Woofer efficiency revisited

Heya. I am taking some time to peek inside the driver efficiency and implications of that. While here and on AVS, there is lots of knowledgeable people, this topic is still not general knowledge. Firstly, high efficiency means low Qts, which is big no-no for oldschool people and hi-fi people. Then there are other compromises to be made, and then, there are details of speaker manufacturers approach to this, that I would like to know.

This graph below is just a starter, work in progress, and will show 1Watt SPL output (kind of efficiency in decibels)of some known drivers, which I will add. Just from seeing the outcome, a lot of implications were understood immediately. Compromise is being made by setting the reference box volume and a port. I will try to add closed box comparison of the same driver to see, what that one does to the system efficiency. Looking at ported graphs, it looks like the port doesn't do a thing.

https://ibb.co/DfXXnG3

I wonder why high end driver manufacturers decide to use stiffer suspension, to lose on both sensitivity and efficiency, especially in the upper range of bass. Any ideas?
Yes, high end high excursion drivers with narrow magnetic gap prolly need to solve rocking modes, but is that it, or there is more to it?
 
Looking at large signal measurements of PA drivers I have obtained, "there cannot be any discussion" about linearity in this context. I mean, according to the data, linearity was not the goal of the stiff suspension at all. High efficiency is good conversion ratio between real input power and SPL. In the graph, it already shows preliminary efficiency curves. The B&C 18DS115 for example seems to be quite efficient in bottom part of the bass region, while it lacks in the upper bass compared to oldschool model.
 
I wonder why high end driver manufacturers decide to use stiffer suspension
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Historically, high end, low end, it doesn't matter: stiffer suspension = lower Vas spec = smaller box for a given Fs, Qts', a major goal in ever shrinking rooms, rising costs, lower peak SPL requirements; or at the other end, more Qts' flexibility and/or flatter response to a lower Fb/Fc just as your chart implies.
 
I mean, according to the data, linearity was not the goal of the stiff suspension at all.
The stiff suspension raises the free-air resonance frequency of the driver. The efficiency of a driver is proportional to the cube of the resonance frequency (i.e., Fs^3), while it is inversely proportional to the stiffness of the suspension. However, if we raise Fs, we reduce the ability to obtain an extended low-frequency response. To get high efficiency and an extended flat bass response, we need to have a driver with a low Fs and place it in a large enclosure that suits its Thiele-Small parameters.
The B&C 18DS115 for example seems to be quite efficient in bottom part of the bass region, while it lacks in the upper bass compared to oldschool model.
I'm not clear as to what you have plotted. In the end, it is possible to simulate the low-frequency SPL response of a driver in a chosen enclosure for an applied 2.83 volt driving signal. Comparing the output level above the –3dB point of different designs will clearly show you any differences in efficiency. The fact that there will usually be changes in the low-frequency cut-off point simply illustrates the bandwidth–efficiency tradeoff that is inherent in any driver design.

Have you studied the papers by Thiele, Small, Keele, etc, which cover many of the aspects of driver design and selection for particular response shapes?
 
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stiffer suspension = lower Vas spec = smaller box for a given Fs, Qts'; and/or flatter response to a lower Fb/Fc just as your chart implies.
I cannot agree on that. Lower Vas does not allow you to have smaller box with my approach. It gets very close to irrelevant parameter. Or at least, big Vas not counterproductive.
Yes, for flatter response in small box, but that is not what we need anymore, do we? We just need displacement, power, efficiency. The frequency response can be shaped afterwards with little to no consequences probably.

Witwald: Why would you say that low driver Qts is a "big no-no"? Can you elaborate a bit?
Because many people say so. It is not me saying that. Low Qts usually means low bass output with conventional handling/tuning. I hope, that for some people step behind, I would also like to debunk this for them, politely, but it was not main reason of my post.
Low Qts mark is possible the one where you need to additionaly shape the frequency response for it to be flat/desired.

