the volume of air moved by the cone woofer per second vs. by the TRW fan per second.

B.2. Air Volume per Second

       To make this conversion, we first have to pick some bass frequency being reproduced. So let's start with 60 Hz, which is certainly at the high end of the spectral range any subwoofer might be expected to cover. At 60 Hz, the cone woofer makes 60 cyclic excursions per second, so its total volume of air pushed per second is 60 times the amount of air it pushes in each excursion. The TRW fan makes about 12 revolutions per second, and it has 5 blades (not just the one blade we considered above). So its total volume of air pushed per second is 12 times 5 = 60 times the amount of air that one of its blades pushes in each revolution.
       Thus, at 60 Hz, the two types of woofers are equivalent again, only this time we are comparing apples to apples, and they are equivalent in terms of air volume pushed per second (as well as still being equivalent in terms of the above apples to oranges comparison, the volume of air pushed by the cone woofer per excursion vs. by one of the TRW fan blades per revolution).

B.2.a. Lower Bass Frequencies

       Then, let's see what happens when we cut the bass frequency in half, to 30 Hz. The TRW fan continues to rotate at a constant velocity, so its total bite of air volume per second remains constant, and is the same at 30 Hz as it was at 60 Hz. The radiation resistance of the TRW fan falls linearly with frequency, so its coupling to the room air is half as good at 30 Hz as it was at 60 Hz. Thus, the effective total bass output of the TRW is half as much as it was at 60 Hz (later we'll discuss how the phenomenon of room gain kicks in to make the TRW pretty flat to very low frequencies).
       The cone subwoofer driver, however, in contrast to the TRW fan, does not keep taking a constant number of bites per second as the bass frequency goes lower. Thanks to the fundamental conceptual fact that the cone driver has to multitask (as discussed above), the cone woofer has to track the frequency of the bass signal, so it only makes half as many cyclic excursions per second at 30 Hz as it did at 60 Hz. So this factor already cuts the cone subwoofer driver's output per second in half at 30 Hz, compared to its output at 60 Hz, and compared to the TRW's output at 30 Hz. Then, to make matters worse for the cone subwoofer driver, its radiation resistance falls as the square of frequency (rather than linearly with frequency, as the TRW fan does). Thus the coupling of the cone subwoofer driver to the room air falls by a factor of 4, when the bass frequency goes down by half. So now the bass output of the cone subwoofer driver has fallen by a factor of 8 (2 times 4) at half the frequency.
       Now, the cone subwoofer driver can make up some of this lost ground, if it can increase its excursion dramatically. In cone drivers, as discussed above, the excursion does tend to increase as the bass frequency goes lower. The cone excursion tends to increase by about 4 times (oversimplifying here), for each halving of frequency. Thus, if the cone subwoofer driver were capable of making this much larger (4 times) excursion, it would recapture 4 out of the 8 times poorer output we just saw it suffer. This would mean that the cone subwoofer driver would net out at 2 times poorer output (half the output) at half the frequency, 30 Hz instead of 60 Hz, and that would again make the cone subwoofer driver equivalent to the TRW subwoofer. But can the cone subwoofer driver make this 4 times larger excursion? If its cone excursion was 1 inch at 60 Hz, then it would have to be able to make a 4 inch excursion at 30 Hz, just to stay equivalent to the TRW subwoofer. Very few cone drivers (if any) can make a 4 inch excursion.
       Of course, we could cut the bass volume level, so that the cone subwoofer driver was making say only a 1/4 inch excursion at 60 Hz, and thus would be making merely a 1 inch excursion at 30 Hz, which it could surely manage. But then the cone subwoofer driver would still have to make a 4 inch excursion at 15 Hz, just to keep up with the TRW subwoofer at 15 Hz. You see the problem. At some low bass frequency the conventional subwoofer cone driver is simply going to abruptly run out of excursion capability, regardless of how far we reduce the bass volume. And at this low bass frequency, the TRW will charge ahead of the conventional cone subwoofer, for this bass frequency and for all lower bass frequencies.
       The TRW subwoofer, in complete contrast and opposition to the conventional cone subwoofer driver, can happily go lower and lower and lower in bass frequency (and at very high bass volume levels), without strain or effort, and without being constrained or curtailed by any excursion limits. Indeed, the TRW subwoofer can effortlessly play all the way down to (and including) zero Hz, i.e. DC.
       Furthermore, since the TRW can happily and effortlessly play lower and lower and lower in frequency, there is no need to reduce its bass volume level to keep it within its excursion limits. Thus, we could easily play the TRW loudly by having its blade pitch set at a full 1 inch at 60 Hz, and keeping it there for all lower frequencies.
       Therefore, to be fair in comparing the two subwoofer technologies, we should re-state the above conditions of the starting point at 60 Hz. The TRW still has its blade pitch set at a full 1 inch, but we had to re-set the excursion of the cone subwoofer driver at 60 Hz to just 1/4 inch, so that it could still play 30 Hz within its 1 inch excursion capability. Thanks to the cone subwoofer driver's excursion curse, the penalty that it has to pay, for being able to extend its response, just down to 30 Hz from 60 Hz, is to cut its maximum loudness to 1/4 (for all frequencies) of what it had been, when it was equivalent to the TRW at 60 Hz. Thus, already at 60 Hz, the TRW in this re-set example can move 4 times more volume of air than the conventional cone subwoofer driver can, and the TRW would retain this 4 times advantage all the way down to 30 Hz. Then, somewhere below 30 Hz, when the conventional subwoofer driver finally, inevitably does run out of excursion capability, the TRW will charge even farther ahead of the conventional subwoofer, for this frequency and for all lower bass frequencies.

