For a shallow overhead conductor span with supports at equal height, sag can be estimated as f = wL2/(8H). Here w is weight per unit length in N/m, L is horizontal span in metres, and H is the horizontal component of tension in newtons. The formula describes one stated condition; it does not determine a safe stringing tension, predict every operating temperature, or approve ground clearance. A useful overhead conductor sag calculation therefore starts by defining the geometry and load case, then checks whether the simplified model is appropriate.
Overhead conductor sag calculation starts with three inputs
For the level-span model, sag is the vertical drop from the straight line joining the attachment points to the conductor at midspan. The span is the horizontal distance between those points, not the length of conductor paid out from a drum.
- w: distributed gravitational load for the stated case. A catalogue mass in kg/km is not yet a force in N/m.
- L: horizontal span length. Use metres consistently with the other SI inputs.
- H: horizontal tension for that same condition. It is not rated breaking strength, and it is not necessarily the resultant force at the support.
The parabolic approximation and distinction between tension components are explained in USDA’s RUS Bulletin 1724E-152, Sections 2.2 Ve 2.3. That historical reference is used for mechanics, not current statutory clearance values. CIGRE'ler calculation-methods overview describes the broader analysis scope; its public summary is not the full design procedure.
For a conventional reinforced construction, the ACSR conductor specification supplies the product context. The exact offered construction still needs its own mass and mechanical data. A material acronym alone cannot supply the inputs to a line calculation.
A 200 m example, with units kept visible
The following values are deliberately hypothetical. They are not an XWA product rating, a customer installation or an approved tension schedule. Assume level rigid supports, still air, no ice, a shallow span and a horizontal tension already established for the selected condition.
| Input | Illustrative value | Meaning |
|---|---|---|
| Mass per unit length | 800 kg/km | Total mass of the complete conductor |
| Gravitational acceleration | 9.81 m/s2 | Rounded value used throughout this example |
| Horizontal span L | 200 M | Attachment-point separation |
| Horizontal tension H | 20,000 N | Assumed input, not a recommended setting |
Convert mass before calculating the sag
800 kg/km = 0.800 kg/m. Multiplying by 9.81 gives w = 7.848 N/m.
Then f = (7.848 × 2002)/(8 × 20,000) = 1.962 M, or approximately 1.96 M.
The unit check is useful: (N/m) × M2 / N leaves metres. Entering 800 directly as N/m would produce 200 M, an obviously different result caused by a unit error rather than conductor behaviour. Entering 20 instead of 20,000 would mix kN with N and create another thousandfold error.
Check the approximation against the catenary
For the corresponding ideal flexible conductor with uniform self-weight, the level-span catenary expression is:
f = (H/w)[cosh(wL/(2H)) – 1].
Using the same inputs gives approximately 1.96225 M. The parabolic result is lower by about 0.00025 M, veya 0.013%. This agreement checks only the approximation for these chosen inputs. It says nothing about whether the assumed tension, temperature or surveyed geometry represents a real line.
What changes the result most?
The example can be reused as a sensitivity check without pretending to predict a new installation. Change one variable at a time:
| Change from the example | Held constant | Parabolic sag | Interpretation |
|---|---|---|---|
| No change | All inputs | 1.962 M | Reference case |
| L rises from 200 ile 400 M | w and H | 7.848 M | Twice the span gives four times the sag in this model |
| H rises from 20 ile 40 kN | w and L | 0.981 M | Twice the horizontal tension halves the sag |
| w rises from 7.848 ile 9.810 N/m | H and L | 2.4525 M | A 25% load increase produces a 25% sag increase |
These are mathematical comparisons, not instructions to increase tension. In an actual fixed-length span, a changed load or temperature generally changes tension as well. Strength limits, bağlantı parçaları, supports and vibration considerations must remain satisfied. Holding H constant in a table deliberately removes those interactions to explain the formula.
Nor does the table rank conductor families. Örneğin, an all-aluminum AAC conductor needs its own construction data and permissible design conditions; assigning it the assumed 20 kN merely to compare products would not establish an acceptable design.
Why one sag value cannot describe an operating line
Temperature changes the state, not just a label beside the answer. The geometric formula contains no explicit temperature term because H is already an input for a particular state. To move to another conductor temperature, the analysis must account for the corresponding change in length and tension. Air temperature and conductor temperature are not interchangeable. The separate explanation of weather-dependent ACSR current capacity addresses the thermal side of that relationship.
Initial and final conditions are different. Long-term creep and permanent extension after loading can alter conductor length. CIGRE Science & Engineering No. 30 reports experiments showing that temperature affects creep in the tested aluminum and aluminum-alloy specimens. It also identifies limitations when wire tests are used to represent whole conductors. Its numerical coefficients must not be assigned indiscriminately to another construction.
Wind and ice introduce other load cases. Ice adds weight and changes the exposed diameter; wind introduces lateral load. A vertical, self-weight-only curve cannot describe every displaced position or support force. CIGRE Teknik Broşür 324 frames sag-tension analysis across temperature, wind and ice conditions. Technical Brochure 643 separately addresses elevated-temperature behaviour and conductor hardware. Their scope explains why a one-line calculator is not a complete operating assessment.
Initial and final states must be evaluated under the relevant weather cases; these are intersecting checks, not three mutually exclusive choices.
Stop the simple calculation at these boundaries
Unequal attachment elevations: the lowest point is no longer necessarily at midspan. The level-support formula cannot simply be relabelled for a steep crossing. The actual elevation difference belongs in the geometry.
Multiple connected spans: neighbouring spans and support behaviour affect the tension state. CIGRE Teknik Broşür 763 identifies multi-span calculation errors as a relevant issue in high-temperature uprating. A single isolated-span example should not be treated as a complete section model.
Clearance: sag is measured from the support chord; clearance is measured to the relevant ground, crossing or object. Even an accurate sag value needs the surveyed profile and applicable design requirements before it can establish clearance. No universal clearance is implied by the 1.96 m result.
Kurulum: the example must not be used as a field tension setting. Stringing requires the approved project sag-tension schedule for the specified conductor, span arrangement and conductor temperature, applied by the responsible qualified team.
For XWA’s conductor data submission, the useful boundary is clear: yığın, construction and mechanical information must describe the offered product; the line calculation must describe the actual route and operating states. If the source of H is unknown, the result is only an arithmetic exercise. Resolve that missing input before treating the number as a design conclusion.