Over engineering without over engineering

If you have done all the steps, you have properly sized the amplifier.  

Here's another way to think about it.  If you sized it perfectly and purchase an amplifier that is exactly the calculated size, the volume attenuator on the amp should be set x dB down from max.  The x dB should be your headroom.

In the real world, you will purchase an amplifier the next size up from your calculation.  The attenuator will be turned down past the headroom level.

Actually, you will set the amplified with an SPL meter at the listening position with program audio.

If you are not getting sufficient level, double check that the source signal to the amplifier is what the amplifier wants to see.

Another thing to consider is the EQ to the loudspeaker chain.  Transformers don't pass lower frequencies.  If you roll these off, you won't load your amplifier down.  This leaves more energy for the frequencies that are required.

I hope this helps.

What's up with the 1.5 upsizing?

If you calculate an impedance for a loudspeaker chain and then you actually measure the loudspeaker chain, your numbers probably don't match very well.  Why?  Mostly because of transformers.

When you look at loudspeaker specifications, it is rare to find a spec on the transformer.  Every transformer has loss, and we need to account for it.  A multiplier of 1.5 is approximately, 10log(1.5/1)=1.8dB difference.

If you didn't keep track of the transformer loss, you could under power your amplifier.

Another factor is the nominal impedance of the loudspeaker is a form of averaging all the impedances at all the frequencies, while your impedance measurement was done at 1kHz.   

RMS v Peak levels - which and why?

RMS - is where we sample the signal, square the measurement (converts negative numbers into positive numbers), find the mean or average of the samples, and now find the square root of the number (to undo the squaring but leaves the numbers as positives).  Basically averaging the signal, as opposed to finding the peak values.

Average verses peak is really, the normal signal that you want, including headroom.  The peaks need to fit into the headroom or you can use peaks to find your headroom.  Many digital mixers give you an average meter and peak meter in one.  Sometimes known as a peak hold display.  This type of display will help ensure that you are not clipping in the mixer or giving you an indication of what you are feeding the amplifier.

Loss over distance and loudspeaker sensitivity.

We must take into account the loss of sound over a given distance.  The two points to look at are the reference point of the loudspeaker given on the spec sheet and the listener's ears.  Many times the loudspeaker will have a sensitivity rating of x-dB at 1 watt and 1 meter.  Meaning if I put 1 watt of energy into a loudspeaker and measured at a distance of 1 meter, I should get a certain level.  The formula for the difference is dB = 20log(D1/D2).

If you had a loudspeaker that had a sensitivity rating of 89dBspl @ 1W, 1m, and you had a loss of 4dB coming from the loudspeaker to the listener's ears, the level at the human should be 89dBspl - 4dB = 85dBspl.

If we know the level that we want at the listeners ears, the headroom required, the loss over distance, and the sensitivity of the loudspeaker, we can use the ERP formula to size our taps for each loudspeaker.

In cases where the ceiling is relatively low, the tap setting is almost always the lowest tap setting available.  We should do the math anyway.

Choosing the proper headroom for your program audio.

Simply put, 10dB for voice and 20dB for music.  That is VERY simplistic, but are a really good place to start.  Running out of headroom is where distortion occurs.

All the things you mentioned are to be taken into account.  If you really know your content, you can make more accurate guestimates on the headroom you actually need for your systems.  The adage, it depends, is true.

If you run live sound for a symphony, you should expect that there will quiet passages and some very loud passages.  What is the total range, in dB, does that represent?  Is 20dB out of bounds or do you need more?  Are you using compression in your signal chain?  Music coming from a streaming channel has been preproduced and most likely has a lot of compression, how much variability is in that stream?  Maybe 5dB?  If you know the variability, you can use that number, if you don't, it's better to use the 10dB and 20dB numbers to get you started. 

If the amplifier provides more power than you need, you are generally better off.  Distortion usually happens when you don't have enough power available and the amp struggles to keep up. 

If you are getting distortion and you think it you have calculated the system properly, double check the level entering the amplifier is correct.  It could be the level is too low and the amplifier can't deliver enough level to the loudspeakers.

Christopher,

That's a big topic!  We teach all of this in our Design school, it takes several hours to get through it all, but I will try my best to address your questions.  

Generally speaking, we want to setup a system that delivers the appropriate level of audio at the listeners ears, with very low distortion and very low noise.  Sizing the amplifier properly should give great results.

When developing AV systems, we always start from the human and work back from there.  We need to figure out, or assume, a desired dBspl A weighted level at the human's ear.  Then apply some headroom so that the amplifier doesn't distort when a higher level signal enters the amplifier.  Now we need to find the loss over distance from the loudspeaker to human's ear.  The loudspeaker's rated sensitivity and a given distance.  Perform the calculation to arrive at your tap setting.  Find the sum of all loudspeaker tap settings in the chain.  Upsize the total wattage by a 1.5 factor, to make up for the loss in the transformers.  Use that final calculation for your amplifier size.  One more thing, the signal feeding the amplifier needs to be a voltage that is specified for the amplifier, generally 0dBu or +4dBu (0.755V or 1.23V).  Always check your spec sheets.  

Let's breakdown your questions individually so if we have follow-up discussions, we don't get a crazy thread going.

Yes.  All transformers have a limit to what power they can handle.  It just comes down to wire gauge really.  The thinner the wire, the less current it can handle.  A 100W transformer will be bigger and heavier than a 20W transformer due to the wire size.

Chris,

Here's a bit more about that 100W rating.  Looking at a spec sheet for an attenuator, ATS001063D-Commercial-Attenuators-Datasheet.pdf (atlasied.com), we can see that the power rating is really the maximum power or current the transformer can pass, without over-heating and burning up.

The question then goes to, how much power needs to go to the loudspeakers that are fed from the attenuator?  A simple calculation is to add up your tap settings on the loudspeakers and make sure you are below the rating of the attenuator.  In practice, you will probably far less power than the tap settings.

Here is a video on how to calculate how much power you need for your loudspeakers.
https://www.youtube.com/watch?v=jQaYxLEchLk

Paul