Linearteam WinISD Pro

Port terminology: Physical/acoustical length, end correction

If you have read articles on port design on the Internet, you have probably stumbled on various terms involving ports. This document is to explain some of those terms.

Effective radius/diameter

If your port has some other shaped cross-section than circular, then we'll need to calculate effective radius or diameter. Effective radius is radius of the circle, which has same cross-section area than non-circular object. For ports, only inside area contributes to port area, not it's walls. For calculating effective port radius/diameter, use following formulas:
effective radius = sqrt(S/pi) and
effective diameter = sqrt(4·S/pi),
where sqrt means square root.

For example, you have square port which has 100 square inches of cross-section area, what is effective diameter and radius?

Now, just plugging the values to above formula we get:
radius = sqrt(100/pi) = 5.642 inches
diameter = sqrt(4·100/pi) = 11.284 inches.

Of course, diameter could have been easily obtained from radius by just multiplying radius by two.

Acoustical length

First, we need to discuss what is the idea behind port, and how it works. Basically, port forms a mass-spring resonance circuit with enclosure volume compliance. Helmholtz was first to discover such a resonator, hence it was named after him. Mass in port resonates with compliance of box air. By tuning the enclosure, we chose mass in port, so that resonates at desired frequency. As our port will have some area, we can calculate, how long this "tube" should be to have desired mass. This length is so called "acoustical length" of our port.

Physical length

Unfortunately, effect of the port doesn't stop at the end of our port. Moving mass extends somewhat beyond of the port. Researchers of acoustics say that radiation impedance has reactive component, mass. So if we make our port length equal to calculated acoustical length, we'll find out that tuning frequency is lower than what was expected. We can make good approximation to this extra mass by adding this radiation load mass from desired port mass and then calculating required port length.

By default, WinISD assumes that you are going to mount your port above way. And therefore gives you physical length of your port assuming mounting like in above figures. See also FAQ 3.1.

End correction

End correction factor is analytically or empirically determined factor, how much port extends beyond its physical ends. For free end, end correction is 0.30665 times port effective diameter. For flanged end, more analytical expression is available, 4/(3·pi) ~= 0.42441 times port effective diameter. Flanged end is calculated assuming that tube terminates to infinite baffle. Which is not exactly true, but.. Following table summarizes various port configuration types and their total end correction factors (refer to above picture to various end types):

Physical port length is obtained by subtracting port effective diameter multiplied by suitable end correction value from port's acoustical length.