Vertical driver orientation like inverted W-Frame used in S19 requires specific requirements as follows:

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:

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.

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:

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

Note that you can use the following table for rough Sd estimates for drivers:

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

Size | Sd |

8" | 230 cm^{2} |

10" | 330 cm^{2} |

12" | 480 cm^{2} |

15" | 780 cm^{2} |

18" | 1150 cm^{2} |

Mms = 1 / ((2*pi*Fs)^2 * Cms)where

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:

pi = 3.1415927... Fs is the resonant frequency, in Hz Cms is as calculated above

Sag = Cms * Mms * gwhere

This will give us the sag in meters. So, multiply by 1000 to get to millimeters. Here's an example, using our Shiva subwoofer:

Cms is as calculated above Mms is as calculated above g is the acceleration of gravity (9.81 m/s ^{2})

Vas = 136.6 litersSo, we calculate the Cms as:

Fs = 21.6 Hz

Sd = 481 cm^2

Cms = Vas / (1180 * c^2 * (Sd/10000)^2)So, now we calculate the Mms:

Cms = 136.6 / (1180 * 343^2 * (481/10000)^2)

Cms = 0.0004253

Mms = 1 / ((2*pi*Fs)^2 * Cms)or 127.66 grams. Lastly, we need to calculate the sag of the driver:

Mms = 1 / (2 * 3.1415927 * 21.6)^2 * 0.0004253)

Mms = 0.12766 kilograms

Sag = Cms * Mms * gSo, 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 rule-of-thumb, we use the following:

Sag = 0.0004253 * 0.12766 * 9.81

Sag = 0.0005326 metersSag = 0.5326mm.

**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!

## 1 comment:

I tried computing if Dayton SD270A-88 10" would be suitable for use in a W-Frame and I came up with 6.13%. I then tried changing the

sdandvasparameters and noticed that It didn't change the outcome. To verify my spreadsheet, I then tried your Shiva example and came up 3.35%, the same result that you did. It looks like thecmsis being canceled out since it's used in the denominator of the mms equations and then is multiplied in the sag equation.This is what I used for my values:

vas 107.6

fs 26Hz

sd 346.4

Xmas 6mm

My percent sag = 6.13%

Any ideas of what I may be going on?

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