Source: https://guthlabs.ai/docs/instruments/dual-sabathe-cycle-efficiency-calculator/
instrument / verified-clean
# Dual (Sabathé) Cycle Efficiency Calculator
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Thermodynamics, Fluids & Aero
**Tranche**: tranche-4
**Evidence ID**: t4-012
**Ledger rows**: 1
No ledger note is attached.
## Review findings
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.
### Formula and scope findings
- 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.
### Unit assumptions
- 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.
## Boundary hardening
**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.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"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."
}
````
## Related workflows
[Engine Cycle Comparatorreal-engine blend]()
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche4/tranche4-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`