In a piston-reciprocating engine, geometric compression ratio only takes into consideration compression of a cylinder's contents into the clearance volume above the piston at TDC and assumes equivalent compression and expansion. Effective compression ratio also takes into consideration intake and exhaust valve events and intake boosting. For example, the effective compression ratio can be different from the effective expansion ratio by changing valve timing events with late intake valve closing (e.g., Atkinson Cycle - with expansion ratio > compression ratio). Boosting the intake pressure above atmospheric pressures (turbocharging, mechanical supercharging) increases the effective compression ratio above the geometric compression ratio by adding a stage of compression upstream of the cylinder.

Geometric compression is just what is sounds like, and assumes the gas is ideal. But, 'effective compression' takes into effect the fact that gasses are not ideal, especially at high pressure and temperatures. That is, real atoms/molecules have finite, non-zero volumes; real atoms/molecules have finite, non-zero interaction forces.

For low compression ratio's and high thermodynamic temperatures, the effective compression approaches the geometric compression. That is, the gas is following the ideal gas law: PV=nRT. Example: Helium near 300K and with a 2:1 compression ratio.

But, when the compression ratio is high and/or the thermodynamic temperatures are low, and the gas is non-ideal and behaves approximately as described by van der Waal's equation: P = ((nRT/(V-nb)) - a(n/V)^2, where a,b are temperature invariant and known as the "van der Waals coefficients" and are tabulated for many gasses. (Refer to any good physical chemistry textbook.) Example: Nitrogen gas (N2) at 150K and 1 atmosphere. (Indeed, N2 deviates from ideal gas law behavior at much milder conditions, but I'm trying to make a point.)

There are other empirical descriptions of non-ideal gasses, like that of Berthelot or Dieterici, or Onnes (Virial coefficients). But the result will be the same, the effective compression ratio will be different (generally less) than that for an ideal gas.

In a piston-reciprocating engine, geometric compression ratio only takes into consideration compression of a cylinder's contents into the clearance volume above the piston at TDC and assumes equivalent compression and expansion. Effective compression ratio also takes into consideration intake and exhaust valve events and intake boosting. For example, the effective compression ratio can be different from the effective expansion ratio by changing valve timing events with late intake valve closing (e.g., Atkinson Cycle - with expansion ratio > compression ratio). Boosting the intake pressure above atmospheric pressures (turbocharging, mechanical supercharging) increases the effective compression ratio above the geometric compression ratio by adding a stage of compression upstream of the cylinder.

Following from Joseph, the rpm (hence the piston speed) of the engine a,so contributes to the effective compression. At higher rpm, the time for the gas to get compressed (or decompressed) is reduced, thus at places further away from the piston top, the effective compression is less than the "geometric value", as the wave front will reach the point at slower speed than the piston itself.

Wan Zaidi

Thanks a lot everyone to contribute your well defined answers.

How can we represent effective compression ratio mathematically?

For representing effective compression ratio there are two methods, one is theoretical and other is experimental.

Theoretically, you need valve timing diagram of engine. You need find crank angle before TDC, when valves are closing.

Then follow following steps:

1. Find volume at crank angle BTDC, using relation for crank rod and stroke to find volume. (Remember to take TDC at compression as reference).

2. Find clearance volume using usual compression ratio, Take ratio of volume at BTDC closed intake valve to clearance volume. You will have effective compression ratio.

Experimentally, you need a pressure transducer with trusted performance (Tested on some other engine successfully).

Follow these steps:

1. Obtain motored curve (Pressure Vs Crank Angle), by removing inductor connection from spark plug and disconnect fuel pipe.

2. Your peak pressure should coincide with TDC marker of crank encoder. Note value of peak pressure.

3. Assume Pressure before intake valve closing as 1 bar.

3. Use PV^n= constant. Take n=poly tropic constant as 1.2.

4. From above correlation Effective Compression Ratio=(Ppeak/Pintakeclosed)^(1/n).

From effective compression ratio, you can reverse calculate volume of chamber when intake valve is closed. From that you can calculate crank angle before TDC and check it with valve timing diagram.

Vishal:

Now I'm wondering if you were originally asking about an Atkinson cycle internal combustion engine. In that case, the compression ratio is much different than a simple Otto cycle engine. In an Atkinson cycle engine, the intake/compression and exhaust/power strokes are asymmetric. That is, the power stroke is much longer than the compression. This produces an improvement in thermodynamic efficiency, but at the expense of power density. Most of the very high gas mileage cars out there today (50mpg) are using Atkinson cycle engines.

Everyone's comments so far (including my previous one) are concerning the effects of non-ideal gases. But an Atkinson cycle engine is a different case.

I think that the geometric compression ration of a IC engine is just for the engine designing process, and the effective compression ration is for the real engine opreating process. In general, the geometric compression ration is not equal to the effective compression ration because of blow-by or valve clearance.