B.2.b. Alternative Starting Frequency

       Incidentally, we could alternatively have started the above comparison at a frequency other than 60 Hz. We chose 60 Hz because, at this frequency, the two subwoofer technologies are approximately equivalent, so this makes a conceptually useful starting point, with the two subwoofer technologies diverging somewhere below this frequency, as conventional subwoofer drivers start running afoul of their inherent limitations. For example, if we had used 30 Hz as a starting point for our comparison, then the TRW's performance would have been twice as good as the conventional subwoofer driver, right out of the starting gate, instead of being equivalent as it is at 60 Hz.
       Why is this? Because of the fundamental conceptual contrast between the two subwoofer technologies, wherein the conventional subwoofer driver has to multitask but the TRW does not, the conventional subwoofer driver has to track the bass signal it is modulating, so its excursion cycling has to slow down at lower frequencies. This means that, at 30 Hz, the conventional subwoofer driver can only make 30 excursion cycles per second. Meanwhile, since the TRW does not multitask, its fan (that is responsible for creating the volume airflow) does not slow down for lower frequencies, so at 30 Hz the TRW is still making 60 blade-revolutions per second (12 fan revolutions per second times 5 blades). Just as we did above, we are assuming here, for our starting point, that the cone subwoofer driver is making a 1 inch excursion, and that the TRW has its blade pitch set to the same 1 inch, and that the driven area of the 18 inch cone woofer per excursion is equivalent to the driven area of one of the TRW's fan blades per revolution as it sweeps its 19 inch diameter circle. Thus, the volume of air driven by the cone driver in one excursion is equivalent to the volume of air driven by one TRW fan blade in one revolution, just as it was above when we used 60 Hz as the starting point for our comparison. And of course the TRW fan still has the same 5 blades as it did above.
       Thus, the fact that the TRW fan has a 2 times superiority over the conventional subwoofer driver, when we use 30 Hz as the starting frequency for our comparison, is due entirely to one key factor, namely the fact that the TRW fan does not slow down its revolutions per second when playing lower bass frequencies, here 30 Hz instead of 60 Hz, whereas in contrast the conventional subwoofer driver does have to slow down its excursion cycling per second when playing lower bass frequencies, here 30 Hz instead of 60 Hz. And this key factor, this contrast, is in turn due to the fundamental conceptual contrast between the TRW subwoofer technology and conventional subwoofer technology, namely that the conventional subwoofer driver has to multitask whereas the TRW subwoofer does not.
       The conventional subwoofer driver has to also perform the second task of modulating the bass signal, so it has to slow down its excursion cycling in order to track and accurately modulate the bass signal that is now cycling more slowly (at 30 Hz instead of 60 Hz), and thus cannot optimally perform the task of blowing maximum air volume (it has to perform the second task of articulating a thank you speech, while attempting to blow out the candles, so it becomes less effective at blowing out the candles). In contrast and opposition, the TRW fan rotation has only the single task of blowing maximum air volume, so this fan rotation can continue at full speed, even while the bass signal cycling gets slower at lower bass frequencies. The TRW fan rotation can continue to be maximally effective, even at lower bass frequencies, since it does not have to worry about performing the distinct task of modulating the bass signal (this modulation is performed by a separate engine in the TRW, the motor that modulates blade pitch). The TRW fan rotation can concentrate on optimally performing its single task of blowing out the candles, without having to worry about slowing down to perform the distinct task of articulating a thank you speech.
       As you can readily appreciate, this last example, wherein the TRW is 2 times more effective when we use 30 Hz as the starting point for our comparison, naturally extends to yet lower frequencies as well. For example, if we were to use 15 Hz as the starting point for our comparison, the TRW's air volume would be 4 times larger than the conventional subwoofer cone driver (this assumes, on behalf of the conventional subwoofer, the unlikely scenario that its bass resonance frequency is below 15 Hz, so that it has flat frequency response to below 15 Hz).


