
Often
times, you'd like to mount a driver facing down, such as in a
Sonotube™ enclosure. However, you may not be sure whether the
driver you have is suitable for such an arrangement. Will the
driver hold up to horizontal mounting? Will the relentless pull of
gravity be too much, and cause intolerable amounts of sag? Well,
there's actually a way to calculate the sag a driver will exhibit
when mounted in a downfiring (or upfiring) position! And you don't
need anything more than the Fs, Vas, effective surface area (Sd),
and the Xmax of the driver.
To calculate the sag, we first need to calculate the acoustic
compliance of the driver. That is, how soft is
the suspension? This
parameter is called Cms, and is related to Vas. Cms is the
acoustic compliance of the driver, and has the units of meters per
Newton. It is calculated as:
Cms = Vas / (1180 * c^2 * (Sd/10000)^2)
where
 Vas is the equivalent compliance of the
driver, in liters 
 c is the speed of sound, in m/s (use
343 m/s as a good approximation) 
 Sd is the effective surface area of the
driver, in square cm 
Note that you can use the following table for rough Sd estimates
for drivers:
Size 
Sd 
8" 
230 cm^{2} 
10" 
330 cm^{2} 
12" 
480 cm^{2} 
15" 
780 cm^{2} 
18" 
1150 cm^{2} 
Now that we have the Cms of the driver, we'll need to calculate
the effective mass of the driver, Mmd. For this, we'll need Cms and
Fs.
Mms = 1 / ((2*pi*Fs)^2 * Cms)
where
 pi = 3.1415927... 
 Fs is the resonant frequency, in Hz

 Cms is as calculated above 
So, with the Mms and Cms, we're almost there. To calculate the
actual sag, you'll need to multiply the stiffness of the suspension
times the mass of the diphragm times the pull of gravity:
Sag = Cms * Mms * g
where
 Cms is as calculated above 
 Mms is as calculated above 
 g is the acceleration of gravity (9.81
m/s^{2}) 
This will give us the sag in meters. So, multiply by 1000 to get
to millimeters. Here's an example, using our Shiva subwoofer:
Vas = 136.6 liters
Fs = 21.6 Hz
Sd = 481 cm^2
So, we calculate the Cms as:
Cms = Vas / (1180 * c^2 * (Sd/10000)^2)
Cms = 136.6 / (1180 * 343^2 * (481/10000)^2)
Cms = 0.0004253
So, now we calculate the Mms:
Mms = 1 / ((2*pi*Fs)^2 * Cms)
Mms = 1 / (2 * 3.1415927 * 21.6)^2 * 0.0004253)
Mms = 0.12766 kilograms
or 127.66 grams. Lastly, we need to calculate the sag of the
driver:
Sag = Cms * Mms * g
Sag = 0.0004253 * 0.12766 * 9.81
Sag = 0.0005326 meters
Sag =
0.5326mm.
So, that's all fine and dandy. We can calculate sag. But what
does it mean, and how can it tell us if the driver is OK for
horizontal mounting? Well, as a general ruleofthumb, we use the
following:
If the sag is more than 5%
If
the sag is more than 5% of
the Xmax of the driver, then it's not meant for horizontal mounting.
Simply put, if you lose more than 1/20th of your Xmax from sag,
then it shouldn't be mounted that way. To finish off the example,
let's look at Shiva:
Xmax = 15.9mm
one way
Sag = 0.5326mm
Percent Sag = (Sag / Xmax) * 100
Percent Sag = (0.5326 / 15.9)
* 100
Percent Sag = 3.35%
So, Shiva would be OK for horizontal mounting. And now you can
calculate the suitability of your favorite driver, too! Just run
the numbers, and if you're less than 5% of Xmax, you're sitting
pretty! 
