subwoofer.  We need to get the sound we want, while keeping a reasonably sized box, a reasonably sized port, and a reasonably simple port.  We also need to design the system so we don't have any port noise (a.k.a. "chuffing").

  

Tuning Frequency

This is the resonate frequency, expressed in hertz (HZ) of the subwoofer enclosure.  Sometimes we call this Fb, or the box frequency.  We could have an entire blog post dedicated to understanding this concept.  But for now all you need to know is that if you want your subwoofer to play lower then you need to to tune the box lower.  For a given enclosure volume and port cross section you can adjust the tuning frequency by adjusting the length of the port.  As the port gets longer the tuning frequency gets lower, As the port gets shorter the tuning frequency gets higher.  This can be clearly seen in in this plot, which is based on a 4" diameter port in a 2 cubic ft box.

Port Length VS. Tuning Frequency, 2 CU FT Enclosure, 4" Diameter Port

For those that have a hard time visualizing a plot consider these images, each shows an identical sized enclosure (2 Cu FT), each with a 1 x 12 slot port.  The first image shows a 25 3/16" long port, which corresponds to a 24 HZ tuning frequency.  The second image shows a 17 3/4" long port, this enclosure is tuned to 28 HZ.  The third image shows a 12 59/64" long port, and a 32 HZ tuning frequency.  The key take away here is that a lower tuning frequency requires a longer port, holding everything else constant.  The ports are shown outside of the enclosure so that the relative size of the ports are easier to visualize. 

24 HZ Fb, 2 CU FT, 1X12 Slot Port

28 HZ Fb, 2 CU FT, 1X12 Slot Port

 

32 HZ Fb, 2 CU FT, 1X12 Slot Port

 

The ports in the above three images are relatively small and can be quite easily folded into their respective enclosures (obviously the enclosures will need a slight redesign in order to maintain the same airspace).  But, port design is not quite that simple.  There are several other factors that must be considered.  

Enclosure Volume

Now consider a slightly different scenario, let's hold the tuning frequency constant, along with the port cross section and look at what happens when we adjust the box volume.  As the enclosure volume gets larger the port gets smaller, and vice versa.  This plot shows the relationship for a 4" diameter port tuned to 40 Hz.

Port Length Vs. Box Volume, 4" Diameter, 40 HZ Fb

 

 

Again, for those that find it difficult to visualize this consider these two images which both show two absurd enclosures.  Neither of these is very good design, they were just selected for.  The first is a 1 CU FT enclosure tuned 28 HZ with a 1X12 slot port, and the second is a 4 CU ft enclosure tuned to 28 HZ with a 1X12 slot port.

1 CU FT, 28 HZ Fb, 1X12 Slot Port

4 CU FT, 28 HZ Fb, 1X12 Slot Port

The 1 CU FT enclosure has two main problems.  First the port is comically long.  It would be very difficult to build that port (it is over 3' long) into the enclosure.  This is the result of using an undersized box.  As the box gets smaller, holding everything else constant, the port must get longer.  Second, the small size of the box will have adverse effects on low frequency response.  The 4 CU FT box, on the other hand is not a reasonable solution.  For starters it is a comically oversized enclosure.  With a box this large the port length becomes trivial.   

Port Cross Section

The port cross section, which rather the cross sectional area is another important factor.  The port needs to be large enough to prevent port noise, also called chuffing.  This happens when the air in the port moves fast enough to create turbulence.  As a general rule of thumb the air speed velocity needs to be less than 5% of the speed of sound.  There are two solutions to this problem, the first is to flare one or both ends of the port.  The second is a larger port opening.  But, that presents a problem.  As the cross sectional area of the port increases, holding everything else constant, the port length increases.  Here is yet another chart showing the relationship.  This example uses a 2 CU FT enclosure tuned to 30 HZ.

Port Length vs Port Cross Sectional Area, 2 CU FT, 30 HZ Fb

Here is a example of a comically long port.  This was designed to show the absurd result you wold get if you were to take things to the extreme in order to get rid of port noise.  This design uses a 2 CU FT enclosure, tuned to 28 HZ with a 3X12 slot port.  The end result is a port that is almost 5'.

3X12 Slot Port, 2 CU FT, 28 HZ Fb

So there you go, now you know how box tuning, port area, and enclosure size impacts the length of you port. Hopefully you found this post interesting and informative.  I am planning a few more posts that dig deeper into the port tuning formula, so make sure you check back in frequently.  If you want to learn more you can also check out this video on the DIY Audio Guy YouTube channel: