INFLUENCE OF SMALL LAYERS 257 



We can use this equation to calculate the corresponding field strength, 

 for the Illinois paths, in terms of lA'/m for 1 kW radiated from a half- 

 wave dipole. We have the following relations: 



A (X/2 dipole) = 0.127 X^ (6.9) 



p, (X/2 dipole) = ^2X2/300^2 (6.10) 



where E is the field strength in volts/meter if Pr is in watts. From 

 (6.8), (6.9), and (6.10), we can calculate E for the two layers specified 

 above. The results obtained are shown in figure 6.17 for various layer 

 heights and the following models of reflection coefficient: 



(a) \p\ = An • \/8ira^h 



(b) IpI = An/2a\ 



Model (b) is the Fresnel discontinuity equation which gives the limiting 

 value of \p\ towards which all models tend as the layer thickness de- 

 creases. The curves in figure 6.17 show that the calculated field strength 

 depends considerably on the assumed n-profile. If | p | = An • X/Sira^h, 

 values of field strength comparable with the long-term median value may 

 be produced by layers of about 10 km in lateral dimensions in the height 

 range 0.5 to 1 km. If |p| = An/2a^, similar field strength may be pro- 

 duced by layers in this height range if the lateral dimension is of the order 

 of 2 km. The effect of the layer decreases with increasing height, but 

 even with layer heights of 3 km, the field strength is still 1 /LtV/m or 

 greater at both wavelengths for a 10 km layer with \p\ — An/2a'^. How- 

 ever, it should be pointed out that the assumed value of An = 10~* is 

 probably somewhat large for layers as high as 3 km. The results also 

 show that model (b) (i.e., p = An/2a:-) gives field strength values which 

 are higher at X = 1.67 m (/ = 179.75 Mc/s) than at X = 4.18 m (/ =71.75 

 Mc/s). 



6.2.8. Conclusions 



Any departure of refractive index structure from a smooth monotonic 

 decrease with height produces an increase in field strength on a 200-km 

 path in the frequency band 70 to 180 Mc/s. In the particular case 

 studied, elevated tilted layers result in signal enhancement of 10 to 25 dB 

 over the values for unstratified conditions, at all percentage levels. (The 

 importance of the tilted layer is possibly a consequence of the asymmetry 

 of the path, the transmitting antenna being 200 m above ground and the 

 receiving antenna 30 m.) 



The predicted field strengths, for conditions classified as unstratified 

 in terms of sonde data, are in approximate agreement with observed 

 results, although the scatter of the points (plus the tendency to predict 



