rank loudness of common cab/driver configs

[Arjank]

With all things being equal?

Easy, then it's +3dB with any doubling of the cone-area

And with things being equal I mean the following:
-xmax
-compression
-baffle size
-tuning frequency
-2pi - 4pi transition
-off-axis response 1khz and up
-the overall frequency response (including rolloff on the lowend)
-impedance
etc......

Oh, and about the BLxVd....what counts is the real xmax(total harmonic distortion lower then 10%, Klippel measurements) and powercompression. The suspension should be linear(to avoid unwanted distortion) within the xmax region, after that it's good (at least for us bassists) to have a progressive suspension (it creates a larger counter force after hitting xmax).

[tom-g]

Don't know what "sq cone area" is and what multiplying BL with Vd is supposed to mean.

8x10 628.3 square inch
6x10 471.2
4x12 452.4
2x15 353.4
4x10 314,2
1x18 254,5
3x10 235.6
2x12 226.2
1x15 176.7
2x10 175.1
1x12 113.1
1x10 78.5

That would be my ranking.

[obimark]

Tom-Q, this looks correct all other things being equal.

I know the reason a 2x10 and 1x15 will SOMetimes play well together is they both will usually take around the same amount of watts without blowing out.

If you blow one likely you will blow both cabinets.

[PlungerModerno]

How does this figure into the preceding calculations and estimates?

http://barefacedbass.com/technical-i...splacement.htm

Goes into some detail on how to estimate the influence of driver size etc.

The upshot is a 115 has more cone area than a 210 -

115 estimation:
Nominal cone diameter = 15" PI(15/2)^2 = PI x 56.25
Actual cone diameter = 13" PI(13/2)^2 = PI x 42.25

112 estimation:
Nominal cone diameter = 12" PI(12/2)^2 = PI x 36
Actual cone diameter = 10.3" PI(10.3/2)^2 = PI x 26.5225

110 estimation:
Nominal cone diameter = 10" PI(10/2)^2 = PI x 25
Actual cone diameter = 8.3" PI x (8.3/2)^2 = PI x 17.2225


By extension:

cab Nominal[Actual]*

110 = 25[17.2225]
112 = 36[26.5225]
210 = 50[34.445]
115 = 56.25[42.25]
212 = 72[53.045]
310 = 75[51.6675]
410 = 100[68.89]
215 = 112.5[84.5]
412 = 144[106.09]
610 = 150[103.335]
810 = 200[137.78]

Thats by my brief run with the figures. Note the Actual areas aren't all that consistent as drivers vary. I took a single sample from the barefaced figures... The fact that the Nominal and Actual estimates don't fall in the same order is interesting. Try some other values if you want.
When you introduce more parameters then it gets murkier. I'm not keen to get into that - considering the level of complexity.

*multiples of PI

[Bassmec]

Originally Posted by Tuned

Xmax is part of "all things being equal", like I said, they're actually not. In reality you have to figure Vd and BL, the motor force behind the cone.

Let's borrow Eminence's stock ratings:

Both the 10" Basslite CH2010 and 15" C2515 have an 11.1 BL product, which is typical between bass speakers of different sizes from the same company. The CH2010 has an Xmax of 7.5mm for a 120cc Vd and the C2515 Xmax is 8.5mm for a 381cc Vd, again typical.

So here's how it plays out:
4x10 = 44.4 BL x 480cc Vd = 21312
2x15 = 22.2 BL x 762cc Vd = 16916

So all things really being equal, a 4x10 has 26% more "output capacity" than a 2x15. Can we get past this already? There's no such thing as a magic 2x15 that blows away 4x10's because the exact same advances in the 15's can and will be applied to the 10's made by the same company. 4x10 is just a better configuration. Deal with it.

Unlimited power changes things dramatically, so do these sums with a 200 watt tube amp and the apparent headroom from a super efficient 2 X 15 like a JBL k140 or Altec 418 driver'd unit, is going to be louder than the 4 X 10 before amp clipping becomes apparent.
The extra coupling of the high power 4x10 does not equate in this case to higher SPL and any spare X max and thus displacement beyond the 200 watt limit is pointless.
This is the difference between effortless efficiency and brute power.

[truebenjaman]

Just saying all speakers of different diameter having the same x_max seems a little off. Imagine a 1" driver with the same x_max as a 15" woofer.

