Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

There are several types of freight cars and many sizes for each
type. For each size and type of car, one can determine the cargo
capacity in cubic feet, the light weight, and the load limit. 1 Load
limits, set by the Association of American Railroads (AAR), may not
be exceeded and are generally much less than the actual cubic capa-
city would permit. For example, a 50-foot general box car may have
a capacity of 5000 cubic feet but a load limit of 70 tons. A typi-
cal medium density commodity, such as corn, may weigh 45 pounds per
cubic foot. This means that if the above box car were loaded to
capacity, the cargo weight would be 112.5 tons which far exceeds the
load limit. However, a low density commodity like oats, which weighs
about 26 pounds per cubic foot, would be space-limited rather than
weight-limited, for the freight car when filled to capacity would
weigh 65 tons, less than the load limit of 70 tons.
To put this argument into symbols, the following definitions
are needed:
Kij
= capacity of ith car for jth commodity, in tons
L. = load limit of ith freight car, in tons
x 4 = cargo volume oi ith car, in cubic feet
g 3 . = weight of jth commodity per unit volume, in tons
per cubic foot
k. = proportion of capacity of ith car utilized, 0 k i
C. = cargo weight of ith car, in tons.
Capacity is defined as follows:
K.. = min (L., x g.).
ij L i j
1
(5.1)
195