358 BELL SYSTEM TECHNICAL JOURNAL 



system is V and the wind velocity relative to the wire at any instant is 

 therefore the vector difference V — ya which has the magnitude 



VF" + {yaY — IVya COS a. 



It is assumed that the wind pressure against this element is propor- 

 tional to the square of this vector and acts along its direction. The 

 moment about the axis of the wind pressure on the element ds is 

 therefore given by: 



^[F- + (3'a)" — ly'aV COS a\y cos ^ds, 



where U is the ratio of wind pressure per unit length to square of veloc- 

 ity. Evaluating cos ^ and noting that ya is small compared with F, 

 this reduces to: 



kdsy V^ cos a 1 — 4t ( cos a -\ i • 



L F \ cos a / J 



Putting 



y = 



and 



ds = dx 

 and integrating, the total moment of wind pressure is 



4 16 



-kV^aC cos a — -r-EkVa^Ca (cos^ a -{- 1). 



If the line through the supports is inclined to the horizontal by angle 

 7 this expression becomes: 



4 16 



-kV^aC cos a cos y — ■r-rkVa'^Ca (cos- a -\- 1) cos^ y 



The dynamic equation for the motion of the loop then becomes: 



a H (1 + COS" a)a -\- -r- s\n a = -; , 



m 4 a 4 ma cos y 



where m is the mass of unit length of wire. 

 Static equilibrium is then given by: 



tan a = 



mg cos 7 

 Proceeding with the analysis, an equation is found for small motions 



