A correction to Maekawa's curve for the insertion loss behind barriers

Maekawa's curve is one of the most established methods for predicting the insertion loss (IL) behind barriers. For the simple case of a barrier modeled as a half plane, the IL is given versus a single parameter, the Fresnel number (N1). Predictions obtained by Maekawa's curve deviate largely from experimental data, and from predictions obtained by analytical solutions, when the receiver is either close to the barrier or at the boundary separating the illuminated from the shadow zone. It is shown that if a second Fresnel number (N2) is appropriately defined, the IL obtained by the existing analytical solutions can be expressed versus N1 and N2 for several types of incident radiation (plane, cylindrical, and spherical). Accordingly, the single curve in Maekawa's chart can be replaced by a family of curves. Each curve corresponds to a different N2 and provides the IL versus N1 . The Kurze-Anderson formula (a mathematical expression of Maekawa's curve) is also modified to describe this set of curves. Besides providing increased accuracy in the areas where Maekawa's curve does not, the graph proposed here addresses the more general problem of combining the simplicity of empirical models like Maekawa's with the accuracy of sophisticated mathematical models.