What, the logarithms and powers of 10?
Ok, so let's take 1300 W peak and 121 dB. Not sure what your target average SPL is, but if it is 110 dB at 1 m:
SPL = 110 dB
power_w = (1/0.90)*(1300 W)*10^((SPL - 121 dB)/10) = 115 W
battery_energy_Wh = 253 Wh
battery_run_time_h = battery_energy_Wh / power_w = 253 Wh / 115 W = 2 hours
I still kind of doubt the 1300 W peak number. Suppose it is something more reasonable like 600 W.
Then you would have 2 hours * 1300 W / 600 W = 4.4 hours
But wait -- your power pack can only deliver 250 W out of an outlet, and it looks like it would do it for about an hour. So there you go -- you are limited to 1 hour at an SPL of
121 dB - 10*log(250/1300) dB = 121 - 7 dB = 114 dB
or if we take 600 W instead of 1300 W for 121 dB:
121 dB - 10*log(250/600) dB = 121 - 4 dB = 117 dB
For every -3 dB, you halve the power and double the run time.
So with the 1300 W you would get 2 hours at 111 dB, 4 hours at 108 dB, 8 hours at 105 dB, 16 hours at 102 dB, etc.
With the 600 W producing 121 dB, you would get 117 dB for 1 hour, 114 dB for 2 hours, 111 dB for 4 hours, 108 dB for 8 hours, etc.
If you have two speakers, that means you can only run each one at 150 W with this power pack. That will produce -6 dB below peak for one speaker, but since there are two, it will produce -3 dB total below 121 dB, or 118 dB for one hour.
So with this, you can adjust to more correct info. If you really want to know, you can measure the dB SPL at 1 m on-axis of the speaker, outdoors with your cell phone, and use an AC ammeter to to measure the AC RMS current drawn. Or, maybe your camping power pack has a readout of the power draw. Try several volume levels and plot dB vs. AC current (you really just need one SPL to project the battery life, though). Then the power draw will be 120 V * (measured RMS current draw in A) if you don't have a direct readout of it. Plug those dB and power numbers into the formulas I gave, but leave out the 1/0.90 efficiency factor.
Well, you asked : )
lol.. that made my head hurt.
I don’t trust the Mackie power output at all - they claim 1300 peak watts whatever that is. It can get some volume going but the peak spl isn’t that amazing. 121 or 118.
For some reason I do trust the QSC numbers - that thing puts out some serious volume. I think I read something about their amps being a new class of very high efficiency tech.
The power bank is my camping SHTF box until I get a proper generator.
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