Electric Power Generation, Transmission, and Distribution

Note thatxis considered positive in either direction from the low point.

The horizontal distance, xL, from the left support point to the low point in the catenary is:

xL¼

S

2

1 þ

h

4 D



(14:10)

The horizontal distance, xR, from the right support point to the low point of the catenary is:

xR¼

S

2

1 

h

4 D



(14:11)

whereS¼horizontal distance between support points.
h¼vertical distance between support points.
Sl¼straight-line distance between support points.
D¼sag measured vertically from a line through the points of conductor support to a line tangent
to the conductor.
The midpoint sag,D, is approximately equal to the sag in a horizontal span equal in length to the
inclined span,Sl.
Knowing the horizonal distance from the low point to the support point in each direction, the
preceding equations fory(x),L,D, andTcan be applied to each side of the inclined span.
The total conductor length,L, in the inclined span is equal to the sum of the lengths in the xRand xL
sub-span sections:

L¼Sþ x^3 RþxL^3

w^2

6 H^2



(14:12)

In each sub-span, the sag is relative to the corresponding support point elevation:

DR¼

wxR^2

2 H

DL¼

wxL^2

2 H

(14:13)

or in terms of sag,D, and the vertical distance between support points:

DR¼D 1 

h

4 D

 2

DL¼D 1 þ

h

4 D

 2

(14:14)

and the maximum tension is:

TR¼HþwDR TL¼HþwDL (14:15)

or in terms of upper and lower support points:

Tu¼Tlþwh (14:16)

whereDR¼sag in right sub-span section
DL¼sag in left sub-span section
TR¼tension in right sub-span section
TL¼tension in left sub-span section
Tu¼tension in conductor at upper support
Tl¼tension in conductor at lower support