B.2.c. Further Limitations of Conventional Subwoofers

       This last example, at 15 Hz, raises a further point. The above discussion does not even take into account a yet further limitation conventional subwoofers suffer in moving air at low frequencies, namely the frequency barrier due to their inherently reactive nature. Their bass frequency response hits a brick wall at their resonance frequency (usually 20 Hz or higher), and plummets below that frequency. In contrast, the TRW does not have any reactive nature at very low frequencies, so its frequency response stays substantially flat to indefinitely low frequencies, indeed down to and including DC. In other words, at (and below) whatever frequency a conventional subwoofer hits its reactive resonance, the TRW's bass quantity performance charges ahead of the conventional subwoofer in two distinct and huge ways. First, the conventional subwoofer has (or soon will) run out of excursion capability, so its volume for all bass, including very low frequencies, must be reduced. Second, the conventional subwoofer's bass output rolls off severely below its resonant frequency, which even further reduces its bass output for very low bass frequencies. Meanwhile, the TRW faces neither of these limitations. The TRW never faces any excursion limitation, so it can play arbitrarily low bass frequencies, and play them very loudly. And the TRW never faces any frequency response rolloff at very low frequencies, so it continues to put out strong, substantially flat bass response, to arbitrarily low bass frequencies.
       Incidentally, in conventional subwoofer designs that use vented enclosures, the cone driver excursion beneficially decreases at the frequency of vent resonance, when the vent beneficially loads the driver. But this benefit disappears at bass frequencies below the vent resonance frequency, where the vent unloads, and the cone driver's excursion increases dramatically. Program material actually contains frequencies well below the vent resonance frequency (as we'll discuss below), especially film soundtracks, which contain this very low frequency energy at very strong, loud levels, so excessive excursion and severe excursion limits are still a problem, even for vented conventional subwoofer systems.

