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Evaluation of noise in flared ports

Subwoofer ports have to flow a lot more air than their conventional speaker counterparts. Since increasing the area of a port quickly produces very long ports, the most effective means of moving more air is to increase the air velocity.

Ports operating below about 10 m/sec generally have no problems with turbulence and compression. As velocity is increased beyond this, turbulence occurs as air exiting the port is forced to slow too quickly as it encounters the surrounding still air.

Flared ports cause the airflow to expand and loose speed in a controlled fashion, allowing higher speeds without turbulence. This method targets the air in the "boundary layer", which is close to the walls of the port.

Increasing velocity even further, the air in the "core" of the port becomes turbulent. Flares are unable to help with this problem, which represents the limiting velocity for the port. By this stage the port is beginning to present a different load to the system, resulting in de-tuning and subsequent loss of output, known as compression.

 

A series of experiments were done to quantify this behaviour ...

Round one, November 2005, concentrated on a range of 86mm ports, and measured how usable velocity increases with flare size.
Round two, February 2006, duplicated these findings for 103mm ports, and more importantly, measured the limiting velocity for both diameters. In addition, changes in performance at different frequencies were investigated. Several measurements were also taken for 152mm ports.
Round three, March 2007, examined whether the inside flare could be smaller than the outside flare, without affecting performance.

All the results are incorporated into the downloadable Flare-it calculator

To keep load time for this page to a reasonable value, much of the content has been moved to additional pages. This is particularly true for the derivation of the various equations. Follow the ">>more" links to see the full content.

 

Summary of findings

 

Definition of Area Ratio:

Photo - defining Area Ratio
Area Ratio is the cross-sectional area (CSA) of the port opening, divided by the CSA of the unflared section of the port. It gives an indication of how quickly the air has to change velocity as it exits a flared port, and is a more useful measure than flare radius alone. It allows comparisons to be made for ports of different diameters, and is the measure used to describe the ports used in these tests.

 

Method

A sine wave was applied to each port / flare combination, and the signal level slowly increased. Care was taken not to use high power for longer than several seconds, particularly for the 30hz tests (at the tuning frequency excursion is at a minimum = less cooling)

When "chuffing" was first detected, the voltage across the drivers was recorded.
From the voltage, the input power was calculated >> more
The input power was entered into WinISD and the velocity at the test frequency was read from the "Air Velocity" graph

Fifteen ports were tested for a range of frequencies. (15, 20, 25, 30 and 35hz, power and excursion permitting ) The ports ranged in diameter from 51mm to 152mm, and the flares ranged from 10mm to 75mm.

Several boxes were required to optimise velocity and port length for the different port diameters. Round one utilised 50 litre box with two 10 inch drivers. Round two used a four-driver box that could be configured for 70, 100 or 160 litres.
See the Test Ports and Boxes page for more details, including the WinISD project files for all the alignments used

 

Definition of Chuffing:

"Any audible noise, other than the intended signal, detected by listening with the ear close to the port"

The onset of "chuffing" is unmistakable and a change of 1dB in input power is usually enough to hear it clearly. Where the transition occured over a range of values, the average of "I think I can just hear it" and "I can definitely hear it" was recorded
I'm confident that anyone who repeated the tests would find their results very close to those presented here. Even if a different threshold for chuffing was chosen, the relationships found in these tests would still be present.

The main area of subjectivity is in deciding how to translate results based on barely audible chuffing, into recommendations for typical music and home theater applications.
A test was done to see how much the port velocity could be increased before the "chuffing" became audible at the seating position.
For a seat 2.5 metres from the sub in a room 5m * 4m, the velocity could be increased by 25%.

An allowance for the masking effect of content can also be used.
The actual amount is based on the performance of sub's I've built, and on existing industry recommendations.
I estimate that reasonable values for masking allowance are an additional 15% for music and 30% for Home Theatre usage.
The equations developed below are based on designing for music, so a total allowance of 25+15 = 40% is used

 

Results for 30hz

See raw data page for the voltage measurements, power calculations and alternate frequency results
Graphing the data for all fifteen ports, highlights the limiting velocities and linear relationships

Graph - 30hz results
Results for all the ports @30hz
Light grey shaded area indicates round one results

The measured figures are for just audible "chuffing" detected by listening at close range
As stated above, an additional 40% of input power can be utilised for listening to music.
This 40% allowance isn't applied once the limiting velocity is reached, because core turbulence begins to cause compression and de-tuning.
A graphical approach was used to add this allowance, and then find equations describing operation at, and below the limiting velocity.

The following set of equations were developed. >> more (Part one)

Limiting velocity at 30hz (onset of core turbulence and compression)

For ports smaller than 103mm in diameter
Limiting velocity = 10 +[ (diameter squared) * (19.5 / 10,000) ]
For ports larger than 103mm in diameter
Limiting velocity = 31 + [(diameter squared - 10,600) * (8.5 / 15,000)]

Usable velocity at 30hz when operating below the limiting velocity (onset of boundary layer turbulence or "chuffing")

equation

 

Results variation with frequency

The ports were tested for a range of frequencies. (15, 20, 25, 30 and 35hz, power and excursion permitting )
It was found that departing from the 30hz test frequency changed the usable velocity.
Here's the results for the 86mm diameter ports.....

Graph - 86mm port at different frequencies
Performance of 86mm diameter ports at different frequencies

The limiting velocity falls as frequency is reduced, stabilising at 25hz

From this data, plus that for the other diameters, the following set of relationships was developed. >>more (Part two)

Limiting velocity

At 35hz, the limiting velocity is higher than the 30hz figure by +23%.
At 25hz, and below, the limiting velocity is lower than the 30hz figure by -33%

Usable velocity

At 35hz, the usable velocity is higher than the 30hz figure by +29%
At 25hz, the usable velocity is lower than the 30hz figure by -28%
At 20hz, the usable velocity is lower than the 30hz figure by -37%
At 15hz, the usable velocity is lower than the 30hz figure by -44%

These results can be visualised in the following graphic. The spacing between the two lines will depend on what flares are fitted


Changes in port performance with frequency

 

Inside flare requirements

The third round of tests examined whether the inside flare could be smaller than the outside flare, without affecting performance.
All the test details can be found here and conclude that:
For speeds below 70% of the core limit, the radius of the inside flare can be 15 - 20% smaller than that of the outside flare

 

At last, the tool

The findings of these tests have been incorporated into the Flare-it calculator

Small screenshot of "Flare-it" calculator
Flare-it calculator

 

You can help to improve this site - use the feature request page to suggest changes to content or navigation.      Last update to this page 22nd April 2009