Abstract
Rolling sphere and lightning protection angle ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> ) are two well-established methods of designing lightning protection systems (LPS) mentioned by IEC 62305-3, international standard for lightning protection. Because of its simplicity, Designers tend to use lightning protection angle ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> ) method. However, this method is just an estimation of rolling sphere method, which makes it less reliable and efficient in some cases. In this paper, a novel mathematical equation is proposed based on rolling sphere in order to optimize the height and protection radius of lightning air terminals. Maintaining the precision of the rolling sphere method, the modern proposed equation makes application of this method more convenient; there would be no need to roll the sphere in 3D space. The major benefit of the innovative equation is that it is precise and is not approximation of rolling sphere method. Moreover, the practical application of the proposed equation to two different buildings for designing LPS is explained in the essay. The results demonstrate that the proposed equation can be employed in a verity of industrial projects.
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