I therefore propose another interpretation of "all things being equal": Fix x_max in proportion to the speaker diameter. We would approximate the air moved by a speaker by the volume of a cone with base a circle with the speaker radius r and height some fixed factor c times r. The factor c will cancel out in any comparison of two given cabs, so it is sufficient to compare the cubes of the speaker radiuses.

In cube inches:
10": 125
12": 216
15": 422

This would make a 215 move almost the same amount of air as a 810, which is more in line with recent developments (think fearful 1515/66). It also supports the experience by some of you that a 115 outperforms a 210.

DISCLAIMER: I'm a mathematician, not an audio engineer, so feel free to shoot me down if my reasoning is not sound or my assumptions invalid.

[Arjank]

Originally Posted by truebenjaman

It also supports the experience by some of you that a 115 outperforms a 210.

Nothing strange about a 115 outperforming a 210 when it comes to pure bassperformance. A 210 has slightly less cone area then a 115. On average most 15"s have a slightly higher xmax then 10"s. You do the math....

[Bassmec]

Originally Posted by truebenjaman

Just saying all speakers of different diameter having the same x_max seems a little off. Imagine a 1" driver with the same x_max as a 15" woofer.

I therefore propose another interpretation of "all things being equal": Fix x_max in proportion to the speaker diameter. We would approximate the air moved by a speaker by the volume of a cone with base a circle with the speaker radius r and height some fixed factor c times r. The factor c will cancel out in any comparison of two given cabs, so it is sufficient to compare the cubes of the speaker radiuses.

In cube inches:
10": 125
12": 216
15": 422

This would make a 215 move almost the same amount of air as a 810, which is more in line with recent developments (think fearful 1515/66). It also supports the experience by some of you that a 115 outperforms a 210.

DISCLAIMER: I'm a mathematician, not an audio engineer, so feel free to shoot me down if my reasoning is not sound or my assumptions invalid.

You make a very valid point but since we don't even have a power figure at which a fair comparison can be made, none of this makes any sense in a practical application.

[Tuned]

Originally Posted by RockDoc

"However:
6x10 = 66.6 BL x 720cc Vd = 47952
^ almost twice the output capacity of a 4x12"

Forgive me if I'm overlooking something, and understand that math isn't my forte, but if the quotation above is accurate, then couldn't we divide that by two and get: 3x10 = almost the output capacity of a 4x12? That somehow doesn't seem right....

3x10 = 33.3 BL x 360cc Vd = 11988
^ 1/4 the output capacity of a 6x10

You're right, that can't be right. At best doubling the speakers (and amp) can't result in more than 3x the output, and that's only if the system maximizes the acoustic loading effect for a 3dB bonus for a total of 9dB gain. Either the BL product or the Vd has to be rooted for this to work:

If it's the BL factor then:
3x10 = rt33.3 BL x 360cc Vd
= 5.77 x 360 = 2077.4
6x10 = rt66.6 BL x 720cc Vd
= 8.16 x 720 = 5875.8
That's 2.8x more output.

If it's the vD then:
3x10 = 33.3 BL x rt360cc Vd
= 33.3 x 19.0 = 631.8
6x10 = 66.6 BL x rt720cc Vd
= 66.6 x 26.8 = 1787.1
That's also 2.8x more output.

I figure the difference will only become apparent when comparing different sized drivers. You can't just go by the sensitivity specs of the drivers, since in a bass configuration the driver's ability to force a mechanical load is more important than its free-air sensitivity.

This begs another question. When a mechanical load is introduced, it increases the electrical impedance of the speakers too, so perhaps cabs with more smaller drivers are actually higher impedance than indicated. Horn loading does exactly that, the Yorkville LS808 is rated at 8 ohms but uses a 4 ohm driver. I've talked to a Yorkville tech about it on the phone, they insist they've measured their AC impedance at 7.8-8.2 ohms. Maybe 4x10's should use 6 ohm drivers found in 3x10's...

[Bmorefoozler]

There is nothing typical about a 7.5 mm xmax for a 10" driver.

That is intentionally skewing the results to make 10" drivers look superior.

[Passinwind]

Originally Posted by Bassmec

none of this makes any sense in a practical application

Exactly right.