/ 



ECONOMICS OF TKLKPIIOXK UKLAV A I'PLH'ATION'S 241 



ing cost for a certain wire gauge \'arics while the curve labelled CV shows 

 how power plant cost is changing. ^J'he desirable end result is a coil with 

 resistance value to permit the sum of these to be as low as possible, as 

 in the curve marked Cr ■ I'hc following methods will give such a design. 

 The value of Cr , made up of power cost, Cp , and winding cost, Cw , 

 represents the cosit of all the parts of the central office which are influ- 

 enced by a change in resistance of the coil. Thus we wish to minimize 

 this e(iuati()n: 



where, from the previous relations, 



^ _ ^1 

 ^^- -R' 



Cw = K2R, 



Ki = CphE\ 



/Vo = Cfl I 1 + — -5- 

 \ Cr K 



The resulting expression for this total cost is 



Cr=^ + K2R. (21) 



In this equation Ki is a constant, but /v2 ^'aries both with resistance 

 and wire size, as the latter affects the values of Cn , Cr , and the quantity 

 N/R, which is determined by the coil design equation 



R = AN (h + d), 



in which, using the special notation common to coil design problems: 



N = turns in winding = h(/K, 



R = coil circuit resistance, 



A = IT times the resistivity of wire in ohms per inch length, gi\-en in 

 tables for each size of wire, 



h = depth of coil space occupied by wire, 



/ = length of winding space, 



d = inside diameter of coil, 



K = effective cross-sectional area required by one turn of wire, given in 

 tables for each size. 



