Transactions of the American Society of Civil Engineers, Vol. LXX, Dec. 1910 | Page 2

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