Vent tuning of ported systems
Copyright 2005-15 © Troels Gravesen

The following study is only related to port tuning. I hope to have time to dig a little more into optimum box volume and optimum tuning frequency for ported systems in future studies.
I rush have to say that thick books and papers have been written on these subjects and I'm not going to solve the problem of vent tuning here. We very soon run into heavy math and as most drivers are very un-linear mechanical devices, they don't follow rules. So, from a practical viewpoint I'm going to test some of the formulas available for calculating vent dimension and show you my measurements.

For example, Apple's newest MacBook Pro models feature several Thunderbolt 3 USB-C ports. But the standard MacBook's single USB-C port lacks Thunderbolt 3 support. Because of all this, USB-C is a bit confusing. The port can either be a basic USB port similar to the ones above, or it can be a multi-purpose jack. This depends on the device. Some common port facilities provided by the most common sorts of ports throughout the world are as follows: a) Special Warehouse: This is available on all the ports, for storing the shipment and for maintaining regular stock. B) Port Reception: Reception has details of all the shipment scheduled and moreover it is a guide for the port facilities. The port on the right side of each pair (as you face the intake flange surface) is longer and directs the inlet charge more to the center of the chamber, and is referred to as the “good” port; the one of the left, obviously referred to as the “bad” port, dumps the air/fuel mix toward the cylinder wall and usually doesn’t flow as well. In this video I answer a few questions you guys have had about ports. I give examples of the most common types of ports and all the different ways to channel.

A number of people have commented that my recommendations for vent dimensions do not meet their calculated values - and no wonder, read on...

In all the ported systems I have made, I have used box simulation programs suggesting optimum cabinet volume (Vb) and vent tuning (Fb). However, port calculations have never been in accordance with real world measurements. Usually the port has to be shorter than predicted. In the following study I have used the formulas available at: http://www.diysubwoofers.org
This is an excellent site with a wide range of information related to box calculations. And here you can find the following information regarding port calculation:
Port Length
The port length required to tune a volume of air to a specific frequency can be calculated by using the following equation: Lv = (23562.5*Dv^2*Np/(Fb^2*Vb))-(k*Dv), where:
Dv = port diameter (cm)
Fb = tuning frequency (Hz)
Vb = net volume (litres)
Lv = length of each port (cm)
Np = number of ports
k = end correction (normally 0.732)
The value for k, the end correction, can be fine-tuned by using the following values to derive the appropriate end correction figure for each end of the port, then adding them together
Both ends flanged: k = 0.425 + 0.425 = 0.850
One end flanged, one end free: k = 0.425 + 0.307 = 0.732
Both ends free: k = 0.307 + 0.307 = 0.614
Normally, k=0.732 is assumed.

So, the tricky part here is the value of k being dependent on the vent ends being flared or not. This site does not specify what size the flaring must have in order to be regarded a flange. Nor does it specify any damping material or the impact on measuring performance from this. Thus, in order to have both ends flared I have made a flange from a 25 x 25 cm panel and I have made initial measurements with and without damping material.
Before we get to actual measurements, here's the set-up: A 29.5 litre box was constructed and a number of vents were cut from 72 mm (internal diameter) PVC tubing: 10, 15, 20, 25 and 30 cm lengths were chosen for measurements.
The CLIO was set at +12 dB output and drivers were driven directly from the CLIO board.

Vent tuning is only related to the mass of the air in the box and vent and the dimension of the vent has nothing to do with the driver and in practical terms any driver can be used for these experiments, but don't use a tiny 4' driver for a 29.5 litre enclosure.
I'll demonstrate what happens to the Scan-Speak 21W/8555-01 bass driver from applying various vents as depicted below.

Fig. 1. 29.5 litre box, 8' driver and 5 vents of different length.

Fig. 2. Vents were attached to the box to have one end flared by the internal
panel of the box and an additional flange could be added by the shown panel.

