Source: https://guthlabs.ai/docs/instruments/belt-friction-capstan-equation/implementation/

instrument implementation / implementation-contract

# Belt Friction (Capstan Equation) implementation

A source-bound implementation contract for Belt Friction (Capstan Equation); deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/belt-friction-capstan-equation/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/belt-friction-capstan-equation/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/belt-friction-capstan-equation/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`