Source: https://guthlabs.ai/docs/instruments/dual-sabathe-cycle-efficiency-calculator/mechanism/

instrument mechanism / verified-clean

# Dual (Sabathé) Cycle Efficiency Calculator mechanism

The inspectable method record for Dual (Sabathé) Cycle Efficiency Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/dual-sabathe-cycle-efficiency-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/dual-sabathe-cycle-efficiency-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/dual-sabathe-cycle-efficiency-calculator/qualification/>)

## 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`