Fig. 3. 'Flanged' is when the vent end is 'sharp',
'flaring' is when the vent end is chamfered e.g. 45 deg. or rounded.

Driver tested with various vent lengths.

Fig. 4. 29.5 litre box with no damping material.
Vents: red = 300 mm, blue = 250 mm, green = 200 mm, yellow = 150, purple = 100 mm.
As can be seen, a very high tuning frequency from this un-damped
box creates a spurious peak around 50 Hz.

Fig. 5. 29.5 litre box including damping material.
Vents: red = 300 mm, blue = 250 mm, green = 200 mm, yellow = 150, purple = 100 mm.
(4 sheets; 30x60x3 cm mixture of sheep's wool and polyester were placed on internal surfaces of the box)

Adding damping material to the cabinet decrease the vent tuning by creating a 'larger' cabinet. No surprise here either, all in accordance with expectations.

Results, damped box:

Fig. 6. The table shows the tuning frequencies from the chosen vent lengths
compared to the calculated lengths with the k value set at 0.732.
As can be seen, there's a major discrepancy between measured
and calculated values and the vent has to be much shorter than predicted.

Results, un-damped box:

Round Port Vs Slot Port For Split Rail Fence

Fig. 7. The table shows the tuning frequencies from the chosen vent lengths compared to the calculated lengths with the k value set at 0.732.
As can be seen, the difference between actual and calculated vent length has diminished.

Vent flange - does it have an impact on Fb?

The results from the un-damped box and k = 0.732 should fit for a port flanged at one end as has been performed. So, apparently something is wrong. It has to be said that the difference between a double-flanged vent and two free ends was less than 0.6 Hz, so when the vent is - at least - sharply flanged this does not make a whole lot of difference.
As the vent is placed outside the box it does not change the volume of the box. The driver may count for a minor volume and the suggestion that you place the driver in a plastic bag and submerge it in water to measure the volume is a little funny. I wouldn't do it, and as a lot the 'driver' is actually air, it wouldn't be correct either. Even if the driver would count for 1 litre volume, this would only have minor impact on the calculations. 1 litre = 3.3% of the total volume. Insignificant.

Fig. 8. Flanged vent: Red = no flange, blue = flaged at one end, green = flanged at both ends,
yellow = flanged of one end - but vent inserted into cabinet (normal position).

Tuning frequency vs. flanging:
No flange: 34.6 Hz
One end flanged: 33.9 Hz
Both ends flanged: 33.7 Hz.
Well, not much to write home about from this study! From no flange to double flange we lower the vent tuning by 0.9 Hz.

Most softwares - to my knowledge - are well in accordance when it comes to calculating vent dimensions and in some cases even damping material can be included (JBL software, e.g. no damping, minimal damping, normal damping (whatever that is...) and heavy damping.
The JBL software is in accordance with the calculation based on the formula shown at www.diysubwoofers.org.
Example: Vb = 29.5, Fb = 28.7, vent diameter = 7.2 cm.
1. JBL: vent = 7.2 (ID) x 46.79 cm with no damping.
2. 'diysubwoofers': 7.2 x 45.00 (with k = 0.732).
Even with heavy damping the JBL software predict a vent of 7.2 x 37.79 cm, where the actual measurement says 30 cm.

Damping material:
Vb = 29.5 litre
Scan-Speak 8' bass driver.
vent: 72 (ID) x 200 mm

Fig. 9. Impedance of bass driver with no damping (blue) and heavy damping (red).
Heavy damping here means 10 mm polyester foam on all internal panels and 2 sheets of Monacor MDM-3
added - and not blocking the passage to the vent!
The MDM-3 is a great material consisting of 2/3 sheeps' wool and 1/3 polyester fibre.

As can be seen, the addition of damping material has a significant impact on the impedance profile and the vent tuning is lowered from 37 Hz (no damping) to 33 Hz (heavy damping) and no surprise here. Again damping material increases the virtual volume of the cabinet and has to be taken into account when deciding Fb and vent length.

