# Compression ratio

The compression ratio 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.

Picture a cylinder and it's combustion chamber with the piston at the bottom of its stroke containing 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. High ratios place the available oxygen and fuel molecules into a reduced space along with the adiabatic heat of compression - causing better mixing and evaporation of the fuel droplets. Thus they allow increased power at the moment of ignition and the extraction of more useful work from that power by expanding the hot gas to a greater degree.

Higher compression ratios will however make gasoline engines subject to engine knocking, also known as detonation and this can reduce an engine's efficiency or even physically damage it.

Diesel engines on the other hand 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

The ratio is calculated by the following formula:

$\mbox{CR} = \frac { \tfrac{\pi}{4} b^2 s + V_c } {V_c}$, where
$b\;$ = cylinder bore (diameter)
$s\;$ = piston stroke length
$V_c\;$ = volume of the combustion chamber (including head gasket). This is the minimum volume of the space at the end of the compression stroke. Because of the complex shape of this space, it is usually measured directly rather than calculated.

## Typical compression ratios

### Petrol/gasoline engine

Due to pinging (detonation), the CR in a gasoline/petrol powered engine will usually not be much higher than 10:1, although some production automotive engines built for high-performance from 1955-1972 had compression ratios as high as 12.5:1, which could run safely on the high-octane leaded gasoline then available.

A technique used to prevent the onset of knock is the high "swirl" engine that forces the intake charge to adopt a very fast circular rotation in the cylinder during compression that provides quicker and more complete combustion. Recently, with the addition of variable valve timing and knock sensors to delay ignition timing, it is possible to manufacture gasoline engines with compression ratios of over 11:1 that can use 87 MON (octane rating) fuel.

In engines with a 'ping' or 'knock' sensor and an electronic control unit, the CR can be as high as 13:1 (2005 BMW K1200S). 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.

### Petrol/gasoline engine with pressure-charging

In a turbocharged or supercharged gasoline engine, the CR is customarily built at 9:1 or lower.

### Petrol/gasoline engine for racing

Motorcycle racing engines can use compression ratios as high as 14:1, and it is not uncommon to find motorcycles with compression ratios above 12.0:1 designed for 86 or 87 octane fuel.

Racing engines burning methanol and ethanol often exceed a CR of 15:1. Consumers may note that "gasohol", or 90% gasoline with 10% ethanol gives a higher octane rating (knock suppression).

### Gas-fueled engine

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

### Diesel engine

In an auto-ignition diesel engine, (no electrical sparking plug—the hot air of compression lights the injected fuel) the CR will customarily exceed 14:1. 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 16:1 for direct injection engines and between 18:1 and 20:1 for indirect injection engines.

## 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:

$p = p_0 \times C_r^\gamma$

where $p_0\;$ is the cylinder pressure at bottom dead center (BDC) which is usually at 1 atm, $C_r\;$ is the compression ratio, and $\gamma\;$ 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 is 10:1, the cylinder pressure at top dead center (TDC) is

$p_{TDC} = (1 bar) \times 10^{1.4} = 25.1 bar$

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 enough oil to facilitate reasonable piston ring seal artificially give a misleadingly high figure, on engines with compromised ring seal.

This 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 effect 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 (> 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.

## Saab Variable Compression engine

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).

To alter Vc, the SVC 'lowers' the cylinder head closer to the crankshaft. It does this by replacing the typical one-part engine block with a two-part unit, with the crankshaft in the lower block and the cylinders in the upper portion. The two blocks are hinged together at one side (imagine a book, lying flat on a table, with the front cover held an inch or so above the title page). By pivoting the upper block around the hinge point, the Vc (imagine the air between the front cover of the book and the title page) can be modified. In practice, the SVC adjusts the upper block through a small range of motion, using a hydraulic actuator.

## Variable Compression Ratio (VCR) Engines

The SAAB SVC is an advanced and workable addition to the world of VCR engines, the first being built and tested by Harry Ricardo in the 1920s. This work led to him devising the octane rating system that is still in use today. SAAB has recently been involved in working with the 'Office of Advanced Automotive Technologies', to produce a modern petrol VCR engine that showed an efficiency comparable with that of a Diesel. Many companies have been carrying out their own research in to VCR Engines, including Nissan, Volvo, PSA/Peugeot-Citroën and Renault but so far with no publicly demonstrated results.[1]

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 powerstroke compared to the intake stroke ultimately altered the compression ratio at different stages of the cycle.

## Dynamic Compression Ratio

The calculated compression ratio, as given above, presumes that the cylinder is sealed at the bottom of the stroke (bottom dead centre - BDC), and that the volume compressed is the actual volume.

However: intake valve closure (sealing the cylinder) always takes place after BDC, which causes 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. 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

Note: this section is contested for the relevance of the math, the lack of references/explanation, and the values in the table. see the talk page

Compression ratio and overall pressure ratio are interrelated as follows:

 Compression ratio Pressure ratio 1:1 2:1 5:1 10:1 15:1 20:1 25:1 35:1 1:1 3:1 10:1 22:1 40:1 56:1 75:1 110:1

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

$CR=\frac{V_1}{V_2}$,

Pressure ratio is defined as the pressure increase

$PR=\frac{P_2}{P_1}$.

From the combined gas law we get:

$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \Rightarrow \frac{V_1}{V_2}=\frac{T_1}{T_2} \frac{P_2}{P_1} \Leftrightarrow CR=\frac{T_1}{T_2} PR$ Since T2 is much higher than T1 (compressing gases puts work into them, i.e. heats them up), CR is much lower than PR.