Sag & Tension Calculator

Method

Catenary. Each condition is solved on the exact catenary for horizontal tension H and resultant unit load w. Conductor length between supports is L = √(h² + (2a·sinh(S/2a))²), with a = H/w, horizontal span S and height difference h.

Change of state. The zero-tension length L₀ is fixed by the tension basis. Every other condition solves for the H where the catenary length equals L₀·(1 + α·ΔT + H/EA + ε_p). The solver uses bisection. This is the Linear Elongation (LE) model of CIGRE TB 324 §5.2, using the published final modulus E.

Initial and final. Initial uses ε_p = 0. Final adds a fixed permanent-elongation allowance (creep plus settlement) of 600 µε. This is TB 324's Simplified Plastic Elongation (SPE) model, §5.3. All-aluminium conductors (AAC, AAAC) usually creep more than ACSR, so adjust the allowance to your data.

Loads (NESC Rule 250B, Table 250-1). w = √((w_c + w_ice)² + (P·(D + 2t)/12)²) + k, with ice at 56 lb/ft³ (Rule 250B). Values checked against NESC 2023 Tables 250-1 and 251-1:

• Heavy: 0.50 in ice, 4 lb/ft², 0 °F, k = 0.30 lb/ft
• Medium: 0.25 in ice, 4 lb/ft², 15 °F, k = 0.20 lb/ft
• Light: no ice, 9 lb/ft², 30 °F, k = 0.05 lb/ft

250C is extreme wind at 60 °F with no ice and k = 0 (Table 251-1): P = 0.00256·V²·kz·GRF·Cf, entered as one factor. The default 1.15 is the simplified kz·GRF that Rule 250C Note 2 allows for structures up to 165 ft and spans up to 2000 ft, with Cf = 1.0 (Rule 251A2); use Tables 250-2 and 250-3(b) for a closer value. V is the Figure 250-2 basic wind speed (Grade B 100-yr or Grade C 50-yr map). 250D is the Figure 250-3 radial ice with concurrent wind at 15 °F, k = 0, ice 56 lb/ft³. The pressure is taken from Table 250-4 at 30–80 mph (otherwise 0.00256·V²). For Grade C, multiply the map ice by 0.80 before entering it (Rule 250D2).

Tension basis. In %RBS limits mode, the largest stringing tension is found that keeps the maximum support tension within all of these:

• the 250B loaded limit (initial)
• the initial unloaded limit
• the final unloaded limit, at the chosen temperature
• the 250C/D limit (80%, can be cleared)

The defaults follow NESC 2023 Rule 261H1: 60% RBS under the 250B load and 80% under 250C/250D (Rule 261H1a), and, where tension limits are used for Aeolian-vibration mitigation, 35% initial and 25% final unloaded at the Table 251-1 temperature of the district (Rule 261H1c): 0 °F Heavy, 15 °F Medium, 30 °F Light. The unloaded temperature follows the district automatically and can be overridden. The binding limit is reported. In Design tension mode, the entered horizontal tension is applied at the chosen temperature and condition.

Multi span (ruling span). For a tangent section between two dead ends with suspension supports, the horizontal tension is taken as equal in every span and the section is solved on the ruling span S_r = √(ΣS_i³ / ΣS_i) (CIGRE TB 324 §4.3; IEEE Std 524 ruling-span method). All NESC cases and limits above are applied to S_r, level. Each span's sag is then the catenary sag of that span at the ruling-span H and load, which is close to sag_r·(S_i/S_r)². Span lengths are horizontal components. Each pole is entered by its length (stick length); a blank length is the same as the previous pole (the first defaults to 40 ft). Setting depth = 0.10 × length + 2 ft (the common 10%-plus-2-ft embedment rule; confirm against the utility standard and soil), and the attachment height is taken as the height above ground, AGH = length − setting depth (pole top; framing offsets are not modelled). Each span's rise is h = AGH of the right pole − AGH of the left pole on level ground, and its sag and profile use that rise. The ruling-span method assumes free-swinging suspension insulators and similar spans; very unequal adjacent spans, large height differences or short sections need a finite-element check.

Inclined spans. Midspan sag is measured vertically from the chord. Low-point sag is measured below the lower support. If the low point falls outside the span, there is none in the span: the conductor rises the whole way from the lower support, which is a possible uplift case.

Assumptions & limits

• Single span is one level-or-inclined dead-end span. Multi span uses the ruling-span approximation (equal H in every span); insulator strings and structure flexibility are not modelled.
• The stress-strain relation is linear and uses a constant final modulus. There are no SAG10 / IEC polynomial curves, no load-history plastic stretch, and no ACSR "knee point" or aluminium compression at high temperature. So high-temperature sag of ACSR may be underestimated; see TB 324 Table 9.
• Composite α for ACSR comes from TB 324 eq. (20), with E_A = 55 GPa, E_S = 190 GPa, α_A = 23.0 and α_S = 11.5 µε/°C. AAC and AAAC use α = 23.0 µε/°C.
• Elastic strain uses horizontal tension H, as in the TB 324 worked examples.
• Tensions are in lb, and loads exclude any NESC overload factors.

Validation

The engine was checked against the worked examples in CIGRE TB 324 §6:

• Arbutus AAC, 300 m span, 15.33 kN. Bare sag is 8.00 m (TB 324: 8.0 m). Under 15.6 N/m wind, H is 20 745 N and sag 8.47 m (TB 324: 20 745 N and 8.5 m).
• Drake ACSR, 300 m span, 48 MPa at 15 °C, 600 µε (SPE). Final tension at 15 °C is 19.9 kN with 9.05 m sag (TB 324, read graphically: 20.1 kN, 8.95 m). Final at 100 °C is 15.7 kN with 11.5 m sag (TB 324: 15.9 kN, 11.3 m).

Sources

Published conductor values (OD, weight, rated strength, AAC/AAAC area) are copied from the datasheets above. ACSR area, modulus and α are derived as described in data/README.md.

Disclaimer

For illustration and preliminary checks only. This is not a substitute for PLS-CADD, the manufacturer's stress-strain data, the governing NESC edition or the judgment of a qualified engineer. No warranty is given.