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Transactions of the American Society of Civil Engineers, Vol. LXX, Dec. 1910 - Locomotive Performance On Grades Of Various Lengths, Paper No. 1172 by Beverly S. Randolph
page 3 of 21 (14%)
likely to be changed much as long as steam-driven locomotives are in
use. What will obtain with the introduction of electric traction is
"another story."

These results have also been platted, and are presented in Fig. 1, with
the lengths of grade as abscissas and the percentages of weight utilized
as ordinates. The curve sketched to represent a general average will
show the conditions at a glance. The results may at first sight seem
irregular, but the agreement is really remarkable when the variety of
sources is considered; that in many cases the "reputed" rate of grade is
doubtless given without actual measurement; that the results also
include momentum, the ability to utilize which depends on the conditions
of grade, alignment, and operating practice which obtain about the foot
of each grade; and that the same amount of energy due to momentum will
carry a train farther on a light grade than on a heavy one.

There are four items in Table 1 which vary materially from the general
consensus. For Item 9, the authorities of the road particularly state
that their loads are light, because, owing to the congested condition of
their business, their trains must make fast time. Item 10 represents
very old practice, certainly prior to 1882, and is "second-hand." The
load consisted of empty coal cars, and the line was very tortuous, so
that it is quite probable that the resistance assumed in the calculation
is far below the actual. Items 15 and 17 are both high. To account for
this, it is to be noted that this road has been recently completed,
regardless of cost in the matter of both track and rolling stock, and
doubtless represents the highest development of railroad practice. Its
rolling stock is all new, and is probably in better condition to offer
low resistance than it will ever be again, and there were no "foreign"
cars in the trains considered. The train resistance, therefore, may be
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