Transactions of the American Society of Civil Engineers, Vol. LXX, Dec. 1910

Transactions of the American
Society of
by Beverly S.
Randolph

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Title: Transactions of the American Society of Civil Engineers, Vol.
LXX, Dec. 1910 Locomotive Performance On Grades Of Various
Lengths, Paper No. 1172
Author: Beverly S. Randolph
Release Date: July 3, 2006 [EBook #18747]
Language: English
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AMERICAN SOCIETY OF CIVIL ENGINEERS
INSTITUTED 1852
TRANSACTIONS
Paper No. 1172
LOCOMOTIVE PERFORMANCE ON GRADES OF VARIOUS
LENGTHS.
BY BEVERLY S. RANDOLPH, M. AM. SOC. C. E.
WITH DISCUSSION BY MESSRS. C. D. PURDON, JOHN C.
TRAUTWINE, JR., AND BEVERLY S. RANDOLPH.

In the location of new railways and the improvement of lines already in
operation, it is now well recognized that large economies can be
effected by the careful study of train resistance due to grades and
alignment, distributing this resistance so as to secure a minimum cost
of operation with the means available for construction.
While engaged in such studies some years ago, the attention of the
writer was attracted by the fact that the usual method of calculating the
traction of a locomotive--by assuming from 20 to 25% of the weight on
the drivers--was subject to no small modification in practice.
In order to obtain a working basis, for use in relation to this feature, he
undertook the collection of data from the practical operation of various
roads. Subsequent engagements in an entirely different direction caused
this to be laid aside until the present time. The results are given in
Table 1, from which it will be seen that the percentage of driver weight
utilized in draft is a function of the length as well as the rate of grade
encountered in the practical operation of railways.

In this table, performance will be found expressed as the percentage of
the weight on the drivers which is utilized in draft. This is calculated on
a basis of 6 lb. per ton of train resistance, for dates prior to 1880, this
being the amount given by the late A. M. Wellington, M. Am. Soc. C..
E.,[A] and 4.7 lb. per ton for those of 1908-10, as obtained by A. C.
Dennis, M. Am. Soc. C. E.,[B] assuming this difference to represent the
advance in practice from 1880 to the present time. Most of the data
have been obtained from the "Catalogue of the Baldwin Locomotive
Works" for 1881, to which have been added some later figures from
"Record No. 65" of the same establishment, and also some obtained by
the writer directly from the roads concerned. Being taken thus at
random, the results may be accepted as fairly representative of
American practice.
Attention should be directed to the fact that the performance of the
10-34 E, Consolidation locomotive on the Lehigh Valley Railroad in
1871 is practically equal to that of the latest Mallet compounds on the
Great Northern Railway. In other words, in the ratio between the ability
to produce steam and the weight on the drivers there has been no
change in the last forty years. This would indicate that the figures are
not 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