Calculating Sag for Distribution Lines

v I think it would be a catenery equation. you can consult any physical handbook. If you are going far enough like devised by yourself, you can use force balance equation to get a diferential equation and solve it..

It is a 'hanging chain' type of problem (A chain is used because it has no stiffness)

The catenary route already suggested should get you to the answer. But allow for elasticity (stretch) as well.

The sag follows a hyperbolic path - but I do not know the formula.

Dear Mr. horace40,

To my knowledge, the sag will follow the profile of CATENERY and not Hyperbola.

The formula for catenery is y = Cosh (H.x/c) and for Hyperbola is x^2/a^2 - y^2/b^2 = 1. This we have studied long back in the college.

DHAYANANDHAN.S

Level span sag can be calculated by the approximate parabola method:

S = WcL^2 / 8Th

Where: S = Sag @ center of span in meters or feet; Wc = Weight of the conductor in kilograms per meter or pounds per foot; L = Span length in meters or feet and Th = Horizontal tension in Newtons or pounds. Obviously, the units chosen must be consistent.

The exact formula is S = Th / Wc (cosh WcL/2Th - 1)

The final stringing tension on transmission and distribution lines is typically less than 25% of the rated breaking strength of the conductor and usually in the range of 15 - 20%. That is done to reduce the possibility of fatigue due to aeolian vibration.

Re Bluestone formula.

Does it matter if the tops of the poles/pylons are at different heights.

Where would the sag be measured from ?

The overall height of the poles is unimportant. Sag is determined relative to the height of the conductor attachment point at the tangent and deadend poles or structures. Sag is the lowest point of the conductor which, for level spans will be midway between consecutive poles or structures. In that case, sag is the vertical distance between the conductor attachment points and the conductor at mid-span. For spans on which the conductor attachment points are at different elevations on consecutive poles, sag is the distance between the conductor and a straight line drawn between the attachment points.

There are many factors associated with determining sag including stringing tension, ambient temperature, average temperature of the coldest month in the line location, surrounding terrain, etc. Line tension varies with temperature with maximum tension and minimum sag occurring at the coldest temperature and vice-versa.

Typically lines are tensioned based on sag templates that include all those factors.

It gets a bit more complicated when there are elevation changes between poles and, in that case, nomographs are typically used to convert the resulting non-level span sags to equivalent level span sags.

Do you mean that Sag is independent of overall height of poles for same elevation attachment points? If not, how does sag depend upon the overall height of poles for span on which conductor attachment points are at same elevation?

This is not exactly my field, but to anticipate some issues that may arise:

First - everything that Bluestone says seems to be correct; but I have heard (reliably??) that even the 15% figure needs to be approached with caution if wind conditions are extreme and the cable span is approaching the maximum that can be achieved. This is why you sometimes see balls and other vibration-damping structures attached along long spans of cable.

The usual design method is to derive the sag you should leave after installation starting from the allowable tension, the cable parameters, and the required spacing.

You will find a ready-built calculator at
http://www.spaceagecontrol.com/calccabl.htm

Let me try.

In your case, H = maximum applicable tension (kg) / cable section (mm2).

Maximum tension = breaking load (dates available from cable manufactures in kg) / safety factor(ice, snow, normally 2-3).

Do not forget to multyply with overload coefficient, in my case (m).

m = P´/ P(weight)

P´= P(weight) + Ph

Ph(kg/m) zone B = 0.18^d, 500 - 1000m

Ph(kg/m) zone C = 0,36^d, >1000m

i think H stands for the height of the conductor from the ground

It is a long story, but certainly you will gain some insight if you read my book (presently under construction). The chapter on sag is almost done. I can send you this if you give me your email ID. Your formula is correct but it computes sag if tension is given. Normally several tensions are known at various specified temperature and wind/ice loading. So you have to use a loooooooonger equation called equation of state. I don't know your location but you can always download from: http://www.lulu.com/product/paperback/mechanical-design-manual-for-overhead-distribution-lines/54108?productTrackingContext=center_search_results You may have to cut-paste this link into your browser address window. The price listed is 35$. The name of the document is Mechanical Design Manual for Overhead Distribution Lines By USDA Rural Electric Administration

My chapter on sag tension Parabolic- Full theory is ready. Any body can get it for the asking only.

CR4 Admin - email address removed

From the CR4 Rules: Do not post phone numbers or email addresses. The CR4 Admin will delete all phone numbers posted in threads or comments, and we strongly urge you not to put up email addresses. You can share this information via the CR4 internal messaging system.

Good day brothers. My book on Transmission line engineering with the spreadsheet is making some progress. Most of its content is mechanical and civil design of Transmission lines. This is to be in public domain. I will be posting from time to time its contents. Any one can ask for emailing the content of his or her choice by sending me a message (Internal CR4 messaging) with their email. I will try to respond ASAP if possible.

Engr. Abdul Aziz

www.tlengr.com