Subwoofer Qualification Formulae For Downfiring Configurations
We are often asked if a particular driver is suitable for using in a down-firing configuration. Below is a formula that takes into consideration the effects gravity will have on the "sag" of the cone structure of any woofer. You will need the Fs, Vas, Sd (surface area of the cone), and the Xmax to determine the relative long term usefulness of up or down-firing any woofer.
You can calculate the sag of a driver from:
Percentage of Sag = 24,849 / ( Xmax * Fs²)where
- 24,849 is a constant value based on the relationship of acceleration due to gravity and Pi.
- Xmax is the maximum linear excursion of a loudspeaker voice coil while remaining within the magnetic flux field (mm).
- Fs is the free-air resonant frequency of the woofer (Hz).
The following is the same formula, including the relationship of acceleration and Pi in this case:
Percentage of Sag = 981,000 / (Xmax * (2 * Pi * Fs)²)where
- 981,000 is acceleration due to gravity (mm/S²) * 100 (for the percentage).
- Xmax is the maximum linear excursion of a loudspeaker voice coil while remaining within the magnetic flux field (mm). - Fs is the free-air resonant frequency of the woofer (Hz)
- Pi is the ratio of a circle's circumference and diameter, usually rounded to 3.14.
As a general rule of thumb, any time the sag exceeds 5% of the driver's Xmax, it's not recommended for a down-firing subwoofer application.