---
title: "T/F: sag absent with supports at different heights"
subject: "Transmission and Distribution System Design"
chapter: 4
key: "semester_8/transmission_and_distribution_system_design:tf-sag-absent-different-heights"
source: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/tf-sag-absent-different-heights
site: BCT Engineering
---

# T/F: sag absent with supports at different heights

Transmission and Distribution System Design · Chapter 4: Conductor and Support Selection

- Asked in: 2067 Mangsir (old course), 1+3 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/tf-sag-absent-different-heights
- Whole chapter: https://www.bctengineer.com/md/semester_8/transmission_and_distribution_system_design/chapter-4

## Question

For a given amount of power to be transmitted over a given distance, state whether the following statement is TRUE or FALSE. Justify your answer with a brief explanation: In case of support at different heights, the sag may be absent if either the span length or support level difference is small.

## Short answer

FALSE. Sag disappears when the span is short or the level difference is large, not small. If the level difference is small, the lowest point remains inside the span and sag exists.

## Answer

**FALSE.**

The sag "disappears" when the span is **short** or when the level difference between supports is **large**, not small.

For supports at different heights (span $L$, level difference $h$), the lowest point of the conductor lies at a distance

$$
x_1 = \frac{L}{2} - \frac{Th}{wL}
$$

from the lower support. When $x_1 \le 0$, the lowest point falls at or beyond the lower support. The conductor then rises all the way from the lower support to the higher one, and there is **no sag (dip) within the span**. The condition is:

$$
\frac{L}{2} \le \frac{Th}{wL} \;\Rightarrow\; h \ge \frac{wL^2}{2T}
$$

So the sag is absent if:
- the **span L is small** (the right-hand side $wL^2/2T$ is small), or
- the **level difference h is large**, or
- the tension is high relative to the conductor weight.

Example: with $L = 300$ m, $w = 1.2$ kg/m and $T = 3000$ kg, $wL^2/(2T) = 18$ m. A level difference of 20 m (more than 18 m) gives no dip. A level difference of 5 m gives a normal dip with the vertex inside the span. A small level difference therefore does not remove the sag; a short span or a large difference does.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. 'Sag may be absent if either the span or the support level difference is small.' Is this true?
   A. True
   B. False, sag is absent when the span is short or the level difference is large
   C. False, sag is absent only when the tension is low
   D. True for the span, false for the level difference only if T is high
   Answer: B. A small level difference keeps the vertex inside the span; a large difference pushes it out. (Key point: True or false verdict)

2. What is the condition for the lowest point to fall at or beyond the lower support?
   A. h <= wL^2/(2T)
   B. L >= Th/w
   C. h >= wL^2/(2T)
   D. T <= wL
   Answer: C. x1 <= 0 gives L/2 <= Th/(wL), i.e. h >= wL^2/(2T). (Key point: Condition for no dip)

3. For L = 300 m, w = 1.2 kg/m, T = 3000 kg, wL^2/(2T) = 18 m. What happens with a level difference of 5 m?
   A. No dip at all
   B. Sag is infinite
   C. The conductor is straight
   D. A normal dip with the vertex inside the span
   Answer: D. 5 m is below 18 m, so x1 is positive and the vertex lies inside the span. (Key point: Numerical example)

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