CE 353
Lab 7: Rail Design
Part 1: Train Acceleration, deceleration, and impact on Capacity
Part 2: Design of a hump yard / classification facility
Initial Instructions
Get a new partner (i.e., one that you haven't had before).
Work in teams of 2.
Submit only one set of files/results for the entire team.
Part 1: Train Acceleration, deceleration, and
impact on Capacity
For a given 10 mile section of track, there is a proposed speed reduction from 50 mph to 30 mph
for a 5 mile stretch. All trains on this track consist of 50 70-ton, 75’ cars pulled by 4 2000 hp, 100’
diesel-electric units. All needed data on the performance of this train configuration are given on
the following graphs taken from Hey (Table 10.1, Figures 10.3, 10.4, 10.9, and 10.10).
Assume 0% grade throughout the area being examined. Recall flow = density times speed! You may
wish to utilize equations 10.6 and 10.12 shown below (not strictly necessary). Note that the slow speed
section limits capacity.
Figure 1. Visualization of the Problem
L = 70’ (vf2 - vi2) t = 95.6 (vf - vi)
F’
Fa a
Equation 10.6: Length of Acceleration Equation 10.12: Time of Acceleration
Acceleration/Deceleration considerations (cont.)
Acceleration/Deceleration considerations (cont.)
Acceleration/Deceleration considerations (cont.)
Acceleration/Deceleration considerations (cont.)
Acceleration/Deceleration considerations (cont.)
Acceleration/Deceleration considerations (cont.)
Tasks
Part 1
1. Determine the travel time difference between the before case (50 mph everywhere) and the
after case (50 - 30 - 50). Assume train slows to 30 mph prior to 30 mph zone and accelerates to
50 mph after reaching other end of the 30 mph zone (i.e., treat the speed limit as if it only applied to
the lead locomotive - obviously as it accelerates out of the restricted zone, trailing cars will exceed
the speed limit).
2. Determine maximum traffic flow (in trains per hour) with a “block” signaling system. Trains
must never occupy the same block. See p. 126 - 135 in Armstrong for definition of block signaling
system. Assume blocks are 1/2 mile long, with one signal at each end of the given section and
spaced throughout. Trains must be able to come to a complete and safe stop if a train ahead is
stopped. Hint: Compute the flow for 30 and 50 mph sections separately.
3. Determine maximum traffic flow (in trains per hour) assuming trains are equipped with GPS
systems. Run trains as close together as safety (stopping distance) allows. Again, compute the flow
for 30 and 50 mph sections separately.
Part 2
Assume that due to construction, a 1 mile section in the center of the 30 mph zone is reduced to
one track, which has to support two-way traffic.
1. Determine maximum traffic flow assuming alternating trains eastbound then westbound.
a. First, determine time through the zone with the trains having to stop upon reaching the
construction zone, waiting for opposing traffic to pass and then exiting the area.
b. Second, determine the maximum traffic concentration with trains alternating through the
zone without slowing below 30 mph.
Part 3
Consider the effects of a +1% up-grade on the train described. The grade is 2 miles long. Find
the speed of a train at the top of the grade if it enters the bottom of the grade at 50 mph. How long
does it take the train to get back to 50 mph (time and distance)?
Part 2: Design of a hump yard/ classification facility
The vertical and horizontal alignment of a hump yard is affected by several factors
including resistance, acceleration capabilities on grades, maximum impact speed,
safety and more. This summary sheet addresses the principal factors to consider in
vertical alignment. The design concept centers around the change in energy head
(velocity profile) as cars pass along sections of the hump, transition and classification
tracks.
The actual design for gradients will vary dependent on conditions, but as a general
guide, one can expect the following.
- Hump grades of 4% for 100 to 200 feet.
- Transition grades of 1.5%.
- Switching grades of 1.2%.
- Classification track grades of 0.1% to 0.5%.
- Class track spacing of 14to 18 feet.
- Frog turnout numbers of 7 to 10.
