1921 .] Robinson.—Voltage-drop in Circuits. 261 
than 0-05 per cent, of V r . To facilitate the use of the above equation, 
tables of R and ph have been prepared for both annealed and hard-drawn 
copper wire (Table I). The values of ph have been calculated from the 
following formulae* :— 
ph = *232 log. 
ph — -232 log. 
pL = -232 log. 
ph = -232 log. 
ph — -232 log. 
The above are for symmetrical spacing. For unsymmetrical spacing 
use D = Vabc where a , b, and c are the distances between the wires. For 
flat symmetrical spacing D = l*26a. 
Table II, giving values of tan 0 for various values of cos 0, will also 
facilitate the calculations. 
2*57 
D 
d 
2*756 
D 
d 
2*640 
D 
d 
2*61 
D 
d 
2*59 
D 
d 
for single wires ; 
for seven-strand cables ; 
for nineteen-strand cables ; 
for thirty-seven-strand cables ; 
for sixty-one-strand cables. 
As an example of the use of the above table consider the following 
problem :—What will be the voltage-drop with the following conditions : 
Size of wire, No. 8 S.W.G.; spacing, 2 ft. ; distance, 1 mile ; load, 30 kw. ; 
power-factor, *70 ; voltage, 3,300; system, three-phase ? 
Voltage-drop is (2*20 + *600 X 1*020) 
1910 
30 X 1000 X 1 X 2*81 
1910 
= 44 volts. 
By applying the Dwight correction for capacity, for transmission-lines 
of lengths from 30 to 100 miles, the voltage-drop may be found by sub- 
tracting 1*50 V r (i000 ) ^ rom drop f° un( i by the above method. 
As an example consider the transmission of 6,000 kw. at *95 power- 
factor ; voltage, 66,000; spacing, 6 ft., delta; size of wire, 19/13; 
distance, 80 miles :— 
V s - V r = 
2000 X 1000 X 80 
38100 
v, / 80 \ 2 _ 160000 X -550 
X (,1000/ “ 38d“ 
(•355 + *328 X -607) - 1*5 X 38100 
- 366 = 2310 - 366 = 1944. 
The above method will give results accurate to about the same degree 
as an ordinary slide-rule. 
* H. B. Dwight, Transmission-line Formulae. 
