When to use: Estimate the midspan sag of an overhead transmission or distribution conductor using the standard parabolic approximation D = wS²/(8T) for a level span, then check the resulting ground clearance against a minimum clearance you supply for your jurisdiction/voltage class. This approximation is accurate when sag is small relative to span (roughly D/S below ~5%); longer or more sagging spans need the full catenary solution.
Sag increases with conductor temperature (thermal elongation) and with ice/wind loading (added weight, reduced effective tension). This calculator uses a fixed tension you supply for one condition — repeat with the tension and weight for your governing high-temperature or heavy-loading case. Precise final-sag-at-any-temperature work requires the full catenary equation and a stress-strain (creep/elastic) analysis, not this parabolic approximation.
This tool estimates the midspan sag of an overhead transmission or distribution conductor for a level span using the parabolic approximation, and checks the resulting ground clearance against a minimum you supply. It's intended for preliminary line design and teaching — final sag-tension design uses the full catenary equation with stress-strain (creep and elastic elongation) data for the specific conductor and every governing loading/temperature case.
For a level span with horizontal tension T (lb) and conductor unit weight w (lb/ft, including any ice/wind loading), the midspan sag is D = wS²/(8T), where S is the span length in feet. This comes from approximating the true catenary curve — y = (T/w)[cosh(wx/T) − 1] — as a parabola, which is an excellent approximation whenever the sag-to-span ratio D/S is small (a common rule of thumb is below roughly 5%). Overhead transmission lines are almost always designed within this range, which is why the parabolic formula is the standard hand-calculation method taught for preliminary sag-tension work.
Horizontal tension is typically set as a percentage of the conductor's rated breaking strength (RBS) at the initial unloaded, everyday condition — commonly in the range of roughly 15–25% RBS, with the exact value driven by the utility's design criteria, vibration/aeolian-fatigue limits, and the governing NESC/utility loading district. This tool lets you enter tension directly or derive it from RBS and a %RBS design value you choose.
Sag is not fixed — it changes with conductor temperature and with ice and wind loading. As conductor temperature rises (from current-carrying I²R heating and ambient conditions), the conductor elongates thermally and sag increases; this is why the maximum-operating-temperature case, not the everyday (25°C) case, governs minimum ground clearance. Ice accretion and wind loading add weight and transverse force, changing the effective tension and increasing sag under the combined ice/wind load case used in NESC loading districts (heavy, medium, light).
This calculator computes sag for one weight/tension pair at a time — to find the governing clearance case, run it once for everyday conditions and again for your maximum-temperature and maximum ice-loading cases, using the conductor manufacturer's sag-tension chart or a full stress-strain (creep-corrected) analysis for the tension at each condition. This parabolic tool does not perform that stress-strain analysis itself.
Actual clearance at midspan is approximately the support attachment height minus the sag (for a level span): clearance = H_attach − D. Compare this against the minimum clearance required for your voltage class, terrain, and crossing type — these values come from ANSI/IEEE C2 (the National Electrical Safety Code) Rule 232 tables or the equivalent governing code in your jurisdiction, and vary by voltage, whether the span crosses roads/rail/waterways, and vertical vs. horizontal clearance case. Enter the exact value that applies to your project rather than relying on a single generic number — the required clearance is jurisdiction- and case-specific.
The parabolic approximation D = wS²/(8T) assumes the sag is small relative to the span. As the sag-to-span ratio grows (long spans, low tension, or heavy loading), the true catenary shape deviates more from a parabola and the approximation error grows. For long spans, deep river/valley crossings, or any case where D/S exceeds roughly 5-10%, use the full catenary equation instead.
Utilities typically limit initial (unloaded, everyday-temperature) tension to a percentage of the conductor's rated breaking strength — often in the range of roughly 15-25% RBS — to control aeolian vibration fatigue over the line's life, with the final loaded tension checked against a higher percentage under the maximum ice/wind design case. The exact limits come from the utility's design standard or NESC district practice, not a single universal number.
Higher tension reduces sag, but it also increases conductor stress, tower/pole loading, and aeolian vibration fatigue risk, and it reduces the margin to the conductor's rated breaking strength under storm loading. Sag-tension design balances clearance against these competing limits — it is not simply "maximize tension."
Use the minimum vertical clearance required by the National Electrical Safety Code (ANSI/IEEE C2) table applicable to your voltage class and crossing type, or your utility's or AHJ's governing standard if more stringent. This tool intentionally does not hard-code a specific NESC clearance value since it depends on voltage, span type, and jurisdiction — enter the value that applies to your project.
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