What is the relationship between sag and horizontal tension?

Under a uniform horizontal load, parabolic midspan sag is inversely proportional to horizontal tension: S = w·L² / (8·H). Halving horizontal tension doubles the midspan sag.

When should the exact catenary formula be used instead of the parabola?

The parabolic formula assumes load is uniformly distributed along the horizontal span. The catenary accounts for weight distributed along the conductor arc length. The 5% sag/span notice is only a screening cue, not a guaranteed error bound; compare both models and use a qualified engineering method for design work.

How does the calculator solve for tension when given a target sag?

For parabolic mode, horizontal tension is obtained analytically: H = w·L² / (8·S). For catenary mode, a bounded numerical root solver finds the catenary constant c such that the exact vertical midspan chord departure equals the target sag.

What is maximum tension vs horizontal tension?

Horizontal tension H is invariant along the horizontal axis. Conductor tension increases along the curve toward each support tower. Maximum tension T_max is the vector sum of horizontal tension and vertical shear force at the higher attachment: T_max = √(H² + V²).

Does this tool replace full ruling-span software like Southwire SAG10?

No. This tool models single-span static equilibrium for specified parameters. Full transmission design requires thermal state changes, conductor elasticity, creep, ruling span distributions, and ice/wind code districts.

Sag Tension Calculator

Solve for midspan sag given tension or solve for required horizontal tension given measured sag, using exact catenary or parabolic models.

Span & Conductor Parameters

Calculation Goal

Governing Model

Parabolic Catenary (Exact)

Horizontal Span Length (L)

Conductor Unit Weight (w)

Horizontal Tension (H)

Support Elevation Difference (h)

Height of right tower relative to left tower (≥ 0).

Midspan Sag

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Max Tension (T_max)

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Catenary Param (c)

—

Sag / Span Ratio

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Conductor Deflection Profile

Chord midspan vertical offset

Static Solution Breakdown

Governing Equations

Standard Unit Definitions & Relationships

1 foot = exactly 0.3048 m (NIST SP 811).
1 lbf = 4.448222 N; 1 lb/ft = 14.593903 N/m.
Catenary Constant: $c = H / w$ in length units, indicating the length of conductor whose weight matches horizontal tension.
Parabolic Departure: Midspan vertical chord sag is $S = \frac{w L^2}{8 H}$ for both level and uniform horizontal projected load inclinations.
Exact Support Tension: True vector tension at support is $T = \sqrt{H^2 + V^2} = H \cosh((x - x_0)/c)$, never simple scalar addition.

Scope & Engineering Limitations

This calculator isolates static single-span catenary and parabolic mechanics. Field transmission line engineering requires comprehensive rulings:

Nonlinear conductor stress-strain, creep elongation, and thermal expansion.
Radial glaze ice, transverse wind pressures, and structural support flexibility.

Authorities: USDA RUS 1724E-152 Southwire SAG10® Osmose O-Calc Pro NIST SP 811

Summary

Solve for midspan sag given tension or solve for required horizontal tension given measured sag, using exact catenary or parabolic models.

How it works

Select calculation mode: solve for midspan sag from horizontal tension, or solve for tension from target sag.
Choose the formula model: Parabolic (governing small sag/span ratios) or Catenary (exact hyperbolic profile).
Enter span length, conductor unit weight, and either horizontal tension or midspan chord sag.
Optionally add elevation difference between support towers for inclined span profiles.
Review calculated horizontal tension, maximum support tension, catenary constant, arc length, and interactive profile diagram.

Use cases

Calculate midspan vertical clearance sag under specified conductor stringing tension.
Determine horizontal and maximum tension from field-measured midspan sag during line inspections.
Compare parabolic approximations with exact hyperbolic catenary formulations across span lengths.
Analyze inclined spans on hilly terrain where tower attachments sit at unequal elevations.
Verify conductor arc length and catenary constant for ruling-span documentation.

Frequently Asked Questions

Last updated: 2026-09-20 · Reviewed by Nham Vu