1 MARCH 2000
RULING GRADE - EXAMPLE PROBLEM
This example of determining a trial ruling grade for a new railroad line follows the material presented in
chapter 3, paragraphs 4, 5, and 6.
A railroad line is to be built from the terminal serving the new training area at Fort Example to the nearest
commercial railroad, about 15 miles away. The most critical traffic, and heaviest loads, will be M-1 tanks
on flatcars. (Each car is 70 feet long and has a maximum loaded weight of 187 tons riding on 6 axles).
The installation has one 1,500 HP, 100-ton locomotive.
To handle movements during larger training exercises and mobilization, the installation wants to use an
engine from the connecting railroad which will be capable of hauling 25 loaded flats over the line at 15
MPH minimum speed. The connecting railroad expects to have a 3,000 HP, 170 ton (340,000 pound)
locomotive available when needed. (Tractive effort curves are not available for either locomotive. For
simplicity, let locomotive length equal car length).
The designer must now determine the maximum effective gradient (and grade length) on the new line to
accommodate these train movements. The first step is to determine how much traction force is available
(using chapter 3, paragraph 5c). Available traction force will be the lesser of locomotive tractive effort or
traction at the wheel-rail adhesion limit, for the commercial locomotive:
Locomotive Tractive Effort at 15 MPH = 300 x 3,000 / 15 = 60,000 lbs.
Wheel-Rail Traction Limit = 340,000 / 4 = 85,000 lbs.
2. Locomotive traction capability governs usable tractive effort.
3. Ruling Grade (from Equation 3-3):
TE =60,000 lbs
WEng = 170 tons