Source: https://guthlabs.ai/docs/instruments/mach-number-calculator/mechanism/

instrument mechanism / verified-clean

# Mach Number Calculator mechanism

The inspectable method record for Mach Number Calculator, kept separate from implementation and qualification.

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

## Model scope

The mathematical formulas pass standard ideal-gas compressible-flow verification, but the specification needs review because γ, R, unit handling, ISA implementation, altitude definition, temperature precedence, valid ranges, and honest labeling are unspecified.

- The formulas M=V/a and a=√(γRT) are standard and correct for Mach number and ideal-gas speed of sound, but γ and R are not specified in the instrument spec.

- Altitude-based temperature is underspecified: the ISA table, altitude reference, atmospheric layer rules, and valid altitude range are not defined.

- The input declaration "altitude or T" does not specify how the calculator selects or validates temperature when both are supplied, nor whether altitude is geometric or geopotential.

## Units and conventions

- Velocity V and speed of sound a must use the same units; test vectors use m/s unless explicitly stated otherwise.

- For the SI calculations, γ=1.4 for air and R=287.05 J/(kg·K).

- T is static absolute temperature in kelvin, not Celsius or Fahrenheit.

- Altitude-based temperatures use the International Standard Atmosphere (ISA): T=288.15−0.0065h for the troposphere up to 11,000 m, with h in meters.

- The knot conversion used is 1 kt=0.514444 m/s.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "velocity": 170.1461435,
    "velocity_unit": "m/s",
    "temperature": 288.15,
    "temperature_unit": "K",
    "gamma": 1.4,
    "R": 287.05
  },
  "expected_outputs": {
    "mach_number": 0.5,
    "speed_of_sound_m_per_s": 340.2923
  },
  "working": "a=√(γRT)=√(1.4×287.05×288.15)=√115798.8405=340.2923 m/s. M=V/a=170.1461435/340.2923=0.5000."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

A zero-temperature input makes the speed of sound zero and the Mach-number denominator vanish; the instrument must reject it instead of exposing a JavaScript Infinity or undefined result. The altitude-based ISA calculation also requires an unstated table/branch convention at 11000 m, and signed velocity creates an explicit Mach-sign convention ambiguity.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/mach-number-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/mach-number-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/mach-number-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-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`