## 4 Application: Windage Yaw of the Jumper Cable over Hilly Terrain  
A jumper cable is a conductive device connecting the tensile clamps on both sides of a tension tower in a transmission line. It is used to maintain a sufficient electrical clearance distance between the live conductor and the conductive portion of the tower (Figure 16). Many accidents in power transmission lines are attributed to the excessive windage yaw of jumper cables, which results in a reduction of the electrical apparatus clearance distance. As the windage yaw of the jumper cable is very sensitive to the wind loadings, the cable is employed herein as an example to clarify the using of the presented contour plots resulting from the hilly terrain-disturbed wind field. The translational displacement responses of the cable subjected to wind loads can be computed via finite element (FE) approach, and the commercial software ANSYS was then utilized. In the FE analysis, the displacement responses can be computed by  
\[\mathbf{F}=\mathbf{K}\mathbf{D} \tag{12}\]  
where \(\mathbf{K}\) is the elastic stiffness matrix, and \(\mathbf{D}\) is the vector of the translational displacement. The \(\mathbf{F}\) in Equation (13) is the vector of the external wind loading, and it has a form of  
\[\mathbf{F}=\{\mathbf{F}_{1},\ldots,\mathbf{F}_{i},\ldots,\mathbf{F}_{N}\}^{ \mathrm{T}}\text{, and }\mathbf{F}_{i}=\{F_{xi},F_{yi},F_{zi}\}^{\mathrm{T}} \tag{13}\]  
Figure 15: Comparison of speed-up Su between tests and various standards. where \(N\) is the number of the nodes. \(\mathbf{F}_{i}\) is the nodal force sub-vector for the \(i\)th node, and in a form of  
\[F_{xi}=0.5\rho V_{0}^{2}S_{u}^{2}\mu_{xs}A_{xi} \tag{14a}\] \[F_{yi}=0\] (14b) \[F_{zi}=0.5\rho V_{0}^{2}S_{w}^{2}\mu_{sz}A_{zi} \tag{14c}\]  
in which \(\rho\) is the density of the air, \(\mu_{xs}\) and \(\mu_{sz}\) are the drag coefficients of the cable in the \(x\) and \(z\) direction, \(A_{xi}\) and \(A_{zi}\) are the projected areas in the \(x\) and \(z\) direction, and \(V_{0}\) is the wind velocity at height of \(z\) in the undisturbed ABL. Thus, the windage yaw angle \(\alpha\) induced by the wind loads can be computed by  
\[\alpha=\tan[D_{x}/(D_{s}-D_{z})] \tag{15}\]  
where \(D_{x}\) and \(D_{z}\) are the streamwise displacement and vertical displacement of the cable, respectively, and \(D_{s}\) is the sag of the cable. In the FE modelling of the cable, the two-node truss element is employed, and each node of the element has three translational degrees-of-freedoms (DOFs). As the cable takes a shape of catenary curve due to its self-weight, the initial coordinates of each node are in accordance with the classic catenary equation [34]. The ends of the jumper cable are hinged. The internal initial tensile force of the cable caused by the self-weight is simulated by prescribing an initial tensile stress for each element. The wind loadings on the structure are simplified as concentrated forces acting on the nodes. The FE model of the jumper cable with boundary conditions and nodal wind loads is illustrated in Figure 17, and the relevant parameters are listed in Table 1. Figure 18 depicts the locations of the jumper cable, along with the wind direction of the oncoming flow, for the following study. A sensitivity analysis was performed in advance to determine an appropriate mesh that would balance the calculation accuracy and the computational cost. Five FE meshes, namely, the cable is divided into 20, 40, 80, 160, and 320 elements, respectively, were thus employed for the sensitivity analysis. Based on these meshes, the streamwise displacement, vertical displacement, and the windage yaw angle of the cable on the hill crest were obtained and listed in Table 2. It is found that the number of the elements affects the wind-induced response of the jumper cable slightly, provided that it is greater than 20. Generally, a denser mesh may result in a better solution, but requires a higher computational  
Figure 16: A picture of the jumper cable. cost.