The efficiency of a driver is proportional to the cube of the resonance frequency (i.e., Fs^3), while it is inversely proportional to the stiffness of the suspension. However, if we raise Fs, we reduce the ability to obtain an extended low-frequency response. To get high efficiency and an extended flat bass response, we need to have a driver with a low Fs and place it in a large enclosure that suits its Thiele-Small parameters.
Not sure if I understood the written text here, but to me it seems like NO. If we benchmark it on close to ad absurdum case, nearly infinitely stiif suspension will certainly not give you more efficiency. That is contrary to my findings. But it depends on where we look and how we even determine efficiency (in frequency response). Yes, placing low resonance driver in big box will indeed raise the efficiency. No denial here. Suiting TS parameters, that is THE can of worms. I would say that these days, there is no such thing without all kinds of (even bad) consequences. This needs to be very specific case by case talk I think.
I'm not clear as to what you have plotted
1Watt of real power response.
In the end, it is possible to simulate the low-frequency SPL response of a driver in a chosen enclosure for an applied 2.83 volt driving signal.
That was absolutely not my point and goal, and that´s what I call oldschool in this context. Why would we want to do that, if we are after efficiency, SPL output and such? It is very bad/incomplete approach for high end SPL goals.
Comparing the output level above the –3dB point of different designs will clearly show you any differences in efficiency. The fact that there will usually be changes in the low-frequency cut-off point simply illustrates the bandwidth–efficiency tradeoff that is inherent in any driver design.
That is not what I do. I am trying to ***** the driver in the whole working range (subwoofer), and implications of speaker efficiency on that. The thing is, that at peak SPL efficiency in my graphs, where the speaker resonance lays, there is not much power going into the speaker. For that reason, it gets close to irrelevant. One does not need to care in high power applications, if the driver is efficient or not, if 50Watts are flowing there. But down at -3, -6, -9dB marks huge amounts of power flow in the speaker due to the much lower impedance and phase deviation, causing lots of strain, heating and nonlinearities. That is the part of the graph, that one really should pay attention to.
As long as the driver has power dissipation capabilities and cone displacement available, not much is determining frequency cutoff. We can be almost freed from that now.
Have you studied the papers by Thiele, Small, Keele, etc, which cover many of the aspects of driver design and selection for particular response shapes?
Not sure what exactly what you are referencing here. Yes, I have. Paid AES.org membership, read and downloaded metric F ton of materials, also read some Powersoft, H&K, JBL and other white papers and documents. Some writings of Vance Dickason, Tom Danley, In touch with B&C speakers about stuff, following good explorers of sound like Ricci and such.
 
I will try to add closed box comparison of the same driver to see, what that one does to the system efficiency. Looking at ported graphs, it looks like the port doesn't do a thing.
I am unsure of what you mean when you say that "it looks like the port doesn't do a thing". In fact, in an appropriately designed vented-box loudspeaker, the port supplements the output of the loudspeaker at the port resonance frequency. In addition, this electrodynamic system results in very low driver displacement at the port resonance frequency. Without the port, the driver in a sealed enclosure of the same size will produce a bass frequency response function that begins to roll off much earlier. So how does the port not achieve anything?

Of course, the efficiency of an individual driver is independent of the enclosure type, be it a ported, passive radiator, or sealed enclosure.
 
The B&C 18DS115 for example seems to be quite efficient in bottom part of the bass region, while it lacks in the upper bass compared to oldschool model.
The information provided by the manufacturer of the 18DS115 seems to provide a somewhat different outlook.