Fig. 10. Fb vs. amount of damping material:
Blue = no damping, purple = 1 sheet of MDM-3, green = 2 sheets of MDM-3,
red = 10 mm polyester foam + 2 sheets MDM-3.

Signal input:

Fig. 11. Impact of signal input on vent tuning.
Speaker driven directly from CLIO board at red:
+12 dB, blue = 0 dB, green = -10 dB, purple = -20 dB.

Obviously Fb is unaffected by the signal input, whereas the height of the impedance peaks decreases with increasing voltage. It may indicate that even the 72 mm vent is too small for high signal levels.

Fig. 12. Nearfield SPL measurement at different input levels. The speaker is here driven from a power amplifier between the CLIO and the speaker. Setting the output level to -20 dB normally produces a signal level around 80-90 dB at 1 meter distance - depending on the sensitivity of the driver. The dip in response between 30 and 40 Hz is due to the vent being in resonance with the drivers, thus damping the cone movement. Interestingly the Fb decreases with increasing signal applied to the driver. The CLIO output was set at: red = -30 dB, blue = -20 dB, green = -10 dB, purple = 0 dB (YES, I'm using ear protection!)

Fig.13. 2.2 mH coils of different resistance inserted between CLIO and driver.
Red = No coil, purple = 0.16 ohm cored coil (Monacor), green = 0.47 ohm (Mundorf),
blue = 1.09 ohm (small Intertechnik coil, cored and 0.6 mm wire).
Obviously the coils with higher resistance display higher overall impedance,
otherwise only minor difference.

Round Port Vs Slot Port For Splash

Flaring of vent:

Round Port Vs Slot Port For Split

This will be the last addition to this page: Impact on Fb from flaring the vent. The data were collected during fine-tuning of the SP38/13 construction:

The Fb for the SP38/13 construction was targeted at 33-35 Hz and a vent of approx. 20 cm length was from practical experience found to be suitable.
When inserting the vent the Fb was measured from three different scenarios:
1. Inner end was free and outer end was flanged.
2. Inner end free and outer end flanged and flared.
3. Inner end flanged + flared and outer end flanged and flared (see fig. 3).

Fig. 14. SP38/13 vent tuning.

Round Port Vs Slot Port For Splitter

The reading here is blown up to view the minor changes from this exercise: Red = one end free, outer end flanged (sharp). Blue = one end free, outer end flanges and flared. As can be seen flaring the vent opening rises the Fb slightly, approx. 1-1½ Hz, apparently reducing the vent length slightly. Green = both end flanged and flared. This adds some 10 mm to the total vent length and lowers the Fb approx. 1 Hz. Not much. The router bit used for flaring the vent has a radius of 13 mm.

Flanged vent to the left. Flanged and flared vent to the right.

As can be seen from this SP38 work, not a whole lot is happening from flanging and flaring the vent. This does not imply that flaring the vent is not worthwhile. Rounding the edges significantly reduces vent noise when a large amount of bass is reproduced, and well...looks nicer I think.

From this vent-tuning study is can be seen that calculating the vent dimensions is tricky business. From practical experience I have learned to multiply the vent length by 0.6-0,7 to get the targeted Fb. Quite some deviation from all the nice math. So, no clear recommendation but get help from someone with measuring equipment if you want it right.

15-01-2006:
Some time ago I had a mail from Bjorn Johannesen telling me about the acoustic impedance at the vent opening. Bjorn has written an excellent article on Martin J. King for Dummies, look here:
http://www.t-linespeakers.org/design/MJK-for-dummies/index.html

Bjorn states:
Effective Length versus Physical Length -- At the opening, there is an acoustic impedance which makes the line behave as if it were slightly longer than the physical line at low frequencies. MathCad includes this impedance so depending on the geometry of your cabinet the actual tuning frequency might be a little lower than you would expect.

Thanks to Bjorn for his comments.
If this goes for TLs, it's a likely explanation for bass reflex designs as well and should explain the discrepancy between calculated and actual vent length.