SINGLE-PHASE COMMUTATOR MOTORS 411

That is:

The commutation current, ig, can be made to vanish at any
speed, S, at given impedance factor, X4, by choosing the phase
angle of the impedance of the short-circuited coil, <5, or the resist-
ance component, X', provided that X4 is sufficiently small, or the
speed, S, sufficiently high, to conform with equations (133).

From (132) follows as the minimum value of speed, St at which
the commutation current can be made to vanish, at given X4:

and:
hence:

•*•

For high values of speed, S, it is, approximately:
cos ((7 — 5) = 0,
a - 5 = 90°,
5-
tan or — —,
Co
hence: o- = 90°
5~^~0~'
X'4 - X4.
That is, the short-circuited coil under the brush contains no
inductive reactance, hence:
At low and medium speeds, some inductive reactance in the
short-circuited coils is advantageous, but for high speeds it is
objectionable for good commutation.
225. As an example are shown, in Figs. 189 and 192, the char-
acteristic curves of series-repulsion motors, for the constants:
Impressed voltage: e = 500 volts,
Exciting impedance, main field: Z = 0.25 + 3j ohms,
Exciting impedance, cross field: Z'= 0.25 +2.5 j ohms,
Self-inductive impedance, main
field: Zo= 0.1 + 0.3 j ohms,
Self-inductive impedance, cross
field: £2= 0.025 + 0.075 j ohms,