The frequency response curve for the B&C Speakers 18DS115 is shown below (from their web page). According to the manufacturer, this driver has a 2.83-volt sensitivity of 98dB, but the graph below seems to indicate it is closer to 93dB, assuming that the curve below is meant to represent the 2.83-volt response measured at 1 metre. The B&C ported enclosure simulations indicate a sensitivity of 94dB, which seems to match up with the curve presented below.
1650235545435.png

With a low Qts value of 0.20 and an Fs of 30Hz, this driver will only produce a maximally flat frequency response when mounted in a quite compact enclosure of less than 100litres. If a non-maximally-flat tuning is chosen instead, in a 100litre enclosure with Fb of 40Hz, we obtain a much more extended low-frequency response, which is –3dB at 41Hz. The efficiency of the driver is identical in both these systems. The B&C simulation is shown below. This example shows that this particular driver can produce quite extended bass response, which is quite flat in the region 40Hz and 135Hz, with around 93dB sensitivity. That's excellent small-signal performance, and with an Xvar of ±14mm, it's capable of quite high levels of low-frequency output in that frequency range.
1650236715040.png

From the above data, it appears that the B&C 18DS115 driver is capable of plenty of bass output using conventional tuning parameters, even though it has a low Qts of 0.20.
 
I think the OP is referring to actual power delivered to the voicecoil. Around resonance, where the impedance is high the actual power delivered is very low. The 18DS115 for instance has a free air impedance above 20 ohms below 50Hz, peaking at 100 ohms at its resonant frequency. 2.83V RMS in at resonance is only 80mW of input power. Now at resonance (30Hz) the driver is generating 73dB at 1M / 2.83V, half space. This is 84dB/W/M.

This is the idea behind the IPAL system by powersoft. The B&C IPAL drivers are even more efficient than the 18DS115 when looking at true power in Vs acoustic power out, delivering over 92dB with 1W in at Fs. They have higher true efficiency at 40Hz than they do at 200Hz. They are very low Qts drivers too.
 
