Every ADSS cable span is a catenary curve — the shape a flexible cable takes under its own weight when suspended between two points. Calculating the sag and tension for that curve is the most fundamental engineering task in any ADSS deployment. Get it wrong, and the cable either sags below clearance limits or carries tension that shortens its life. This guide walks through the calculation step by step.
The Catenary Equation
The catenary curve is described by:
y = (H/w) × [cosh(wx/H) – 1]
Where:
- y = vertical sag at distance x from the lowest point (meters)
- H = horizontal component of tension (Newtons) — constant along the span
- w = cable weight per unit length (N/m) — cable mass in kg/km × 9.81 / 1000
- x = horizontal distance from the lowest point (meters)
For a span of length L between supports at the same height, the maximum sag at mid-span (x = L/2) is:
Sag_max = (H/w) × [cosh(wL/(2H)) – 1]
For the full engineering methodology including MAT and RTS, see our MAT calculation guide.
Simplified Parabolic Approximation
For spans where the sag is less than 10% of the span length (which covers most ADSS installations), the catenary can be approximated as a parabola:
Sag = w × L² / (8 × H)
This simplified formula gives results within 1% of the full catenary for typical ADSS spans (sag < 5% of span). Use it for initial sizing; use the full catenary for final design verification.
Step-by-Step Calculation Example
Given: 48-core ADSS cable, 48-core, span L = 500 meters, cable weight = 150 kg/km
Step 1: Convert weight to N/m
w = 150 × 9.81 / 1000 = 1.4715 N/m
Step 2: Determine target sag
For a 500m span, a maximum sag of 2% of span is typical → target sag = 10 meters at mid-span.
Step 3: Calculate tension using parabolic approximation
H = w × L² / (8 × sag) = 1.4715 × 500² / (8 × 10) = 4,598 N
Step 4: Verify tension against MAT
If the cable’s MAT is 8,000 N, the calculated tension of 4,598 N provides a safety factor of 8,000/4,598 = 1.74 — adequate (target > 1.5).
Step 5: Apply wind and ice loads
Under IEC 60826 heavy loading (ice + wind), the effective weight per meter increases by a factor of 2-5×. Recalculate — if the loaded tension exceeds 60% of MAT (4,800 N for this cable), the span design fails and either a higher MAT cable or reduced span length is required.
How Wind and Ice Loads Change the Calculation
Under combined wind and ice loading, the effective weight per meter is:
w_eff = √[(w_cable + w_ice)² + w_wind²]
Where:
- w_ice = weight of ice accretion (N/m) — depends on ice thickness (typically 10-30 mm radial) and ice density (900 kg/m³)
- w_wind = wind force on the iced cable (N/m) — depends on wind speed, cable diameter, and drag coefficient (~1.0 for cylindrical shapes)
For extreme weather design considerations, see our extreme weather ADSS design guide.
Key Takeaways
- Use the parabolic approximation (sag = wL²/8H) for initial sizing — it’s accurate within 1% for typical ADSS spans.
- Always apply wind and ice loads per IEC 60826 (or local equivalent). The loaded tension typically governs the design, not the bare-cable tension.
- Maintain a safety factor of at least 1.5 between the loaded tension and MAT. Below 1.5, the cable is overstressed and will fatigue prematurely.
- For spans over 1,000 meters, use the full catenary equation. The parabolic approximation diverges by more than 2% at large sags. See our large-span design guide.
Need Sag and Tension Calculations for Your Project?
Send us your span lengths, cable specifications, and local wind/ice data — our engineering team will run the full catenary analysis and provide a span-by-span tension report.
Frequently Asked Questions
What is the formula for ADSS cable sag?
For typical spans (sag <10% of span), use the parabolic approximation: Sag = w × L² / (8 × H), where w is cable weight (N/m), L is span length (m), and H is horizontal tension (N).
What is the difference between catenary and parabolic sag formulas?
The catenary is exact but complex. The parabolic approximation is simpler and accurate within 1% for spans where sag is less than 10% of span length. Use parabolic for initial sizing, catenary for final design.
How do wind and ice loads affect ADSS sag and tension?
Combined wind and ice loading can increase effective cable weight by 2-5×, significantly increasing tension. Always verify the loaded tension against MAT with adequate safety factor.
What is a safe sag percentage for ADSS cable?
Typical maximum sag is 2-5% of span length. The exact limit depends on ground clearance requirements, conductor clearance, and local electrical codes.
How do I verify installed sag matches the design?
Measure sag with a laser rangefinder from the support point to the cable at mid-span. Compare to the design value. A 10% sag deviation can indicate incorrect installation tension.
