Atkinson / Miller Cycle

Modified Otto cycle where the expansion stroke exceeds the compression stroke. The gas expands isentropically all the way to intake pressure, extracting more work before isobaric heat rejection — improving efficiency at the cost of specific power.

Atkinson: mechanical linkage makes compression shorter than expansion.  Miller: same thermodynamic effect via early/late intake-valve closing, often paired with a turbocharger to restore power density. γ = 1.4, T₁ = 300 K, Qin = 800 kJ/kg.

Compression ratio rc10

Efficiency vs Otto

Atkinson efficiency
65.6%
Otto at same r = 10
60.2%
Efficiency gain
+5.4 pp
Expansion ratio re
19.12
Otto+Atkinson gainlosses

Engine States

State 1→ compressState 2→ igniteState 3→ expand past V₁State 4→ exhaust
1→2 Isentropic compression
(starts before BDC in Miller)
2→3 Constant-volume heat addition
(combustion at TDC)
3→4 Isentropic expansion
past V₁ until P = P₁
4→1 Constant-pressure heat rejection
(exhaust at ambient P)

Cycle Diagrams

1→2 Isentropic compression
2→3 Isochoric heat addition
3→4 Isentropic expansion (overexpanded)
4→1 Isobaric heat rejection
Volume V (norm.)0100kPressure P (Pa)V₁1234P–V Diagram
0326652Entropy s (J/kg·K)4008002kTemperature T (K)1234T–S Diagram
0326652Entropy s (J/kg·K)0500k1.6MEnthalpy h (J/kg)1234H–S Diagram

On the P–V diagram, the dashed vertical marks V₁ (compression-start volume). State 4 lies to the right of V₁, showing the overexpansion. The isobaric 4→1 leg on the T–S diagram is shallower than the isochoric 2→3 leg (slope ∝ T; /cp vs /cv).

State Properties

StateT (K)P (kPa)V (norm.)s (J/kg·K)h (kJ/kg)
1300101.31.00000.0
27542545.20.1000455.8
318686308.40.1006521575.6
4574101.31.912652275.1
Thermal efficiency η = 65.6%= 1 − γ·(T₄−T₁)/(T₃−T₂)

Key Relations

Thermal efficiency
η = 1 − γ·(T₄−T₁)/(T₃−T₂)
Expansion endpoint (P₄ = P₁)
V₄ = V₃·(P₃/P₁)1/γ
Isobaric heat rejection (4→1)
Qout = cp·(T₄−T₁)
vs Otto at same rc
ηAtkinson > ηOtto (lower Qout)