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I cannot agree on that. Lower Vas does not allow you to have smaller box with my approach. It gets very close to irrelevant parameter. Or at least, big Vas not counterproductive. Yes, for flatter response in small box, but that is not what we need anymore, do we?
But don't we want the low-frequency response to be relatively flat and extended? Then, if the enclosure size is bigger than we can live with, something has to be traded away. That's where that Vas parameter becomes very important, as it directly allows us to compute the actual physical enclosure size needed for a selected tuning, be it of a sealed, ported or passive radiator enclosure type. So to say that Vas is very close to being an irrelevant parameter seems somewhat inaccurate.
We just need displacement, power, efficiency.
The need for displacement in low-frequency sound reproduction is a given. And we need good levels of power handling to enable reasonable low-frequency sound pressure levels to be attained. The efficiency is largely to do with the moving mass of the system, and the power of the magnet motor, in combination with the diaphragm size. The Thiele-Small parameters allow one o easily choose from families of low-frequency alignments to give the low-frequency response shape. The efficiency of the driver is simply embodied in the combination of moving mass, suspension stiffness and magnet motor strength. Knowing the driver Qts, Vas and Fs allows us to determine the low-frequency alignment, and by also knowing Qes we can compute the driver's efficiency. All of that has been made available to us in the available loudspeaker design literature, which is based on the measurement and use of Thiele–Small driver parameters.
The frequency response can be shaped afterwards with little to no consequences probably.
I'm not sure I understand what you're getting at. And how is it proposed to do that? Doesn't one need the driver Thiele–Small parameters to be able to choose a response shape for the low-frequency alignment?
Low Qts mark is possible the one where you need to additionaly shape the frequency response for it to be flat/desired.
Irrespective of the Qts value, it is necessary to choose the box size and tuning parameters appropriately in order to get a chosen low-frequency alignment shape. That's been amply and extensively demonstrated by Thiele back in the 1960s, and Small in the 1970s, and covered by many others such as Bullock, Keele, Newman, and Benson.
Not sure if I understood the written text here, but to me it seems like NO. If we benchmark it on close to ad absurdum case, nearly infinitely stiif suspension will certainly not give you more efficiency.
To take the above example a trifle further, the efficiency of that hypothetical driver will be high, but unfortunately, it won't be able to reproduce adequate sound pressure levels in the audible frequency range. For drivers to operate effectively in the audio frequency range, an appropriate choice must be made concerning their moving mass, suspension stiffness, and magnet motor strength.
Yes, placing low resonance driver in big box will indeed raise the efficiency.
I am not sure that is correct. The driver, as a transducer, has an acoustic efficiency in and of itself, which does not depend on the enclosure. The choice of enclosure affects its frequency response.
That was absolutely not my point and goal, and that´s what I call oldschool in this context. Why would we want to do that, if we are after efficiency, SPL output and such? It is very bad/incomplete approach for high end SPL goals.
Is it really? Why would that be so? If we are after high efficiency for low-frequency drivers (woofers), a strong magnet motor (low Qes), a relatively high Fs., and a large value of Vas are needed. The "old school" Thiele–Small equation for efficiency indicates this quite clearly. The "old school" Thiele–Small parameters reveal that those physical attributes are key. If we also want good low-frequency extension, then those same "old school" Thiele–Small theories reveal that we need drivers with a relatively low Fs. Hence, we have to make a trade-off: lower efficiency for more bass extension. Of course, if we build a large 18" driver, with a large magnet motor, we can get good low-frequency extension as well as good efficiency.
The thing is, that at peak SPL efficiency in my graphs, where the speaker resonance lays, there is not much power going into the speaker. For that reason, it gets close to irrelevant.
Yes, at the driver/system resonance there is not much power going into the driver. But keep in mind that a driver is not simply used just at its resonance frequency. We usually expect a low-frequency driver to produce usable output at frequencies above its free air resonance frequency, don't we? So it's not clear to me what you are alluding to.
One does not need to care in high power applications, if the driver is efficient or not, if 50Watts are flowing there. But down at -3, -6, -9dB marks huge amounts of power flow in the speaker due to the much lower impedance and phase deviation, causing lots of strain, heating and nonlinearities. That is the part of the graph, that one really should pay attention to.
All of that type of thing is related to the power handling of the system. There is power-limited SPL, and there is Xmax-limited SPL. How much power is present at low frequencies depends on the content of the music. That's where the design of the magnet motor becomes very important. In general, if I recall correctly, a loudspeaker system is limited by Xmax at low frequencies, while it is power limited at higher frequencies. Again, this has all been covered by the "old school" Thiele–Small analysis theory.
As long as the driver has power dissipation capabilities and cone displacement available, not much is determining frequency cutoff. We can be almost freed from that now.
To some degree that's true. But even an 18" driver will run out of linear cone excursion when trying to reproduce 15Hz at high sound pressure levels.
Not sure what exactly what you are referencing here. Yes, I have. Paid AES.org membership, read and downloaded metric F ton of materials, also read some Powersoft, H&K, JBL and other white papers and documents. Some writings of Vance Dickason, Tom Danley, In touch with B&C speakers about stuff, following good explorers of sound like Ricci and such.
That's good. You seem to be quite conversant with many of the available published works.
 
I am unsure of what you mean when you say that "it looks like the port doesn't do a thing". In fact, in an appropriately designed vented-box loudspeaker, the port supplements the output of the loudspeaker at the port resonance frequency. In addition, this electrodynamic system results in very low driver displacement at the port resonance frequency. Without the port, the driver in a sealed enclosure of the same size will produce a bass frequency response function that begins to roll off much earlier. So how does the port not achieve anything?

Of course, the efficiency of an individual driver is independent of the enclosure type, be it a ported, passive radiator, or sealed enclosure.
Ah, yes. No. I am well aware about port function. That was not what I meant. I was looking at my efficiency curves. I saw a mild hump located around the speaker(system) resonant frequency, but in the graph, there is no efficiency boost from the port (tuned at 35Hz) visible.
Even more surprisingly, after finishing same closed box efficiency curve, it shows that ported box raises the efficiency across the whole band, and mostly at resonant frequency of the system. Anyways, it seems my points are quite misunderstood, I might go step back to explain what´s up.

