Transactions of the American Society of Civil Engineers, Vol. LXX, Dec. 1910 | Page 5

of
rating its locomotives. The locomotives were first divided into classes
according to their tractive power, this being calculated by the usual rule,
with factors of size of cylinders, boiler pressure, and diameter of
drivers, also by taking one-fourth of the weight on the drivers, and
using the lesser of the two results as the tractive power.
Locomotives of different classes, and hauling known loads, were run
over a freight division, the cars being weighed for the purpose; thus the
maximum load which could be handled over a division, or different
parts of a division, was ascertained, and this proportion of tonnage to
tractive power was used in rating all classes.
Of course, this method was not mathematically accurate, as the
condition of track, the weather, and the personal equation of the
locomotive engineers all had an effect, but, later, when correcting the
rating by tests with dynamometers, it was found that the results were
fairly practical.
There were three hills where the rate of grade was the same as the rest
of the division, but where the length was much in excess of other
grades of the same rate.
Designating these hills as A, B, and C, the lengths are, respectively,
2.44, 3.57, and 4.41 miles. There were no other grades of the same rate
exceeding 1 mile.
In one class of freight engines, 10-wheel Brooks, the weight of the

engine was 197,900 lb.; tender, 132,800 lb.; weight on drivers, 142,600
lb.; boiler pressure, 200 lb.; and tractive power of cylinders, 33,300 lb.
On Hill A these engines are rated at 865 tons, as compared with 945 on
other parts of the division. As the engine weighs 165 tons and the
caboose 15 tons, 180 tons should be added, making the figures, 1,045
and 1,125 tons. Thus the length of the grade, 2.44 miles, makes the
tractive power on it 92% of that on shorter grades.
On Hill B, the rating, adding 180 tons as above, is 1,160 and 1,230 tons,
respectively, giving 94% for 3.57 miles.
On Hill C, the rating, with 180 tons added, is 1,130 and 1,230 tons,
making 92% for 4.41 miles.
Taking the same basis as the author, namely, 4.7 lb. per ton, rate of
grade × 20, and weight on drivers, gives:
Hill A, 18.078%, remainder of division, 19.462% Hill B, 20.068%, " " "
21.279% Hill C, 19.549%, " " " 21.279%
It will be noted that the author uses the weight on the drivers as the
criterion, but the tractive power is not directly as the weight on the
drivers, some engines being over-cylindered, or under-cylindered; in
the class of engines above mentioned the tractive power is 23.35% of
the weight on the drivers.
The writer made a study of several dynamometer tests on Hill C. There
is a grade of the same rate, about 1 mile long, near this hill, and a
station near its foot, but there is sufficient level grade between this
station and the foot of the hill to get a good start.
All the engines of the above class, loaded for Hill C, gained speed on
the 1-mile grade, but began to fall below the theoretical speed at a point
about 2-1/4 miles from the foot of the hill. This condition occurred
when the trains stopped at the station and also when they passed it at a
rate of some 16 or 18 miles per hour, the speed becoming less and less
as the top of the hill was approached.

The writer concludes that the author might stretch his opinion as to
using heavier rates of grade on shorter hills than 10 miles, and indeed
his diagram seems to intimate as much, and that, for economical
operation, the maximum rate of grade should be reduced after a length
of about 2 miles has been reached, and more and more in proportion to
the length of the hill, in order that the same rating could be applied all
over a division.
This conclusion might be modified by local conditions, such as an
important town where cars might be added to or taken from the train.
While it does not seem practicable to the writer to calculate what the
reduction of rate of grade should be, a consensus of results of operation
on different lengths of grade might give sufficient data to reach some
conclusion on the matter.
The American Railway Engineering and Maintenance of Way
Association has a Committee on "Railway Economics," which is
studying such matters, but so far as the writer knows it has not given
this question any consideration.
The writer hopes that the author will follow up this subject, and that
other members will join, as a full discussion will no doubt bring some
results on a question which seems to be highly important.
JOHN