Calculation of cabinets and ports
Copyright 2010-2014 Troels Gravesen
The files available here have been found on the web and the first one, "box simulation and room-gain", is an easy quick-and-dirty file that tells us what's going on.
The second file, SpeakerBoxDesigner, is found at an excellent Dutch website:
http://www.mh-audio.nl/sql7/ViewDownloadFiles.asp
Both files in this zip file:
Download.

Tutorials

Download "box simulation and room-gain" excel file for ScanSpeak 18W/8531-G00 here, and you will find this:

From manufacturer's data sheet you get the TS data and you only need four values to get going, Fs, Re, Vas and Qt. Insert resistance of the coil(s) in series with the bass driver in cell B8, something like 0.2-0.4 ohms. It doesn't make a huge difference.

Now, TS data and their reliability: Basically we can get the data we want depending on the voltage applied during measurement. Here are some examples from an 8" polyprop bass driver:

Above the same driver from four different measurements of impedance: Two are done from stepped sinusoidal measurements and two with a sweep signal. Both are performed by added mass (20 grams) and added volume (33.4 liter).
Now, this all looks pretty nice making the same Qt, but Vas does vary some.

Next I tried added mass/sweep and 4 different input levels:

This looks more interesting as we get a huge variation depending on voltage applied during measurements. So, what is right? Good question! Actually none of these are correct as it was possible here to measure the weight of the the moving mass. This is done by taking the membrane with the voice coil and cutting half the rubber surround and half the spider. At least this is as close as we can get the moving mass. We can always argue if half the rubber surround and half the spider is really the right amount of suspensions adding to the moving mass. Anyway, Mms is closer to 25 grams - and this is close to what we get from maximum CLIO output, added mass and sweep measurements (column 4 in the first illustration). But Qt is really low - and is this really true? Hard to tell. The problem is that the suspension aren't linear. This shows up in Cms and Rms. Cms is the compliance of the suspensions, where Rms is the damping of the suspension and also from e.g. voice coil formers made from aluminum. Using Kapton voice coil former the electrical damping is much less and usually produce a much higher Qm.
The lesson to be learned from this is that TS data you're looking at are not true! They could be something else if the measurements were done with another input voltage. This doesn't mean the TS data aren't useful, in particular if they far outside Qt = 0.35. I also means we have to try different volumes before we finally decide on the final cabinet for our driver. Ideally we should try various volumes and various amounts of damping material before we decide.

 

The box simulation excel file linked above does not tell you optimum cab volume for a given driver and we may question whether this is desirable at all as only a few drivers will fit in nicely when it comes to the math. For ported systems, only drivers with a Qt close to 0.35 will make a perfect match.
Dealing with high-Qt drivers (e.g. Qt > 0.4) we use cabs too small and for low-Qt drivers (e.g. Qt < 0.3) we tend to use too large cabinets. Remember, there's no "right" here. You can use whatever you want, but be aware of the consequences of what you're doing. Too small cabs may mean no bass and too large cabs may produce a boom-box with un-precise bass performance (e.g. 2.5 clone).

Closed system:
Try a cabinet volume making Qtc = 0.7 and see what happens. In this case we reach 24 liters and this is not too far off. Try inserting 30 liters (change cell B11) and you find the response (purple curve) reaching a bit lower. What you also see from the graphs is that the closed box will make much less bass at 40 Hz compared to the vented system. If you're not a bass freak, you may prefer the short and dry bass coming from the closed box compared to the more voluminous bass from the ported system. I often recommend making the ported system and you can always stuff the vent with a sock if the bass becomes too boomy. If you ad a minor amount for e.g. dacron/acoustilus/MDM3 to the port you're having an aperiodic system and this may not be bad at all. Try it out!

Ported system:
The 18W drivers are mostly seen in 28-33 liter ported cabs and we have a nice (almost) flat response down to 40 Hz. Only a minor increase of ~1 dB in the 60-100 Hz range. No problem. We're ~5 dB down at 30 Hz and this is not a common view I can tell. This driver goes deep from a 33 liter vented cab. The price to pay for this is efficiency on the low side.