The information provided by the manufacturer of the 18DS115 seems to provide a somewhat different outlook.
Yeah, that is sensitivity, not efficiency. These are whole different worlds, really. The low sensitivity of Low Qts drivers is caused by high impedance and some other stuff. Simply said, the speaker does not eat as much power there in the bass region, as high Qts drivers. Once we equalize them for real power input, and not voltage, the low Q driver (with usually stronger motor) will do more. And that is what my graphs are about.

With a low Qts value of 0.20 and an Fs of 30Hz, this driver will only produce a maximally flat frequency response when mounted in a quite compact enclosure of less than 100litres.
Yes. But we do not require flat frequency response from the driver anymore. Yes it is nice possibility tu put it in compact box, that´s what I am doing amongst other things, but it is not a requirement. You can put it in about the same large box as oldschool speakers. You will just need to straighten out the frequency response. If the displacement volume, cone area and power are there, there is no logical reason to not do it. People counter with "but frequency response is wrong". And that´s what I will kind of debunk here.

From the above data, it appears that the B&C 18DS115 driver is capable of plenty of bass output using conventional tuning parameters, even though it has a low Qts of 0.20.
That would be partial understatement. This driver is one of these very capable. It´s just the frequency response does not show us the whole picture.

Now the step-back explanation. As you well know, the speaker produces sound pressure level by moving a cone, mounted on the coil. The more it moves (all else being equal), the more sound pressure. For coil to move, it needs a mechanical force F[Newtons] to propel it. The more the force, the further the coil and cone are pushed. And so the more the force, the more sound pressure. Speaker force can be described as conversion ratio, Amount of Newtons per Watt of input. You want most Newtons per Watt, as you can only supply the speaker so many Watts.
For example, 18DS115 and 18PS100.
F[N] = B(magnetic flux) * I(current) * wire length.
We have Bl in the TS parameters, and we need current for 1Watt of power. 18DS115 has 5 Ohm coil, and so 0,448A corresponds to 1VA(W).
Bl on 18DS115 = 39; I = 0,448.
And so for F = Bl * I, we have 17,47 Newtons per Watt with 18DS115.
With 18PS100, we arrive at 9,785 Newtons per watt.

And so by common sense, we have to see that at no point (if all else was equal), the 18PS100 could give you more output (or bass). It is simply not possible by following basic physics. We saw it is possible, because the 18PS100 has weaker suspension, and so around resonance frequency, it pushes through. Not so in the bass region thoug, which is according to the math.

That´s what I am working with.

cowanaudio....
Yes, that is exactly what I mean.
 
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But don't we want the low-frequency response to be relatively flat and extended?
There is Want, and there is Need. We do want that, but the way to get there is complex. Not that easy as frequency response anymore. More work, math and thinking has to be involved. For response extension, we need stronger speaker motors, and the cause is, that it stops being flat. We have to deal with that afterwards. As explained before, I am attempting to show, that we do not reach our extreme goals through flat frequency response based on voltage input.

The efficiency is largely to do with the moving mass of the system, and the power of the magnet motor, in combination with the diaphragm size. The Thiele-Small parameters allow one o easily choose from families of low-frequency alignments to give the low-frequency response shape. The efficiency of the driver is simply embodied in the combination of moving mass, suspension stiffness and magnet motor strength. Knowing the driver Qts, Vas and Fs allows us to determine the low-frequency alignment
Yup. Not applicable anymore for extreme goals. Motor strength is very related to Qes. The stronger the motor (all else being equal), the more output. If the graph shows you otherwise, it is not right. That leads us to the alignment. Alignment is done to get flat frequency response. We do not need that anymore. We can flatten it later, if we get some goodies for that. And indeed, we do.
I'm not sure I understand what you're getting at. And how is it proposed to do that? Doesn't one need the driver Thiele–Small parameters to be able to choose a response shape for the low-frequency alignment?
Great question! So we are getting there! Not anymore. Response shape is not alpha & omega anymore. We can shape the shape after more important design choices now. No alignment. Or at least, very different one. We want more output for given input, and then we shape it afterwads for ears to be happy.

