Belt Friction (Capstan Equation)

Inspectable records

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