SINGLE-PHASE COMMUTATOR MOTORS 407
and herefrom follows:

O\ f I _ \ // •( , ry-v /

— QA 4 -{- CpA 4 __ _____I ^ I ^ OA 4

W2($2 4~ Co2) Co2 + $2 I >?

— CQ\ 4 — /SX 4 _ 1 f CQ #0X^4

° ~ ~~ Sb\42(S*+<rf) "" co2 + £21S
or approximately:

t" = 0 substituted in equation (112) gives S = $0, the value
recorded in equation (108). .

It follows herefrom, that with increasing speed, S, tr and still
more t"', decrease rapidly. For S = 0, t' and t" become infinite.
That is, at standstill, it is not possible by this method to produce
zero commutation current.

The phase angle, 02, of the voltage ratio, T = t' — jt"', is given
by:

tan 62 = -7- = ^r—\-----q° 4 —r-77^;

rearranged, this gives:

Co sin 02 + S cos 02 __ &X42 — X%
Co sin 02 — ^? sin 02 X7/4 7

and, denoting:

(115)

--• = tan 0-, (116)

Co

where o- may be called the "speed angle," it is, substituted in
(115):

L\ 2 \/

tan (92 + a)

a = -,
A 4
= constant;
hence :
02 + <r = 7, (118)
and:
02 = 7 - <r. (119)
TL\ 2 _ W
— !_. - !js a iarge quantity, hence 7 near 90°.
A 4
<j is also near 90° for all speeds, S, except very slow speeds, since
in (116) Co is a small quantity.