MOTION OF TELEPHONE WIRES IN WIND 359 



about any position of equilibrium (deflection a) of the form 



'(p -\- 2eip + n-ip = 0, 

 where 



_ (t + cos^c^) kV 



^ ~ 2m 



and 



7 £, « 



W 



4o cos a 



For cases of practical interest in this investigation n^ > e^ and the 

 motion about equilibrium is periodic and of period 



rp _ ^TT _ kfl cos a 



where a is the sag in feet and g the acceleration of gravity in feet per 

 second per second. The ratio of the period of small oscillations about 



equilibrium to the period when a is zero is given by T/Tq = Vcos a. 

 The damping as measured by the ratio of successive half swings, X, 

 is given by 



log, X = , = - € 



■\n^ — e^ n 



If a wire, held at a deflection a by a steady wind F, is subjected to a 

 gust of wind having maximum velocity V\, the additional throw of the 

 wire will depend on the duration of the gust and may in general be 

 either greater than or less than the increase in steady deflection which 

 Vi, if sustained, would produce. The maximum throw will be given 

 by a gust of most favorable duration and /x,„g has been defined as the 

 ratio of this maximum throw to the increase in deflection that would 

 result if the peak velocity were sustained. Similarly, for a periodic 

 succession of gusts, there is a most favorable timing which in general 

 will produce displacements greater than would a wind which sustained 

 the velocity of the gust peaks. The ratio of the throws produced by a 

 most favorably timed succession of gusts to the increase in deflection 

 which would result if the peak velocity of the gusts were sustained, has 

 been defined as ^imp- 



The formulae derived above have been applied to the practical 

 conditions of the telephone line problem,- where our interest is centered 

 in hard drawn copper wire, commonly of .104" or .165" diameter, with 

 spans ordinarily from 90 to 200 feet and sags commonly from 7" to 20" 



2 This work was carried out in the Bell Telephone Laboratories by Mr. V. 

 Nekrassoff. 



