360 BELL SYSTEM TECHNICAL JOURNAL 



though occasionally considerably greater. The method, which will 

 be described in more detail elsewhere, was to reduce the expressions for 

 wind pressure per unit length of wire, F, angular displacement a, 

 periods of small oscillations, T and Tq, damping constant X, and the 

 effects of single and periodic gusts, /i,„s and ^mp, to explicit functions of the 

 wind velocity in miles per hour, the diameter of the wire in inches, sag of 

 the wire in inches and trigonometric functions of the deflection of the 

 loop a and inclination of the loop 7. The factor k does not appear 

 directly in the equations, having been replaced by fractional powers of 

 wind velocity and wire diameter derived from the experimental results 

 of Relf.3 



The following nomograms have been constructed by this method. 

 Nomogram No. 1 (Fig. 2) gives the steady deflection « of a span of wire 

 inclined to the horizontal at an angle 7 and the force in pounds per 

 linear foot of wire for a normal wind of velocity V. It also gives the 

 ratio of the period of small oscillations about the equilibrium position 

 to the natural period about the vertical position, this ratio depending 

 only on a. The actual value of the period in seconds may be read on 

 nomogram No. 2 (Fig. 3). 



By the use of nomogram No. 3 (Fig. 4), the damping constant X, and 

 the gust ratios n,ns and ju,„p may be computed from the sag a, the wind 

 velocity V and the diameter D. 



These nomograms in short give the numerical solution for our prob- 

 lem for wires of the two diameters assumed, namely .104" and .165". 



Two major assumptions should be noted, first, that the wire loop 

 swings in a plane and second, that the wire is inelastic. The first 

 assumption has a certain justification in that each element of wire if 

 independent of adjacent elements would be in equilibrium in the same 

 deflected angle a as is found for the loop as a whole. Expressing this 

 in another way — if it be assumed that the wind is uniform along the 

 span there would be no forces, considering only first order effects, to 

 distort the loop out of a plane. 



The second assumption is not so readily justified, in fact the sag of 

 the wire may be greatly affected by the wind pressure. The equili- 

 brium deflection a is, however, independent of the sag of the wire and is 

 found to be the same when the elasticity of the wire is taken into ac- 

 count as that derived for an inelastic wire. 



Considering only the case where the line through the supports is 

 horizontal (7 = 0), we define 2r as the unstressed length of wire in the 

 loop and note that this may be either greater or less than the span 

 length 2c depending upon the tension at which the wire is suspended. 



^ British Advisory Committee for Aeronautics — Report Xo. 102. 



