280 
The N.Z. Journal of Science and Technology. 
[Jan. 
CABLE SPANS WITH SUSPENSION INSULATORS. 
By I. R. Robinson, B.E. 
The following is an attempt to derive a formula which will give the tension, 
for different temperatures, of the wire of a high-tension transmission-line 
with suspension insulators. Although numerous formulae and methods have 
been published for determining the tension of the wire when pin insulators 
are used, so far as the author is aware no formula has been published for 
use when suspension insulators are used. With this type of insulator the 
point of support is not fixed, but is free to move, owing to the method of 
suspension, both transversely and longitudinally with respect to the direction 
of the line. The formulae derived for fixed spans with pin insulators, there¬ 
fore, require modification in important respects. The notation here used is 
the same as that in Cable Spans, by Mr. E. Parry,* whose method also 
is closely followed. For all practical purposes the curve in which the wire 
hangs can be taken as a parabola, and for most spans the tension can be 
taken as constant throughout.*)' 
If S be the length of arc in half the span in feet; x, the half-span in 
feet; P, the tension in the span (pounds per square inch); q, the loading- 
ratio ( i.e ., ratio of total load on wire to weight of wire); and S, the weight 
per foot-run per square inch of wire ; then we have for any span 
S, 
x -f- 
x 3 q 2 S 2 
¥p _t 
v q 
Now, if the temperature changes by an amount t° Fahr., and the 
loading-ratio changes to q u the insulators at each end of the span will 
swing slightly along the line and alter the span by an amount 2 A $. 
Then, for each half of the span we have, if St denotes the new length of 
arc for the half-span, 
S t — x —(— A x —f- 
{x -j- A x) 3 q 1 2 S 2 
( 2 ) 
From (1) and (2) 
= A x -{- 
(x + A x) 3 q 1 2 S 2 
“BP? - 
(3) 
but we also have, by considering the change of length due to elastic and 
thermal expansion, 
St 
Sq (1 -j- at) 
i + h i + Pq 
E E 
(4) 
where E is the modulus of elasticity in pounds per square inch, a is 
the coefficient of expansion per degree Fahrenheit, and t is the change 
in temperature. 
* E. Parry, Gable Spans, Public Works Department (N.Z.), 1917. 
f G. P. Anderson, Location of Electric Transmission-lines, N.Z. Jour. Sci. & Tech., 
vol. 2, p. 97, 1919. 
