Chapter 12 

 NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE* 



THE equations given in the preceding chapter 

 have now been thrown into nomographic form. 

 When these nomograms are employed a rapid method 

 for constructing coverage diagrams results. 



Let hi denote the height of the transmitter in 

 feet, /„ R . be the frequency in megacycles, n be an 

 integer (1, 2, 3, • • ■) specifying the number of the 

 lobe, 6(0 ^ b < 1) a "phase" factor specifying the 

 position on the lobe, and r the radius of the earth. 

 Introduce the quantity B defined as follows. 



B = 



150 - b) \/2N (3.281)* 



= 3.676 X 



10 6 (n - b) 



hi'fme 



(1) 



where we have taken r = 8.50 X 10 6 m, as the 

 approximate % earth value. We have to decide on 

 the interval for b. By taking b = 0, %, %, %, %, %, 

 we actually obtain seven points on each lobe, 

 which should be sufficient for the purpose of drawing 

 a coverage diagram. Hence, n — b = 0, %, %, %, 



/3, 



%, 1, %, 



, etc., spaced at intervals of %. 



Equation (1) is represented in the nomogram of 

 Figure 1. We are given hi and / mc , the height and 

 frequency of the transmitter. Connect the appro- 

 priate values on the scales by a straight line and 

 mark the point of intersection on the central vertical 

 line. 



Define a quantity k by the equation 



fc k 



so that k = 3 corresponds to the maximum of the 

 first lobe, k = 6 to the minimum, k — 9 to the next 

 maximum, k = 12 to the minimum, etc. k = 15, 21, 

 and 27 correspond to the third, fourth, and fifth 

 maxima, respectively. Other values of k determine 

 intermediate points on the lobe. 



Now draw a straight line from k = 1 through the 

 point previously determined on the central vertical 

 line until it intersects the left-hand axis of B. Read 

 off B or 1/B, whichever is given. Repeat the process 

 for k = 2, 3, • • • , etc., until a vame of B is obtained 



a By Lt. Comdr. D. H. Menzel and Lt. A. L. Whiteman, Office 

 of the Chief of Naval Operations. 



that exceeds 10; in other words, continue until the 

 straight line runs off the lower edge of the left-hand 

 scale. 



There will be cases, however, usually involving 

 large values of h or f mc) where B will still be small 

 (1/B large) even for k = 27. When this condition 

 exists, the lobes tend to be so closely spaced that 

 the individual maxima are difficult to define and 

 even more difficult to draw on a coverage chart. 

 For such conditions an alternative procedure is 

 recommended, which will be given later. 



If no difficulty is encountered, however, enter the 

 values of B or 1/B (designate the latter with an 

 asterisk) in a table such as Table 1. 



Table 1 



/mc = Frequency in mc 

 hi = Height of antenna in ft 



*Put an asterisk after an entry if the value read off is equal to l/B. The 

 corresponding values of n and b are entered in columns 3 and 4 of the form 

 sheet. 



It should be noted that equation (1) is easy to 

 solve, and the operator familiar with mathematical 

 procedures may prefer to use direct calculation, by 

 slide rule or logarithm tables, as much more accu- 

 rate. In general, however, the nomogram values are 

 sufficiently accurate for the work. 



Next, for the five or six assumed values of decibels 

 for which contours are desired, we solve a subsidiary 

 equation for Y by means of a nomogram (not repro- 

 duced here). We note that 



Y = db + 60 - 10 log (2btA0 , 



95 