Irrespective of the Qts value, it is necessary to choose the box size and tuning parameters appropriately in order to get a chosen low-frequency alignment shape. That's been amply and extensively demonstrated by Thiele back in the 1960s, and Small in the 1970s, and covered by many others such as Bullock, Keele, Newman, and Benson.
That was given the possibilities of their time. What is appropriate and necessary, changed drastically. I don´t deny their work. it´s just the handling and our approach that must change.
I am not sure that is correct. The driver, as a transducer, has an acoustic efficiency in and of itself, which does not depend on the enclosure. The choice of enclosure affects its frequency response.
And efficiency. But as with your resonance claim, doing more math on my side, it seems that you can be righ within the certain case, pass band and so on. It is not absolute. We would need to dig more precisely into some case, and then we would have an outcome for that case.

Is it really? Why would that be so? If we are after high efficiency for low-frequency drivers (woofers), a strong magnet motor (low Qes), a relatively high Fs., and a large value of Vas are needed. The "old school" Thiele–Small equation for efficiency indicates this quite clearly. The "old school" Thiele–Small parameters reveal that those physical attributes are key. If we also want good low-frequency extension, then those same "old school" Thiele–Small theories reveal that we need drivers with a relatively low Fs. Hence, we have to make a trade-off: lower efficiency for more bass extension. Of course, if we build a large 18" driver, with a large magnet motor, we can get good low-frequency extension as well as good efficiency.
Yes, but see the contradiction. Strong motor gives you low Qes. Low Qes gives you great damping. that gives you less extension and less bass.
Yet strong motor obviously is here to give us more, not less. And that is the exact point I am arguing. If the frequency response of the low Qes driver with strong motor gives you less output or bass, something is not right. And what is not right is the frequency response, alluding less output. No. Frequency response here is wrong tool for the assesment.

Yes, at the driver/system resonance there is not much power going into the driver. But keep in mind that a driver is not simply used just at its resonance frequency. We usually expect a low-frequency driver to produce usable output at frequencies above its free air resonance frequency, don't we? So it's not clear to me what you are alluding to.
According to my graph, showing 18PS100 winning around resonance, while 18DS115 winning in the bass region, I put out that claim that higher efficiency of 18PS100 in that resonance range is not important. It is not important if there is 20Watts going in there, compared to 40Watts going into 18DS115. What matters is, that at 35Hz, there goes 1000Watts into the poor thing where 18DS115 with massive coils will eat there only ~500Watts. Sorry for the first 30-32Hz mark jaggie, as I was doing different math on these speakers there. And what´s more, if we undertune such speaker, we get higher impedance and more cone movement in the original frequency. That usually means more cooling, way less power compression, more efficiency under working power.

There is power-limited SPL, and there is Xmax-limited SPL. How much power is present at low frequencies depends on the content of the music. That's where the design of the magnet motor becomes very important. In general, if I recall correctly, a loudspeaker system is limited by Xmax at low frequencies, while it is power limited at higher frequencies. Again, this has all been covered by the "old school" Thiele–Small analysis theory.
With modern speakers and different approach, it can happen that this will sway purely to one side. my RCF LF21N551 design is purely power limited across the whole band (before subsonic filter kicks in). How much power is present in low frequencies also depends on the system design. I am now designing my systems around its resonant frequency (impedance peak), and so way less power goes in there. It usually means significantly lower tuning and cutting at or above tuning. That usually means more cone displacement. But modern speakers with displacement capabilities between 15-20mm can handle that. The "nonexistent" power compression I enjoy easily gains me 1-2dB back, which I lose by lower tuning and system management.

Anyways... :-D

Yup. Seen all his vids, mostly live streamed, where we discussed details. Great guy, lots of deep knowledge for sales rep. He must have spent some months under wings of their engineers.
 
