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This mentioned in almost all standard books that for two stroke we use scavenging efficiency and trapping efficiency, but does not mention the reason, why volumetric efficiency is not used.

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You are misinterpreting what the volumetric efficiency is in 2-stroke engines. You need a better reference, mine is Internal Combustion Engines by Obert, Harper & Row, 1973.

Volumetric (charging) efficiency is the mass of air retained in the cylinder over the mass of air to fill the displacement volume.

The problem in a 2-stroke is that the lack of a specific intake stroke forces us to measure the air masses indirectly. We can't use geometry. So we use delivery and scavenging ratios.

Deliv ratio = mass of air supplied over mass of air to fill the displacement volume.

Scav ratio = mass of air supplied over mass of air to fill the cylinder volume.

Which when combined results in:

Trapping efficiency [that more closely relates to what is going on in the cylinder], mass of air retained over mass of air supplied.

Volumetric (charging) eff = delivery ratio times trapping efficiency.

So there are more variables to making an efficient 2-stroke engine than compression ratio, namely how to get the exhaust gasses out and intake gasses in.

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