III.  Generated  E.M.FS. 

42.  The   formula   for  the  generation  of  e.m.f.  in  a  direct- 
current  machine,  as  discussed  in  the  preceding,  is 

e  = 

where  e  =  generated  e.m.f.,  /  =  frequency  =  number  of  pairs 
of  poles  X  hundreds  of  rev.  per  sec.,  n  =  number  of  turns  in 
series  between  brushes,  and  <£  =  magnetic  flux  passing  through 
the  armature  per  pole,  in  megalines. 

In  ring-wound  machines,  <f>  is  one-half  the  flux  per  field  pole, 
since  the  flux  divides  in  the  armature  into  two  circuits,  and  each 


178     ELEMENTS  OF  ELECTRICAL  ENGINEERING 

armature  turn  incloses  only  half  the  flux  per  field  pole.  In  ring- 
wound  armatures,  however,  each  armature  turn  has  only  one  con- 
ductor lying  on  the  armature  surface,  or  face  conductor,  while  in  a 
drum-wound  machine  each  turn  has  two  face  conductors.  Thus, 
with  the  same .  number  of  face  conductors — that  is,  the  same 
armature  surface — the  same  frequency,  and  the  same  flux  per 
field  pole,  the  same  e.m.f.  is  generated  in  the  ring-wound  as  in 
the  drum-wound  armature. 

The  number  of  turns  in  series  between  brushes,  n,  is  one-half 
the  total  number  of  armature  turns  in  a  series-wound  armature, 

-  the  total  number  of  armature  turns  in  a  single-spiral  multiple- 
wound  armature  with  p  poles.  It  is  one-half  as  many  in  a  double- 
spiral  or  double-reentrant,  one-third  as  many  in  a  triple-spiral 
winding,  etc. 

By  this  formula,  from  frequency,  series  turns,  and  magnetic 
flux  the  e.m.f.  is  found,  or  inversely,  from  generated  e.m.f.,  fre- 
quency, and  series  turns  the  magnetic  flux  per  field  pole  is 
calculated: 

*--!-, 

4/n 

From  magnetic  flux,  and  section  and  lengths  of  the  different 
parts  of  the  rnagnetic  circuit,  the  densities  and  the  ampere- 
turns  required  to  produce  these  densities  are  derived,  and  as  the 
sum  of  the  ampere-turns  required  by  the  different  parts  of  the 
magnetic  circuit,  the  total  ampere-turns  excitation  per  field  pole 
is  found,  which  is  required  for  generating  the  desired  e.m.f. 

Since  the  formula  for  the  generation  of  direct-current  e.m.f 
is  independent  of  the  distribution  of  the  magnetic  flux,  or  its  wave 
shape,  the  total  magnetic  flux,  and  thus  the  ampere-turns  re- 
quired therefor,  are  independent  also  of  the  distribution  of 
magnetic  flux  at  the  armature  surface.  The  latter  is  of  impor- 
tance, however,  regarding  armature  reaction  and  commutation.