# Sag in a Transmission Line: What is it? (And How To Calculate it)

Contents

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Key learnings:
• Sag Definition: Sag in a transmission line is defined as the vertical distance between the highest points of support and the lowest point of the conductor.
• Purpose of Sag: Including appropriate sag protects transmission lines from excessive tension and potential damage, especially under adverse conditions.
• Calculation Methodology: Calculating sag involves understanding the geometric and physical properties of the transmission line, such as span length, conductor weight, and tension.
• Environmental Impact: Wind and ice alter the sag by changing the effective weight of the conductor, requiring recalculations to ensure stability.
• Safety Considerations: Proper sag calculation is vital for maintaining the structural integrity and operational reliability of transmission lines.

## What is Sag in a Transmission Line?

Sag in a transmission line is the vertical gap between the support points, such as transmission towers, and the conductor’s lowest point. The way to calculate this sag and the conductor’s tension relies on the span between these supports.

Span having equal level supports (i.e. towers of the same height) is called level span. Conversely, when the span has unequal levels of support, this is known as unequal level span.

Consider a transmission line conductor AOB suspended freely between level supports A and B at the same level (equal span). The shape of the conductor is a parabola and the lowest point of the conductor is O.

In the above overhead conductor AOB, S is the sag when measured vertically.

## Why is Sag Mandatory in Transmission Line Conductors?

Sag is mandatory in transmission line conductor suspension. The conductors are attached between two supports with the perfect value of sag.

Sag is critical as it prevents the conductor from being overstretched and experiencing unsafe tension levels, thereby enhancing durability.

If the conductor is stretched fully during installation, wind exerts pressure on the conductor, hence the conductor gets a chance to be broken or detached from its end support. Thus sag is allowed to have during conductor suspension.

Some important points to note:

1. When the same leveled two supports hold the conductor, a bent shape arises in the conductor. Sag is very small with respect to the span of the conductor.
2. The Sag span curve is parabolic.
3. At each point along the conductor, the tension is always tangential, maintaining balance across the span.
1. Again the horizontal component of the tension of the conductor is constant throughout conductor length.
2. The tension at supports is nearly equal to the tension at any point in the conductor.

## How to Calculate Sag in a Transmission Line

When calculating sag in a transmission line, two different conditions need to be considered:

1. When supports are at equal levels
2. When supports are not at equal levels

The formula to calculate sag changes based on whether the support levels (i.e. the transmission towers holding up the overhead conductor) are at the same level.

Sag calculation for supports are at equal levels

Suppose, AOB is the conductor. A and B are points of supports. Point O is the lowest point and the midpoint.
Let, L = length of the span, i.e. AB
w is the weight per unit length of the conductor
T is the tension in the conductor.
We have chosen any point on the conductor, say point P.
The distance of point P from the Lowest point O is x.
y is the height from point O to point P.

Equating two moments of two forces about point O as per the figure above we get,

Sag calculation for supports are at unequal levels

Suppose AOB is the conductor that has point O as the lowest point.
L is the Span of the conductor.
h is the difference in height level between two supports.
x1 is the distance of support at the lower level point A from O.
x2 is the distance of support at the upper-level point B from O.
T is the tension of the conductor.
w is the weight per unit length of the conductor.
Now,

So, having calculated the value of x1 and x2, we can easily find out the value of sag S1 and sag S2.

This formula calculates sag under conditions of still air and normal temperature, where only the conductor’s own weight affects it.

## What is the Effect of Ice and Wind on Sag?

Some of the effects of ice and wind on sag include:

• The weight per unit length of the conductor is changed when the wind blows at a certain force on the conductor and ice accumulate around the conductor.
• Wind force acts on the conductor to change the conductor self-weight per unit length horizontally in the direction of the airflow.
• Ice loading acts on the conductor to change the conductor self-weight per unit length vertically downward.
• Considering wind force and ice loading both at a time, the conductor will have a resultant weight per unit length.
• The resultant weight will create an angle with the ice loading down ward direction.

Let us assume, w is the weight of the conductor per unit length.
wi is the weight of ice per unit length
wi= density of ice × volume of ice per unit length

ww is the force of wind per unit length
ww = wind pressure per unit area × projected area per unit length

So, the total weight of the conductor per unit length is

The sag in the conductor is given by

So the vertical sag

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