Source: https://guthlabs.ai/docs/instruments/flywheel-energy-storage-calculator/mechanism/

instrument mechanism / verified-with-binding-errata

# Flywheel Energy Storage Calculator mechanism

The inspectable method record for Flywheel Energy Storage Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**

## Model scope

The core KE and fluctuation formulas are standard under the stated unit and averaging assumptions, but the missing definition of omega_avg, ambiguous KE reference speed, and absent required-inertia formula prevent an unconditional PASS. Add explicit input/output definitions, unit conversion, domain validation, and a division-by-zero policy.

- The kinetic-energy formula is correct only when omega is angular speed in rad/s, but the spec does not define whether omega means average, maximum, minimum, or another operating speed.

- The coefficient formula is standard when omega_avg is the arithmetic mean, omega_avg=(omega_max+omega_min)/2; that definition is missing.

- The stated delta-energy formula is correct for the arithmetic mean speed: 0.5I(omega_max^2-omega_min^2)=I*omega_avg^2*Cs. It is not generally valid for an unspecified alternative definition of average speed.

- The formula for required inertia is missing. For nonzero omega_avg and Cs, it should be I_required=deltaE_target/(omega_avg^2*Cs).

- The output 'KE stored' is ambiguous unless the speed at which stored energy is reported is explicitly identified, normally KE at omega_avg or KE at a specified operating speed.

## Units and conventions

- I is in kg·m².

- Angular speeds are in rad/s; rpm must be converted using omega=rpm*2*pi/60.

- omega_avg is assumed to be the arithmetic mean of omega_max and omega_min.

- Cs is dimensionless.

- KE and deltaE are in joules.

- Required inertia is in kg·m².

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "I_kg_m2": 2.5,
    "omega_min_rad_s": 98,
    "omega_max_rad_s": 102,
    "omega_avg_rad_s": 100,
    "target_deltaE_J": 1000
  },
  "expected_outputs": {
    "KE_at_omega_avg_J": 12500,
    "Cs": 0.04,
    "deltaE_J": 1000,
    "required_I_kg_m2": 2.5
  },
  "working": "KE=0.5*2.5*100^2=1.25*10000=12500 J. Cs=(102-98)/100=4/100=0.04. deltaE=2.5*100^2*0.04=2.5*10000*0.04=1000 J. I_required=1000/(100^2*0.04)=1000/400=2.5 kg·m²."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The zero-average-speed input makes Cs and required inertia undefined because the denominator vanishes; the calculator should reject it. The unit probe also exposes a large numerical error if rpm is interpreted as rad/s without conversion.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/flywheel-energy-storage-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/flywheel-energy-storage-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/flywheel-energy-storage-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`