Skin Effect / Skin Depth Calculator mechanism

Model scope

The two core formulas are standard under SI-unit and high-frequency assumptions. The instrument should be labelled as a high-frequency isolated-round-wire skin-effect approximation, not as a general AC-resistance calculator. The copper resistivity value 1.68×10^-8 Ω·m at 20 °C is used in three vectors, and the aluminium value 2.82×10^-8 Ω·m at 20 °C is used in one; these are widely tabulated textbook entries. NEEDS_REVIEW is required because the input contract does not specify temperature, magnetic-property convention, validity checking for d≫δ, or the fallback method for thin conductors.

• The skin-depth formula δ=sqrt(ρ/(π f μ)) is standard and equivalent to sqrt(2ρ/(ωμ)), provided f is in hertz, ρ is in ohm-metres, and μ is absolute permeability in henries per metre.
• The round-wire approximation Rac/Rdc ≈ d/(4δ) is only a high-frequency asymptote. It requires d/δ to be much greater than 1; it is not valid for thin conductors or at low frequency, where the ratio approaches 1 rather than 0.
• The claimed effective AC resistance increase is underspecified: the result is only an internal skin-effect resistance ratio for an isolated round conductor, excluding proximity effect, external magnetic fields, strand construction, and other geometry effects.
• Material resistivity must be temperature-qualified, and permeability may be frequency- and field-dependent. A material name alone is insufficient for a generally correct result.

Units and conventions

• Frequency f is in hertz.
• Resistivity ρ is in ohm-metres.
• Wire diameter d is in metres; millimetre inputs must be converted before calculation.
• Permeability μ is absolute permeability in henries per metre, calculated as μ=μrμ0.
• For copper and aluminium in these examples, μr=1 is assumed because they are treated as nonmagnetic conductors.
• The tabulated resistivities are assumed to apply at 20 °C.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "material": "copper",
    "resistivity_ohm_m": 1.68e-8,
    "relative_permeability": 1,
    "frequency_hz": 1000000,
    "wire_diameter_m": 0.01
  },
  "expected_outputs": {
    "skin_depth_m": 0.00006523,
    "skin_depth_um": 65.23,
    "rac_rdc_ratio": 38.33
  },
  "reference_data": {
    "copper_resistivity_ohm_m_20C": 1.68e-8,
    "copper_resistivity_source_convention": "widely tabulated standard value; CRC/IEC textbook value at 20 °C",
    "mu0_H_per_m": 0.0000012566370614,
    "mu0_source_convention": "widely tabulated standard value, μ0=4π×10^-7 H/m",
    "copper_relative_permeability": 1,
    "relative_permeability_source_convention": "widely tabulated standard value for nonmagnetic copper"
  },
  "working": "μ=μrμ0=1×1.2566370614×10^-6=1.2566370614×10^-6 H/m. δ=sqrt(ρ/(πfμ))=sqrt(1.68×10^-8/(π×1.00×10^6×1.2566370614×10^-6))=sqrt(4.2555×10^-9)=6.523×10^-5 m=65.23 μm. d/(4δ)=0.010/(4×6.523×10^-5)=0.010/2.6092×10^-4=38.33. Here d/δ≈153.3, so the high-frequency approximation is appropriate."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The instrument can fail or mislead at zero or negative frequency, and it lacks a defined full Bessel-function calculation for the thin/intermediate-conductor branch. Unit and diameter-versus-radius ambiguity can also change the reported resistance ratio substantially.

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-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json