HIGHER HARMONICS 155

92. The space harmonics usually are more important than the
time harmonics, as the space distribution of the winding in the
motor usually materially differs from sinusoidal, while the devia-
tion of the voltage wave from sine shape in modern electric power-
supply systems is small, and the time harmonics thus usually
negligible.

The space harmonics can easily be calculated from the dis-
tribution of the winding around the periphery of the motor air
gap. (See " Engineering Mathematics/' the chapter on the
trigonometric series.)

A number of the more common winding arrangements are
shown in Fig. 58, in development. The arrangement of the
conductors of one phase is shown to the left, under F, and the
wave shape of the m.m.f. and thus the magnetic flux produced
by it is shown under $ to the right. The pitch of a turn of the
winding is indicated under F.

Fig. 58 shows:

Full-pitch quarter-phase winding: Q — 0.

Full-pitch six-phase winding: S — 0.

This is the three-phase winding almost always used in induction
and synchronous machines.

Full-pitch three-phase winding: T — 0.

This is the true three-phase winding, as used in closed-circuit
armatures, as synchronous converters, but of little importance
in induction and synchronous motors.
%, % and ^-pitch quarter-phase windings:

a ~ M; Q - M; Q - M.

%, % and J^-pitch six-phase windings:

8-Hi s-H; s-H.

%-pitch true three-phase windings: T — %.

As seen, the pitch deficiency, p, is denoted by the index.
Denoting the winding, F, on the left side of Fig. 58, by the
Fourier series:

F = Fo (cos o> + a3 cos 3 a> + a5 cos 5 co + a? cos 7 a> + . . .). (13)
It is, in general:

(14)

= - I F cos nu do).

If, then: p = pitch deficiency,
q = number of phases