Amplifier Power Ratings & Speaker Sensitivity


We often hear comments about amplifier X does not have sufficient power to drive speaker Y or speaker Z requires minimum 200W to come alive. I am trying to figure out if there is a correlation between amplifier power ratings and speaker sensitivity in the prevention of over-driving of speakers when listening at high volume levels since stressing an amplifier beyond its intended output will cause the amp to clip that may subsequently cause damage to the coils of the speaker.

From what I have read, below is my understanding but please correct me if any of my interpretations are wrong.

1) For a manufacturer's stated sensitivity of say 86dB/W/m, 1W of power is required to produce 86dB SPL at a distance of 1m away from the drivers.

2) In the doubling of power, the SPL will increase by 3dB. For example :-
1W @ 86dB
2W @ 89dB
4W @ 92dB
8W @ 95dB
16W @ 98dB

3) For every distance added, the SPL will decrease by 6dB. For example :-
86dB @ 1m
80dB @ 2m
74dB @ 3m
68dB @ 4m
62dB @ 5m

4) Close placement to rear wall will boost 3dB in the bass

5) Close placement to a corner will boost 6dB in the bass

To determine whether an amplifier is capable of driving the speakers at a given loudness and distance without causing damage to either the speakers and/or the amp, can we use the power rating of the amp and the sensitivity of speakers as a basis in controlling the level of loudness we are getting from the system? Let say a 50W amp is used to drive a speaker with 86dB sensitivity and the listening distance is approximately 4 meters away. Can we work backwards from the peaks we are getting in the SPLs from the listening position? With the assumption of 90dB as the absolute peak SPL when listening at insane volume levels at 4 meters away(-18dB){at least in my case although I am aware some folks listen past 100dB}, the SPL at 1m away is 72dB.

At 4 meters listening distance,
1W @ 72dB
2W @ 75dB
4W @ 78dB
8W @ 81dB
16W @ 85dB
32W @ 88dB
64W @ 91dB

64W of power is required to produce 91dB SPL. If using lesser powered amplifiers of 60W and below, the amp will have potential to go into clipping. If listening at 88dB SPLs(peaks) and lower there would not be any concern on speaker or amplfier damage.

I do know that room conditions, amplifier gain, power supply and some other factors will play a part as well but the above should at least give a basic idea by providing a rough estimate on how loud should one be listening so as to prevent any damage to the components?

I understand that people with high-powered amps will not need to worry so much when cranking up the volume but it can be useful for some other folks who have flea-powered amps(especially tube amps), particularly those who like to listen loud.

Any advice or feedback would be most appreciated.
ryder
This is all done for one speaker (unless I missed that point. In that case: sorry!). Since most of use two speakers in the room, what does that mean? I seem to recall that you can add 3 dB (A) to the equation.

As for quality/quantitiy: 1 Watt is 1 Watt, from whatever amp it comes. Whether or not it will sound as good... that's an other debate.
Hi Ryder, I just looked at your system page and noticed all of the room treatment including the diffusion. Well done!
If you are interested in measuring your in room response, I would recommend the free program REW )Room EQ Wizard which is available for free at the Home Theater Shack. Besides freq response it also measures RT60 times and does waterfall plots and a few other nice features. Let us know when you do it and then you can post a graph here. I am sure it will be superb!

Bob
Satch, re: Watt quality; yes, no one is arguing the criterion of the measurement, it's about what sounds better. I, perhaps incorrectly, assumed that would be understood.
Only 1 fly in the ointment.

If you need say .... 100 watts to produce the desired SPL, there is another factor to consider.
IF the speaker presents a bad load to the amp, in the sense of large phase angle, you can cut in to available power badly. If you need a calculated 100 watts and the speaker is 45' phase angle, you really need 141 watts to deliver 100 watts.
Large phase angle and low impedance at same or near-same frequency is a deal breaker for many amps.
I simply don't know where to draw the line. Are 'cheap' good watts really cheaper than a speaker with a more moderate load? Can you find a speaker you enjoy that has easier electrical characteristics?
I'd personally be willing to try a solution with a smaller amp than my ICE amp of 250/side and more sensitive speakers than my panels....though electrically, they are not as bad as most.
Magfan, that's certainly a plan. FWIW, and with all due respect to those who feel that they've succeeded with that approach, I've yet to hear high sensitivity speakers that are more compelling than less sensitive speakers across all the paramters that I seem to find important.