# Compression ratio

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A four-stroke engine showing the strokes of the piston with fuel and exhaust airflows

The static compression ratio, (symbol ${\displaystyle \varepsilon }$),[1] of an internal combustion engine or external combustion engine is a value that represents the ratio of the volume of its combustion chamber from its largest capacity to its smallest capacity. It is a fundamental specification for many common combustion engines.

In a piston engine, it is the ratio between the volume of the cylinder and combustion chamber when the piston is at the bottom of its stroke, and the volume of the combustion chamber when the piston is at the top of its stroke.[2]

For example, a cylinder and its combustion chamber with the piston at the bottom of its stroke may contain 1000 cc of air (900 cc in the cylinder plus 100 cc in the combustion chamber). When the piston has moved up to the top of its stroke inside the cylinder, and the remaining volume inside the head or combustion chamber has been reduced to 100 cc, then the compression ratio would be proportionally described as 1000:100, or with fractional reduction, a 10:1 compression ratio.

A high compression ratio is desirable because it allows an engine to extract more mechanical energy from a given mass of air–fuel mixture due to its higher thermal efficiency. This occurs because internal combustion engines are heat engines, and higher efficiency is created because higher compression ratios permit the same combustion temperature to be reached with less fuel, while giving a longer expansion cycle, creating more mechanical power output and lowering the exhaust temperature. It may be more helpful to think of it as an "expansion ratio", since more expansion reduces the temperature of the exhaust gases, and therefore the energy wasted to the atmosphere. Diesel engines actually have a higher peak combustion temperature than petrol engines, but the greater expansion means they reject less heat in their cooler exhaust.

Higher compression ratios will however make gasoline engines subject to engine knocking (also known as detonation) if lower octane-rated fuel is used. This can reduce efficiency or damage the engine if knock sensors are not present to modify the ignition timing.

On the other hand, diesel engines operate on the principle of compression ignition, so that a fuel which resists autoignition will cause late ignition, which will also lead to engine knock.

## Formula

Static compression ratio (${\displaystyle CR}$) is calculated by the formula

${\displaystyle {CR}={\frac {V_{d}+V_{c}}{V_{c}}}}$

Where:

${\displaystyle V_{d}}$ = displacement volume. This is the volume inside the cylinder displaced by the piston from the beginning of the compression stroke to the end of the stroke.
${\displaystyle V_{c}}$ = clearance volume. This is the volume of the space in the cylinder left at the end of the compression stroke.

${\displaystyle V_{d}}$ can be estimated by the cylinder volume formula

${\displaystyle V_{d}={\tfrac {\pi }{4}}b^{2}s}$

Where:

${\displaystyle b}$ = cylinder bore (diameter)
${\displaystyle s}$ = piston stroke length

Because of the complex shape of ${\displaystyle V_{c}}$ it is usually measured directly. This is often done by filling the cylinder with liquid and then measuring the volume of the used liquid.

## Typical compression ratios

### Gasoline (petrol) engine

The compression ratio in a gasoline (petrol)-powered engine will usually not be much higher than 10:1 due to potential engine knocking (detonation) and not lower than 6:1. Some production automotive engines built for high performance from 1955–1972, used high-octane leaded gasoline or '5 star' to allow compression ratios as high as 13.0:1.

A technique used to prevent the onset of knock is the high "swirl" engine that forces the intake charge to adopt a fast circular rotation in the cylinder during compression that provides quicker and more complete combustion. It is possible to manufacture gasoline engines with compression ratios of over 11:1 that can use 87 (MON + RON)/2 (octane rating) fuel with the addition of variable valve timing and knock sensors to delay ignition timing. Such engines may not produce their full rated power using 87 octane gasoline under all circumstances, due to the delayed ignition timing. Direct fuel injection, which can inject fuel only at the time of fuel ignition (similar to a diesel engine), is another recent development which also allows for higher compression ratios on gasoline engines.

