formation, which takes lace only within a very limited temperature
range, is practically unknown under conditions of maximum wind.
The relation of wind velocity to pressure in case of a suspended
wire or cable may be approximately expressed by the equation
P=0-0025V2, where P is the pressure per square foot of projected
area of cable, and V is the actual wind velocity in miles per hour.
Except for sleet conditions the wind pressure is, then, a matter of
little concern. At times sleet may accumulate on bare wires to a
thickness of half an inch to an inch. Even under these conditions
the lateral stability of the line is a matter of less concern than
the added component of stress in the catenary. The third element
of line stress, the actual crushing stress of the wire load, is of no
consequence in high voltage transmission work.
In scientific line design the best example has been set by the
Italian engineers, who, realizing that the longitudinal strains, which
are very severe in case of breakage of spans rigidly supported from
pole to pole, are immediately relieved by a slight increase in catenary
drop, have introduced the principle of longitudinal flexibility.
The poles or towers of structural steel are so designed as to be
fairly stiff against lateral pressure and are given secure foundation
against overturning, but are deliberately designed to deflect lengthwise
the line in the extreme case of breakage of wires so as at once to
relieve the catenary tension without passing their elastic limit.
In this way complete security is attained with a miniinum of material
and expense.
In recent construction both in America and Europe the tendency is to use steel poles or towers of ample height, 40 to 60 ft. and spans ranging from 300 to 600 ft., occasionally more. The catenary drop allowed is considerable, often 3 to 4% of the span length. Crossarms and pins, when used, are commonly of iron or steel, and the interiors of the insulators are therefore fairly at earth potential. The insulators are of dense and hard-baked porcelain, built up of three or four shells cemented together to form a whole, with several deep petticoats to protect the inner surfaces from wettin . Such insulators may be 12 to 18 in. in diameter over all, and iom top groove to base a little more. If well designed and made, insulators of this type can endure even under very heavy precipitation alternating voltages of 60,000 to 100,000 effective without Hashing over, and double these figures when dry. For line voltages above 60,000 to 70,000 it is apparent that the insulating factor of safety would be seriously reduced, and some recent lines have been equipped with suspension insulators. These are in effect porcelain bells from 10 in. diameter upward strung together like a string of Japanese gongs. The bells are all the same size and are spaced about a foot apart, the suspensions being variously designed. These insulating groups can be as large as need be, and it is easy to push the aggregate insulation resistance, both dry and wet, far beyond the figures just mentioned. This suspension requires higher poles than the ordinary, but allows a considerable amount of longitudinal back lash, in case a wire burns off. T00 extensive slip along the line is checked by guys fitted with strain insulators, like the suspension ones, at suitable intervals. The suspension insulator gives promise of successful use of voltages much higher than 100,000 volts. The wires on high voltage systems are generally widely spaced: very seldom less than 2 ft. between centres, and for the higher voltages something like 1 ft. for each 10,000 volts.
Voltage.-The most important factor in the economy of the conducting system is the actual voltage used for the transmission. This varies within very wide limits. For transmissions only a few miles in length the pressures employed may be from 2000 to 5000 volts, but for the serious work of power transmission less than 10,000 volts are now seldom used. This pressure, under all ordinary conditions and in all ordinary climates, can be and is used with complete success, and apparently without any greater difficulty than wouldbe encountered at much lower voltage. It is regarded as the standard transmission voltage in American practice for short distances up to 10 or 15 m. Beyond this, and sometimes even on shorter lines, it is greatly increased; up to 20,000 volts there seems to be no material difficulty whatever in effecting and maintaining a sufficient insulation of the line. In the higher voltages there were in 1908 more than fifty plants in regular operation at 40,000 volts and above. Of these more than a score are operated at 60,000 volts and above. The highest working voltage employed in 1909 was 110,000 volts, which was successfully used in two American plants: that of the Grand Rapids-Muskegon (Michigan) system, and in the transmission work of the Central Colorado system. These both employ suspension insulators with five bells in series, and operate with no more trouble than falls to the lot of systems using ordinarily high voltages. The Rio de ]aneiro transmission system, operates at 88,000 volts with large porcelain insulators, I7-5 in. in over-all diameter and 19-75 in height, carried on steel pins; the Kern River (California) plant at 75,000 volts with similar construction; the Missouri River Power Co. (Montana) at 70,000 volts, using glass insulators on wooden pins saturated with insulating material. There is no especial difficulty in building transformers for