Source: https://guthlabs.ai/docs/instruments/cable-catenary-sag-tension-calculator/
instrument / verified-with-binding-errata
# Cable/Catenary Sag-Tension Calculator
The current ledger marks this instrument verified with errata that must be applied at binding time.
Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified with errata that must be applied at binding time.
**Area**: Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration
**Tranche**: tranche-6
**Evidence ID**: t6-140
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The uniform-load parabolic formulas are mathematically sound under the stated assumptions, and the exact catenary test uses a fully specified symmetric equal-support interpretation. However, the specification omits the cable-length formula, exact-catenary parameter relations and convergence details, and claims point-load capability without providing a point-load algorithm. These ambiguities require review before catalog approval.
### Formula and scope findings
- The parabolic formulas for horizontal tension and maximum tension are standard for a level-span cable with uniform load w per unit horizontal span, but that load convention is not stated.
- The cable-length formula is missing. Under the parabolic approximation, the standard length is S=(L/2)sqrt(1+(4d/L)^2)+(L^2/(8d))asinh(4d/L).
- The exact catenary equation y=a·cosh(x/a) requires a vertical datum and horizontal origin; for a symmetric cable with its lowest point at x=0, the sag-referenced equation is y=a[cosh(x/a)-1].
- Exact catenary mode must define the relation used to solve a: d=a[cosh(L/(2a))-1], assuming equal-level supports and uniform load per unit horizontal length. It must also define T_h=w·a, T_max=w·a·cosh(L/(2a)), and S=2a·sinh(L/(2a)).
- Point loads are claimed in the description, but no point-load statics equations, load locations, or piecewise cable geometry are specified. The listed uniform-load parabolic and catenary formulas do not handle arbitrary point loads.
- The parabolic approximation becomes inaccurate for large d/L; no numerical validity threshold is specified despite the honest label referring to small sag-to-span ratio.
### Unit assumptions
- L and d use the same length unit.
- w is force per unit horizontal span, such as kN/m or N/m; it is not force per unit cable length.
- T_h and T_max have the same force unit as w multiplied by the length unit.
- For the exact catenary vectors, the cable is symmetric, supports are at equal elevation, and the lowest point is at midspan.
- Inverse hyperbolic sine is dimensionless and is evaluated as asinh(x)=ln(x+sqrt(1+x^2)).
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
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.
## Errata and corrections
### Tranche errata
**cable_length_m** · vector 2
94.542454
29.578857
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 example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"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."
}
````
## 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_WITH_ERRATA`
- `evidence-tranche6/tranche6-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`