The port: Insert your port diameter in cell B22 and you can read the port length in cell B23 and you don't have to be nit-picking on this value. Anything from 13-14 cm length will do perfect. If you have a slightly conical port, use diameter at outlet (and not maximum diameter of a flared port).

Do not feel tempted to make a 50 liter ported system for this driver if you find you can get -3dB @ 30 Hz and think YES, this is what I want. There's a price to pay for this in terms of a boomy and un-precise bass performance. You may ask what the heck is the optimum size cab for this driver? Hmm.... read on.


SpeakerBoxDesigner:

Download Speaker-Box-Designer for 18W/8531-G00 here, and you will see this:


I don't have a password for this file, but we can view the formulas used for calculation. The port length is not corrected to fit reality and if you use this file, multiply port length by 0.7.

This is a more sophisticated program telling you optimum cabinets based on TS parametres. You need to add more data (cells with blue font) and we read a recommended closed box of 24 liters and a calc. ported box of 48 liters, making F3 = 31 Hz!

Now, we would never place the 18W driver in a 48 liter vented box. Or, it would be like making a modern 2.5-clone getting deep, deep bass although boomy, sloggish, one-note, etc. Not a good choice.

So, how do we really decide which volume we should use for a given driver? Only practice can tell. We need to try out the driver in various volumes, experiment with various Fb and we need to listen. We also need to listen to the midrange in case we making a 2-way with the 18W handling anything from the lower bass to 2.5-3 kHz. I've tried the 18W in 22 liter volume and I didn't like the midrange being flat with too much presence. The 18W as midrange in a 3-way system is another story, here 22 liters do really well.

What makes the whole thing even worse is that manufacturers' TS data may not always be right. Sometimes even very much wrong, so we have to measure TS data ourselves and see if this makes a more likely scenario. There's no international standard for measuring TS data, so the results will vary enormously depending on the voltage applied during measurements. Speakers are highly un-linear devices.

So, I use the manufacturers' data and I use my own data. Next I model the driver in LspCAD to see if this driver is really possible! In LspCAD you can fiddle with all driver parametres and make cross-calculation to see it what we measure makes sense and not least if what the manufacturer claim is really plausible. Here you can also explore more ported tunings like SBB4/BB4, QB3/SQB3 and SC4/S4. An SBB4 tuning will typically use a large box with a low tuning with a more shallow rool-off and extended at the low-end.
QB3 uses a smaller cab and a high tuning resulting in a flatter response and a steeper roll-off profile. SC4 uses a sligtly larger cabinet compared to the QB3 with a fairly low tuning, not too different from the SBB4 tuning.

Here's the LspCAD results based on SS data:

QB3, SBB4 and SC4 all prescribes boxes of 15-20 liter volume!

Here's what we usually do: 33 liter and a port tuning of 30-33 Hz. Confused? No wonder!
Considering the impact of damping material on virtual volume as shown below, I'd make a 28 liter cab for the 18W reaching a virtual volume of 32-34 liter when properly damped.


The impact of damping materials on box volume

Adding damping materials to a recent construction I started wondering if the dense green felt I often use really doesn't reduce box volume rather than increase box volume.
So, time for a small study:

Materials: test cab, 33.4 liter net volume, internal dimensions 460 x 280 x 260 mm (volume of two fillets for mounting front panels subtracted)
Driver: ScanSpeak 21W/8555-01, Fs = 17 Hz, Vas = 169.5 liter
Green felt, approx. 10 mm thickness.
Egg crate foam, 30 mm
Monacor MDM3, 33% polyester foam and 67% sheep's wool.

To cover internal walls with 0.5 m^2 of damping materials were used.

Results:

- As can been seen the green felt did not reduce volume, rather increased virtual volume by 6%.
- For egg crate foam and MDM3 we see an increase in virtual box volume of around 15%.

As always: Take into account the impact of damping matrials on your box volume.


Red = unit in free air, empty box (blue), green felt (green), egg crate foam (brown) and MDM3 (yellow).