66 PRINCIPLES OF ELECTRICAL DESIGN 



Let us therefore decide upon this dimension. The diameter 

 of the inner core is obtained from the equation 



whence D = 9.16 in. It will be better to provide a 2-in. hole 

 through the center of the magnet, and have a conical face to the 

 core, as shown in sketch. The diameter of the central pole core 

 may be 10 in., and the edges can be slightly bevelled off so that 

 the polar surface shall not exceed 66 sq. in. 



In order to introduce a factor of safety, and permit of the iron 

 ball being lifted even when the contact between magnet and 

 armature is imperfect, the specification would probably call for 

 a magnet powerful enough to attract the ball through a distance 

 of, say, )4 in- Let us further assume that, the action being 

 intermittent, the current will flow through the exciting coil dur- 

 ing only half the time that the magnet is in action. This will 

 probably permit the use of a current density of 1,000 amp. per 

 square inch of copper section. Thus, if the winding space factor 

 may be taken as 0.5, it will be necessary to provide 2 sq. in. of 

 cross-section of coil for every 1,000 ampere-turns of excitation 

 required. 



The ampere-turns necessary to overcome the reluctance of the 

 double air gap are 



l (SI) g = 2.02J5 X l"' g 



= 2.02 X 7,240 X M 

 = (say) 8,000, which includes a small 



allowance for the reluctance of the iron in the circuit. The 

 required section of coil is therefore about 16 sq. in. One of the 

 dimensions should, if possible, be kept within the limit of 3 in. 

 in order to avoid excessive internal temperatures. A cross- 

 section of 5 in. by 3 in. = 15 sq. in. will probably be large enough 

 to accomodate the winding. 



The average length per turn of wire is 7r(10 + 5) = 47.2 in., 

 and (by formula 26, Art. 10, page 42) the cross-section of 

 the wire, in circular mils, will be 



47.2 X 8,000 

 (m) = --- 



where E is the voltage across the terminals of the magnet. 

 Assuming this to be 120 volts, the value of (m) will be 3,140. 



1 Art. 4, formula (5). 





