Static compression ratio is determined using the cylinder volume when the piston is at the top and bottom of its travel.

The compression ratio is the ratio between the volume of the cylinder and combustion chamber in an internal combustion engine at their maximum and minimum values.

A fundamental specification for such engines, it is measured two ways: the static compression ratio, calculated based on the relative volumes of the combustion chamber and the cylinder 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.^[1]

The dynamic compression ratio is a more advanced calculation which also takes into account gasses entering and exiting the cylinder during the compression phase.

Effect and typical ratios

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 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.

Mathematical formula

In a piston engine, the static compression ratio (${\displaystyle CR}$) 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.^[9] It is therefore calculated by the formula^[10]

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

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.

Variable compression ratio engines

Most engines use a fixed compression ratio, however a variable compression ratio engine is able to adjust the compression ratio while the engine is in operation. The first production engine with a variable compression ratio was introduced in 2019.

Variable compression ratio is a technology to adjust the compression ratio of an internal combustion engine while the engine is in operation. This is done to increase fuel efficiency while under varying loads. Variable compression engines allow the volume above the piston at top dead centre to be changed.^[11]

Higher loads require lower ratios to increase power, while lower loads need higher ratios to increase efficiency, i.e. to lower fuel consumption. For automotive use this needs to be done as the engine is running in response to the load and driving demands.

The 2019 Infiniti QX50 is the first commercially available car that uses a variable compression ratio engine.

Dynamic compression ratio

The static compression ratio discussed above — calculated solely based on the cylinder and combustion chamber volumes — does not take into account any gasses entering or exiting the cylinder during the compression phase. In most automotive engines, the intake valve closure (which seals the cylinder) takes place during the compression phase (i.e. after bottom dead centre, BDC), which can cause some of the gasses to be pushed back out through the intake valve. On the other hand, intake port tuning and scavenging can cause a greater amount of gas to be trapped in the cylinder than the static volume would suggest. The dynamic compression ratio accounts for these factors.

The dynamic compression ratio is higher with more conservative intake camshaft timing (i.e. soon after BDC), and lower with more radical intake camshaft timing (i.e. later after BDC).^[12] Regardless, the dynamic compression ratio is always lower than the static compression ratio.

Absolute cylinder pressure is used to calculate the dynamic compression ratio, using the following formula:

${\displaystyle P_{\text{cylinder}}=P_{\text{atmospheric}}\times {\text{CR}}^{\gamma }}$

where ${\displaystyle \gamma }$ is a polytropic value for the ratio of specific heats for the combustion gasses 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 ratio of specific heats 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. 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 (relative to atmospheric pressure).

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 dynamic compression ratio similar to an engine with lower compression but earlier intake valve closure.

See also

• Mean effective pressure

References