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

instrument / verified-clean

# Belt Friction (Capstan Equation)

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/belt-friction-capstan-equation/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/belt-friction-capstan-equation/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/belt-friction-capstan-equation/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/belt-friction-capstan-equation/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration

**Tranche**: tranche-4

**Evidence ID**: t4-178

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The core capstan limiting relation is standard, but the specification needs an explicit impending-slip/maximum-ratio label and an exact definition of the alternative "max holding load" output. The empty honest_label is a concern because the equality is a limiting condition, not a universal operating tension ratio.

### Formula and scope findings

- T1/T2 = e^(μθ) is the limiting capstan relation at impending slip, not the general tension ratio during static no-slip operation; generally T1/T2 ≤ e^(μθ).

- The claim that the instrument outputs a "max holding load" is underspecified: the loaded side, applied load, anchor condition, and whether T1 or T2 is solved must be defined.

- The formula requires positive tension values and a nonnegative friction coefficient; these input constraints are not stated.

### Unit assumptions

- θ must be supplied in radians; degrees must be converted using θ_rad = θ_deg × π/180.

- μ is dimensionless and is assumed to be a constant friction coefficient over the contact surface.

- T1 and T2 use the same force units, such as newtons; the ratio is dimensionless.

- The equality assumes a flexible belt or rope, uniform contact, negligible bending stiffness and centrifugal effects, and impending slip under a Coulomb-friction model.

## Boundary hardening

### Recorded hazards

- 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.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "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."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche4/tranche4-results.json`