 elsewhere on the Earth's surface, is liable to make losses greater than those derived from the simple screens assumed for the Deygout approximations. To overcome this, the profile can be assumed to consist of geometric shapes, for which calculations are possible, such as spheres, cylinders, or wedges. Rounded Hilltops One method of stylizing the profile is to assume a rounded top on each of the obstructions rather than a knife edge. This technique has a problem in its application because it requires the radius of a hilltop to be known and, with most maps in common use, it is not possible to determine this radius with sufficient accuracy. However, a useful analysis of this method is given in an IEE paper by Hacking (1970), where extra terms are derived to add to the knife edge loss. Diffraction over a Sea Path If it is only sea that interrupts the line-of-sight path, a spherical diffraction calculation can be made from a method that has its origins in work by Van der Pol and Bremmer (1937, 1949). These methods have a complicated formulation and will not be detailed here. However, for many applications a simplification, based on a paper by Vogler (1964), is of value for frequencies above 400 MHz. Approximating a Land Path to a Cylindrical Surface On a land path with many diffraction edges, a useful prediction is made with a cylindrical surface stylization of four radii joining each other with common tangents, as shown in Figure 7.21. Point a is the transmitter horizon, and point b is the receiver horizon. Arc ac just clears the terrain between point a and the transmitter site, and it has a tangent to the horizon line, Ta, at point a. This condition defines the radius rt. Radius rr is defined similarly at the receiver end. The radii r1 and r2 are defined such that arcs ae and be form tangents with The Space Wave Fig. 7.21 Geometry for a curved- surface diffraction calculation. horizon lines Ta and Rb at points a and b, respectively, and have a common tangent at e. The curved surface attenuation can then be approxim