## Compression Ratio – Otto Engine

The **compression ratio**,** CR**, is defined as the ratio of the volume at the bottom dead center and the volume at the top dead center. It is a key characteristic of many internal combustion engines. In the following section, it will be shown that the **compression ratio** determines the **thermal efficiency** of the used thermodynamic cycle of the combustion engine. It is desired to have a high compression ratio because it allows an engine to reach higher thermal efficiency.

For example, let assume an Otto cycle with compression ratio of CR = 10 : 1. The volume of the chamber is 500 cm³ = 500×10^{-6} m^{3} (0.5l) prior to the compression stroke. For this engine** a**ll required volumes are known:

- V
_{1}= V_{4}= V_{max}= 500×10^{-6}m^{3}(0.5l) - V
_{2}= V_{3}= V_{min}= V_{max}/ CR = 55.56 ×10^{-6}m^{3}

Note that (V_{max} – V_{min}) x number of cylinders = total engine displacement.

## Thermal Efficiency for Otto Cycle

In general, the **thermal efficiency**, *η***_{th}**, of any heat engine is defined as the ratio of the work it does,

**W**, to the heat input at the high temperature, Q

_{H}.

The **thermal efficiency**, *η***_{th}**, represents the fraction of

**heat**,

**Q**

**, converted**

_{H}**to work**. Since energy is conserved according to the

**first law of thermodynamics**and energy cannot be converted to work completely, the heat input, Q

_{H}, must equal the work done, W, plus the heat that must be dissipated as

**waste heat Q**

**into the environment. Therefore we can rewrite the formula for thermal efficiency as:**

_{C}The heat absorbed occurs during combustion of fuel-air mixture, when the spark occurs, roughly at constant volume. Since during an isochoric process there is no work done by or on the system, the **first law of thermodynamics** dictates *∆U = ∆Q. *Therefore, the heat added and rejected is given by:

**Q _{add} = mc_{v} (T_{3} – T_{2})**

**Q _{out} = mc_{v} (T_{4} – T_{1})**

Substituting these expressions for the heat added and rejected in the expression for thermal efficiency yields:

We can simplify the above expression using the fact that the processes **1 → 2** and from **3 → 4** are adiabatic, and for an adiabatic process, the following p,V,T formula is valid:

It can be derived that:

In this equation, the **ratio V _{1}/V_{2}** is known as the

**compression ratio, CR**. When we rewrite the expression for thermal efficiency using the compression ratio, we conclude the

**air-standard Otto cycle**thermal efficiency is a function of

**compression ratio**and

**κ = c**

_{p}**/c**

**.**

_{v}It is a very useful conclusion because it is desirable to achieve a **high compression ratio** to extract more mechanical energy from a given mass of the air-fuel mixture. A higher compression ratio permits the same combustion temperature to be reached with less fuel while giving a longer expansion cycle. This creates more mechanical power output and **lowers the exhaust temperature**. Lowering the exhaust temperature causes the lowering of the energy rejected to the atmosphere. This relationship is shown in the figure for κ = 1.4, representing ambient air.