Thanks Abraham for the kind words and consistently good posting. It would be nice if you could also post some details of your system, on which you did a superb job. I'm sure your playback results are just as good.
Here are the brass tacks:
1) Signal chain: Flat to 3 Hz. Without this, there will be no success <10 Hz.
Here are some versions of signal chain using the required L/T configuration accomplished through various hardware options from the player to the AVR/Preamp to the signal shaper to the amplifier. All have a 2nd order LPF @ 250 Hz in line. NOTE The light blue trace is through a DCX using only a shelf filter, as some suggest using. Obviously, there can be variations of that single curve based on what AVR/Amplifier is used:
It should require no comment as the graph tells the story of how the final response will be influenced by what signal chain is employed.
2) Driver displacement: .01 liters per cubic foot of listening room. Example: 2000 cubes = 20 liters of displacement minimum. That requirement's met by employing 3 UXL-18s, 4 SI-18s, 6 SI 15s, 7 Dayton HO-18s, 6 Dayton 15 Ultimax, 7 SA-15s, etc.
Alignment: Sealed. Ultimate "efficiency" <20 Hz is determined by box size, but must be balanced with excursion protection, which is an investigation, like the signal chain investigation, requires careful thought and final testing and will be dependent on the parameters of the driver chosen vs the Vb
chosen with caution being exercised against the need to alter the signal chain in a way that eliminates the bandwidth of interest.
Amplification: Approximately 5W peak per cubic foot of listening space. This is based on a system designed with proper signal shaping to mate the system with the room. This requires a fairly accurate measurement of the naked system response compared to the system response in-room, from which comparison the Room Gain profile may be determined. The input signal may be altered to affect a new system FR that's designed to mate the system so that the result is a flat response to the desired frequency. . It's assumed that the amplifier(s) will be supplied by the proper AC and that the system will be operated only by responsible persons after proper setup, calibration and limits testing in-room using the actual program source of interest.
Transmission loss calculation: A debatable subject when speaking about <100 Hz, but the losses will obviously vary by construction method. This is the part of the equation that most folks confuse with "a sealed room".
All of my own imperial evidence from 10 years of measuring suggests that how sealed a room is, regarding air tightness, is largely irrelevant. Contrary to conventional wisdom, a drivers motion does not affect a change in the ambient pressure of a room. Rather, the drivers motion creates a sound pressure wave that travels through the air in the room. The air in any particular room may vary in temperature and/or humidity which both effect the behavior of the pressure wave, but the differences in that variable are unmeasurable unless one lives in a tent in the woods in the mountains or some similar unrealistic and irrelevant extreme.
The gain from the rooms boundaries increases as frequency decreases because the longer the sound wave vs the distance to boundaries, the more interference becomes constructive and conversely, the less the chance reflections can be destructive. Using this premise to explain 'room gain', a completely enclosed room may actually have less room gain than one which is partially open. The pertinent factors are; Item 1) above, item 2) above, transmission losses in the bandwidth of interest, the coincidence of resonant frequencies of the structure with the BW of interest and the placement of the system within the listening space.
Transmission losses through the boundaries will determine how much gain you realize at any given frequency, assuming all of the above have been considered and executed optimally. Obviously, if half the pressure wave is lost through the boundary to outside the room, then only 1/2 can be reflected back into the room to continue reflecting as it decays.
In any case and regardless of one's personal opinions regarding the mechanics of the phenomenon known as "Room Gain", measured responses of systems taken outdoors at GP vs in-room from Ilkka, Ed Mullen, Josh Ricci, MKT, notnyt and myself in rooms ranging from <2000 cubes to >4000 cubes show that "Room Gain" begins around 30 Hz and continues to increase in a similar pattern as frequency decreases down to the signal chain rolloff, which then dominates in-room response at the lowest octaves.
Using 2000 cubes listening room and DIY boxes loaded with 4 SI-18s (21.2 Liters), MiniDSP, a "clone" amplifier, the system will cost < $2500. It will meet the 4 Hz in-room response requirement at a properly calibrated reference level in any room that size.
In my case:
ROOM: 3500 cubes
DRIVER DISPLACEMENT: 36 Liters (Formula suggests: 3500 X .01 = 35 Liters)
SIGNAL CHAIN: (FR shown in graph) Oppo BDP-105 as pre/pro/player ==> SEQSS analog signal shaper =>> clone amplifier version (2)
AMPLIFICATION: 2 amplifiers, each @ 9KW peak (18KW total). Formula suggests: 3500 cubes X 5W = 16,500W peak.
IN-ROOM results: (shown in graph).
Playback Accuracy at Reference Level graphed from the LP:
This is the basic formula. It will work for any room. If more output is desired, more displacement/amplification is required, which is scaled at +6dB per 2X. The formula can be deviated from only if the desired bandwidth is truncated on the low end by design or by deviating from any single point of the formula.