Belt Friction (Capstan Equation) implementation

Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

Record owner

Guth Instruments

Lifecycle

verified-clean

Evidence ID

t4-178

Effect

Computation or source lookup only

Input and validation requirements

• If T2 = 0, the stated ratio T1/T2 is undefined, even though direct evaluation of T1 = T2e^(μθ) gives zero.
• A degree value passed as radians produces an incorrect result; the interface must label the angle unit explicitly.
• Negative θ, negative μ, or negative tensions are physically invalid or reverse the intended tight/slack-side interpretation and should be rejected.
• For very large μθ, e^(μθ) can overflow numerically; an upper input bound or logarithmic handling may be needed.
• The equality should not be presented as an achievable ordinary operating ratio unless impending slip is explicitly specified.

Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "inputs": {
    "T2_N": 500,
    "mu": 0.2,
    "theta_rad": 1.5707963267948966
  },
  "expected_outputs": {
    "T1_N": 684.5535
  },
  "working": "μθ = 0.2 × 1.5707963268 = 0.3141592654. e^(μθ) = e^0.3141592654 ≈ 1.369107. T1 = T2 × e^(μθ) = 500 × 1.369107 = 684.5535 N."
}

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