Mechanical retarders are used in all hump yards, but the designs may include all three types
drawn on the sketch, any one of the three exclusively, or some combination. The purposes
of the retarders are to adjust the speed of the cars so excessive impact speeds can be
eliminated, and to maintain spacing between cars so switching can be performed smoothly.
The general expression of energy balance for a freight car traveling X feet along a track is
as follows.
The static rolling resistance may vary from 2 pounds per ton for easy-rolling cars
to 18 pounds per ton for hard-rolling cars. The extremes are often considered in the design
process.
Switch losses have typical values ranging from 0.02 to 0.06 feet per switch at the
switch point.
Curve losses may be approximately 0.025 feet of head per degree of central angle.
Air resistance can be calculated from the general relationship below. The value
can be significant if there are strong prevailing winds. K, A, V, W and n are the standard
components of air resistance in the Davis equation for railroad resistance.
Energy extraction capability of the retarders is variable, but a general figure
suggests that a heavy duty system can extract 0.11 foot of head per foot of retarder. Lengths of
20 feet are considered to be the minimum effective length.
If retarders are placed on both rails the extraction rate can be doubled.
Other considerations
Vertical curve lengths should meet the following minimum standards.
L= A * C
Where: L = length in feet
A = Alegbraic difference in grades, in percent
C = constant dependent on curve type
C = 15 for hump crest
C = 40 for summit curve
C = 60 for sag curves
Horizontal curves should be a maximum of 12O30’
Velocity on the grades must be such as to achieve sufficient headway between vehicles as
they are released so the switches can be “thrown” successfully to avoid misclassification. A
general equation is that the velocity at the main switch must be:
A general value for H is 60 feet. If the average car length is 60 feet, the velocity at the
switch would need to be twice as large as the humping velocity.
The maximum desired coupling speed is 6 feet per second.
CE 353 Lab 7
Design of a Hump (Classification) Yard
The attached sketch is a partial plan and profile for a hump yard. The
preliminary layout is to be checked for speed conditions and vertical curve transitions. The
equation for kinetic energy changes given on the handout sheet is applicable. The constants for
the resistance components are given below.
Switches: 0.03 feet of head perswitch at the switch point.
Curves 0.025 feet of head per degree of central angle.
Retarders: 0.11 feet of head per foot of retarder (Retarders are not shown on
sketch)
Wind: Assume wind resistance is 0.
Rolling (Mk ): Hard-rolling car = 18#/ton; easy-rolling car = 3#/ton.
1) Determine the minimum length of vertical curves for each of the grade changes
and include these in the design.
2) The humping speed is 7.0 ft per second. Determine the speed at points B through
L for a hard-rolling car. For your calculations you may assume that the car releases when the
center of gravity is at the crest of the hump curve. Further, you may assume that the gradient
changes instantaneously at the PI’s of the vertical curves.
3) Maximum impact speed at L is 6 feet per second. Determine the length of
retarder needed (if any) to extract excess energy before impact.
4) Car lengths are 60 feet. If a hard-rolling car is followed by an easy-rolling car
from the hump, would there be a problem at the first switch if you need at least 60 feet between
the cars. State all assumptions and calculate the time of arrival at the switch for both cars if no
retarding force is used on the cars.
5) The calculations in (2) used some simplifying assumptions regarding gradient changes along
the curves. Examine carefully a sketch of a car on the hump and discuss why an adjustment in
potential energy would be appropriate in this area.
Switches begin here
130’
See Turnout handout and Hints and Annotations on next page!
HINTS and ANNOTATIONS:
• distance HI minimum = length of switch rail + length of closure rail + toe length
(see figure from Turnout and Crossover Data handout) -- this distance is the same as
that prior to point C for the beginning of the switch
• distance CD minimum = heel length (see figure from Turnout and Crossover Data
handout)
• degree of curvature and curved closure length for rail between C and D can be
obtained from Turnout and Crossover Data handout
•distance IJ and JK depends on the frog angle (see Turnout and Crossover Data
handout)
•distance KL includes heel length
•gradient from KL is -0.25%