Flywheel Energy Storage Calculator mechanism

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

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