Volume displacement - it's (almost) all about moving air

Oh no, not another spec for the marketeers to play fast and loose with...

Bear with us, there is some logic to unveiling a 'new' spec. If you've ever had the pleasure of standing next to a large bass rig or been pinned against a club subwoofer by an amicable binge drinker you may have noticed your clothes moving as if in a breeze or felt your innards being massaged by an invisible force. This invisible force is caused by changes in air pressure created by the movement of the woofer(s), and the more air each woofer can move, the greater the potential for air pressure changes (and therefore the greater the potential SPL - Sound Pressure Level).

So where are these numbers coming from?

Most bassists will be familiar with the importance of cone area if you want big loud lows - but that's only half the picture. However, let's concentrate on that half of the picture for now. Firstly there are often some basic arithmetic issues when comparing cone area - for instance some claim that a 4x10=40 whilst a 2x15=30 so the 4x10 is 10 better. Wrong. Cone area is proportional to diameter squared so 4x10x10=400 whilst 2x15x15=450 so the 2x15 is 50 better. More accurate but still not entirely precise. Why not? Because speaker diameter is merely nominal diameter - basically the approximate size of the frame / baffle hole. The actual size of the cone is less because you have to subtract the frame width and some of the cone surround (the corrugated or rolled fabric bit around the edge of the cone). For one of our 15" woofers the actual cone diameter is 13" whilst for the other it's 13.2". For our 12" woofers it's 10.3" and 10.4". We don't currently use any 10"s but one of the best out there has an actual diameter of 8.3". For nominally 8"s it's about 6.5" whilst for 6" woofers it's about 5". So if we do those sums again we see that  two 15"s have equal area to five 10"s, whilst two 12"s matches three 10"s.

The second and oft forgotten part of the picture

When we're talking about moving air we're talking in three dimensions - it is a volume of air we are moving, not simply a flat sheet of air. When we talk about cone area we only have two dimensions so we need another parameter to get a volume of air. That parameter is clean cone excursion, often called Xmax. There are three ways that Xmax is determined - two methods are arithmetic and based on measuring the actual dimensions of the voice coil and the magnetic gap and one is based on measuring the maximum cone excursion in usage where THD reaches 10%. The latter method is the most accurate whilst the simple arithmetic method is overly conservative for most drivers and the more complex arithmetic method is slightly over-optimistic. To get an truly accurate comparison you should check that Xmax has been determined the same way for all cabs - but either the measurement or complex arithmetic method will give you sufficiently similar figures to be of real value.

This is all starting to seem more trouble than it's worth

Honestly, it isn't! Because once your kindly cab manufacturer has done their sums they can state an absolute figure for Volume displacement (aka Vd) and in fact they don't need to do the complicated sums as their loudspeaker supplier will do that for them (just as they provide cab builders with the all important for marketing but almost completely useless in the real world power rating (more accurately the thermal power handling). And as we play bass and thus need relatively large quantities of bottom, the usual limiting factor in how loud a gig a given cab can play is its Volume displacement. If you've ever tried to compare cabs based on the usual power rating you'll know that tells you next to nothing about how loud they can go, and likewise if you've just looked at 2x12" cabs then some will be great, some will be ok and some will be pretty awful, it totally depends on the specific speakers and how well the cab is designed - and you might miss out on checking out a 4x10", 3x10", 1x15", etc that could be perfect for you.

One more part to the puzzle

A ported cab uses a tuned resonator to help move more air in the lowest frequencies. A correctly tuned port can almost double the Vd. A port that is tuned too high or a cab that is oversized will sound boomy and slow but will more than double Vd but not in a good way. A lower tuned port or undersized cab will still increase Vd substantially but not by as much. Why are we mentioning this? Because a sealed cab has no port assistance and therefore is at a substantial disadvantage when it comes to moving air - which is why almost all sealed cabs are big - 8x10"s, 6x10"s and 2x15"s - they have the Vd to move plenty of air with their cones alone - no 'turbocharging' required from a tuned port.

And now to the Barefaced figures!

These figures are calculated from both of the more accurate Xmax methods, from the official cone area figures, and should help with comparisons between the model range. To help with other comparisons the most popular premium neo 10" and 12" woofers have a Vd of 147cc and 255cc respectively (by the measurement method) whilst a typical ferrite 10" will have a Vd of ~100cc and typical ferrite 12"s vary between about 150cc and 240cc. A couple of notable manufacturers of nicely designed cabs which broke quite a few boundaries over the last decade or so used high excursion ferrite magnet 10"s which exhibited more than twice as much Vd as from a typical ferrite 10" - hence the huge lows they could produce.

By the measurement method:

Midget = 330cc
Big Baby = 496cc
Compact = 505cc
Super Twelve = 660cc
Big Twin = 992cc
Super Fifteen = 1010cc
Dubster = 1692cc

By the complex arithmetic method:

Midget = 340cc
Big Baby = 566cc
Compact = 566cc
Super Twelve = 680cc
Big Twin = 1132cc
Super Fifteen = 1132cc
Dubster = 1830cc

Complex arithmetic method is: Sd x (((Hc-Hg)/2)+(Hg/4)) = Vd

where Sd equals cone area (Pi x D^2)/4, Hc equals voice coil winding length (or height but definitely not diameter) and Hg equals magnetic gap height (or length or depth depending on your perspective). Note that it's purely a bizarre coincidence that the complex arithmetic method gives the same Vd for both our low tuned 12" and our higher tuned 15"!

So why does it say "it's (almost) all about moving air"?

Because although we play bass which requires sufficient bottom to sound fat and like a bass, not a guitar, much of the tone of a bass is actually in the midrange. If your cab cannot produce enough midrange to punch your tone through the mix then all the air moving in the world won't do you any good. Fortunately the vast majority of bass cabs have enough continuous thermal power handling and broadband midrange sensitivity for their midrange output to keep up with their excursion limited output (i.e. Volume displacement limited output) so Vd remains the limiting factor. An exception would be if you tried to use a Baby Sub for a rock gig - plenty of bottom for a reasonably loud gig but because it is solely designed to be used with a Big Baby stacked on top (which has an additional midrange speaker) then it wouldn't have the midrange output to keep up. But that's an unusual cab designed for a very specific purpose! (It's fine as a reggae standalone though). So although it's not ALL about moving air, it's close enough to the truth.

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