The expansion ratio R is the ratio of

Where v₁ = volume at the beginning of expansion and v₂ = volume at the end of expansion.

Concept:

For the Diesel cycle:

Processes involved in compression engine (diesel cycle) are:

3-4: Reversible adiabatic compression

4-1: Constant pressure heat addition

1-2: Reversible adiabatic expansion

2-3: Constant volume of heat rejection

Now 

The compression ratio is given by

.....(V2 = V3)

The cut-off ratio is given by

The expansion ratio is given by 

but we know that, 

∴ rc × re = r