Source: https://guthlabs.ai/docs/instruments/cable-catenary-sag-tension-calculator/implementation/

instrument implementation / implementation-contract

# Cable/Catenary Sag-Tension Calculator implementation

A source-bound implementation contract for Cable/Catenary Sag-Tension Calculator; deployment and executable qualification remain separate.

Status: **VERIFIED_WITH_ERRATA**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-with-binding-errata

**Evidence ID**: t6-140

**Effect**: Computation or source lookup only

## Input and validation requirements

The calculator breaks on zero span because T_max and cable length become undefined through division by zero; it also has a physical-convention hazard when a signed negative load is supplied and the interface does not specify whether load means signed force or nonnegative magnitude.

## Required corrections

````
[
  {
    "vector": 2,
    "field": "cable_length_m",
    "wrong": 94.542454,
    "correct": 29.578857,
    "cause": "10× slip inside her own Correction: writes 5*1.443635475=72.1817738 (true 7.218); a 20 m span with 10 m sag cannot be 94.5 m of cable"
  }
]
````

## Inspectable interface fixture

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

````
{
  "inputs": {
    "mode": "parabolic",
    "L_m": 100,
    "sag_d_m": 5,
    "load_w_kN_per_m": 1
  },
  "expected_outputs": {
    "T_horizontal_kN": 250,
    "T_max_kN": 254.950976,
    "cable_length_m": 100.662723
  },
  "working": "T_h=wL^2/(8d)=1·100^2/(8·5)=10000/40=250 kN. 4d/L=20/100=0.2. T_max=T_h·sqrt(1+(4d/L)^2)=250·sqrt(1+0.2^2)=250·sqrt(1.04)=250·1.019803903=254.950976 kN. Using the standard parabolic arc-length formula, S=(L/2)sqrt(1+(4d/L)^2)+(L^2/(8d))asinh(4d/L)=50·1.019803903+250·asinh(0.2)=50.9901952+250·0.198690110=100.662723 m."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/cable-catenary-sag-tension-calculator/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/cable-catenary-sag-tension-calculator/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/cable-catenary-sag-tension-calculator/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-tranche6/tranche6-results.json`

- `tranche errata record`