Originally Posted by JohnR_IN_LA
This is a false analysis. Lets assume your running a 7.1 setup, each channel putting out a REAL 100 RMS a channel simultaneously. To get this level of performance, expect to spend at least 1000 bucks for an amplifier that can push 700 RMS simultaneously.
Now when your adding a subwoofer, you are adding the lower frequencies for the other 7 channels. Hence you need a subwoofer that can also push at least 700 RMS simultaneously.
One could argue that you actually need more than 700 RMS of power, because lower frequencies require more watts than upper frequencies.
To be pedantic the spectral balance of music favors lower frequencies above 40Hz, so if you split up the frequencies you require more total power at low frequencies. At a given speaker sensitivity it takes no more power to reproduce low frequenies.
So it would be entirely reasonable to designate 1050 RMS of power for the bottom frequencies, and 700 RMS of power for the mid and upper frequencies to achieve a nicely balanced setup.
You're neglecting placement (you're theoretically picking up a 4X output increase for each surface a sub-woofer is near, although with leakage through the walls means the real number is somewhere between that and only 2X - which still gets you an 8X boost for corner placement) and sensitivity differences (small speakers that aren't efficient can be paired with a big sub woofer that is).
I got curious about this once and made some measurements with sub (corner loaded) and center (on a short stand 3' off my screen wall) both with claimed sensitivity a bit over 90dB/2.83V/1 meter and nominal impedance arround 6Ohms. The sub was about 12' away and center 9' away, although this is well beyond the critical distance at which direct sound and reverberant fields are equal so only room size should be significant. The sub is a Citation 7.4 with a 14.5" driver in a ~3 cubic foot ported box and should be typical for reasonably sized subs; the center a Definitive C1 which should be typical for a medium sized MTM speaker. I used my Rat Shack SPL meter with C-weighting so sub-output may be a little under reported . I used an HP true RMS volt meter which is spot on at no worse than -2% against the calibration terminal on my Tek scope which is .17dB. The sub tune is arround 30Hz so the voltage within the sub's pass-band may be over-reported. Any errors led to sub sensitivity being measured as less than it really was. Extrapolation to reference level output disregards thermal compression although the Citation 7.4 uses a JBL pro-sound driver with a 4" voice coil and shouldn't suffer too much arround just 100W.
My mains were actively tri-amplified dipoles that would be too messy to make sense of so I didn't measure them.
I measured .88 VRMS for pink noise at 75dB SPL (at my listening position) from my 6 Ohm center which is .13W. A 101dB peak (reference level Dolby Digital main channel maximum with typical encoder settings) would take 50W. 4dB less efficient speakers (not atypical) would get this up to 125W.
I measured .34 VRMS to produce pink noise at 76dB SPL (at my listening position) from my 6 Ohm corner loaded sub-woofer which is .02W. A 101dB peak would take 6W, 111dB (reference level Dolby Digital LFE maximum with typical encoder settings) 60W.
Mixing in uncorreleated bass from 7 other channels with 10dB less headroom could get me 2.3dB more output which is a factor of 1.7 - meaning I'd need 102W . Using correlated bass would increase my total power requirement 4.6dB which is a hair less than a factor of three to 173W. Both numbers assume there is nothing but bass below the 80Hz sub-woofer XO in the other channels which is completely unrealistic since you need higher frequency energy for the transients to have any impact.
This all assumes that you want/need reference level output which does not work well in overly reverberant rooms (many untreated areas) or with small mid-bass drivers that distort too much to be useable at reference level. Reference -5dB would cut that by a factor of 3, reference -10 a factor of 10.
Obviously things change with small (spouse-friendly) and therefore inherently inefficient sub-woofers. A small design like Sunfire's which produces flat output for a given amplifier input will be inefficient throughout its entire opreating range. A small sealed sub-woofer can be efficient down to its natural cut-off, below which you must boost amplifier output to compensate if you want low bass.