The problem is, you are confused.
The compression ratio is strictly the ratio as I originally described. Boosting does not change this. They are not comparable. The compression ratio is a mechanical volumetric ratio. It irrelevant how dense the air is which it mechanically compresses. The engine in a vacuum maintains the same compression ratio as it does at the bottom of the sea.
Boosting is a measurement of density. The volume is irrelevant. It is not a ratio. They describe two different attributes.
Let's consider turbo normalization. This is more commonly used in aircraft. The purpose is to maintain sea level manifold pressure up to the turbo's maximum output. At sea level it provides zero boost. At 10k ASL, it might provide 10lbs boost (relative to atmospheric pressure) but manifold pressure remains at sea level.
In this way, we can see that boost increased manifold pressure (amount of scavengible air available to compress), buy did not effect the compression ratio of the engine in any way.
The crutch of the misunderstanding is you believe air density is interchangeable with volumetric capacity. They are two very different things.
Which means your question is flawed, based on flawed assumptions of what's going on.
Volume is not pressure.
Pressure is pressure, changing volume and changing density both change pressure. That pressure can be measured and expressed as a ratio relative to atmospheric pressure. Do you know what BMEP is? Do you understand that it takes different things and combines them into a time average? Things that have nothing to do with each other, why isn't there something like that for compression ratio when both piston and turbo compressor achieve the same thing in practice, that is increase the pressure of the air.
Boosting is not a measurement of density, boosting is a measurement of pressure ratio.
https://www.grc.nasa.gov/www/k-12/airplane/compth.html
In either design, the job of the compressor is to increase the pressure of the flow**. We measure the increase by the compressor pressure ratio (CPR), which is the ratio of the air total pressure pt exiting the compressor to the air pressure entering the compressor.
https://www.speednik.com/wp-content/blogs.dir/1/files/2015/04/efr_91s74.jpg
When reading turbo maps there is no mention of density, there is only pressure ratio on the y axis.
You keep saying I'm confused, but I'm not inventing anything, this is standard nomenclature using accurate technical terms.
Again, pressure increase is the same whether it's done by a compressing piston or compressing aerofoil stages. A scroll compressor, screw compressor, axial compressor, centrifugal compressor and piston pump all do exactly the same thing.
I'm not disagreeing with much of your point. But a RATIO is not pressure or volume. Pressure is not volume. Volume is not pressure.
MAPs frequently make assumptions and can short circuit because they can infer based on a specific engine. This is why ECUs cater to specific engines.
Pressure doesn't care about volume. This is why I keep asking you what you're trying to figure out? I believe you're simply not asking the right question and I can't figure out what you're trying to ask.
Are you asking how to correlate manifold pressure with a given boost?
But a RATIO is not pressure or volume.
The ratio is of pressure, expressed in kpa or psi or bar to atmosphere, only. My question is if there's a theoretical calculation like BMEP, or torque ratio, to compare engine performance, why can't there be a total compression ratio per cylinder? Not of volume, not of density, but the two combined into their related pressure, and measured as a ratio to the static air pressure. Then you could have a way to compare engines, based on their boost pressure and compression ratios.
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