Calculator
Example data table
| Case | Span L (m) | Load w (kN/m) | H (kN) | Sag f (m) | Tmax (kN) | Cable length S (m) |
|---|---|---|---|---|---|---|
| Sample (catenary) | 30 | 0.45 | 25 | 2.04 | 25.92 | 30.37 |
| Sample (parabolic) | 30 | 0.45 | 25 | 2.03 | 25.80 | 30.37 |
Formula used
This calculator supports two common representations for a messenger wire between level supports. Choose the method that matches your required accuracy and sag range.
Catenary method (exact)
For a flexible cable under uniform distributed load along the cable length, the curve follows a catenary. Let L be span length, w load per unit length, and H horizontal tension.
- f = (H / w) [ cosh( (w L) / (2 H) ) − 1 ]
- S = 2 (H / w) sinh( (w L) / (2 H) )
- V = H sinh( (w L) / (2 H) )
- Tmax = √(H² + V²)
Parabolic method (approx.)
For relatively small sag, a parabola provides a quick approximation. The midspan sag is estimated by:
- f ≈ (w L²) / (8 H)
- Tmax ≈ √(H² + (w L / 2)²)
- S ≈ L + (8 f²) / (3 L)
How to use this calculator
- Select a solve mode: compute sag from a known tension, or compute tension for a desired sag.
- Choose the method: catenary for higher accuracy, parabolic for quick checks.
- Enter span length and distributed load, then provide the required tension or sag.
- If available, enter breaking strength and a safety factor to check allowable tension.
- Press Submit to show results under the page header.
- Use Download CSV or Download PDF to export the latest results.
Professional guidance article
1) Why messenger wire sag matters
Messenger wires support bundled services and attachments, so sag directly affects clearance, component stress, and installation safety. On a 30 m span, even a 0.45 kN/m line load can produce about 2 m sag if horizontal tension is near 25 kN. Using a consistent approach helps teams align field setpoints with design intent.
2) Data you should prepare
Collect the span length, the total distributed load per length, and either a target sag or a known horizontal tension. For load, combine self‑weight of the messenger wire plus brackets, clamps, cable trays, or temporary rigging. If loads vary by segment, use a conservative average for preliminary checks, then refine for critical spans.
3) Selecting catenary vs parabolic
The catenary method models the exact curve for a flexible cable under uniform load along its length and is recommended when sag is moderate to large. The parabolic method is faster and works well when sag is small relative to span. If your sag is more than roughly 1/20 of the span, prefer the catenary option.
4) Reading the outputs professionally
Midspan sag indicates clearance impact, while the maximum support tension governs anchors, dead‑ends, and fittings. The vertical component at the support helps estimate reactions transferred to structures. Cable length supports ordering, cutting, and allowances for hardware take‑up, but always add project‑specific waste factors.
5) Example workflow for documentation
Start with the desired clearance and convert it into a target sag. Solve tension from sag using the catenary option, then compare the computed maximum tension against an allowable limit derived from breaking strength and a safety factor. Export the result set and attach it to lift plans, method statements, or inspection records for consistent traceability.
FAQs
1) What does “distributed load” represent?
It is the total load per unit length carried by the messenger wire, including self‑weight and attachments. Use consistent units and include any temporary rigging loads when checking installation stages.
2) When should I use the catenary method?
Use it when sag is not very small compared to span, or when you need higher accuracy for tension and length. It better represents the true curve of a loaded flexible cable.
3) Is the parabolic method wrong?
No. It is an approximation that performs well for small sag-to-span ratios. For large sag, it can under‑ or over‑estimate key outputs, so switch to catenary for critical decisions.
4) What is the difference between H and Tmax?
H is the horizontal component of tension. Tmax is the combined tension at the supports, accounting for both horizontal and vertical components. Hardware and anchors are usually governed by Tmax.
5) How do temperature and installation affect sag?
Temperature changes wire length and therefore sag and tension. Installation practices, clamp positions, and pre‑tensioning also shift results. Use this tool for baseline checks and confirm with field measurements.
6) How do I use breaking strength and safety factor here?
Enter the rated breaking strength and a safety factor to compute an allowable tension. Compare allowable tension to Tmax. If utilization exceeds 1.0, revise sag, span arrangement, or hardware selection.
7) Can I model unequal support elevations?
This page assumes level supports and a symmetric span for clarity. For unequal elevations, the low point shifts and tensions change. Use a dedicated asymmetrical catenary analysis when elevations differ significantly.