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 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
naturally assumed to be much less than that of roads hauling all classes
of cars, many of which are barely good enough to pass inspection. As the
grades are light in both cases, this feature of train resistance is
larger than in items including heavier grades. Attention should be
called to the fact that a line connecting the two points representing
these items on Fig. 1 would make only a small angle with the sketched
curve, and would be practically parallel to a similar line connecting
the points represented by Items 13 and 16. There is, therefore, an
agreement of ratios, which is all that needs consideration in this
discussion.
[Illustration: FIG. 1.--DIAGRAM SHOWING PERCENTAGE OF WEIGHT ON DRIVERS
WHICH IS UTILIZED IN TRACTION ON GRADES OF VARIOUS LENGTHS]
Wellington, in his monumental work on railway location, presents a table
of this character. The percentages of weight on the drivers which is
utilized in draft show the greatest irregularity. He does not give the
length of the grades considered, so that it is impossible to say how far
the introduction of this feature would have contributed to bring order
out of the chaos. In his discussion of the table he admits the
unsatisfactory character of the results, and finally decides on 25% as a
rough average, "very approximately the safe operating load in regular
service." He further states that a number of results, which he omits for
want of space, exceeds 33 per cent. The highest shown in Table 1 will be
found in Item 1 (0.06 mile, 0.066 grade), showing 33 per cent. There is
no momentum effect here, as the grade is a short incline extending down
to the river, and the start is necessarily a "dead" one. The reports of
Item 3, which shows 31%, and Item 5, which shows 27%, state specifically
that the locomotives will stop and start the loads given at any point on
the grade.
The results of a series of experiments reported by Mr. A. C. Dennis in
his paper, "Virtual Grades for Freight Trains," previously referred to,
indicate a utilization of somewhat more than 23%, decreasing with the
speed.
All this indicates that the general failure of locomotives to utilize
more than from 16 to 18% on long grades, as shown by Table 1, can only
be due to the failure of the boilers to supply the necessary steam.
While the higher percentage shown for the shorter grades may be ascribed
largely to momentum present when the foot of the grade is reached, the
energy due to stored heat is responsible for a large portion of it.
When a locomotive has been standing still, or running with the steam
consumption materially below the production, the pressure accumulates
until it reaches the point at which the safety valve is "set." This
means that the entire machine is heated to a temperature sufficient to
maintain this pressure in the boiler. When the steam consumption begins
to exceed the production, this temperature is reduced to a point where
the consumption and production balance.
The heat represented by this difference in temperature has passed into
the steam used, thus adding to the energy supplied by the combustion
going on in the furnace. The engines, therefore, are able to do
considerably more work during the time the pressure is falling than they
can do after the fall has ceased.
The curve in Fig. 1 would indicate that the energy derived from the two
sources just discussed is practically dissipated at 15 miles, though the
position of the points representing Items 16, 18, 19, 20, and 21 would
indicate that this takes place more frequently between 10 and 12 miles.
From this point onward the performance depends on the efficiency of the
steam production, which does not appear to be able to utilize more than
16% of the weight on the drivers. The diagrams presented by Mr. Dennis
in his paper on virtual grades, and by John A. Fulton, M. Am. Soc.
C. E., in his discussion of that paper, indicate that similar results
would be shown were they extended to include the distance named.
From this it would appear that a locomotive is capable of hauling a
larger train on grades less than 10 miles in length than on longer
grades, and that, even when unexpectedly stopped, it is capable of
starting again as soon as the steam pressure is sufficiently built up.
Conversely, it should be practicable to use a higher rate of ascent on
shorter grades on any given line without decreasing the load which can
be hauled over it. In other words, what is known as the "ruling grade"
is a function, strictly speaking, of the length as well as the rate of
grade.
In any discussions of the practicability of using a higher rate on the
short grades, which the writer has seen, the most valid objection has
appeared to be the danger of stalling and consequent delay. As far as
momentum is relied on, this objection is valid. Within the limits of the
load which can be handled by the steam, it has small value, as it is
only a question of waiting a few minutes until the pressure can be built
up to the point at which the load can be handled. As this need only be
an occasional occurrence, it is not to be balanced against any material
saving in cost of construction.
The writer does not know of any experiments which will throw much light
on the value of heat storage as separated from momentum, though the
following discussion may prove suggestive:
A train moving at a rate of 60 ft. per sec., and reaching the foot of a
grade, will have acquired a "velocity head" of 56.7 ft., equivalent to
stored energy of 56.7 × 2,000 = 113,400 ft-lb. per ton. On a 0.002
grade (as in Item 15 of Table 1) the resistance would be, gravity
4 lb. + train 4.7 lb. = 8.7 lb., against which the energy above given
would carry the train through 113,400 ÷ 8.7 = 13,034 ft., say, 2.5
miles, leaving 5 miles to be provided for by the steam production.
Examining the items in the table having grades in excess of 10 miles, it
will be noted that 16% is about all the weight on drivers which can be
utilized by the current supply of steam. In Item 15 the energy derived
from all sources is equivalent to 24.3%; hence the stored heat may be
considered as responsible for an equivalent of 24.3% - 16% = 8.3% for a
distance of 5 miles.