Diffraction of Plane Radio Waves by a 

 Parabolic Cylinder 



Calculation of Shadows Behind Hills 



By S. O. RICE 



(Manuscript received April 3, 1953) 



Expressions are given for the diffraction field far behind, and the surface 

 currents on, a parabolic cylinder. Approximate values for the field strength 

 and current density are given when the radius of curvature of the cylinder is 

 large compared to a wavelength. The formidas may have value in predicting 

 the chadows that are cast by hills in microwave propagation. The idea of 

 representing hills by knife-edges has been used successfully by a number 

 of investigators. The theory of the parabolic cylinder indicates that such a 

 representation is valid even for gently rounded hills when the angle of diffrac- 

 tion is small. On the other hand, when the angle of diffraction is so large 

 that the knife-edge calculations do not apply, the residts presented here may 

 be used. 



1. INTRODUCTION 



A number of investigators have studied the effect of hills on the 

 propagation of short radio waves. Experiment has shown that the field 

 far behind a hill may be computed, to a reasonable degree of accuracy, 

 by assuming that the hill acts like a knife-edge (half-plane) \ The ques- 

 tion naturally arises as to the conditions under which such an assump- 

 tion is permissible. Here we attempt to throw some light on this ques- 

 tion by taking the hill to be a parabolic cylinder. 



Our results indicate that, for small angles of diffraction, even gently 

 curved hills act like knife-edges. However, for larger angles correspond- 

 ing to points deep in the shadow or to points high in the illuminated re- 

 gion, it may be necessary to use the more exact formulas which take the 

 curvature of the hill into account. 



* See, for example, Ultra-Short-Wave Propagation, J. C. Schelleng, C. R. 

 Burrows and E. B. Ferrell, Proc. I.R.E., 21, pp. 423-463, 1933. 



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