Simple points that bear repeating.
Constant voltage response is much less important than it used to be.
Sensitivity is not efficiency.
At higher output levels, such as subs usually get used at, efficiency becomes affected by things like: Thermal buildup, eddy currents and non linearities in the suspension and BL. At some point it is possible that a driver with lower small signal efficiency than an alternative driver unit, but greater: Power handling, linear excursion and effective shorting measures, may have higher effective efficiency once the drive level is increased.

One major reason that suspensions are often very tight on powerful sub drivers is simply for durability, centering of the coil in the gap and control of overshoot. Modern high power subs can often have 250-500g moving mass. Some are over 1kg. On paper for the most efficiency the weight of the moving parts would be as low as possible and the suspension as soft as possible. Ideally. This doesn't happen because modern drivers require power handling, long excursion and some safety margin against bad things appearing at the input jacks. The mass is required for the purposes of strength, durability, etc. Imagine that you have a very soft suspension subwoofer with 400g worth of moving parts that sits on a warehouse shelf for >year with gravity acting on it.
 
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I don't understand what you mean by that. Can you please elaborate a little?
Voltage response does not correlate directly with either efficiency nor output capabilities. That way it cannot be taken as a reference data piece to make a decision about speaker output.

@Ricci: I am aware. I just wonder if it really is IT. It seems that there is some variance between models on purpose. On the other hand, it seems that the DS line gets the same spider frim 15" to 21". The DS line would benefit from 2-3mm longer throw tremendously. I am little cinfused with their LSI data, with excursions reaching over 20mm. Not only that past 15mm the woofer sounds bad, but there is hella lot more thermal compression, as the spider is limiting everything.
 
Voltage response does not correlate directly with either efficiency nor output capabilities. That way it cannot be taken as a reference data piece to make a decision about speaker output.
Can you expand on that a little? For example, if I run a 2.83V frequency sweep of a driver plus enclosure combination, it produces a certain SPL response. Of course, as you allude, a 4-ohm driver will draw more power than an 8-ohm driver, speaking in nominal terms. Hence, although the drivers are equally sensitive the one with the higher impedance is more efficient, is it not? As we go towards higher frequencies, there will generally be a flattening off in the response (before the cone breakup modes), and the height of that plateau in dB_SPL will be strongly related to the sensitivity of the loudspeaker plus enclosure combination, won't it?

For a driver with a highish BL, we usually find that it has a low Qes, leading to a low Qts, and a highly damped natural low-frequency response. Would that be a reasonably accurate observation?

On another tack, we can equalize the low-frequency response of the enclosure, using a high-power professional amplifier's voltage swing output capability to boost the bass response. For example, we may need to make up a 20dB shortfall in output at, say, 40Hz when using a high-BL driver. How much power is actually needed depends of course on the impedance of the system, and how much (reasonably) linear output is available will depend on the excursion limits of the driver. This is simply a filter-assisted low-frequency alignment, and is no doubt quite amenable to simulation.

For a woofer, all of the above seems to rely on the voltage response of the driver, and its maximum linear excursion capability across the operating frequency range. I don't think that the efficiency of a driver, nor its sensitivity, ever implied the available output capabilities of the low-frequency enclosure system, except possibly in an entirely empirical sort of way. Hence, why would anyone use these values as reference data to make a decision about speaker output capability?
 
Sorry to come in here as I have no meaningful experience into this subject , but I'm highly interested in finding the best speakers or grasp the meaningful theory of useful speakers for a small germanium amplifier that's barely able to drive 6 watts into 8 ohms with about 0.2 thd on resistive loads, so very ,very modest vintage setup, but for a while I'm gonna watch you and derive the best of this theoretical knowledge 🙂 .I don't care how the speakers would be built but I want the best experience out of it with only 6watts available into 8 ohms.I can't for the moment translate your language into something meaningful for my ears but I promis I'll be listening to you and google every term until I get it.
 
I went for Seas W26FX002. I haven't listened to them yet, but they sure do look nice. When I tap them, they have a low, doof! that is absolutely amazing. I doubt and 15"-18" PA woofer can sound that good and relaxed in the bass. But we will see.