28 PRINCIPLES OF ELECTRICAL DESIGN 



in the sketches 1 provided the cross-sections are similar, apart 

 from the actual magnitude of the dimensions. Thus, if the 

 exciting ampere-turns were to remain constant, the leakage flux in 

 similar designs of apparatus would be proportional to the first 

 power of the linear dimension Z; but since the cross-seclion of 

 the winding space is proportional to I 2 , the exciting ampere- 

 turns would not remain of constant value, but would also vary 

 approximately as I 2 . Given the same size of wire which 

 obviates the necessity of considering changes in the winding space 

 factor the number of turns, S, will be proportional to I 2 , 

 and the resistance, R } will vary as I 3 . For the same rise of 

 temperature on the outside of the windings, the watts lost in 

 heating the coil must be proportional to the cooling surface. 

 Thus, 



PR cc l* 



whence 



and 



The total leakage flux in similar designs of magnets will be pro- 

 portional to I X I 1 - 6 or Z 2 - 5 , and as a rough approximation it 

 may be assumed that, with a proportional change in all linear 

 dimensions, the leakage flux will vary as the third power of the 

 linear dimension, or as the volume of the magnet. 



7. Leakage Coefficient. The leakage coefficient, or leakage 



,. useful flux + leakage flux 

 factor, is the ratio -- ,. , a 



useful flux 



or 



7 ,_ $.+ $i 



where $/ is the total number of leakage lines calculated for every 

 path where an appreciable amount of leakage is likely to occur. 

 When designing electromagnets or the frames of dynamo 

 machines, a fairly close estimate of the probable leakage factor 

 is necessary in order to be sure that sufficient iron section will be 



1 The sections shown in Figs. 9 and 10 have, for convenience, been taken 

 through the axis of length instead of at right angles to this axis as in the 

 other examples. 



