GENERALIZED COVERAGE DIAGRAMS 



147 



value of rfo determines the lange of the lobe for 

 specified values of r. In Figure 14, the various 

 values of do used in constructing the charts are 

 specified as A, B, C, • • ■ , M, N, and are shown as 

 functions of hi as ordinate and 20 log A — 20 log X 

 as abscissa. 



6.8.3 



Determination of r 



Figure 15 shows r for various values of transmitter 

 height hi and wavelength X where 



1 2hidr hi"^^2ka 2hi 



!^ J2_ 



V (57) 



\ka \ka X ka 



The values of r determine how the path-difference 

 ciu'ves intersect the envelopes corresponding to 

 assigned ^-alues of sin- ( n/2) in the equation 



I, = 4- = doVG'i \l a - DY- + 4D sin^ - . (58) 



: -T- = dpVG'i \l (1 - Dy- + 4D sin^ 



The generalized coverage charts are designated as 

 1, 2, • • • , 11, 12 in Figures 16 to 39, with the chart 

 number being given bj^ Figure 15. 



6 (,.4 Use of Charts 



Figures 16 to 39 give 24 basic charts developed 

 by the Radiation Laboratory and presented in 

 report 702. On each chart are complete lobes oi- 

 lobe outlines labeled A, B, C, ■ • ■ , M, N. In the 

 following description these letters are referred to as 

 lobe letters and the numbers 1 to 12 as chart num- 

 bers. It will be noted that each chart number is 

 plotted to two scales, giving 24 charts in all. 



The problem of constructing coverage diagrams 

 resolves itself into finding the chart number and lobe 

 letter corresponding to given values of gain factor A , 

 transmitter height hi, and wavelength X. As stated 

 in Section 6.8.1, the basic parameters of the general- 

 ized coverage diagrams are R and du or r and da. 



The value of r is given in Figure 15 as a function of 

 X and hi. Figure 15 was constmcted from equation 

 (51) which, after the substitution of numerical 

 values, becomes: 



1030X /, , 4\ 

 r = — .—^ I forfc = - . 

 /(/'- \ 3/ 



(59) 



The value of r determines the chart number. The 

 lobe letter is found from the do corresponding to the 

 given gain factor, transmitter height, and frequency. 

 Figure 14 gives the lobe letters A, B, C, ■ • •, M, N 

 as functions of 20 log A — 20 log X and the trans- 

 mitter height. The relationship for plotting these 

 lines is given by equation (56). 



As an illustration of the use of the generalized 

 coverage diagrams, assimie 20 log A = —83, /ii = 

 33 meters, and / = 200 mc (X = 1.5 meters). If a 

 straight line is drawn connecting hi = 33 and X = 1.5 

 in Figure 15, it ^\^ll intersect the r scale at r = 8. 

 Thus the chart number is 5. Now the lobe letter 

 to be used in chart 5 must be found. For this case, 

 20 log A - 20 log X = -86.48. The coordinates 

 20 log A - 20 log X = -86.48, and /;, = 33, de- 

 termine the lobe letter to be E in Figure 14. Figure 

 24 shows lobe E on chart 5. The first lobe is shown 

 completely, together with the lower half of the second 

 lobe. It must be noted that the coordinates of these 

 charts, v = d/dx and u = ho/hi, are dimensionless. 

 To convert to height /;.. and range d, the vertical 

 distances must be multiplied by hi and the hori- 

 zontal distances by df. In this case hi = 33 meters 

 and dr = ^2kahi = 23.6 km. The actual coordi- 

 nates of the position of maximum range are h^ = 

 375 X 33 = 12.4 kna and rf = 15.4 X 23.6 = 365 km. 



The charts given in Figures 16 to 39 may be used 

 for drawing coverage diagrams where the reflection 

 coefficient is assumed equal to — 1 and when the 

 directivity factor F2/F1 is equal to unity. Each 

 chart may be used for values of r near that for 

 which the chart is drawn. For intermediate values, 

 interpolation between charts is necessary. Errors 

 inherent in interpolation limit the accuracy attained. 