B.3. Air Volume per Cycle

       We have just discussed the performance comparison, between the two subwoofer technologies, in terms of air volume moved per second. It is also instructive to look at the TRW's performance in terms of air volume moved per cycle of the bass signal. As the bass frequency being reproduced goes lower, the time period of each cycle gets longer, with half the frequency (e.g. 15 Hz instead of 30 Hz) taking twice as long a time period. Since the TRW's fan rotation keeps going at the same speed, regardless of bass signal frequency, this means that the TRW's fan makes twice as many revolutions per signal cycle, when the bass signal goes to half the frequency, four times as many revolutions when the bass signal goes to one-fourth the frequency, and so on, without limit. Thus, the TRW automatically and effortlessly takes more and more revolution bites of air per signal cycle, as the bass frequency goes lower. In contrast, a conventional subwoofer driver can make only one excursion per signal cycle, even as the bass frequency goes lower, and so can take only one excursion bite of air per signal cycle, even as the bass frequency goes lower. As we saw above, the TRW fan takes one blade-revolution bite of air per signal cycle at 60 Hz, two bites per signal cycle at 30 Hz, four bites per signal cycle at 15 Hz, eight bites per signal cycle at 7.5 Hz, etc.
       As you can see, the TRW subwoofer moves twice as much air volume per signal cycle for every halving of frequency. And the volume of air moved per signal cycle, by the TRW, automatically and effortlessly keeps increasing, without limit, as the bass frequency being reproduced goes lower. Indeed, as the bass frequency reproduced by the TRW approaches zero Hz (DC), the TRW fan's number of bites per signal cycle, and hence volume of air moved per signal cycle, automatically and effortlessly approaches infinity. This also means that the TRW's effective excursion (per signal cycle, which is also how we look at the excursion of conventional subwoofer drivers) automatically and effortlessly increases, without limit, as the bass frequency goes lower, and also approaches infinity as the bass frequency approaches DC. These dramatic increases per signal cycle are automatic and effortless for the TRW because they are a simple result of the fact that the TRW fan, creating the airflow and bass energy, just keeps rotating at the same speed, regardless of frequency (thanks to the fact that the fan's rotation is not also assigned the distinct task of signal modulation).
       In contrast to the TRW's fan rotation, a conventional subwoofer driver cannot keep cycling its excursions at the same speed, as the bass frequency being reproduced goes lower. Instead, it must slow down its excursion cycling as the frequency goes lower, to track the slowing down of the bass signal cycling (thanks to the fact that the single cone driver engine must multitask, and must modulate the signal as well as creating airflow and bass energy). Thus, the only way that a conventional subwoofer driver can increase its volume of air per signal cycle, to compete with the TRW's intrinsic and automatic ability to do this, is to increase its cone velocity and thereby hugely increase its excursion distance, within each excursion cycle and signal cycle. But, as we discussed above, this huge increase in excursion distance increase is very stressful on cone drivers, and very soon drives them to their modest excursion limits, as the bass frequency goes lower.
       Because the TRW does not have any excursion limits, it automatically and effortlessly keeps increasing its effective excursion per signal cycle as the bass frequency goes lower, so its bass performance capability does not have any limitations whatsoever as a function of the bass frequency going lower. In contrast, the conventional subwoofer driver has very modest excursion limits, so in attempting to stay competitive with the TRW as the bass frequency goes lower, it very quickly runs afoul of its modest excursion limits per signal cycle, and thereby hits the absolute ceiling of its bass performance capability.

C. Comparisons with Conventional Subwoofers in Coupling to Air

       There's another interesting benefit that the TRW realizes, from the fact that the number of air bites it takes per signal cycle keeps increasing, as the bass signal frequency goes lower. As the TRW fan takes progressively more bites of air per signal cycle, the effective radiating area of the fan keeps growing. Thus, the effective area of the TRW's fan "diaphragm" keeps growing, without limit, as the bass frequency goes down. In contrast, the radiating area of a conventional subwoofer driver's diaphragm of course stays constant as the bass frequency goes lower.
       This progressive growth, in the TRW's effective radiating area, at progressively lower bass frequencies, is of enormous benefit in the TRW's ability to couple to the air, and to thereby generate real acoustic bass energy in your room, especially at low bass frequencies. You see, as the bass frequency goes lower, the acoustic wavelength in the air gets longer, so a driver diaphragm of a given fixed diameter couples to the air in a weaker and weaker fashion. At low bass frequencies where subwoofers operate, the acoustic wavelengths become so long that an ordinary cone driver, even of 18 inch diameter, couples very weakly to the air, and thus cannot be effective at actually driving the air and creating acoustic bass energy, regardless of how much the tiny cone might flail about.
       As a simple analogy, imagine flicking a cherry pit into the air. However fast you flick it, and however far it might travel in its excursion, that cherry pit is not going to push or move much air,

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