1919 .] Jenkinson.—Balancing of Locomotives. 23 
outside, and the nosing-couple is correspondingly increased ; yet they 
are wonderfully smooth - running. Further, on the Canadian Pacific, 
Vaughan built some outside-cylinder engines with the nosing-couple of the 
reciprocating weights entirely unbalanced,* and these engines gave great 
satisfaction ; while the same practice was followed with marked success 
in the Ab engines recently built in New Zealand. 
The nosing-couple of the revolving parts can, of course, be balanced 
without increasing the hammerblow, but not so with reciprocating parts ; 
and the writer claims that nosing-couple should be ignored when designing 
modern fast engines with leading bogies. The resisting-couple of the 
adhesion of all the wheels is in such cases much greater than the nosing- 
couple. Locomotives without bogies or carrying-axles (0-6-0 and 0-8-0 
type) should probably be balanced by the Rankine (or Dalby) method, but 
such engines usually run at slow speeds. 
The nosing-couple consists of primary and secondary couples of different 
phase, the secondary couple not being affected by ordinary balancing. The 
minimum value of the nosing-couple is therefore secured when the primary 
couple vanishes, and from equation (2) we see that this occurs when 
D , 2, • ^G “1“ (K\ 
B (cos 6 — sin 8) = -g... (5). 
Combining this with equation (4) we get the values of B and 8 for this 
condition of minimum nosing. Unfortunately the hammerblow is then 
very large, and it is only in very special cases that this method of balancing 
should be resorted to. Articulated engines of the Mallet, Garrett, Fairlie, 
or Meyer type, where the cylinders are carried on easily swayed swivelling 
bogies, give a great deal of trouble with ordinary balancing, and equation (5) 
should certainly be worked to for these engines wherever possible. 
Equation (3) for the hammerblow is of the type— 
p sin 0 — q sin 6 — X where p — q = constant. 
Its maximum value for a revolution is therefore of the form Vp 2 -f- q 2 , and 
its minimum range of values occurs when p = — q. In the special case 
where 
B (cos 8 -j- sin 8) = M 
and B b (cos 8 — sin 8) = Mu 
the value of the hammerblow is zero ; but this is the case where none of 
the reciprocating weight is balanced. In other cases the hammerblow 
has its minimum range when 
. Mg 
B (cos 8 — sin (>) = y 
this representing the case where the nosing-couple of the 
weight is unbalanced ; and the hammerblow is then given by 
V 2 r 
Hammerblow in pounds = 2‘268 -jj- sin {Q — 45°) Ml. 
In general, the greatest value of the hammerblow during a revolution 
is given by 
Hammerblow in pounds = 2-268 ^ V | Ma ~ B6 < c ° s 8-jinS)| » + ^ , 
and it will be noticed that this does not occur when the balance-weight 
is at its lowest point, but when the crank is at the angle 
Mg — B6 (cos 8 — sin 8) + glcR 
reciprocating 
Tan ~ 1 cf> = 
Mg — Bo (cos 8 — sin 8) — gk R 
* American Engineer, November, 1910, p. 435. 
