Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Transmission line length changes

Transmission line length changes

Transmission line length changes

How much does the physical length of a transmission line change with temperature and physical loading?

RE: Transmission line length changes

You may start with sag equation:
S=w*L^2/8/T where:
S = mid-span sag (m)
w = conductor weight (N/m)
L = horizontal span length (m)
T = conductor tension (N)
The conductor tension T is the tension at the low point of the cable
Usually To=0.2-0.3 NBL [Nominal Break Load]
The difference in distance between the straight line between the supports and the distance along the parabola arc (the stretched conductor length) is called the slack. For a level span the slack is given by:
K = slack (m)
S = mid-span sag (m)
L = span length (m)
As the temperature increases, the unstretched conductor length will increase by an amount equal to: Δ L = α*dT* S where:
α = the coefficient of thermal expansion
dT = the temperature increase in deg C
S = the span length in metres
wind load on the conductor will increase the apparent weight of the conductor resulting in an in increase in tension.
Ice build up on the conductor will increase the apparent diameter and weight of the conductor
Aging: conductor sag over time may increase due to the effects of strand settling in and
metallurgical creep.
The increase in tension will increase the cable length due to elastic stretch by an amount given by: dL=(T-To)/E/A where:
To = the initial tension in newtons
T = the final tension
E = the coefficient of elasticity
A = the cross section of the conductor in metres.
See-for instance:

RE: Transmission line length changes

As a less mathematically rigorous answer: The change in length for a typical span is on the order of centimeters, the change in sag is on the order of meters.

RE: Transmission line length changes

Hey HamburgerHelper, don't know if it will help or not, but here's a quote of what I wrote in a recent post entitled Sag Protection, since I misunderstood the intended subject. I reproduce it here since I know I for sure don't read every single eng-tips post made, so you may not have seen it either...

My utility has a conductor sag detection facility used to derive realistic continuous and limited time ratings for specific 230 kV circuits that are often very heavily loaded, especially during the summer months [these circuits collectively comprise a "flowgate"]. Ultrasonic proximity detectors are used in conjunction with known line loadings and local ambient temperatures to calculate very accurate effective wind speeds which can then be plugged into the thermal monitoring program to enable said lines to be loaded to their maxima without crossing the fateful line into overload and premature conductor aging.

Anecdote, as all the formulae in the world can't correct a lack of situational awareness:

The Toronto Transit Commission once decided that better lighting was needed in its vehicle parking lots, and to that end subbed out a contract to have newer, taller, more efficient light standards installed.

One of these parking lots was located within a 230 kV right-of-way running roughly parallel to the 401 freeway; the contractor duly took their measurements from the conductors to the ground, determined there was no violation of clearances or limits of approach, and late in the fall of one year completed the installation to the satisfaction of the TTC, got paid, and the matter was closed...supposedly.

The following summer, on a hot, sticky day with lots of air conditioning load, there was a contingency involving a companion circuit, leading to a much heavier loading on the circuit in question, resulting in significant but nevertheless not unexpected or unacceptable conductor sag...with the predictable result including high-profile customer interruptions.

What was interesting was to watch the fur flying after the fact, with the different entities accusing each other of failing to exercise the appropriate due diligence, arguments over who was going to pay the additional cost of relocating the light standard in question, whether shortening it and using different luminaires with appropriately different light throws was a viable alternative, etc., etc.

RE: Transmission line length changes


I am getting thrown off by your comment. If the conductor sags meters in a span, the conductor length has to be in the least near the length to go down and come back up. When I used this equations, Δ L = α*dT* S I was seeing length changes on the order of 0.2%. How do you get something that you can physically see sag when it is heavy loaded but its length only changes a small fraction of a percent. If a span is 300 M, I am maybe looking at 1 meter in length change. Does physical tension account for what I see more than its length change due to it being hotter?

RE: Transmission line length changes

Quote (HamburgerHelper)

the conductor length has to be in the least near the length to go down and come back up
Not really. Consider 7Anoter4's equation for slack. For a 300m span with 3m of sag, the slack in the conductor is only 8*3^2/3/300 = 0.08m. That's not anywhere near down 3m + up 3m. A small change in length translates to a large change in sag.

Increasing temperature causes an increase in the conductor length, but that increase lowers the tension, which reduces the conductor length. The equilibrium point between the increase from temperature and the decrease from lower tension determines the change in slack and sag. The answer to the OP's question in short is "not much".

RE: Transmission line length changes

Or, to put jghrist's response in different terms, the change is less than the uncertainty of the original measurement.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members! Already a Member? Login


White Paper - Reshoring Prototyping and Production
In this whitepaper, we'll provide insight into why and when it makes sense for U.S. manufacturers to reshore prototyping and production, and how companies can leverage the benefits of working with local design, prototype, and manufacturing partners during the pandemic and beyond. Download Now
Engineering Report - Top 10 Defect Types in Production
This 22-page report from Instrumental identifies the most common production defect types discovered in 2020, showcases trends from 2019 to 2020, and provides insights on how to prevent potential downtime in 2021. Unlike other methods, Instrumental drives correlations between a variety of data sources to help engineers find and fix root causes. Download Now
White Paper - Addressing Tooling and Casting Requirements at the Design Stage
Several of the tooling and casting requirements of a part can be addressed at the design stage. If these requirements are not addressed at the design stage, lot of time is spent in design iteration when the design reaches the die caster. These design issues lead to increase in time and cost of production leading to delay in time to market and reduced profits for the organization. Download Now

Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close