CHAP. XIII] TORQUE AND TRACTIVE EFFORT 249 



to eq. (171), the vertical component of the pull upon the strip of the 

 width da is. 



dF ex "(B^/24.7)(A/2^da-cos a. 



The horizontal component of the pull is balanced by the corresponding 

 component on the other half of the armature. The total pull downward is 



F ex =[2.4/(27rX24.7)]j* a 'cos a da. 



Putting tan a =z and integrating we get the so-called Sumec formula 

 for the eccentric pull, in kg. : 



F,,-(4B.//V24.7)(e/o)[l-(e/a)'H-*. . . . (175) 



The integration is simplified; if, before integrating, the difference is 

 taken between the vertical forces at the points corresponding to 

 and to n a. The limits of integration are then and i*. 1 



Prob. 13. The average flux density under the poles of a direct - 

 current machine is 6.5 kl/sq.cm.; the poles cover 68 per cent of the 

 periphery. The diameter of the armature is 1.52 m.; the effective 

 length is 56 cm. What is the magnetic pull when the eccentricity is 

 10 per cent and when it is 50 per cent of the original air-gap? 



Ans. 3.2 and 24 metric tons. 



Prob. 14. The 22/2-kv., 2500-kva., transformer specified in prob. 

 5, Art. 64, had a total impedance drop of 73.5 volts at full load current 

 on the low-tension side. What average force is exerted on each coil- 

 face during a short-circuit, provided that the line voltage remains 

 constant? The transformer winding consists of 12 hi^h-tension coils of 

 100 turns each, and of 11 low-tension coils interposed between the high- 

 tension coils, together with 2 half-coils at the ends. Two of the dimen- 

 sions of the coils arc repeated here: O m -2.6 m.; f-18 cm. Hint: The 

 short-circuit current is equal to 2000/73.5 = 27.2 times the rated current. 



Ans. About 22. metric tons. 



Prob. 15. What is the mechanical pressure on the surface of the 

 conductors in prob. 3? 



Ans. 47.6 and 5.8 milligrams per sq.cn i. 



71. The Determination of the Mechanical Forces by Means 

 of the Principle of Virtual Displacements. In order to 1 -tc Tininr 

 th< mechanical Inn. or torque between two parts of a mag- 

 netic circuit the general method consists in giving these parts 

 an infinitesimal relative .: . nt and applying the law of 



1 J. K. Sumec. Hrrorhnung dc* rinsritiRrn magnet i-.-lirn Zuges bei Excen- 



trizititt, Zeitscfai/t far EUktrotcchnik (Vienna), Vol. 22 (1904), p. 727. This 



al ia continued now under the name of EUctrotochnik vnd Maschin- 



