Compression ratio describes the efficiency of a heat engine to extract thermal energy into mechanical work and has nothing to do with the more commonly used context of compressing something to get more of it in the same space. All compression ratio is is a measure of efficiency, it's value has zero effect on the volume of air entering the engine.
Compression from a turbo/blower serves to increase the density and volume of the air/fuel available for combustion regardless of the compression ratio.
Two completely different concepts. To put it into perspective, put a piston at bottom dead center, then fire it off. Nothing will happen because 0 work is being performed, regardless if the intake is at 14.7 psi atmospheric pressure or 28 psi of pressure with a turbo. The intake is compressed, but the engine does nothing because it captures 0% of the thermal energy as mechanical motion.
Right on, simply put: the compression ratio describes the geometry of the engine and can be used to calculate the ideal Otto cycle efficiency.
The reason why a piston at BDC won't extract any work is because work is pressure*volume through which it expands, and there is no volume expansion in that case. Keep this in mind.
To answer your original question, the reason to use a turbo or supercharger is to essentially increase the displacement of the engine. Doubling the intake pressure by boosting doesn't exactly double the power output, but it's close. Also, a smaller boosted engine will have lower losses (like pumping, bearing friction, etc) than those of a larger engine, increasing the power available to the wheels. This is a very complex subject...
I think I'm starting to understand, but not quite. Increasing the compression by changing the stroke would leave less area for things to explode; would that severely affect burning efficiency?
Feeding compressed air into the cylinder then compressing the compressed air would leave a lot more space for things to burn.
My understanding is that you want the highest possible cylinder pressure when the air/fuel mixture is ignited because the burn rate of the mixture increases with pressure and the engine performance will get closer to an ideal Otto or Diesel cycle.
^^ PV diagram of an otto cycle, the area enclosed by the loop is the work per engine cycle that the engine could extract. The way to look at boosting an engine is to double the pressure at each point (imagine stretching the image to be 2x as high to represent 2atm of boost). The area surrounded by the loop is now bigger, so more work is done per engine cycle. Remember that work is pressure*volume, so super/turbo-charging is increases the pressure throughout the cycle, resulting in more work. There is an amount of extra air and fuel consumed commiserate with the increased work output, so the efficiency of the engine remains unchanged.
Now, if the compression ratio was increased, the pressure at points 2, 3, and 4 would increase (1 is simply the intake pressure), also increasing the amount of work produced by the cycle. The same amount of air and fuel was used but more work was done, so the engine is more efficient.
I'm talking in ideal terms here, there are other losses associated with a forced induction engine that I'm skipping. It's a very complex subject... The main advantage of forced induction is a higher power output without the increased weight/volume of a larger engine.
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