1. What is a Sag Calculator for Overhead Conductors (Wind and Ice Effects)?

Definition: This calculator estimates the sag (vertical dip) in an overhead conductor suspended between two equal-level supports, accounting for wind and ice loading. It uses a safety factor (default 2) to compute the working tension (\( T_{\text{work}} = T / \text{safety factor} \)) and calculates the total sag, angle of the resultant force, and vertical sag component. Options are provided to calculate the conductor's self-weight based on material and diameter or input the weight directly.

Purpose: It helps engineers ensure safe tension in transmission lines under environmental loads, preventing conductor breakage and maintaining adequate ground clearance.

2. How Does the Calculator Work?

The calculator computes sag for equal-level supports, incorporating wind and ice effects and a safety factor, and determines the angle and vertical sag. The conductor length is assumed equal to the span length.

Formulas: \[ A = \pi \left(\frac{d}{2}\right)^2 \quad (\text{cross-sectional area from diameter}) \] \[ w = \text{density} \times A \quad (\text{if calculating self-weight}) \] \[ p_w = \frac{1}{2} \rho v^2 \] \[ w_i = \rho_{\text{ice}} \cdot \pi \cdot t \cdot (d + t) \] \[ w_t = \sqrt{(w + w_i)^2 + w_w^2} \] \[ T_{\text{work}} = \frac{T}{\text{safety factor}} \] \[ S = \frac{w_t \cdot L^2}{8 \cdot T_{\text{work}}} \] \[ \tan \theta = \frac{w + w_i}{w_w} \] \[ S_v = S \cos \theta \] Where:

• \( A \): Cross-sectional area (m²)
• \( w \): Conductor weight per unit length (kg/m)
• \( \text{density} \): Copper (8920 kg/m³) or Aluminum (2700 kg/m³)
• \( p_w \): Wind pressure (Pa)
• \( \rho \): Air density (kg/m³, default 1.29 kg/m³)
• \( v \): Wind speed (m/s)
• \( S \): Total sag (m)
• \( S_v \): Vertical sag (m)
• \( \theta \): Angle of resultant force (degrees)
• \( L \): Span length (m)
• \( T \): Input tension (kg)
• \( T_{\text{work}} \): Working tension (kg)
• \( \text{safety factor} \): Safety factor (default 2, unitless)
• \( w_w \): Wind loading weight (kg/m)
• \( d \): Conductor diameter (m)
• \( t \): Ice thickness (m)
• \( g \): Acceleration due to gravity (9.81 m/s²)
• \( w_i \): Ice loading weight (kg/m)
• \( \rho_{\text{ice}} \): Density of ice (917 kg/m³)
• \( w_t \): Total effective weight (kg/m)

Unit Conversions:

• Length (Span, Diameter, Thickness):
• 1 km = 1000 m
• 1 cm = 0.01 m
• 1 mi = 1609.344 m
• 1 ft = 0.3048 m
• 1 in = 0.0254 m
• Weight per Unit Length:
• 1 lb/ft = 1.48816 kg/m
• Tension:
• 1 lb = 0.453592 kg
• Air Density:
• 1 lb/ft³ = 16.0185 kg/m³
• Wind Speed:
• 1 km/h = 0.277778 m/s
• 1 mph = 0.44704 m/s
• 1 ft/s = 0.3048 m/s

Steps:

• Select whether to calculate the conductor’s self-weight or input the total weight per unit length.
• If calculating self-weight: Choose the material (Copper or Aluminum), and the calculator computes the cross-sectional area from the diameter and then \( w \).
• If inputting weight: Enter the conductor weight per unit length (\( w \)) directly.
• Enter the span length (\( L \)), tension (\( T \)), safety factor (default 2), conductor diameter (\( d \)), air density (\( \rho \), defaults to 1.29 kg/m³), wind speed (\( v \)), and ice thickness (\( t \)), selecting the appropriate units.
• Convert all inputs to metric units (meters, kg/m, kg, kg/m³, m/s).
• Calculate the working tension \( T_{\text{work}} = T / \text{safety factor} \).
• Calculate the wind pressure \( p_w \), wind loading weight \( w_w \), ice loading weight \( w_i \), and total effective weight \( w_t \).
• Calculate the total sag, angle \( \theta \), and vertical sag \( S_v \) using \( T_{\text{work}} \).
• Display the results: total sag in meters, angle in degrees, and vertical sag in meters, all rounded to 2 decimal places.

3. Importance of Sag Calculations with Wind and Ice Effects

Calculating sag with wind, ice effects, and a safety factor is crucial for:

• Safety: The safety factor reduces the working tension, ensuring the conductor can withstand environmental loads without breaking.
• Clearance: Maintaining adequate ground clearance during adverse weather, using the vertical sag component.
• Design: Optimizing conductor material usage while ensuring structural integrity under varying conditions.

4. Frequently Asked Questions (FAQ)

Q: Why is sag necessary in overhead conductors?
A: Sag prevents excessive tension that could break the conductor, especially under varying conditions like wind and ice loading.

Q: How do wind and ice affect sag?
A: Wind adds a horizontal force, and ice adds vertical weight, increasing the effective weight and thus the sag.

Q: What does the angle \( \theta \) represent?
A: The angle \( \theta \) is the angle of the resultant force (due to vertical and horizontal loads) with respect to the horizontal.

Q: Why calculate vertical sag?
A: Vertical sag \( S_v \) represents the actual vertical displacement of the conductor’s lowest point, critical for ground clearance.

Q: What is the safety factor?
A: The safety factor (default 2) reduces the input tension to a working tension (\( T_{\text{work}} = T / \text{safety factor} \)) to ensure the conductor can handle unexpected loads safely.

Q: Can this calculator handle unequal support levels?
A: No, this calculator assumes equal-level supports. For unequal levels, additional calculations are needed.

Reference

https://www.electrical4u.com/sag-in-overhead-conductor/

https://www.rcet.org.in/uploads/academics/rohini_43235565283.pdf

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