I'll try but I do not believe you understand what you're saying.
Boosting does not change the compression ratio. Period. It changes density. Or another way to look at it is air flow.
50000000psi into a 8.5:1 engine is still 8.5:1. It will move a shit ton of air through it, but the compression ratio is unchanged.
Again, what is it you are really trying to figure out? Because the statements in OP is in error, resulting in a position which cannot be resolved.
Boosting does not change the compression ratio. Period.
The compression ratio is a ratio that the air has been pressurized to, relative to atmospheric conditions. 10:1 compression ratio is the same whether achieved by a piston squeezing air or a compressor raising the pressure in the manifold.
In a cyliner, volume goes down for a given air mass, pressure increases. In a turbo, volume is constant for an increasing air mass, pressure increases. In both cases the pressure increases, that compression ratio above atmospheric can and should be expressed as a combined effective compression ratio. Instead we use the cylinder pressure ratio which must be measured directly.
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.
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