56 



PRINCIPLES OF ELECTRICAL DESIGN 



excessive temperature rise. It is usual to assume a value for the 

 thickness, t, greater than one-third of the diameter of the core, 

 with the previously mentioned limit of about 3 in. Thus, even 

 if d were greater than 9 in., the depth of winding should, prefer- 

 ably, not exceed 3 in. In the present case we shall try a small 

 value of coil thickness of about 1.875 -f- 3 = 0.625 in. or, say, 

 * = H in. 



Current Density in Windings. If a suitable value for the 

 current density in the windings can be chosen, it will be an easy 

 matter to determine the length, I, of the winding space, and so 

 complete the preliminary design. 



Let A = the current density (amperes per square inch). 



R" = the resistance, in ohms, between opposite faces of an 

 inch cube of copper. By formula (21) of Art. 9, 

 1 



R 1 



at 60C. 



1,273,000 

 sf = the winding space factor, as given in Fig. 15, page 40. 



As the size of wire is not yet known, a probable value 



of 0.5 will be chosen for this factor, in the preliminary 



calculations. 

 T = The allowable temperature rise, being 40C. in this 



example. 



k = the cooling coefficient, being denned in Art. 11 form- 

 . ,__. cooling surface 



ula (30), as T X ' An avera * e 



be dissipated 

 value of 180 may be taken for k. 



Equating the I 2 R losses with the watts that can be dissipated 

 without exceeding the temperature limit, we can write, 



T 



total surface of coil X T = watts to be dissipated 



= #"A 2 X cubic inches of copper X 



ou 



or 



whence 



+0X2 



t] = 



X 2Uir(d + X sf X 



hT(i : 



\kR"U 



i+ O.JKW 



/XA 



(35) 



In order to eliminate I, we may consider t in the numerator to 

 be negligible, since, in this particular design, with an air gap of 



1 Where h has the same meaning as on p. 47, being less than 60 if heating 

 is intermittent. 







