DVC subwoofers, theories-discussions-etc

OK gang, lets put our thinking caps on and ponder henceforth this>

I was looking at some subwoofer specs and recommended box designs last PM for some dual v.c. subs, and noticed something worth discussing. I also have some questions concerning the physics that govern the performance aspects of these subs. So we can all join the fun, I will start in simplistic layman's terms, then get into the "meat-n-potatoes"..cool?

So here we go.
DVC subs typically have dual 4 ohm coils, but can be 2X8ohm, 2X2ohm, 2X1ohm or any combination the manufacturer can design. I've even seen triple and quad-coil designs (mainly for the SPL crowd). The benefits of this design offer increased power handling, the possibility of multiple total ohm load configurations, including lower overall impedances to get the most power from higher-current amp designs, and *usually* dvc subs can require less total enclosure volume than svc subs, making for installation in tighter places possible.
These dual coils can be wired in 4 different ways on any given subwoofer, and the performance of the woofer is affected to certain degrees by the different wiring configs. It is this very topic that I would like to address in this discussion, so I will post the 4 different configs, then mechanical and sonic characteristics of each config, then questions specific to the different configuration wiring schemes....here we go.

>>> PARALLEL COILS.
Basically, the two "+" terminals hooked together, and the two "-" terminals hooked together, and a single speaker wire going to the amp. This config will yield a nominal impedance of 1/2 the Znom of one coil...so for a 4 ohm dvc woofer this will yield a 2 ohm total load (1/2*4ohms=Ztotal). This config yields the highest woofer sensitivity rating, mainly due to the decreased electrical resistance of the coils. This config will yield increased overall THD specs in the system due to the typical amplifiers' damping and distortion specs decreasing by a factor of 1/2 as well (lower impedance = lower damping factors and higher THD in amplifiers). However, with regard to power output level, high current amplifiers that double power as the output impedance drops by a factor of ? provide additional output with this wiring configuration, helping get the most actual wattage out of your amplifier. In essence, you trade control and low distortion for higher power and output with this configuration. Parallel configurations also tend to RAISE the resonant frequency(Fs) of the woofer , most likely due to variances in inductance, Qes, or other parameters.

>>>SERIES COILS
Series connection is formed by making a complete ìcircuitî through the voice coils, where one coilís ì+î terminal is connected to the other coilís ì-ì terminal, and then the remaining two opposing terminals are hooked to the single speaker wire coming from the amp. This config yields a nominal impedance of the sum of the ohm load of each coil (Zcoil1 + Zcoil2= Total system impedance). This config has the lowest woofer sensitivity and highest resistance. However, this higher impedance means your amplifier will DOUBLE itís damping characteristics over what it does with a single coil woofer, and the ampís THD spec will double as well. As for power output, the amplifier will see a higher impedance than the woofer in single-coil state, so output power of the amp used will be roughly ? what it would do with the same woofer in svc model. Series wiring scheme will allow only 1/4th the total amplifier output as compared to the same woofer wired in parallel, given the amplier is capable of higher-current low impedance loads. With series wiring, you gain low distortion and high damping at the expense of decreased overall output levels. Series coils tend to lower the woofer's normal Fs.

>>>BI-AMPING
Bi-amping a DVC woofer is simply wiring one coil to a mono-bridged amplifier, and the other coil to another mono-bridged amplifier. This can be tricky and should not be attempted by a novice, as the amplifiers must be carefully level-matched so as to provide the same electrical supply to each coil. If done improperly, the voice coils will ìfightî each other, distortion will rise, and the coils can become damaged, burn, or fail completely. Also, output level and performance will both drop. So , if all this bad can happen, what's the benefit? Well for starters, if you use a pair of amps in bi-amp config rather than a single amp in parallel config, you realize the benefit of increased damping factors for said woofer and decreased THD and yet you still have the same output power coming from the pair of amps as you would from running a single amp at lower impedance. Furthermore, having two power supplies instead of one can provide increased performance on transients (attack, dynamics, etc) and overall subwoofer resolution may be enhanced.
Bi-amping can also help get maximum woofer output and/or maximum power levels when using amplifiers that are NOT capable of lower impedance loads. This is one reason bi-amping is used for SPL systems.

>>>SINGLE-COIL WIRING
This is merely hooking up only a single coil rather than both coils of the DVC woofer. This yields a resistance equal to the Znom of one coil, and can be used when an amplifier is not capable of lower-impedance parallel wiring, and/or the amp simply is not powerful enough to perform well with a series configuration of the coils. A benefit is the THD and damping characterstics of the amp will be ìmid-lineî, as it is better at this load than it would be in parallel, yet worse than it would be in series. Also, if this woofer is a dual 4 ohm sub, the number of possible amplifiers one could get to power the thing in single v.c. config is VASTLY increased as the majority of 12V power amps are optimized for 4ohm mono-bridged operation. Fs drops when only a single coil is used to drive a DVC woofer, and the required enclosure volume also drops, but why??? Obviously, woofer sensitivity specs (db/1watt/1meter) will be least for the woofer in series, highest for the woofer in parallel, and mid-line for the single coil wiring.

OK, now that the explanations are over, letís discuss >;
My first question is how are factors like Qes (electrical Q factor), Le (voice coil inductance), BL (magnetic field strength), and Xmax (as it pertains to the number of windings in the voice coil gap) affected when we use only ONE of the coils of a dual-voice coil driver???

My second question is directed at the performance of said driver Ö.specifically, WHY does this wiring scheme lower the wooferís Fs? WHY does this wiring scheme lend to reduced enclosure volume requirements?

Of course, the wooferís parameters are changed by using only a single coil, and the additional weight of the Mms (moving mass) of the dual coil windings vs. the decreased Qes that the single coil exhibits vs. both coils will affect the Fs, but are these the ONLY factors that change?

I will give an example of what Brand X claims are the required enclosure volumes for their DVC subwoofer wired in parallel
1.21 cubes with an F3 (db down point) of 57Hz in anechoic (out of car)
Now the same woofer wired as an SVC
.75 cubes with F3 of 42Hz anechoic.

This is a VAST difference, and I want to completely understand why. Let's discuss