24 The N.Z. Journal of Science and Technology. [Jan. 
It will be remembered that when this fact was experimentally de¬ 
monstrated by Dr. Goss, at Purdue, by means of wire strips,* the majority 
of the critics asserted that a severe blow had thereby been dealt to the 
“ mathematical theory ” of balancing ! 
Hammerblow is the ruling factor in balancing, yet no definite rules 
are commonly formulated to determine its allowable maximum. In Ger¬ 
many and Sweden! it is restricted to 15 per cent, of the wheel-load at 
maximum speed, but in other countries the permanent-way engineers, 
whose function it is to state axle-load restrictions, continue to ignore it. 
It often amounts at high speeds to 50 per cent, of the static wheel-load, and 
this cyclical variation of rail-pressure, between the limits of 50 per cent, 
and 150 per cent, of the static load, must surely merit consideration. The 
variation in axle-load as distinct from wheel-load is independent of 8, and 
depends only on /rE . 
Its value is given by— 
V 2 r 
Variation of axle-load in pounds = 4*535 s i n (0 — 44)°) JcR. 
The limit of hammerblow from a locomotive point of view might be 
said to be the static load on the wheel, but at high speeds the imperfections 
of the track cause continual movement of the engine on the springs, and 
from this cause alone the spring-load on any wheel may probably vary 
down to 50 per cent, of the static load. A maximum hammerblow when 
V = d of 30 per cent, of the static wheel-load would thus be well within 
the safety limits, and, if possible, this restriction should not be exceeded, 
as otherwise the wheel may possibly be lifted from the rail. In all cases 
the balance-weight for the reciprocating parts should be divided among 
the coupled wheels either equally, as is most usual, or, better still, in such 
a way that the coupled-wheel loads are equalized at the highest speeds. 
No ill effects can possibly be produced by this procedure, as the total 
horizontal components for the engine are unaltered, while the hammerblow 
is divided among-the wheels and its effect correspondingly reduced. 
To sum up, the following rules are formulated :— 
(1.) In every case, balance all the revolving and as much of the recipro¬ 
cating weight as possible, consistent with hammerblow limits. 
(2.) Divide the balance-weights for reciprocating masses among the 
coupled wheels. 
(3.) U, the reciprocating mass left unbalanced, must not exceed 
W d 2 W 
27rV 2 9r ’ lf V ~ d > 27 r 
(4.) For ordinary locomotives the minimum hammerblow position of 
balance-weights should be adopted; for locomotives without 
bogies or carrying-axles the Rankine position should be used ; 
for locomotives with cylinders carried on a light swivelling bogie 
use the minimum nosing-couple position. 
(5.^Restrict the hammerblow, if rule (3) can still be satisfied, to 30 per 
cent, of the static wheel-load ; but in any case the hammerblow 
should not exceed 50 per cent, of the wheel-load. 
In conclusion, Table 1 is presented, showing the form to which the 
equations reduce for the standard positions of the balance-weight; also 
Table 2, showing the data, and Table 3, the results, of balancing for different 
arrangement of cylinders applied to engines of the same weight and tractive 
power. This clearly shows the superiority of three- and four-cylinder 
* W. F. M. Goss, Locomotive Performance, p. 329, 1909. 
f E. L. Ahrons, loc. cit., p. 38. 
