Need advice/information on boxes and response for two subs

[SubSchmub]

Hi,

New here on DIYaudio but not new to DIY nor to DIY speakers.

In my car camper van I integrated a dual 6.5" woofer system to support two satellite speakers. The technical advise was given to me by Reckhorn. So all I had to do was make sure the physical speicifations were the same as I was told. With some EQ-ing this sounds good, not sure if it is objectively good but with the engine noise that is not really something I care about.
Recently I bought some pairs of full range speakers for my living room. I will be able to switch between different speaker setups but want the bass to come from two subs.

I have been reading quite a bit and I feel like the more I read the more confused I get. So here is where I'm at:

Things to know/what I want

1. Two subs, that I will use solely for music, maybe three in the future.
2. Preferably flat from 30-80hz.
3. No need for loud listening/high SPL (prefer smaller/more flat over high SPL)
4. Sealed.
5. Not too large.
6. Preferably passive subs with external amps.
7. miniDSP is an option.
8. Living roomd is 25m² with semi-open kitchen of 13m².

So the goal is to have two subs to support my full range speakers (HPF at 80hz) for listening to music.

I played around with an online calculator for some drivers that I found interesting.
Focal SUB12
Vas = 90 lts
fs = 24 Hz
Qts = 0.484
Qtc = 0.707

This tells me to build a 80 liter box for f3 of 35hz, I read that by EQing them you can get to 30hz at the cost of some SPL. The reason for this focal driver is that I have giftcards left at some webshop so it would be nice to spend some of that.

GRS 12SW-4HE
Vas = 2.84 ft3
fs = 22 Hz
Qts = 0.43
Qtc = 0.707

This would allow for f3 of 36hz with a 47L box.

Also, I found the GRS 12SW-4 to offer a flatter frequency response from 30hz onward and higher output at 30hz, however the Xmax of the HE is 12.5mm while the non HE version has Xmax 8.5mm, higher Xmax is supposed to be better for a closed sub. Yet another thing that I need to understand better.

So this is where Im at and I have a lot of questions. I read that a lower Qts is better. I dont understand why and I dont really understand why the Focal needs such a bigger box than the GRS?
It however seems that if I am willing to spent 600-€700 I can easily get two subs that are better when doing DIY than getting something pre built. I have the tools and skills to build something, so that is not a problem. I like to build and learn but the alternative would be 2 x SVS SB 1000 for €900, which includes 5 years of warranty. So I guess what I really want to know. What are my options to achieve my goals? Two subs with the GRS driver seem like good value for money but I guess there is more to it than this?

Hope you guys can help me out!
Feel free to share good articles/book chapters on the basics of what I need to know (technically)

 

[GM]

Greets!

Driver Qt dominates for a given box Qt, hence the focal's higher Qts requires a bigger box for a given Qtc.

The lower the driver Qt, the more powerful (over damped*) the motor, ergo for an otherwise given set of specs makes for a smaller box for a given Qtc.

* leading edge of note is stopped short of completion (transient perfect = 0.5 Qt, ergo higher Qt = under damped, i.e. 'hangover'/'boom')

Right, 'there's no replacement for displacement' (driver Sd*Xmax) since Xmax needs to quadruple for every octave (-6dB SPL)

Octaves math (inverse square law):

Fh = Fl*2^n

Fl = Fh/2^n

n = ln(Fh/Fl)/ln(2)

where:

Fh = upper frequency

Fl = lower frequency

n = octave spread

ln(2) = 0.6931

 

[GM]

The above is the basics; now we ideally want the (sub) woofer to fully load the box all the way to its upper mass corner (Fhm) = 2xFs/Qts' and further we ideally normally want it somewhat over damped since the room's acoustics will add to it to a greater or lesser extent depending on the 'sub's location(s) along with thermal power distortion from 'fast' (high amplitude) transients up to +30 dB with some recording's 'attacks', sustain notes, many bluray music, movies.

(Qts'): (Qts) + any added series resistance (Rs): https://web.archive.org/web/20220707003028/http://www.mh-audio.nl/Calculators/newqts.html

Re GRS, historically = junk, though recently they seem to be getting a bit more serious, but personally would stick with known prosound or at least SVS quality.

 

[YSDR]

now we ideally want the (sub) woofer to fully load the box all the way to its upper mass corner (Fhm) = 2xFs/Qts'

Why and how can this be achieved?

 

[SubSchmub]

Greets!

Driver Qt dominates for a given box Qt, hence the focal's higher Qts requires a bigger box for a given Qtc.

The lower the driver Qt, the more powerful (over damped*) the motor, ergo for an otherwise given set of specs makes for a smaller box for a given Qtc.

* leading edge of note is stopped short of completion (transient perfect = 0.5 Qt, ergo higher Qt = under damped, i.e. 'hangover'/'boom')

Right, 'there's no replacement for displacement' (driver Sd*Xmax) since Xmax needs to quadruple for every octave (-6dB SPL)

Thanks!!

So I read through those links last week and today again, I understand part of it. Thanks for that! Your math and the concept of fully loading a box I did not understand, nor could I find an article explaining it.

