Sag in transmission lines

A catenary.

most beautiful!

The name catenary is associated with the curve because it describes the shape formed by a chain or rope freely suspended by its endpoints.

`` A bridge [...] is a very special thing. Haven't you seen how delicate they are in relation to their size? They soar like birds; they extend and embody our finest efforts; and they utilize the curve of heaven. When a catenary of steel a mile long is hung in the clear over a river, believe me, God knows. [...] the catenary, this marvelous graceful thing, this joy of physics, this perfect balance between rebellion and obedience, is God's own signature on earth. I think it pleases Him to see them raised.''

http://en.wikipedia.org/wiki/Catenary

http://mathworld.wolfram.com/Catenary.html

http://www-history.mcs.st-andrews.ac.uk/history//Curves/Catenary.html

The catenary equation is where a is determined by the linear density and tension of the chain. This is a transcendental curve rather than an algebraic curve like the parabola. The catenary is a hyperbolic function: .

Dear friend '

The equation for Catenary is y = a cosh(x/a) where y is the y Cartesian coordinate, x is the x Cartesian coordinate, cosh is the hyperbolic cosine function and a is the scaling or constant.

DHAYANANDHAN.S

Another point to consider is the co-efficient of linear expansion for the given material.

That is, when the wires are hot they will grow in length and therefore sag more.

When it is cold they will shrink (contract) and therefore reduce the sag.

If the catenary (sag) isn't large enough when the wire is installed then the wire may be in a great deal of tension as the temperature drops. Conversely as the temperature increases the sag increases and may allow contact or bridging of the air gap to occur.

Also keep an eye on the tensile strength of your chosen material for the weight of the wire plus wind loading plus snow/ice loading. The voltage drop for the length and cross sectional area need to be considered also.

Normally this comes on Hilly terrains. Calculation is same except that sag point may be beyond the tower in which case it gives an upthrust.Lot software is available used by many of the transmission line construction or tower manufacturing companies .try contacting them .

What is the maximum horizontal load that your pylon can take? Is this load determined by the pylon strength or the connection detail or by the cable strength? Or maybe it is a problem of head height or vehicule height beneath the cable?

You can then treat it as a simple arch/catenary calculation for a first approximation (even treat it as a beam then divide by the sag you require as a rough approximation). The sag can be deduced from the maximum allowable load. Remember that the cable is still a part of the catenary in spite of being at different support heights. Graphical methods also work quite well; these are often found in classical text books but some of the better modern text books have them too.

As mentioned previously, ice/snow load cases coupled with wind (the cross section of the cable increases 3 to 5 fold depending on the climate) will be the worst load case for the connection and cable design; this will also give rise to horizontal forces and put the cable in an inclined plane although still catenary in that plane. For the pylon it is generally the case where one of the cables is attached only (maintenance or accidental load case).

Hi! better to consulta text book, than getting confused by so many software and replies.

Hello Electric friends, I was thinking of improving the efficiency of the transmission lines by de-sagging them. Is it worth??

Could explain more clearly how u plan to improve efficiency by de sagging the line?

Very simple. Exactly like the Hanging Bridges (Cable Stayed Bridges) and the electrical line used for traction.

In a cross country transmission line no of towers has a impact on the cost.If u want to eliminate sag like the traction overhead conductor the no of towers required will be more.Traction is normally at 25KV and lines can be anywhere between66-400kv.Imagine towers of the size and nos.Then to keep the line taut without sag and also considering expansion and contraction due to temp variation,towers will need extra strength compared to normal towers, insulators with higher mechanical strength,and so on.If after all these costs if the line impedance is lower and losses are less why not?

My idea is not to increase the no. of towers but remove the sag with the method used in traction. Desag by using suspender cables exactly like the suspension type bridge among the cable stayed bridges. May be it is high time I will do the calculation myself and let you know.

The voltage difference is high.Conductor sizes (ACSR) is far higher and tension is high already to string the conductor.You will need a catenary wire.The load has to come on towers which will have to be made stronger.Towers will increase as spans are too large compared to traction.For instance in a400KV line span is 400m phase to phase clearance is 11 m.In traction it is the requirement of application of a straight conductor.Have u observed that though the conductor is straight the wire holding it is a catenary with sag.The sag is transmitted to the suspension wire whether bridge or traction.My idea is to draw ur attention to various problems as transmission line is a field by itself.Any how nothing wrong .Best of luck and keep us all posted.we eagerly await the out come.