SINGLE-PHASE COMMUTATOR MOTORS 335

and the angle of lag, 0, is given by:

^o + 61

= -
/o

or, denoting the ratio of armature turns to field turns by

(9)

(10)
and this is a minimum; that is, the power-factor a maximum, for:

or:

go =

JL
Vb

(ii)

and the maximum power-factor of the motor is then given by:

(12)

/ 2
tan do = ~ —

Jo

Therefore the greater b is the higher the power-factor that
can be reached by proportioning field and armature so that

n,

Since 6 is the ratio of armature reluctance to field reluctance,
good power-factor thus requires as high an armature reluctance
and as low a field reluctance as possible; that is, as good a mag-
netic field circuit and poor magnetic armature circuit as feasible.
This leads to the use of the smallest air gaps between field and
armature which are mechanically permissible. With an air gap
of 0.10 to 0.15 in. as the smallest safe value in railway work, 6
can not well be made larger than about 4.

Assuming, then, 6 = 4, gives q = 2, that is, twice as many
armature turns as field turns; HI = 2 n0.

The angle of lag in this case is, by (12), at synchronism: /0 = /,

tan 00 = 1,

giving a power-factor of 70.7 per cent.

It follows herefrom that it is not possible, with a mechanically