Also read some other stuff and looked into using WinISD. I think I managed to simulate a subwoofer enclosure but I have the feeling I'm doing something wrong. I have lowered "system input power" because of EQ applied, keeping cone excursion below Xmax. I'm confused how this relates to "Amplifier apparent load power (VA)".
System input power is at 19,8Watts, while load power peaks at 50 VA which I understand is 50Watts? From what I understand, boosting some frequencies +3dB requires twice as much power (if I remember correctly). What I understand from this is that I would need a 50 watt RMS amplifier for this sub, but it just seems wrong to me that this would lead to an SPL of 98dB. Or does this allow for -1 SPL from the 1watt 1m SPL (86dB), in other words, the Focal would be able to produce 30hz at 85dB only? That makes more sense to me than 98dB but I cant find any confirmation on this and I could be all wrong here. That would mean that the driver with the highest "system input power", would be the best driver for my sub, as that would be the one that can be pushed closer to 90dB (which would be the GRS, by far - I simulated some more speakers and found some alternatives but I dont want to make this a more complex question than it already is by adding them all) .

I have added my project in the attachment, hope somebody can see if I made mistakes and or help me with my new questions.

 

[weltersys]

It however seems that if I am willing to spent 600-€700 I can easily get two subs that are better when doing DIY than getting something pre built. I have the tools and skills to build something, so that is not a problem.

DSP, amplifiers that are guaranteed for 5 years, materials for good boxes and drivers probably add up to more than €700.
The experience of DIY can be priceless..

I like to build and learn but the alternative would be 2 x SVS SB 1000 for €900, which includes 5 years of warranty. So I guess what I really want to know. What are my options to achieve my goals? Two subs with the GRS driver seem like good value for money but I guess there is more to it than this?

Simply put, sealed boxes can be equalized to any response desired, and high passed to limit excursion at very low frequencies.
The driver displacement (excursion times Sd) determines the output.
Each doubling of excursion allows +6dB more output, and requires +6dB (four times) the power, without accounting for thermal compression.
Amplifiers are a voltage source, power in watts is voltage squared divided by the impedance, which varies with frequency.
Thermal compression occurs as the voice coil heats up, it's impedance rises, and the amplifier delivering less power into the higher impedance.
If you are listening at moderate volumes, thermal compression is probably not an issue.
This calculator makes it easy to determine the output:
http://www.baudline.com/erik/bass/xmaxer.html

For 90dB at 30Hz, under 3mm excursion would be required from one 12", a pair would half that.

The Focal Sub12 does not list it's Xmax, but comparing the driver's magnet structures, I'd say 8mm might be in the ballpark. The GRS at 12.5mm Xmax (70% Bl, Klipple verified) could achieve an easy +3dB clean output.
From actual measurements of output at relatively low distortion, the SVS SB-1000 driver has around 19mm Xmax, a single would probably beat a pair of the Focal Sub12 for clean output.

System input power is at 19,8Watts, while load power peaks at 50 VA which I understand is 50Watts?

https://forum.speakerplans.com/winisd-apparent-power-question_topic108409.html
Fudge22 explains:
"The nominal electrical input power to a loudspeaker driver is defined as the power delivered by the amplifier into a resistor having the same value as the driver’s voice coil resistance. This is usually calculated by simply squaring the input voltage and dividing by the driver’s voice coil resistance or rated impedance. This definition of input power yields a nominal efficiency vs. frequency response curve that is similar to the SPL response curve you get when driving the system with a constant voltage source.

However, the impedance of a loudspeaker coil is not constant, so if you plot a graph of the input voltage squared divided by the actual impedance, with relation to frequency, you end up with the VA curve shown in winisd. This curve is essentially the inverse of the impedance curve, modified by any filters that you have added. It is also an inverse of the real efficiency of the drive unit."

From what I understand, boosting some frequencies +3dB requires twice as much power (if I remember correctly).

Yes, +3dB requires double the power.
Doubling voltage is 4 times the power.
+10dB is ten times the power.
+10dB sounds "twice as loud" at 1000Hz, while due to our hearing's equal loudness contours, +5dB sounds around twice as loud at 30Hz.

What I understand from this is that I would need a 50 watt RMS amplifier for this sub, but it just seems wrong to me that this would lead to an SPL of 98dB. Or does this allow for -1 SPL from the 1watt 1m SPL (86dB), in other words, the Focal would be able to produce 30hz at 85dB only?

Can't open your files to see what you see, or answer directly.
My guess would be the Focal Sub12 would be closer to 80dB 1w/1m@30Hz.
The Focal Sub12 is a nominal 4 ohm driver (3 ohms DC resistance) so 2.83v applied is "2 watts", not 1.
The driver's impedance may change by an order of magnitude (4 ohms to 40) between 30 and 100Hz.
If 2.83v(2w)=86dB, 4v(4w)=89dB, 12.6v(40w)=99dB.
That said, my guess would be the Focal Sub12 would be closer to 80dB 1w/1m@30Hz, so would require ~100w to reach 100dB at 30Hz, equivalent in "loudness" to 60dB (a quiet conversation) at 1000Hz.

Art

 

[SubSchmub]

Thanks! I will read into that tomorrow. From a quick scan of your message it seems the GRS is the better choice and that the SPL values in WinISD won't be reached with an amp that does 50w (Focal) or 100w (GRS). Took some quick screenshots, might be more useful than project files.

Both are calculated with max cone excursion (12.5mm for the GRS and I found 8.5mm for the Focal somewhere).