CE 353Lab 7: Rail Design

Part 1: Train Acceleration, deceleration, and impact on CapacityPart 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 mphfor 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 - vi

2)Fa

’

Equation 10.6: Length of Acceleration

t = 95.6 (vf - vi)Fa’

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 1230’

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%