# Practical Compression Calculations

If you are doing a compression test, air in the cylinder is compressed during the compression stroke and that pressure is registered on your compression gauge or pressure transducer. When everything is good the numbers should match the ones listed in the service manual for the engine. But if the engine is not running right, can those values help to reveal what the issue is (hence "practical" in the title)?

Let's try to answer this question. There will be some math involved, but I'll try to keep it straightforward.

When the compression process is described, Boyle's law is often used as an illustration: Pressure x Volume remains constant if the quantity and temperature of gas do not change. So, when volume is reduced, pressure goes up. Sometimes it is mentioned that during the actual compression stroke temperature also increases, but this point is rarely stressed enough, even though it completely invalidates use of Boyle's law in realistic calculations at cranking speeds and above.

Instead, I prefer to turn to the Ideal Gas Law directly:

If the volume decreases (blue arrow) and the temperature increases (red arrow), for the left- and right-hand sides to remain equal the pressure should rise a lot (two red arrows).

How does the temperature rise during the process? The work performed by the piston is transferred into the amount of gas. Some of that energy escapes as heat loss to the cylinder walls, the rest goes to increase the temperature of the gas:

If we assume that at any point throughout the compression process a fixed proportion of the piston's energy goes to increase the temperature of the gas, it is possible to derive the solution explicitly. Physicists called such a process Polytropic, and mathematicians figured out that it is described by equation: P x V^nu = const, where nu is a parameter. Automotive engineers found that this relationship holds fairly well throughout most of the compression process, with nu depending on the RPMs of the engine and how well the cylinder is sealed (search 'SAE paper polytropic' to see how popular the topic is).

Ballpark values for parameter nu? From what I've seen, for cranking speeds (~300rpm), nu=1.25-1.3; for fast idle nu=1.3-1.35. For high RPMs, nu can be as high as 1.4, but will be smaller if there are any leaks in the cylinder.

How does this help us? If we know what the pressure and the volume are at the start of the compression process, and what the volume is at its end, we can then calculate the final pressure. Here we have to be careful: while it is tempting to use the Compression Ratio (CR) of the engine, that would not be correct as the intake valve typically closes quite a bit later than the BDC point. Also, we might need to take into account additional volume introduced by our pressure testing equipment.

1. To account for the IVC event, consider a Slider Crank Model. diag.net/file/f27bwe5fn… For example, for IVC at 60 degrees after BDC the cylinder volume is around 80% of the volume at BDC, so, for this case, we will need to use the so-called Dynamic Compression Ratio (DCR): DCR = 0.8*CR.

2. If we are using a compression gauge, it adds very little extra volume because of the Schrader valve. However, in-cylinder pressure transducers add noticable amount of volume, V_extra. It is claimed that for WPS500 (with the supplied hose) V_extra=5mL, which would reduce DCR further by about 8% (that is, multiplied by a factor of 0.92) for engines with cylinder volumes 500-600mL and CR=9-11. But don't try to use this rule of thumb for Mazda SkyActiv or diesel engines -- better calculate the corrected DCR ratio as (V_IVC + V_extra) / (V_TDC + V_extra) and use it in the formula. The same applies if you are using a different pressure transducer or compression hose.

And, so, the formula is: P_TDC = P_IVC * DCR^nu, where all pressures are measured relative to absolute vacuum (and, thus, are 14.7psi higher than what is displayed on the gauge). Also, we should be really careful while determining P_IVC, as even 1 psi difference is a lot when the values are just 5-15 psi above absolute vacuum (use properly calibrated transducers and zoom into waveforms). For those interested in math, here is a video I prepared that provides the derivations:

What we are going to do next is to apply this formula to waveforms collected by Eric O. for Chevy Malibu 2.4. The vehicle has a problem with cam timing, but what about compression?

Example 1. Cranking compression:

Engine's compression ratio is CR=10.4. Cranking speed is 220rpm. Let's try to use nu=1.3. From the waveform's cursors we see that there is an inflection point where the actual compression starts around 600 deg mark, with pressure: P_IVC = 14.7 - 1.4 = 13.3 psia, so P_TDC = 13.3 * (0.8*10.4*0.92)^1.3 = 187 psia. Converting this value to gauge pressure gives: 187 - 14.7 = 173 psi. This matches the waveform suspiciously well! The compression is good.

Example 2. Running compression:

Engine speed is 1200 rpm, so let's use nu=1.35. What is the initial pressure? The pressure is not very stable in this region, so let's zoom in into the inflection point at 600 degrees and make sure we fetch the precise value:

P_IVC = 14.7 - 5.8 = 8.9 psia, so P_TDC = 8.9 * (0.8*10.4*0.92)^1.35 = 139 psia. Converting this value to gauge pressure gives: 139 - 14.7 = 124 psi. So, again, the cylinder is doing its job properly, but this time it is fed with bizarre initial pressure. Thus, the peak pressure is abnormally high, and this technique allows to quantify the observed value. Here there are no issues with the compression process but the high initial pressure, and you can focus on the other parts of the waveform to figure the reason for that.

In general, I think this technique should be most useful if the other parts of the waveform or previous tests do not provide definitive diagnosis, and you are looking for extra clues. In this case you will be able to establish a baseline of what to expect from the the compression process, compare it to the observed value, and check what potential problems can explain such deviation. For example, if the final pressure is higher than expected (for a given initial pressure), you might want to check if the intake valve closes early, as in that case DCR would be higher, and so would the final pressure.

Applying the method can be complicated by the following issues:

- the pressure transducer has to be precise (especially for pressures below atmospheric) and be properly calibrated;
- the compression hose and adapters should be high quality and their parameters should be known;
- the pressure before the intake valve closes should be fairly stable so that the initial pressure reading is precise enough;
- effects such as cylinder wash can make calculation results non-repeatable and confusing.