TELEPHONE LINE WIRE SPACING PROBLEMS 227 



where Li = Horizontal displacement of wires, 



a' = Corrected stretched sag of wires, and 



a' — Angle of deflection determined experimentally as distin- 

 guished from the theoretical angle (a). 



The details of the method of determining the equilibrium position 

 of the wires for a particular natural wind velocity were as follows: 



The horizontal displacement of the two wire images on the film 

 at each wave crest and trough was determined. The displacement 

 for the two wire images at each crest and at each trough was 

 averaged. Next the mean displacement on the film of the crest 

 and trough was calculated and also the mean velocity * was 

 determined for this particular time interval. The mean dis- 

 placement on the film was then converted to actual wire displace- 

 ment through the use of equation (2) and the experimental angle 

 Avas determined by equation (4). This average angle was taken 

 as the equilibrium position of the wires for this mean velocity. 



APPENDIX II 



Empirical Equations 



From natural wind tests on arrangements of wires in which both 



wires of a pair were maintained at equal sags it was found that in 



the absence of glaze threshold velocities increase with the spacing 



between the wires and the span length and decrease as the sag increases. 



An empirical equation obtained from an analysis of the results is 



as follows: 



" ro. I CO. 3 "12.1 

 ^'« = 22.4|^-^J , (5) 



where F„, = Natural wind threshold velocity (miles per hour), 

 L = Span length (100 to 260 feet), 

 5 = Wire spacing (3 to 12 inches), and 

 d = Sag of wires at rest (4 to 45 inches). 



The data upon which this equation was based comprised approximately 

 fifty cases where swinging contacts actually occurred. Regarding the 

 degree to which this equation represents these data, there were only 

 about five cases which deviated as much as five miles per hour in 

 terms of threshold velocity and of these only one deviated as much as 

 seven miles per hour. The nomogram given in Fig. 8 was constructed 

 for this equation (5). 



* When the direction of the wind uas not normal to the Hne the normal component 

 of the velocity was determined by multiplying the wind velocity by the cosine of 

 the angle between the actual direction of the wind and the normal to the line,- 



