Source: https://guthlabs.ai/docs/instruments/normal-shock-relations-calculator/
instrument / verified-with-binding-errata
# Normal Shock Relations Calculator
The current ledger marks this instrument verified with errata that must be applied at binding time.
Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**
## 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 with errata that must be applied at binding time.
**Area**: Thermodynamics, Fluids & Aero
**Tranche**: tranche-5
**Evidence ID**: t5-086
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The supplied M2 and static-pressure formulas are standard for a perfect-gas normal shock. The specification fails because three claimed outputs lack formulas and the stagnation-pressure-loss label is undefined. The implementation should add the missing standard relations, define the loss convention, validate gamma>1 and M1>1, and clearly identify the perfect-gas normal-shock assumptions.
### Formula and scope findings
- The supplied formulas correctly define M2² and P2/P1 for a perfect-gas normal shock, assuming M1 and gamma are dimensionless and M1 is in the supersonic regime.
- Formulas are missing for the claimed outputs T2/T1 and rho2/rho1. Standard formulas are rho2/rho1=((gamma+1)M1²)/((gamma-1)M1²+2) and T2/T1=(P2/P1)/(rho2/rho1).
- The formula for stagnation pressure loss is missing. If the intended output is the stagnation-pressure ratio P02/P01, the standard formula is [((gamma+1)M1²)/((gamma-1)M1²+2)]^(gamma/(gamma-1))*[((gamma+1))/(2gamma M1²-(gamma-1))]^(1/(gamma-1)).
- The phrase 'stagnation pressure loss' is ambiguous: it must specify whether the output is the ratio P02/P01, fractional loss 1-P02/P01, or percentage loss 100(1-P02/P01).
### Unit assumptions
- M1 is dimensionless Mach number.
- gamma is dimensionless ratio of specific heats, normally constant with gamma>1; air is commonly modeled with gamma=1.4.
- All pressure, temperature, and density outputs are dimensionless ratios, so the upstream and downstream quantities must use matching units.
- The supplied relations assume a perfect gas and an adiabatic, one-dimensional normal shock with negligible body-force effects.
- The honest-label restriction M1>1 must be enforced for a physical compressive normal shock; M1=1 is the zero-strength limiting case, not a finite shock.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
The calculator breaks or must reject several edge inputs: the exact M1=1 boundary violates the strict validity condition, gamma=1 and M1=0 causes a zero denominator and undefined results, and a subsonic input produces formal algebraic values despite being outside the normal-shock branch. Signed Mach-number handling is also convention-dependent.
## Errata and corrections
### Tranche errata
**T2_T1** · vector 2
1.0641115702
1.0649380165
T2/T1 must equal her own correct P2/P1 ÷ rho2/rho1 (1.245/1.169082)
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"M1": 2,
"gamma": 1.4
},
"expected_outputs": {
"M2": 0.5773502692,
"P2_P1": 4.5,
"T2_T1": 1.6875,
"rho2_rho1": 2.6666666667,
"P02_P01": 0.7208738615
},
"working": "M1²=2²=4. M2²=(1+((1.4-1)/2)×4)/(1.4×4-(1.4-1)/2)=(1+0.2×4)/(5.6-0.2)=1.8/5.4=1/3, so M2=√(1/3)=0.5773502692. P2/P1=1+[2×1.4/(1.4+1)]×(4-1)=1+(2.8/2.4)×3=1+3.5=4.5. rho2/rho1=((1.4+1)×4)/((1.4-1)×4+2)=9.6/3.6=2.6666666667. T2/T1=4.5/2.6666666667=1.6875. P02/P01=(2.6666666667)^3.5×(2.4/10.8)^2.5=0.7208738615."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_WITH_ERRATA`
- `evidence-tranche5/tranche5-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`