Catenary Curve Effect Calculation

Calculate the cable sag error and cable length for given values.




The catenary curve represents to shape the displacement cable takes under uniform force such as gravity, in case of overhead line, it is important that conductors are under safe tension.

If the conductors are too much stretched between supports to save conductor material, the stress in the conductor may reach to unsafe level and conductor may break due to excessive tension.

In order to permit safe tension in the conductors, they are not fully stretched but are allowed to have a dip or sag due to gravity acted. Difference in level between supports point and the lowest point on the conductor is called sag.

Due to gravitational force the cable get catenary curved, the difference in level between supports point and the lowest point on the conductor is called sag as shown in picture.

The word catenary is derived from Latin word "chain" and the curve is also called the Alysoid and Chainette.

The tightening force is acting at every point of cable. The weight of the cable is directed downwards, so we can say parallel to y-axis.


If the mass of the cable per unit length is small and cable tension is relatively high then the cable sag does not produce much significant error unless the cable length is exceptionally long say over 60 feet.

In this calculator we calculate the cable sag and cable length for given cable tension, straight line distance, force perpendicular to cable length and mass of the cable per unit length.

Factors affecting sag

Conductor weight Sag of the conductor is directly proportional to weight of the cable.
Tension The sag is inversely proportional to the tension in the conductor. Higher tension increases the stress in the cable and supporting structures.
Span (lenght) Sag is directly proportional to the square of the span length. Longer span increases sag.
Wind speed Wind speed increases sag in the inclined direction.
Temperature The sag is reduced at low temperatures and is increases at higher temperatures.