134 ELECTRICAL APPARATUS
mum torque point, m, and a stable branch, from the maximum
torque point, m, to synchronism.
83. It must be realized, however, that this instability of the
lower branch of the induction-motor speed curve is a function of
the nature of the load, and as described above applies only to a
load requiring a constant torque, L. Such a load the motor
could not start (except by increasing the motor torque at low
speeds by resistance in the secondary), but when brought up to
a speed above d would carry the load at speed, c, in Fig. 51.
If, however, the load on the motor is such as to require a
torque which increases with the square of the speed, as shown
by curve, (7, in Fig. 51, that is, consists of a constant part p
(friction of bearings, etc.) and a quadratic part, as when driving
a ship's propeller or driving a centrifugal pump, then the induc-
tion motor is stable over the entire range of speed, from standstill
to synchronism. The motor then starts, with the load repre-
sented by curve C, and runs up to speed, c. At a higher load,
represented by curve B, the motor runs up to speed, 6, and with
excessive overload, curve A, the motor would run up to low
speed, point a, only, but no overload of such nature would stop
the motor, but merely reduce its speed, and inversely, it would
always start, but at excessive overloads run at low speed only.
Thus in this case no unstable branch of the motor curve exists,
but it is stable over the entire range.
With a load requiring a torque which increases proportionally
to the speed, as shown by C in Fig. 52, that is, which consists
of a constant part, p, and a part proportional to the speed, as
when driving a direct-current generator at constant excitation,
connected to a constant resistance as load—as a lighting sys-
tem—the motor always starts, regardless of the load—provided
that the constant part of the torque, p, is less than the starting
torque. With moderate load, C, the motor runs up to a speed,
c, near synchronism. With very heavy load, A, the motor starts,
but runs up to a low speed only. Especially interesting is the
case of an intermediary load as represented by line B in Fig.
52. B intersects the motor-torque curve, D, in three points,
&i, &2, 63; that is, three speeds exist at which the motor gives the
torque required by the load: 24 per cent., 60 per cent., and 88
per cent, of synchronism. The speeds 61 and 68 are stable, the
speed 62 unstable. Thus, with this load the motor starts from
standstill, but does not run up to a speed near synchronism, but