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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 11 of 21 (52%)
23|Baldwin Loco. Wks. Record, No. 65, p. 29|
24|Baldwin Loco. Wks. Record, No. 65, p. 29|
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In proportioning grade resistance for any line, therefore, a locomotive
may be counted on to utilize 24.3% of the weight on the drivers for a
distance of 5 miles on a 0.002 grade without any assistance from
momentum, and, in the event of an unexpected stop, should be able, as
soon as a full head of steam is built up, to start the train and carry
it over the grade. This is probably a maximum, considering the condition
of the equipment of this Virginian Railway, as previously mentioned.

Treating Item 14 in the same way, a distance of 2,310 ft. is accounted
for by momentum, leaving, say, 5.5 miles for the steam, or the length of
a 0.02 grade on which a locomotive may be loaded on a basis of tractive
power equal to 24.2% of the weight on the drivers.

From these figures it may be concluded that on lines having grades from
12 to 15 or more miles in length, grades of 3 to 5 miles in length may
be inserted having rates 50% in excess of that of the long grades,
without decreasing the capacity of the line. This statement, of course,
is general in its bearings, each case being subject to its especial
limitations, and subject to detailed calculations.

It may be noted that the velocity of 60 ft. per sec., assumed at the
foot of the grade, is probably higher than should be expected in
practice; it insures, on the other hand, that quite enough has been
allowed for momentum, and that the results are conservative.

Arguments like the foregoing are always more or less treacherous; being
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