The compression ratio can be as high as 14:1 (2014 Ferrari 458 Speciale) in engines with a 'ping' or 'knock' sensor and an electronic control unit. In 1981, Jaguar released a cylinder head that allowed up to 14:1 compression; but settled for 12.5:1 in production cars. The cylinder head design was known as the "May Fireball" head; it was developed by a Swiss engineer Michael May.

In 2012, Mazda released new petrol engines under the brand name SkyActiv with a 14:1 compression ratio (U.S. models have a 13:1 compression ratio to allow for 87 AKI octane), to be used in all Mazda vehicles by 2015.[3][4][5] The SkyActiv engine achieves this compression ratio with ordinary unleaded gasoline (95 RON in the United Kingdom) through improved scavenging of exhaust gases (which ensures cylinder temperature is as low as possible before the intake stroke), in addition to direct injection.

### Petrol/gasoline engine with pressure-charging

In a turbocharged or supercharged gasoline engine, the CR is customarily built at 10.5:1 or lower. This is due to the turbocharger/supercharger already having compressed the air before it enters the cylinders. Port fuel injected engines typically run lower boost than direct fuel injected engines because port fuel injection allows the air/fuel mixture to be heated together which leads to detonation. Conversely, directly injected engines can run higher boost because heated air will not detonate without a fuel being present. In this instance fuel is injected as late as 60 degrees before top dead center to avoid heating the mixture to the point of compression ignition.

### Petrol/gasoline engine for racing

Motorcycle racing engines can use compression ratios as high as 14.7:1, and it is common to find motorcycles with compression ratios above 12.0:1 designed for 86 or 87 octane fuel. F1 engines come closer to 17:1, which is critical for maximizing volumetric/fuel efficiency at around 18,000 RPM.[citation needed]

### Ethanol and methanol engines

Ethanol and methanol can take significantly higher compression ratios than gasoline. Racing engines burning methanol and ethanol fuel often incorporate a CR of 14.5-16:1.

### Gas-fueled engine

The CR may be higher in engines running exclusively on LPG or CNG, due to the higher octane rating of these fuels.

### Diesel engine

There is no spark plug in an auto-ignition diesel engine; the heat of compression raises the temperature of the air in the cylinder sufficiently to ignite the diesel when this is injected into the cylinder; after the compression stroke. The CR will customarily exceed 14:1 and ratios over 22:1 are common. The appropriate compression ratio depends on the design of the cylinder head. The figure is usually between 14:1 and 23:1 for direct injection engines, and between 18:1 and 23:1 for indirect injection.

### Kerosene engine

A compression ratio of 6.5 or lower is desired for operation on kerosene. The petrol-paraffin engine version of the Ferguson TE20 tractor had a compression ratio of 4.5:1 for operation on tractor vaporising oil with an octane rating between 55 and 70.[6]

## Fault finding and diagnosis

Measuring the compression pressure of an engine, with a pressure gauge connected to the spark plug opening, gives an indication of the engine's state and quality. There is, however, no formula to calculate compression ratio based on cylinder pressure.

If the nominal compression ratio of an engine is given, the pre-ignition cylinder pressure can be estimated using the following relationship:

${\displaystyle p=p_{0}\times {\text{CR}}^{\gamma }}$

where ${\displaystyle p_{0}\;}$ is the cylinder pressure at bottom dead center which is usually at 1 atm, ${\displaystyle {\text{CR}}}$ is the compression ratio, and ${\displaystyle \gamma \;}$ is the specific heat ratio for the working fluid, which is about 1.4 for air, and 1.3 for methane-air mixture.

For example, if an engine running on gasoline has a compression ratio of 10:1, the cylinder pressure at top dead center is

${\displaystyle p_{\text{TDC}}=1{\text{ bar}}\times 10^{1.4}=25.1{\text{ bar}}}$

This figure, however, will also depend on cam (i.e. valve) timing. Generally, cylinder pressure for common automotive designs should at least equal 10 bar, or, roughly estimated in pounds per square inch (psi) as between 15 and 20 times the compression ratio, or in this case between 150 psi and 200 psi, depending on cam timing. Purpose-built racing engines, stationary engines etc. will return figures outside this range.