still higher pressures, the real problem lying in the insulation of the line. Taken as a whole these high voltage lines have given good service, those near the upper limit doing apparently as- well as those near the lower, owing to more careful precautions in construction. Likewise the distances of transmission have steadily risen. There are, all told, nearly a score of power transmissions over 100 m. in length, the longest distance yet covered being from De Sabla to Sausalito (California), a distance of 232 m. This, like most other long American transmissions, is at 60~, and it is interesting to note that even over such distances there seems to be very little evidence of trouble due to frequency. In point of fact, those who have had the most experience with long distance transmission are the last to worry about the difficulties of using alternating current. Some unusual phenomena turn up in high voltage work, but they are rather interesting than alarming. The lines become self-luminous from “ coronal ” discharge at a little above'20,000 volts, and at 40,000 or 50,000 volts the phenomenon, which is sometimes aggravated by resonance, becomes of a striking, not to say startling, character. At above 100,000 volts this coronal discharge must be given serious consideration. Resonance, in substance, is due to synchronise of the periodic electromotive force, or a harmonic thereof, with the electro-magnetic time-constant of the system. The frequency of the currents actually employed in transmission work is so low that resonance with the fundamental frequency must be extremely rare; resonance with the harmonics is, however, common-much commoner than is generally supposed. In every electromotive force wave the odd harmonics are more or less in evidence, particularly the third, fifth and seventh. If the electromotive force wave departs notably from a sinusoidal form, traces of harmonics up to at least the 15th may generally be found; the third, seventh and the alternate higher harmonics are manifest in iiattening the crest of the wave. Supposing, what is seldom quite true, that the harmonics are symmetrically disposed in phase with the fundamental, all the harmonics tend somewhat to elevate the shoulders of the wave; a wave, therefore, with peaked shoulders and a depression in the centre is certain to be affected by harmonics, while if it has a high central crest, there is evidence of great predominance of the fifth and higher harmonics. Generally the harmonics are slightly out of phase with the fundamental, so that the wave is both deformed and unsymmetrical. As to the amplitude of these harmonics, the third is usually the largest, and may sometimes in commercial machines amount to as much as 20% of the amplitude of the fundamental, and frequently 10%. In machines giving nearly sinusoidal waves it is of course much less, but it is not difficult to find even the seventh and higher harmonics producing variations as great as 5%. Since, other things being equal, the rise in electromotive force due to resonance is directly proportional to the magnitude of the harmonics, and the chance of getting it increases rapidly with the presence of those of the higher orders, the desirability of using the closest possible approximation to a sinusoidal wave is self-evident. The greater the inductance and capacity of the system and the less its ohmic resistance, the greater the chance of getting serious resonance. As regards the distributed capacity and inductance due to the line alone, the ordinary conditions are not at all formidable; the general effect of such distributed capacity and inductance is to produce in the system a series of static waves, their length varying inversely with the frequency. At commercial frequencies the wave length is very great, so great that even in the longest lines at present employed only a small fraction of a single wave length appears; the total length of the line is generally much less than one quarter the complete wave length, and the only notable effect is a moderate rise of potential along the line. The time-constant of the alternating circuit is T=~00629x/ (LC), where L is the absolute self-induction in henrys and C the capacity in micro farads; and if the frequency, or a marked harmonic thereof, coincide with this time-period, resonance may safely be looked for, and resonance of the harmonics may appear conspicuously in lines of ordinary lengths. The following table gives the values, both L and C, per mile of three-phase circuit, of the sizes (American wire-gauge) ordinarily employed for transmission circuits, the wires being assumed to be strung 48 in. apart and about the height already indicated:- 000
4
1
0
nch
IO
2
-2
-2
-22
-204
o-00322
0-003,28
o-oo336
o-oo338
O'O0347
0-00351
0~0164
0'O160
0-0157
0-0154
0-0151
O'O148
Y Size No. Diameter. L. C.
oooo 0-460 O'0O3I2 0-0167
0-4
oo 0-365
0 0-3 5
1 0 89
2 0 58
3 0 9
o-oo358
O'O145
In cases where underground cables form a part of the system, the above values of C are very largely increased, and the probability of resonance is in proportion enhanced. A still further complication is introduced by the capacity and inductance of the apparatus used upon the system, which may often be far greater than that due to the entire line, even if the latter be of considerable length. In point of fact, it is altogether probable that resonance due to the distributed capacity and inductance of the overhead line alone is of rare occurrence and generally of trivial amount, while it is equally probabld
