Dual (Sabathé) Cycle Efficiency Calculator mechanism

Model scope

The stated honest label, "air-standard idealization," is appropriate but should also disclose ideal-gas behavior, constant γ, internally reversible compression/expansion, and idealized heat-addition processes. Efficiency is verifiable from the four listed inputs; net work is not.

• The efficiency formula is the standard air-standard dual-cycle formula: η=1−r^(1−γ)·(αβ^γ−1)/[(α−1)+γα(β−1)], assuming r is compression ratio, α is the constant-volume pressure ratio, β is the constant-pressure cutoff volume ratio, and γ=Cp/Cv is constant.
• The claimed net-work output has no formula and cannot be determined from only r, α, β, and γ. Additional state data such as mass and heat input, or a specified initial pressure, temperature, and volume, are required.
• The formula requires explicit domain constraints: r>1, α≥1, β≥1, and γ>1. The simultaneous boundary case α=1 and β=1 makes the displayed fraction 0/0 and requires a limiting-case implementation.

Units and conventions

• r, α, and β are dimensionless ratios: r=V1/V2, α=P3/P2, and β=V4/V3.
• γ=Cp/Cv is dimensionless and assumed constant; for an air-standard model it is commonly approximately 1.4.
• All pressures and volumes used to form α and β must use consistent units, although the resulting ratios are unitless.
• η is dimensionless and should be reported as a fraction or percentage.
• No numerical net work can be computed from the listed inputs alone; work would need a mass basis and thermodynamic state or heat-input specification.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "r": 8,
    "alpha": 1.5,
    "beta": 1,
    "gamma": 1.4
  },
  "expected_outputs": {
    "eta": 0.564725,
    "net_work": null
  },
  "working": "β^γ=1^1.4=1. Numerator=αβ^γ−1=1.5×1−1=0.5. Denominator=(α−1)+γα(β−1)=(1.5−1)+1.4×1.5×(1−1)=0.5+0=0.5. r^(γ−1)=8^0.4≈2.297397, so r^(1−γ)=1/2.297397≈0.435275. η=1−0.435275×(0.5/0.5)=1−0.435275=0.564725. β=1 is the boundary case reducing to the Otto-cycle result. Net work is undetermined."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The formula has a direct 0/0 undefined-result trap at alpha=1 and beta=1, which must be rejected. Additionally, the advertised net-work output cannot be computed from the supplied dimensionless inputs because no heat-input or energy scale is specified. The specification also omits the pressure-ratio direction and physical-domain rules.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json