Factors including late intake valve closure (relatively speaking for camshaft profiles outside of typical production-car range, but not necessarily into the realm of competition engines) can produce a misleadingly low figure from this test. Excessive connecting rod clearance, combined with extremely high oil pump output (rare but not impossible) can sling enough oil to coat the cylinder walls with sufficient oil to facilitate reasonable piston ring sealing. In engines with compromised ring seals, this can artificially give a misleadingly high compression figure.

This phenomenon can actually be used to some slight advantage. If a compression test does give a low figure, and it has been determined it is not due to intake valve closure/camshaft characteristics, then one can differentiate between the cause being valve/seat seal issues and ring seal by squirting engine oil into the spark plug orifice, in a quantity sufficient to disperse across the piston crown and the circumference of the top ring land, and thereby affect the mentioned seal. If a second compression test is performed shortly thereafter, and the new reading is much higher, it would be the ring seal that is problematic, whereas if the compression test pressure observed remains low, it is a valve sealing (or more rarely head gasket, or breakthrough piston or, rarer still, cylinder-wall damage) issue.

If there is a significant (greater than 10%) difference between cylinders, that may be an indication that valves or cylinder head gaskets are leaking, piston rings are worn, or that the block is cracked.

If a problem is suspected, then a more comprehensive test using a leak-down tester can locate the leak.

## Variable Compression Ratio (VCR) engines

Because cylinder-bore diameter, piston-stroke length and combustion-chamber volume are almost always constant, the compression ratio for a given engine is almost always constant, until engine wear takes its toll.

One exception is the experimental Saab Variable Compression engine (SVC). This engine, designed by Saab Automobile, uses a technique that dynamically alters the volume of the combustion chamber (Vc), which, via the above equation, changes the compression ratio (CR).

The Atkinson cycle engine was one of the first attempts at variable compression. Since the compression ratio is the ratio between dynamic and static volumes of the combustion chamber, the Atkinson cycle's method of increasing the length of the power stroke compared to the intake stroke ultimately altered the compression ratio at different stages of the cycle.

On August 15, 2016 Nissan Motor Company announced a new variable compression engine that can choose an optimal compression ratio variably between 8:1 and 14:1. That lets the engine adjust moment by moment to torque demands, always maintaining top efficiency. Nissan says that the turbo-charged, 2-liter, four-cylinder VC-T engine averages 27 percent better fuel economy than the 3.5-liter V6 engine it replaces, with comparable power and torque.[7]

## Dynamic compression ratio

The calculated compression ratio, as given above, presumes that the cylinder is sealed at the bottom of the stroke, and that the volume compressed is the actual volume.

However: intake valve closure (sealing the cylinder) always takes place after BDC, which may cause some of the intake charge to be compressed backwards out of the cylinder by the rising piston at very low speeds; only the percentage of the stroke after intake valve closure is compressed. Intake port tuning and scavenging may allow a greater mass of charge (at a higher than atmospheric pressure) to be trapped in the cylinder than the static volume would suggest ( This "corrected" compression ratio is commonly called the "dynamic compression ratio".

This ratio is higher with more conservative (i.e., earlier, soon after BDC) intake cam timing, and lower with more radical (i.e., later, long after BDC) intake cam timing, but always lower than the static or "nominal" compression ratio.

The actual position of the piston can be determined by trigonometry, using the stroke length and the connecting rod length (measured between centers). The absolute cylinder pressure is the result of an exponent of the dynamic compression ratio. This exponent is a polytropic value for the ratio of variable heats for air and similar gases at the temperatures present. This compensates for the temperature rise caused by compression, as well as heat lost to the cylinder. Under ideal (adiabatic) conditions, the exponent would be 1.4, but a lower value, generally between 1.2 and 1.3 is used, since the amount of heat lost will vary among engines based on design, size and materials used, but provides useful results for purposes of comparison. For example, if the static compression ratio is 10:1, and the dynamic compression ratio is 7.5:1, a useful value for cylinder pressure would be (7.5)^1.3 × atmospheric pressure, or 13.7 bar. (× 14.7 psi at sea level = 201.8 psi. The pressure shown on a gauge would be the absolute pressure less atmospheric pressure, or 187.1 psi.)

