16 



TRANSMISSION EXPERIMENTS OVER MASSACHUSETTS BAY 



ft, etc.) Note that fur the biliuear model, unless the 

 slope of the bottom portion be extreme, the duct height 

 must be of order 200 ft or higher before there is any 

 appreciable effect at this frequency. 



Figure 12 is a similar theoretical diagram for the 

 high S-band path. The scale in this case is to 100 ft. 

 At X band the corresponding changes occur over a 

 height range of only about 30 ft. For the low patlis 



•■ DUCT HEIGHT IN FEET 



Figure 12. Theoretical field strength versus duct 

 height, bilinear index, first mode, high S band. 



at any given freqixency the curves are similar, but the 

 increases in field strength occur more rapidly, so that 

 the free space value is reached at essentially the same 

 duct height for both high and low paths. 



In a few special cases for S and X bands contribu- 

 tions of a number of modes (as many as 18 in one case) 

 have been added in phase. In no case did the calculated 

 field strength reach a value more than 15 db above the 

 free space value, and iti most cases it was between 

 —5 and +10 db. 



The calculations check well with ol)sorvations in a 

 qualitative way in spite of the fact that the bilinear 

 curve is not in general a good approximation to the 

 true IL curve and that the assumption of a uniform M 

 curve along the entire transmission path is an ex- 

 treme idealization. They show the order of magnitude 

 of duct heights at which appreciable increases in field 

 strength first occur at a given frequency. They demon- 

 strate also the important fact that the field strength 

 is increased even at considerable heights above the 

 duct. This is so because with a leaky mode the height- 

 gain function does not decrease with height above the 

 duct but instead liecomes practically constant over an 

 appreciable range. This is illustrated in Figure 13, 

 where the normalized height-gain function for a leaky 

 case is compared with the standard. The decrease in 

 absolute value of the height gain is compensated by 

 the reduction in the attenuation. It is thus clearly 

 not necessary to put a transmitter inside the low duct 

 in order to take advantage of it; nor does the first 

 mode need to be actually trapped as indicated by ray 



tracing, but merely less attenuated than the standard. 



As to character of the signal, the theory suggests 



that steady signal is obtained with low ducts because 



only a single mode is important. With large ducts fad- 



50 



40 



20 



40 60 



20 LOG |U| 



Figure 13. Height-gain functions, standard and leaky 

 first modes. (Ordinate: height. Abscissa: gain.) 



ing may be caused by interference among many modes 

 which change rapidly in amplitude and phase with 

 small changes in refraction. Even with very large 

 ducts, for terminals well above the duct, steady signal 

 might again be expected because the field strength 

 there would probably again result from a single leaky 

 mode, in this case not the first mode. 



Figure 14. Height-gain functions within a duct com- 

 pared with standard first mode. (Ordinate: height. 

 Ab.scissa: gain.) 



Finally, the calculations agree with observations in 

 showing that even when many modes are strongly 

 trappcfl, the field strength at a fixed point does not 



