Editing Diesel cycle (section)

=== Maximum thermal efficiency ===
The maximum thermal efficiency of a Diesel cycle is dependent on the compression ratio and the cut-off ratio. It has the following formula under cold [[Standard state|air standard]] analysis: 

<math>\eta_{th}=1-\frac{1}{r^{\gamma-1}}\left ( \frac{\alpha^{\gamma}-1}{\gamma(\alpha-1)} \right )</math>

where
:<math>\eta_{th} </math> is [[thermal efficiency]]
:<math>\alpha</math> is the cut-off ratio <math>\frac{V_3}{V_2}</math> (ratio between the end and start volume for the combustion phase)
:{{math|r}} is the [[compression ratio]] <math>\frac{V_1}{V_2}</math>
:<math>\gamma </math> is ratio of [[specific heat capacity|specific heats]] (C<sub>p</sub>/C<sub>v</sub>)<ref>{{cite web| url = http://230nsc1.phy-astr.gsu.edu/hbase/thermo/diesel.html| title = The Diesel Engine}}</ref>

The cut-off ratio can be expressed in terms of temperature as shown below:
:<math>\frac{T_2}{T_1} ={\left(\frac{V_1}{V_2}\right)^{\gamma-1}} = r^{\gamma-1}</math>

:<math> \displaystyle {T_2} ={T_1} r^{\gamma-1} </math>

:<math>\frac{V_3}{V_2} = \frac{T_3}{T_2}</math>

:<math>\alpha = \left(\frac{T_3}{T_1}\right)\left(\frac{1}{r^{\gamma-1}}\right)</math>

<math>T_3</math> can be approximated to the flame temperature of the fuel used. The flame temperature can be approximated to the [[adiabatic flame temperature]] of the fuel with corresponding air-to-fuel ratio and compression pressure, <math>p_3</math>.
<math>T_1</math> can be approximated to the inlet air temperature.

This formula only gives the ideal thermal efficiency. The actual thermal efficiency will be significantly lower due to heat and friction losses. The formula is more complex than the [[Otto cycle]] (petrol/gasoline engine) relation that has the following formula:

<math>\eta_{otto,th}=1-\frac{1}{r^{\gamma-1}}</math>

The additional complexity for the Diesel formula comes around since the heat addition is at constant pressure and the heat rejection is at constant volume. The Otto cycle by comparison has both the heat addition and rejection at constant volume.