The two corrections for dynamic compression ratio affect cylinder pressure in opposite directions, but not in equal strength. An engine with high static compression ratio and late intake valve closure will have a DCR similar to an engine with lower compression but earlier intake valve closure.

Additionally, the cylinder pressure developed when an engine is running will be higher than that shown in a compression test for several reasons.

• The much higher velocity of a piston when an engine is running versus cranking allows less time for pressure to bleed past the piston rings into the crankcase.
• a running engine is coating the cylinder walls with much more oil than an engine that is being cranked at low RPM, which helps the seal.
• the higher temperature of the cylinder will create higher pressures when running vs. a static test, even a test performed with the engine near operating temperature.
• A running engine does not stop taking air & fuel into the cylinder when the piston reaches BDC; The mixture that is rushing into the cylinder during the downstroke develops momentum and continues briefly after the vacuum ceases (in the same respect that rapidly opening a door will create a draft that continues after movement of the door ceases). This is called scavenging. Intake tuning, cylinder head design, valve timing and exhaust tuning determine how effectively an engine scavenges.

## Compression ratio versus overall pressure ratio

Compression ratio versus pressure ratio

Compression ratio and overall pressure ratio are interrelated as follows:

 Compression ratio Pressure ratio 2:1 3:1 5:1 10:1 15:1 20:1 25:1 35:1 2.64:1 4.66:1 9.52:1 25.12:1 44.31:1 66.29:1 90.60:1 145:1

The reason for this difference is that compression ratio is defined via the volume reduction:

${\displaystyle {\text{CR}}={\frac {V_{1}}{V_{2}}}}$,

while pressure ratio is defined as the pressure increase:

${\displaystyle {\text{PR}}={\frac {P_{2}}{P_{1}}}}$.

In calculating the pressure ratio, we assume that an adiabatic compression is carried out (i.e. that no heat energy is supplied to the gas being compressed, and that any temperature rise is solely due to the compression). We also assume that air is a perfect gas. With these two assumptions, we can define the relationship between change of volume and change of pressure as follows:

${\displaystyle P_{1}V_{1}^{\gamma }=P_{2}V_{2}^{\gamma }\Rightarrow {\frac {P_{2}}{P_{1}}}=\left({\frac {V_{1}}{V_{2}}}\right)^{\gamma }}$

where ${\displaystyle \gamma }$ is the ratio of specific heats (air: approximately 1.4). The values in the table above are derived using this formula. Note that in reality the ratio of specific heats changes with temperature and that significant deviations from adiabatic behavior will occur.

## Notes

1. ^ Lutjen, D; Müller, M (1984). Kfz-Rechnen. B.G. Teubner Stuttgart. p. 12. ISBN 9783519067214.
2. ^ Encyclopædia Britannica, Compression ratio, retrieved 2009-07-21
3. ^ gSiteLife.Recommend("ExternalResource","110429942"); Tweet (2011-04-22). "2012 Mazda 3 gets 40-mpg SkyActiv engine option; diesel expected in 2014". Autoweek. Retrieved 2012-05-29.CS1 maint: Multiple names: authors list (link)
4. ^ [1] Archived March 12, 2012, at the Wayback Machine
5. ^ VANDERWERP, DAVE (August 2010). "Mazda Engine News: Mazda Sky Gas and Diesel Details". Car and Driver. Retrieved 2012-05-29.
6. ^ "Tractor Vaporising Oil". Web.archive.org. 2005-04-18. Archived from the original on October 12, 2007. Retrieved 2014-08-10.
7. ^ Blain, Loz. "Turbo power meets extreme efficiency: Infiniti unveils world's first production engine with variable compression ratios". newatlas.com. Archived from the original on 2017-10-12. Retrieved 2018-04-28.