338 APPLIED MECHANICS 
288. Effort of Governors.—By the effort of a governor is meant the 
force which it is capable of exerting at the sleeve for a given percentage 
or fractional change of speed. . 
Consider first the effort of the Porter governor for which 
ow airs 2, 
w h 
Q be applied at the sleeve in a downward direction, Q being just sufficient 
to prevent the sleeve rising. ‘This will evidently be equivalent to increasing 
the central load from W to W+Q. 
Let F = centrifugal force for two balls at the speed o, 
F, =centrifugal force for two balls at the speed zw. 
2Qrww? r Qw0a2w?r r 
F= AW ew) F,= A =UW+Q+w),. 
Let the speed increase from w to #w,-and let a force 
F,-F= aera? SS ee a 
Therefore Q=@t-1)=(W +e) (e—1), If the force Q be 
W+w g 
w au®? 
and the average value of. the effort on the sleeve during the rise will 
be 3Q, or 4(W +w)(x?-—1)=P, and this is the resistance at the sleeve 
which this governor is capable of overcoming with an increase of speed 
from w to ww, For a decrease in speed from o to zw it follows that P, 
now acting in the opposite direction, is equal to }(W+w)(1—2*). For 
a change of speed of 1 per cent. P=0-01(W +). 
Converting the Porter governor into an unloaded governor by 
removing the central load or making W =0, it follows from the foregoing 
proof that P = 42(a? — 1), or 420(1 —a?)= 0°01, for a change of speed of 
1 per cent. If in the unloaded governor the sleeve is suspended, as in 
Fig. 526, then P, as just given, must be increased in the ratio of J: a, 
supposing that the suspension links and the pendulum arms are equally 
inclined to the main axis. 
It is evident that in order that the unloaded governor may have the 
one =W+w, 
where w, is the weight of each ball of the unloaded governor. 
For the loaded governor of the type shown in Fig. 521, 
P=4(W + 2w)(a? —- 1). 
289. Power of Governors.—By the power of a governor is meant the 
amount of work which it is capable of doing at the sleeve for a given per- 
centage or fractional change of speed. The work done at the sleeve is 
equal to the mean effort of the governor multiplied by the distance 
through which the sleeve moves for the given change of speed. Thus if 
P=mean effort, 4=lift of sleeve, and U=the power of the governor, 
then U = P&. . 
For the Porter governor (Fig. 524), P=3(W+w) (2-1), 
An= (= \i k= 2dh=2(2 2) \p, U=Pk=(W+w)(“—*) 2, 
x x 
gradually diminished to zero, the sleeve will rise until h= 
same power as the loaded governor of the Porter type, 
