the field of rod - plan electrodes and partial discharge inception voltage in air

the coordinate transformation allows the exact calculation of some electrode configurations. in this paper the prolate spherical coordination transformation is used to calculate the field of a hyperboloiderod against plan electrode. the exact field is caculated using two new parameters: 1) electrodes spacing and 2) the radius of curvature of the tip of the rod electrode. the partial discharge inception voltage in air is then calculated by numerical integration of the effective ionization coefficient over the gap using these parameters. the pd inception voltage is calception voltage is calculated for constant radius of curvature versus electrodes spacing. the calculation shows that for large electrodes distances the electrodes spacing is not relevant but the radius of the curvature of the tip of the rod electrode is very important. it seems that the form of the rod shaft is likewise not relevant. the result can be used for large electrodes distances for evry form of the rod shaft.