Pitch Factor or Coil Span Factor (Kc)

E.M.F. Equation of an Alternator : Part2 
        In practice short pitch coils are preferred. So coil is form by connecting one coil side to another which is less than one pole pitch away. So actual span is less than 180^o . The coil is generally shorted by one or two slots.

Note : The angle by which coil are short pitched is called angle or short pitched is called angle of short pitch denoted as 'α'.

α       = Angle by which coils are short pitched. As coils are shorted in terms of number of slots i.e. either by one slot, two slots and so on and slot angle is β then angle of short pitch is always a multiple of the slot angle β.

Fig.  1  Angle for short pitch

.^..        α    = β x Number of slots by which coils are short pitched.

      or   α  = 180^o -Actual coil span of the coils.

       This is shown in the Fig. 1.

       Now let E be the induced e.m.f. in each coil side. If coil is full pitch coil, the induced e.m.f. in each coil side help each other. Coil connections are such that both will try to set up a current in the same direction in the external circuit. Hence the resultant e.m.f. across a coil will be algebraic sum of the two.

 .^..         E_R   = E + E = 2E                   .......... for full pitch

Fig. 2  Full pitch coil

 

       Now the coil is short pitched by angle 'α', the two e.m.f. in two coil sides no longer remains in phase from external circuit point of view. Hence the resultant e.m.f. is also no longer remains algebraic sum of the two but becomes a phasor sum of the two as shown in the Fig. 3.

Fig. 3  Phasor sum of two e.m.f.s

       Obviously E_R  in such a case will be less than what it is in case of full pitch coil.

       From the geometry of the Fig. 3, we can write,

       AC is perpendicular drawn on OB bisecting OB.

 .^..     l (OC) =  l (CB) = E_R  /2

and 

∟BOA  = α/2

 .^..    cos (α/2) = OC/OA = E_R/2E

.^..      E_R  = 2 E cos (α/2)                                      ............... For short pitch

       This is the resultant e.m.f. in case of a short pitch coil which depends on the angle of short pitch 'α'.

Note : Now the factor by which, induced e.m.f. gets reduced due to short pitching is called pitch factor or coil span factor denoted by K_c.

       It is defined as the ratio of resultant e.m.f. when coil is short pitch to the resultant e.m.f. when coil is full pitched. It is always less than one.

       where α  = Angle of short pitch