THE DESIGN OF ELECTROMAGNETS 67 



Referring to the wire table on page 34, the calculated size is seen 

 to be only slightly less than the cross-section of No. 15, B. & S. 

 gage. Using this wire, and allowing % in. for insulation be- 

 tween the iron and the coil, there will be about 68 layers of 41 

 turns, making a total of, say, 2,800 turns in the coil. The length 

 of wire will therefore be 2,800 X 47.2 ^ 12 = 11,000 ft., and 

 the resistance hot, i.e., at a temperature of 60C., will be 3.702 

 X 11 = 40.6 ohms. The current = 120/40.6 = 2.95 amp. and 

 the actual ampere-turns = 2.95 X 2,800 = 8,260. 



Rise of Temperature. The watts lost in the field when the 

 current is flowing are El = 120 X 2.95 = 354; but since the 

 current is supposed to be passing through the windings during 

 only one-half the time that the magnet is in operation, we can 

 apply the rule referred to in Art. 12, and assume that the power to 

 be dissipated amounts to only 354/2 = 177 watts. The total 

 surface of the coil is 47.2(10 + 6) = 755 sq. in., and if we use the 

 average value of 180 for the heating coefficient k, as suggested 

 in Art. 11 page 46, the temperature rise will be 



T = 180 X ^ = 42.2C. 

 755 



above the temperature of the air. This figure is a safe one, and, 

 since the iron shell offers a large cooling surface in contact with 

 the air, it is probable that the value of the coefficient k in this 

 particular design might be about 150. The temperature of 

 the windings will therefore not be excessive, and the amount of 

 copper might even be slightly reduced if the greatest economy in 

 manufacturing cost is to be attained. Exact data for the cal- 

 culation of temperatures in coils entirely surounded by iron are 

 not available, because the thickness and radiating surface of 

 the external shell are factors which will have an appreciable 

 influence on the value of the heating coefficient. 



Calculation of Leakage Flux. In order to provide sufficient 

 cross-section in the magnet, and ensure that the flux density in 

 the iron shall not be carried too near the saturation limit, it is 

 necessary to estimate the amount of the leakage flux. 



The permeance of the leakage paths may be calculated by 

 considering two separate components of the leakage flux: (1) 

 the flux which passes between the core and the cylindrical shell 

 through the space occupied by the windings, and (2) the flux 

 which passes between the uncovered portions of the central core 



