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# Subwoofer Design Math Fail

I'm building a subwoofer for my friends art film theater. I'm trying to figure out how much amplifier power I need to drive the drivers to Xmax, but my calculations do not match those made by Win ISD. If Win ISD is right I need about 1000 W and can expect about 121 dB at one meter. If my calculations are right then I can expect about 116 dB at one meter and I need about 500 W to achieve it.

I'm using two Titanic Mk III drivers in a 15 ft³ box tuned to 19 Hz.

Driver Parameters:
fs= 24
Vas= 5.46 ft³ * 2 = 10.92 ft³ (5.46 ft³ per driver)
Qms= 6.75
Qes= 0.52
Qts= 0.49
Xmax= 20.5 mm
Vd≈ 77 in³ * 2 = 154 in³ = 0.00252 m³ (I estimated that the Vd was about 77 in³ per driver since Vd isn't given)
f3≈ 19 Hz

Efficiency:
ƞₒ= ( (2.7 * 10^-8) ( fs^3 * Vas) ) / Qes = 0.00784 W
where Vas is in ft³

112 + 10 * log 0.00784 = 91 dB SPL 1 W/1m

Max SPL:
Par= 3 * f3^4 * Vd^2 = 2.48 W
where Vd is in m³

112 + 10 * log 2.48 = 116 dB SPL @ 1m

Max Input Power:
Per= Par / ƞₒ = 317 W
where Par and ƞₒ are in Watts

Win ISD calculated efficiency at 91 dB 1W/1m which is exactly what I calculated.
Win ISD calculated Max SPL to be about 120 dB which is about 4 dB more than I did.
WIn ISD calculated Max Input Power to be about 875 W which is about 560 W more than what I figured.

What is going on here? Those seem like big discrepancies.

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I think your Vd is wrong, Vd equals Sd (124.65 in^2) * xmax (0.81 in) you should end up with 100.58 in^3 per driver.

Here is what I see in winISD, two 15"MKIII, 15cuft enclosure, 19hz tune, Transfer function:

SPL:

Max Power:

Max SPL:
Thank you mtg90,

You are right I was off on the Vd. According to the spec sheet: http://www.parts-express.com/pdf/295-420s.pdf
Sd is 804.2 cm² which makes Vd about 0.0016 m³ * 2 or 0.0032 m³.

My calculations are still off from what Win ISD predicts though

I calculate max output to be about 118 dB SPL at one meter. Win ISD says about 122 dB. One is off by about 4dB that's a factor of about 2.5.

I calculate max input power to be about 510 Watts. Win ISD is now saying about 1470 Watts. Here somethings off by a factor of nearly 3.

The equations I'm using came from The Loudspeaker Design Cookbook (6th edition)
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